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NIST

PUBLICATIONS

imist United States Department of Commerce

Technology Administration

National Institute of Standards and Technology

NIST Special Publication 918

PROCEEDINGS OF THE 1997

INTERNATIONAL CONFERENCE ON

INTELLIGENT SYSTEMS AND SEMIOTICS

A Learning Perspective

A. M. Meystel, Editor

ISAS '97

World Model

QC

100

.U57

NO. 918

1997

Sponsored by: World

National Institute of Standards and Technology (NIST)

Institute of Electrical and Electronic Engineers (IEEE)

National Science Foundation (NSF)

Army Research Office (ARO)

NIST Special Publication 918

PROCEEDINGS OF THE 1997

INTERNATIONAL CONFERENCE ON

INTELLIGENT SYSTEMS AND SEMIOTICS:

A Learning Perspective

ISAS '97

Gaithersburg, MD

September 22-25, 1997

A.M. Meystel, Editor

Manufacturing Engineering Laboratory

Intelligent Systems Division

National Institute of Standards and Technology

Gaithersburg, Maryland 20899-0001

September 1997

SPONSORS

National Institute of Standards and Technology

The Institute of Electrical and Electronics

Engineers, Inc.

National Science Foundation

Army Research Office

U.S. Department of Commerce

William M. Daley, Secretary

Technology Administration

Gary R. Bachula, Acting Under Secretary for Technology

National Institute of Standards and Technology

Robert E. Hebner, Acting Director
ISBN: 1-88684-02-3

National Institute of Standards and Technology

Special Publication 918

Natl. Inst. Stand. Technol. Spec. Publ. 918

587 pages (Sept. 1997)

CODEN: NSPUE2

U.S. Government Printing Office Washington: 1997For sale by the Superintendent of Documents

U.S. Government Printing Office Washington, DC 20402
SEMIOTICS: THE TOOLBOX OF INTELLIGENCE

Editor's Preface

Intelligent Systems

Intelligence is magic.

We do not call things that we easily understand intelligence. Then, it is considered just an

algorithm and as any algorithm, it seems to be mundane and mechanical.

Yet, magic accomplishes the goals in a presumably non-algorithmic way.

(I mean, magic not sorcery because although they both rely on incantations, i.e. use some kind of

linguistic tools, sorcery employs evil forces, while our focus will be on useful applications like

robotics, intelligent manufacturing, language translation, automated discovery, unmanned

energy systems, large health care programs, analysis of music and poetry, well. ..battlefield too.)

This is why Sukhan Lee, one of the organizers of the Symposium on Computational Intelligence

(Monterey, July 9-11, 1997), was surprised by the discovery that the conference could actually

be called "IEEE International Symposium on Computational Magic." The panel, at which it was

discussed, noticed that the similarity between magic and intelligence is in the depth and clarity of

our knowledge of them.

This reminds us of the commonality between intelligence and quantum mechanics. Manypeople

are looking forward to uncovering the mystery of intelligence by the means of quantum

mechanics. This commonality is in the similarity among them in both the depth and the clarity of

our knowledge of them.

We cannot avoid using the term intelligence. We can even see some benefits in attributing the

term, intelligent system, to many not clearly defined real world systems: the ones that

demonstrate some magic that is typical for intelligence. We are dreaming of intelligent robots that

are capable of getting to the core of an unexpected situation. Say, a particular situation is not

presented in the list of behavior rules. Yet, the robot can figure out how to deal with it. That is

intelligence!

When the famous Deep Blue browses the list of precomputed possibilities with breathtaking

speed, we are disappointed. We would prefer a slower thinker to come up with a winning solution

with no browsing at all—possibly by magic.

in
Michael Botvinnik, the Chess Champion of the Post-WWII era, envisioned a multiresolutional

system of planning in future chess-playing computers. Multi-level decision making was his

interpretation for his own mechanisms of winning.

Intelligent System is a metaphor for the system which functions but yet cannot be fully

understood. To understand it, we have to use another intelligent system —ourselves—which we

cannot fully understand either. The metaphor of intelligent system allows for prediction and

control of the systems of interest, although the properties and the mechanisms of these systems

are not totally clear to us. We are compelled to use this metaphor and this system, although its

algorithm cannot be clear to us now (and maybe will never be clear at all.)

We are interested in scientific and practical benefits in using this metaphor and its theories. The

metaphor of intelligent system maybe is applicable in all domains and at all levels of granularity, or

resolution. We have to show this in the future. If we succeed, then the embedded

incompleteness of our theory will be forgiven by the scientific community, (especially because in

the case of intelligent systems this incompleteness is forever!)

Can we say something substantial about intelligent systems today?

We can say that intelligent systems are generalizing machines. Their way of surviving is to

establish a trade-off between unbearable multiplicity of needs and desires and an unbearable

amount of information processing, which is required for this. They generalize by the virtue of

grouping (clustering), focusing attention, and combinatorial searching.

In the meantime, the procedure of generalization is always associated with a loss of information.

This is why the bottom-up process of re-generalization should be repeated constantly. Sooner or

later, the entities of the upper level would change inadvertently. When new information is

incorporated, the procedure of regrouping, refocusing, and re-searching will be performed.

Thus, the previously created multiresolutional system of representation will be changed as a

partial effect of such a learning process.

(See? Would it be sufficient to look for the explanation for intelligence only within the quantum

physics? Quantum mechanics itself is a product of the multiresolutional system of intelligence.)

Semiotics

Semiotics is the only system of thought that dares to consider itself as an object of its own

analysis. Like intelligence, semiotics is a self-referential and self-reflective system. All

components of intelligence including generalization with its focusing attention, search and

clustering are parts of semiotics. Actually, what we called learning process, in semiotics is called

semiosis.

iv
Semioticians are concerned with the issue "where is our niche?" This is an important issue, but

you have to specify what level of resolution you are talking about. Indeed, you may look for a

niche in one room versus another, in one country or state versus another, or even in one galaxy

versus another.

When I talk about this search for a niche, /imagine crowds of scientists intruding the Wild West of

Intelligence looking for a place to prosper, or the crowd of scientists like gold miners trying to

stake a place in the Klondike of Intelligence. Remember that everything happened literally on our

eyes. Indeed, Ampere's "Kybernetes" and Maxwell's "On Governors" appeared in in the middle

of 19th Century. At about the same time, C. Peirce wrote his papers on semiotics. Wiener's

"Cybernetics" was published a century later. We did not even have enough time to properly

digest these works.

The invariance of results in different scientific domains is not in looking for answers to the

question "What?" but rather in looking for answers to the question "How?"

Semiotics is the one which is looking for "How?" for all domains together because our intelligence

is common for all domains.

The well-known saying is that mathematics is the language of Science.

Yes, but it uses Semiotics as its Toolbox, the Metalanguage.

Semiotics supplies its Metalanguage to all disciplines of Science that are therefore dialects of

Semiotics.

Semiotics is mathematics that aspires for symbol grounding.

Semiotics is mathematics that does not delegate symbol-grounding to engineers.

Semiotics is mathematics that remembers that all axiomatic theories are just alternatives of World

simulation or for World simulation. It teaches engineers how to perform symbol grounding after a

simulation is done.

Let us ask the question, "What is Life, a playground, or a place with situated meaning?" Semiotics

does not follow the temptation to answer "a little bit of both. " Semiotics is looking for, interested

in, and striving toward a situated meaning of Life.

For semiotics, the existentialist issue "I think, therefore I am" does not exist. It is merely a

philosophical question. For semiotics, the insight "I think, therefore I axiomatize" has only a partial

importance. This is a mathematical issue. For semiotics, the issue is, "I think, therefore, I must

understand how do I do it."

v
Yes, mathematics is a dialect of semiotics. But, semiotics always attacks the problem before

mathematics does. Mathematics can be applied only after we understand the system well or can

pretend to understand it well.

Conference ISAS'97

Jourdain, the protagonist of Moliere's play "Le Bourgeois Gentilhomme, " was surprised when he

found out that he speaks prose. Most of the professionals in science and other intellectual areas have no idea that they speak semiotics.

We have a mission: to demonstrate the power of semiotic tools to them, to promulgate

understanding, to diminish confusion, to enhance clarity.

Semiotics is the invariance of all disciplines represented at our conference. Participants of the

conference and readers of this volume will easily recognize the relevance of each discipline both

to intelligent systems and to semiotics.

Some of these quests will be easy; some will require an effort. The theory of games is ultimately

semiotic. It is self-referential. Its implicit component is reflection, and it realizes that known theory

does not guarantee to win the game. When you think about it, the theory of automata can be

considered an attempt to decompose Peircean triangle into its components.

I hope that the toolbox of semiotics will be useful in your particular domain of science, in its

particular dialect. I hope that it will enhance your power of analysis and interpretation, and allow

you to express the meaning we always search for.

I wish you happy semiotic analysis of multiple complex intelligent systems you will encounter aft

this Conference.

A. Meystel

July 26, 1997

vi
Conference Committee

Honorary Conference Chairs - Thomas A. Sebeok, Indiana University

and Lotfi Zadeh, University of California at Berkeley

General Chair - James Albus, NIST

Program Chair - Alex Meystel, NIST/Drexel University

Educational Activities Chair - Kevin Passino, Ohio State University

Local Arrangements Chair - Richard Quintero, NIST

Publication Chair - David Coombs, NIST

Publicity Chair - Elena Messina, NIST

Vice-Chair, Publications - Patricia Flanagan, NIST

International Program Committee

K. Baheti, NSF

Z. Bien, KAIST, Korea

K. Bellman, DARPA

P. Borne, Ecole Centrale de Lille, France

B. Bouchon-Meunier, U. P Et M Curie, France

J. L. R. Chandler, WESS

A. Chikrii, Institute of Cybernetics, Ukraine

M. Coombs, NMSU, USA

B. Dean, Sandia National Laboratories, USA

E. D. Dickmanns, U. der Bundeswehr, Germany

V. Finn, VINITI, Russia

D. Fogel, Natural Selection, USA

K. Furuta, Tokyo Inst, of Technology, Japan

J. Goguen, U. of California at San Diego, USA

J. Gray, U. ofSalford, UK

W. Gruver, SFU, Canada

M. Gupta, U. of Saskatchevan, Canada

M. Herman, NIST, USA

C. Joslyn, Los Alamos Nat'l Lab

M. Jubert, NIST, USA

S. Kawaji, Kumamoto U., Japan

0. Kaynak, Bogazici U., Turkey

Y. Klimontovich, Moscow State University, Russia

L. Kohout, Florida State University, USA

M. Kokar, Northeastern University, USA

V. Kreinovich, U. of Texas at El Paso

S. Lee, U. of So. California, USA

V. Lefebvre, U. of California at Irvine, USA

D. A. Linkens, U. of Sheffield, UK

R. Lumia, U. of New Mexico, USA

R. Mann, Oak Ridge National Laboratory, USA

J. Maulbetsch, EPRI, USA

G. T. McKee, U. of Reading, UK

L. Miller, NGIS, USA

B. Mirkin, DIMACS, Rutgers U., USA

A. Mironov, Moscow State University, Russia

M. Modarres, U. of Maryland, USA

1. Muchnik, DIMACS, Rutgers U., USA

vii
C. Nehaniv, U. of Aizu, Japan

V. Novak, U. of Ostrava, Czech Republic

U. Ozguner, Ohio State University, USA

L. Perlovsky, Nichols Research Corporation, USA

D. Pospelov, Comp. Ctr. Academy of Science, Russia

K. Pourrezaei, Drexel U., USA

T. Reader, WSMR, USA

B. Rieger, O. of Trier, Germany

G. Ritter, U. of Florida, USA

P. Schenker, JPL, USA

K. Schlussel, NGIS, USA

D. Skatrud, ARO, USA

A. Stopp, Daimler-Benz, Germany

M. Sulcoski, NGIS, USA

H. Szu, U. of SW Louisiana, USA

S. G. Tzafestas, NTUA, Greece

J. Umiker-Sebeok, Indiana U., USA

B. Turksen, University of Toronto, Canada

J. C. A. van der Lubbe, Delft U. of Technology, The Netherlands

F.-Y. Wang, U. of Arizona, USA

P. Wang, Duke U., USA

J. M. Weiss, EPRI, USA

P. Werbos- National Science Foundation, USA

F. Zhao, Ohio State U.

viii
ISAS 97 CONFERENCE PROCEEDINGS

TABLE OF CONTENTS

Semiotics: The Toolbox Of Intelligence: Editor's Preface Ill

I PLENARY LECTURES

Why Now Semiotics 3

James S. Albus, National Institute of Standards and Technology

Top-Down Engineering 9

Lawrence J. Fogel, Natural Selection, Inc.

Ordinal Optimization and Soft Computing 12

Yu-Chi Ho, Harvard University

Introduction to Quantum Theory of Open Systems 14

Yu.L. Klimontovich, Moscow State University

Information Granulation and its Centrality in Human and Machine Intelligence 26

Lotfi A. Zadeh, University of California at Berkeley

II WORLD REPRESENTATION

The Role of Semiotic Descriptors in Relational Representation of Fuzzy Granular

Structures 31

Ladislav J. Kohout and Eunjin Kim, Florida State University

An Integrated Approach to Fuzzy Learning and Reasoning in Hierarchical Knowledge

Structures 37

Jan C.A. van der Lubbe, Delft University of Technology and

Emile Egbers, Zappwerk

Conceptual Categories as Knowledge Structures 44

Christopher Landauer, The Aerospace Corporation

Knowledge Representation Language in Semiotic Systems 50

V.N. Vagin and E.Yu. Golovina, Moscow Power Engineering Institute

ix
Ill NEURAL NETWORK MODELS

"Intelligence and Semiotics in Pattern Recognition and Neural Networks" 57

David Casasent, Carnegie Mellon University

Morphological Perceptrons 60

Gerhard X. Ritter and Peter Sussner, University of Florida

Traps and Tricks in Standard Benchmark Problems for Neurocontrol 66

Ludmila M. Dolmatova, Scientific Cybernetics, Inc. Paul J. Werbos, National Science Foundation

Neural Network Based Planner/Learner for Control Systems 75

J. Albus, National Institute of Standards and Technology

A. Lacaze, National Institute of Standards and Technology, University ofMaryland

A. Meystel, National Institute of Standards and Technology, Drexel University

N. DeClaris, University ofMaryland

A Hybrid Hierarchical Neural-AI Model of Mammal-Like Intelligence 82

Paul J. Werbos, National Science Foundation

IV LOGICAL CALCULI FOR SEMIOSIS

Plausible Reasoning and Its Logics 87

Oleg M. Anshakov, Victor K. Finn and Dmitry P. Skvortsov

VINITI - All Russian Institute of Scientific and Technical Information

Application of JSM-Theory of Plausible Reasoning to Social Data Analysis and Social

Actions Prediction 92

V.K. Finn and M.A. Mikheyenkova

VINITI - All Russian Institute for Scientific and Technical Information

Algorithmic Complexity of Generating Hypotheses and Forecasts in Version Spaces

Formed by Concept Lattices 96

S.O. Kuznetsov, Intelligent Systems Laboratory

To the Scaleable Technology of Automated Document Understanding based on

Quasi-Axiomatic Theories 100

M.I. Zabezhailo, Intelligent Systems Laboratory

NonMonotonic Reasoning in the Modal Quantificational Logic Z 103

Frank M. Brown, University of Kansas

V LEARNING

Inductive Theory of Semiotic Systems Ill

Lev Goldfarb, University ofNew Brunswick
Unified Learning/Planning Automaton: Generating and Using Multigranular

Knowledge Hierarchies 117

Alex Meystel, National Institute of Standards and Technology, Drexel University

Alberto Lacaze, National Institute of Standards and Technology, University of Maryland

Structural Learning for Classification of High Dimensional Data 124

Paul M. Baggenstoss, Naval Undersea Warfare Center

Learning from Large Dimensional, Small Data by a Potential Function Method with

Nonlinear Transformation: A Cancer Diagnostic Study 130

Mark Modell, MediSpectra, Inc., Victor Kamensky, Albert Einstein College of Medicine,

Casimir Kulikowski and Ilya Muchnik, Rutgers University and

Louis Burke and Jonathan Niloff, Harvard Medical School

Incremental Learning of Inheritance 137

Jose Neves, Evgueni Smirnov and Cesar Anlide, University ofMinho

VI MULTIRESOLUTIONAL SEMIOSIS

Multi-Resolution Data Processing: It is Necessary, It is Possible, It is Fundamental .... 145

S. A. Starks, V. Kreinovich, University of Texas at El Paso

A. Meystel, National Institute of Standards and Technology, Drexel University

Multiresolutional Planning with Minimum Complexity 151

J. Albus, National Institute of Standards and Technology

A. Lacaze, National Institute of Standards and Technology, University of Maryland

A. Meystel, National Institute of Standards and Technology, Drexel University

Multi-Resolution Data Processing is Optimal: Case Study of Detecting Surface Mounted

Devices 157

A.E. Brito, O.M. Kosheleva, and S.D. Cabrera, University of Texas at El Paso

An Artificial Life View on Intelligent Enterprises - Fuzzy Evolution Multi-Agent

Systems 162

Valery Tarassov, Bauman Moscow State Technical University

VII ORDINAL OPTIMIZATION

Ordinal Optimization for a Class of Combinatorially Hard Problems 173

Christos G. Cassandras, Boston University, Liyi Dai, Washington University and

Christos G. Panayiotou, University ofMassachusetts at Amherst

Three Techniques for Ordinal Optimization: Short Simulation Runs, Crude Analytical

Models, and Imprecise Simulation Models 175

Jeffery E. Wieselthier, Naval Research Laboratory, Craig M. Barnhart, TRW, and

Anthony Ephremides, University of Maryland

xi
Selection Schemes in Ordinal Optimization and Their Computational Advantages 181

T.W. Edward Lau, Harvard University

Intelligent Computing Budget Allocation for Discrete Event Simulation and

Optimization 185

Chun-Hung Chen, Karen Donohue of Pennsylvania

Liyi Dai, Washington University and Enver Yucesan, INSEAD

Comparison of Performance Orders of Different Design for Discrete-Event Dynamic

Systems 191

Liyi Dai, Washington University, and Chun-Hung Chen, University of Pennsylvania

VII ARCHITECTURES

A Case-Based Integrated Learning Architecture and Its Applications 199

Gennady Agre, Bulgarian Academy of Sciences

Computational Embodiment: Software Architecture 205

Christopher Landauer, The Aerospace Corporation, and

Kirstie L. Bellman, Defense Advanced Research Projects Agency

Emergence of Complex Organized Natural Systems, A Hierarchically - Structured

Conceptualization and Notation of Organization 211

Jerry L.R. Chandler, Krasnow Institute for Advanced Studies

A Holonic Approach to Intelligent Control of a Flexible Transfer System for

Manufacturing 217

Mihaela Ulieru, Simon Fraser University

Learning Coordination Patterns from Emergent Behavior in a Multi-Agent-Based

Manufacturing System 225

F. Maturana, S. Balasubramanian, and D.H. Norrie, University of Calgary

IX EVOLUTION

Speculation on the Evolution of Symbols 233

David B. Fogel, Natural Selection, Inc.

The Evolution of Intelligence from the Semiotic Perspective 239

John R. Alexander, Jr., Towson State University

On Hardware Evolvability and Levels of Granularity 244

Adrian Stoica, Jet Propulsion Laboratory

Evolution of Learning: The Merging of Semiotic and Evolutionary-System Theories . 248

Wolfgang Hofkirchner, Vienna University of Technology

xii
The Effects of Biological Aging on Genetic Algorithms 252

Tim Schnelmer and Frank M. Brown, University of Kansas

X AUTONOMY

Adaptive Autonomy: The Key to Dynamic, Responsive Formation of Sensible Agent

Organizations 263

K. Suzanne Barber, The University of Texas at Austin

Finding and Using Multiple Models for Autonomous Learning 269

I.N.P. Davidson, CSIRO

Agent Based Task Viewing in Telerobotic Environments 275

Gerard T. McKee, Bernard G. Brooks, University ofReading

Paul S. Schenker, Jet Propulsion Laboratory

A Unified Approach for Fast Recognition, Learning and Interpretation of the

Environment by an Autonomous Mobile Robot 281

Andreas Stopp and Lars Kiittner, Daimler-Benz AG

Learned Emergence of Functional Symbol Systems in Adaptive Autonomous Agents,

Guided by Skinner's Analysis of Verbal Behavior 287

William R. Hutchison, Behavior Systems LLC

XI LIKELIHOOD, MIXTURES, AND SYMBOLS

Towards Quantum Field Theory of Symbol 295

Leonid I. Perlovsky, Nichols Research Corporation

Semiotic Compounds - Mixtures of Components Invariant Under Specified

Transformations 301

Roy L. Streit, Naval Undersea Warfare Center

Information, Likelihood, and Einstein 307

Leonid I. Perlovsky, Nichols Research Corporation

A Symbolic Representation of Misconceptions 313

Benjoe A. Juliano, Coastal Carolina University

XII SEMIOTICS OF TEXTS AND IMAGES

Mathematical Aspects of Cyberaesthetics 319

Leonid I. Perlovsky, Nichols Research Corporation

xiii
Semiotics and Modeling Computer Classification of Text with Genetic Algorithm:

Analysis and First Results 325

Vincent Rialle, Sofiane Oussedik, Universite Joseph Fourier and

Jean-Guy Meunier, Georges Nault, Universite du Quebec a Montreal

Dynamic Word Meaning Representations and the Notion of Granularity. Text

Understanding as meaning constitution by SCIPS 331

Burghard B. Rieger, University of Trier

Cyberasthetics in Light of Zoosemiotics 333

Victor Dmitriev, Oklahoma State University

Leonid I. Perlovsky, Nichols Research Corporation

The Hole in the System 338

Floyd, Merrell, Purdue University

XIII MULTIDISCIPLINARY APPLICATIONS OF SEMIOTICS

Control Mechanisms for a Nonlinear Model of International Relations 349

Aron Pentek, Jim Kadtke, University of California at San Diego

Suzanne Lenhart, University of Tennessee and

Vladimir Protopopescu, Oak Ridge National Laboratory

Galen in Medical Semiotics 354

Thomas A. Sebeok, Indiana University

Introduction in Physics of Open Systems: Main Principles. Diagnostics on the

"S-Theorem" Criterion. Norm of Chaos. Degradation and Self-Organization.

Phase Transitions 364

Yu. L. Klimontovich, Moscow State University

Non-Equilibrium Themodynamics Explains Semiotic Shapes: Applications to

Astronomy and to Non-Destructive Testing of Aerospace Systems 378

Roberto Osegueda, Carlos Ferregut, Mary J. George, Jose M. Gutierrez, and

Vladik Kreinovich, University of Texas at El Paso

Towards Computers of Generation Omega - Non-Equilibrium Thermodynamics,

Granularity, and Acausal Processes: A Brief Survey 383

M. Koshelev and V. Kreinovich, University of Texas at El Paso

XIV SEMIOTICS OF OPEN SYSTEMS

'Seeing' the Battlefield through Virtual and Constructive Simulation 391

Ken Hunt, Mounted Maneuver Battlespace Lab

xiv
TVA's Kingston Unit 9 Distributed Control System (DCS) Retrofit Benefit

Documentation 395

Dennis Linkins, TVA Technology Advancement

David Lewis, TVA Kingston Fossil Plant, Rob Frank, EPRI U&C Plant and

Joe Weiss, EPRI

Evaluation Measures for the Collective Intelligence of Closed Social Structures 401

Szuba Tadeusz, Kuwait University

The Semiotics of Autonomous Investigations of Natural Systems 407

Paul S. Prueitt, Highland Technologies, Inc.

XV SOFT MODELING

Soft Modeling for Intelligent and Complex Systems 415

Paul P. Wang, Duke University

Computational Embodiment: Biological Considerations 422

Kirstie L. Bellman, Defense Advanced Research Projects Agency

Christopher Landauer, The Aerospace Corporation

The Neurodynamics of Intentionality in Animal Brains Provides the Basis of

Intelligent Behavior 428

Walter J. Freeman, University of California at Berkeley

Hypermedia Integration of Information Resources for Plant Operations 434

Lefteri H. Tsoukalas, Purdue University, and

Robert E. Uhrig, University of Tennessee at Knoxsville

XVI GAMES AND REFLEXION

Game Problem on Soft Landing for Moving Objects 443

Arkadii A. Chikrii, Cybernetics Institute

Game Problems of Control with Delay of Information 450

Greta Ts. Chikrii, Cybernetics Institute

Reflexive Game Theory 455

Vladimir A. Lefebvre, University of California at Irvine

XV
XVII COMPUTATIONAL APPROACHES IN SEMIOTICS

Supporting End-User Programming with Explanatory Discourse 461

Clarisse Sieckenius de Souza, PUC-Rio

An Approach to Computational Semiotics 467

Ricardo Gudwin and Fernando Gomide, DCA-FEEC-UNICAMP

Sequential Algorithm for the Semantic Representation of Actions in Terms of Moving

Parts 471

Hiroyuki Nishina, Saitama University

Solving the Forward Kinematics Problem for the Stewart Platform by Focusing

Attention and Searching 477

A. Lacaze, National Institute of Standards and Technology, University ofMaryland

C. Tasoluk, Drexel University

A. Meystel, National Institute of Standards and Technology, Drexel University

XVIII BRAIN, MENTALITY, AND MEANING

A Neurobiological Interpretation of Semiotics: Meaning, Representation, and

Causality 487

Walter J. Freeman, University of California at Berkeley

Intelligence vs. Mentality: Important but Independent Concepts 493

James H. Fetzer, University ofMinnesota

Functional Organization of Cortico - Basal Ganglia - Thalamocortical Loops 499

K.V. Baev, Barrow Neurological Institute

Learning How to Know: Semiotics and Multiscale Cybernetics 505

A. Meystel, National Institute of Standards and Technology, Drexel University

XIX SEMIOTICS IN INTELLIGENT CONTROL

Semiotics: a Key to Intelligent Control 511

Tariq Samad, Honeywell Technology Center

Intelligent vs. Reflex Control for Complex Dynamical Systems 517

Michel Cotsaftis, LTME/ECE

Introduction to Integrated Learning/Planning Paradigm 522

A. Meystel, National Institute of Standards and Technology, Drexel University

A. Lacaze, National Institute of Standards and Technology, University of Maryland

xvi
XX ISAS '96 PREVIOUSLY UNPUBLISHED PAPERS

A Roadmap to the Future for Intelligent Systems and Semiotics 53

James S. Albus, National Institute of Standards and Technology

Computational Semiotics and Fuzzy Linguistics: On Meaning Constitution and Soft

Categories 541

Burghard B. Rieger, University of Trier

Linguistic Geometry: Model Evaluation 552

Boris Stilman, University of Colorado at Denver

XXI ISAS'96" CONFERENCE REVIEW

ISAS' 96: Conference Review 567

Prepared by A. Meystel, K. Bellman, D. Filev, J. Goguen, C. Hewitt

C. Joslyn, L. Kohout, C. Landauer, I. Muchnik, L. Perlovsky,

V. Stefanuk, and Y. Yufuk

AUTHOR'S INDEX 583

LATE SUBMISSIONS

xvii

I PLENARY LECTURES

Why Now Semiotics?

From Real-Time Control

to Signs and Symbols

James S. Albus

Chief, Intelligent Systems Division

Manufacturing Engineering Laboratory

National Institute of Standards and Technology

albus@cme.nist.gov

Why is NIST hosting a conference on Semiotics?

NIST's primary interest is in intelligent control

systems for manufacturing and in standards and measures for open architecture controllers. What has

that to do with the science (dare I say the philosophy)

of signs and symbols? What has semiotics to say to manufacturing? You can read for a long time in the

semiotics literature before you encounter a reference to

the problem of data communications between a CAD

database and a numerically controlled machine tool. So

where is the connection? What does the engineering of

intelligent real-time control systems have in common

with the science of signs and symbols?

Control

To answer this last question, let's take a look at

the field of control. The history of real-time control

begins with the invention of the fly-ball governor. The

problem was how to regulate the flow of steam to control the speed of a steam engine under variable load

conditions. The solution was feedback. If the engine was running too slowly, the fly-ball arms fell down,

opening a valve and allowing more steam to flow. If the engine was running too fast, the fly-ball arms flew

out, closing the valve and slowing the flow of steam.

The development of feedback control theory

reached a peak during World War II with the

development of radar controlled anti-aircraft guns.

Norbert Wiener was the intellectual leader of this effort. He founded the field of cybernetics. Feedback control

theory matured in the aerospace industry during the

Cold War race for supremacy in the skies and outer

space. Today, feedback control theory provides the

mathematical foundations for servo controllers used in

millions of applications.

Feedforward control is simply a recognition that if you know enough about the system you are

controlling, you can design a pattern of inputs to the

controller that will produce the desired output from the

system.

One example of feedforward control is the control

program for a machine tool. The machine tool and the

metal cutting processes are sufficiently well

characterized so that low level servo controllers can guarantee that the tool will go to the points along the

paths designated in the program. A typical machine

tool program may include thousands of steps which

proceed from start to finish with essentially no feedback

from the machine.

A more interesting example of feedforward control

is the use of plant models (and inverse plant models)

for process control. If you want to get a plant to produce a certain output, first develop a plant model

(transition matrix between inputs, states, and outputs).

Then, invert the model. When you apply the desired

output to the inverse plant model, it will produce the

proper control sequence that if input to the plant will cause it to generate the desired output. In other words, an inverse plant model put in series with a modeled

plant produces a transfer function of unity. Thus, the

desired output applied to the series combination of the

inverse model and the plant itself will produce the

desired output from the plant. It is amazing that this

works. How well it works depends on the fidelity of

the inverse plant model. Bernie Widrow just published

a book on how to use neural nets to develop inverse

plant models even for non-minimum phase plants.

In the field of artificial intelligence (AI) and

robotics, a great deal of research has been done on

planning. A plan expressed as a series of commands is essentially a feedforward control sequence. Thus,

planning is a form of feedforward control. A planner

uses a plant model to predict the results of hypothesized

actions. The ability to predict is a key (perhaps THE

key) to intelligent behavior. The development of

prediction theory was first developed by Kalman for use

in designing recursive filters. A Kalman filter predicts one sample period into the future. An AI planner

requires a model that can predict the future out to a

3
planning horizon which may be many seconds,

minutes, hours, or days into the future.

Recently, controller developers began to combine

feedback and feedforward control techniques to achieve

the advantages of both. AI system designers have begun

to combine deliberative planners (feedforward) with

reactive (feedback) controllers. Control theory is beginning to focus on prediction -- to anticipate the

requirements of the future in addition to compensating

for errors from the past.

Both feedback and feedforward control systems

employ concepts such as signals, states, state variables,

events, and event tokens. Knowledge of plants,

processes, entities, attributes, and plant behavior are stored in a variety of numerical and symbolic formulae,

rules, state-transition matrices, and state graphs

consisting of characters and words, images, frames,

graphs, and pointers.

Control systems must also deal with real-time

issues such as response time, bandwidth, sampling rate,

stability, observability, and controllability. Control

theory has developed an arsenal of mathematical tools

for optimizing designs and for incorporating adaptive

and learning algorithms into the control system. Most

recently, attention has been focused on fuzzy systems,

neural nets, and genetic algorithms.

Semiotics

Semiotics is the science of signs and symbols.

Fundamental to signs and symbols is the notion of

representation. The dictionary definition of the word

"represent" means "to be a symbol for or an image of

something in the world." Representation requires data

structures that represent (and presumably) correspond to

entities and situations in the world.

Symbol grounding refers to the problem of

establishing and maintaining correspondence between

symbols in the data structure and things in the world.

In an intelligent system, signal grounding is achieved

by sensory processing and world modeling functions

that establish and maintain correspondence between the

internal world model and external reality.

It was Immanual Kant who first made clear the

distinction between a representation that exists in the

mind and objective reality that exists in the world. We

need to keep this distinction clear in the design of

intelligent semiotic systems. Entities and situations in

the world are sensed producing observed signals and

images that are segmented into observed entities. Observed entities and images are filtered to form

estimated entities and images. Dynamic models can then produce predicted entities and images. Predicted

entities and images plus desired goals can produce plans

and actions in the world.

Semiotics has a lot to do with language,

particularly regarding semantics, pragmatics, causality,

and plausibility.

Semantics defines the meaning of what is encoded

in grammatically correct strings of symbols and words.

One of the most basic forms of meaning is contained in the logical calculus of deduction, inference, and

probability. Semantics can be formalized in relational

graphs consisting of networks of nodes and edges where

the nodes are words and the edges are relationships.

Relational graphs can also be used to describe

pragmatics (what things are used for) and causality

(what things cause other things). Rules, equations,

formulae, and algorithms can be used to define how

things work and what effect some things have on other

things. For example, F = ma is a formula that

describes the relationship between force applied to a mass and the acceleration that will be experienced by

that mass. The formula F=ma can be used to compute

how much force is needed to produce a desired

acceleration or how much acceleration to expect when a

particular force is applied.

Situations can be represented by words and

narrative text. However, situations can also be

represented by images, drawing, maps, and pictures.

For reasons that I do not fully understand, semiotics seems much less concerned with images and maps than

with words and symbols. Apparently, a strong

preference exists among researchers in semiotics, as well as in artificial intelligence, and linguistics to represent the world in symbolic form ~ i.e., in frames,

relational graphs, and text, rather than in pictures and

maps.

But words are often inadequate to fully describe

the richness and dynamic vibrancy of real world

situations. Especially if we take into account the

totality of the sensory experience ~ vision, hearing,

smell, taste, touch, and gut feelings — words become a cumbersome and sparse medium for representation.

4
Images as Representation

In this presentation, I want to argue the case that

image representations are much more important than

anyone would guess from reading either the semiotic or the control theory literature. I would argue that images

are not just sensory input to be dispensed with as soon

as it is possible to derive a symbolic representation.

Images are repositories of information about spatial and

temporal detail that cannot be represented as efficiently

in any other format.

It is clear that the use of images for representation

of knowledge and computing developed very early in

the evolution of the brain. Visual competence existed

in the brains of sea creatures and insects almost a

billion years ago. Fish, crustaceans, and insects have

eyes and neural computing structures for processing

images. Birds and mammals all represent the visual

world and process images for purposes of locomotion

and manipulation. Vision is crucial to hunting for food

and evading danger in almost every species. There is good neurophysiological evidence from birds and

primates that neurons on the surface of the superior

colliculus are anatomically arranged so as to form a

visual map on which targets of attention are displayed.

Signals from this genetically designed map

representation are then transformed directly into

commands to muscles to move the eyes.

In marked contrast, language comes very late in

the evolutionary history of the brain. Birds, mammals,

and even insects use a variety of signs and symbols to signal their presence and their sexual interests. Many

animals use symbolic gestures or sounds to communicate intentions such as aggression,

submissiveness, friendliness, or fear, or to warn others

of danger. Nevertheless, in all species, language

competence is primitive when compared to visual

processing capabilities. Among humans, the level of

language competence that most occupies researchers

probably did not exist in verbal or sign language form more than 100,000 ago. Written forms of language

first appeared only about 10,000 years ago.

It is said that a picture is worth a thousand words.

Clearly, the capabilities of the brain for representing

and processing visual information far exceeds those for language representation and processing. From this fact alone, I would think that more emphasis should be

placed on the use of images as a mechanism for thinking about and planning for the future. We should

pay more attention to computing with images, rather

than computing on images to extract symbolic data -

and then discarding the images.

Images are derived directly from sensors. The

sensor egosphere is a very natural coordinate frame for

representing knowledge about the world -- especially

knowledge about where things are and how they are moving. We often communicate information through

pointing to things. We show each other how to do

things. We compute where to place our feet based on

where supporting surfaces appear in our visual world.

We visually track targets we intend to pursue and look

directly at things we intend to manipulate. We flee from parts of the egosphere that contain threatening

images.

Images that are overlaid with symbolic

information about objects are called maps. Maps can be used to represent situations and to make plans. For

example, military maps of the battlefield typically

show the elevation and slope of the terrain, the type of

ground cover (trees, grass, buildings, roads), the type of

terrain (lake, mountain, forest, open fields), and the

disposition of friendly and enemy forces. Soldiers

frequently used maps and physical models of the terrain

to plan battles. Travelers rely on maps for planning

and executing trips. Navigators for ships and airplanes use maps to figure out where they are, and to plan what

direction to go, and when to turn.

I intend to pursue this issue of visual (or iconic) versus symbolic (or language based) representations

throughout the body of my talk. I want to suggest that

the study of signals, images, and symbols, and the

processes that transform one into the other form the

basis for integration of semiotics with real-time

control.

Representation to Action

I will argue that intelligent systems can improve

its performance by using both iconic and symbolic

representations and computational methods. Iconic and

symbolic formats can and should be tightly linked so

that information computed in one domain can be

transformed into the other and vice versa. For example,

combining iconic representations with symbolic

information produces maps that can be used to plan and

control behavior. Regions on maps can be specified as goals. Task objects can be specified symbolically by

name and identified visually in images. Goals can also

be defined by means of visual representations similar to

5
"key frames" used in cartoon movies. Situations can be specified on maps showing the desired configuration

of objects relative to each other and the terrain. Attention can be specified in terms of where on the

egosphere to look or where to point high resolution sensor arrays.

I also want to describe a reference model

architecture that incorporates both symbolic and iconic

representations and outline an engineering methodology

for the design and development of intelligent control

systems. I will briefly describe some application

examples developed using this methodology.

But, in the end, I return to the question "Why

Now Semiotics?" Why should real-time control

theorists care about the science of signs and symbols?

And why should semioticists study issues related to real-time control?

The answer, I believe, can be found in those areas where the two fields intersect and address common

problems. These areas include the acquisition,

representation, and use of knowledge about the world.

How can signals from sensors be transformed into

images, maps, and symbols that represent states,

attributes, entities, events, values, and situations in the

world? How can knowledge be used to focus attention,

plan action, and reason about the best course of action?

How does an intelligent system generate and express

goals and intentions? How does it know how to behave in order to achieve goals in an uncertain and

often hostile environment? The answers to these

questions will be found sooner if we combine what is known and is being discovered in the two fields of

semiotics and real-time intelligent control.

I believe semiotics can help control engineers

better understand how to represent images, maps,

entities, actions, rules, situations, and relationships. I think recursive filtering theory and image processing

research can help semioticists better establish

correspondence between the real world and

representations of the world. Given these better representations, intelligent systems can better plan and

execute tasks amid uncertainty. Given a reference

model architecture, researchers can better understand

how to partition the control system so that various

kinds of information can be learned. Learning can only

take place within a prior structure where incremental

improvements in performance can be rewarded and

failures can be incrementally corrected. Given an

engineering methodology, engineers can better understand how to approach the design of intelligent

systems.

Semiosis

I would argue that the combination of real-time

control and semiotics will enable us to build more

intelligent systems for practical applications.

Semiotics gives us a better understanding of semantics,

pragmatics, causality, logic, inference, probability, and

plausibility. Intelligent real-time control theory gives us a better understanding about how sense and process

sensory data into knowledge about the world, and how

to use that knowledge to plan and control behavior.

Combined, these two diverse fields provide insight as

to how better to acquire, represent, and use knowledge

and how to transform knowledge into actions that produce real wealth for the benefit of society.

This then is the answer to "Why Now

Semiotics?" Now is the time to integrate semiotics

with real-time control to produce intelligent systems

for practical applications of great importance to the

future of human kind.

6
Top-Down Engineering

Lawrence J. Fogel, Ph.D.

Natural Selection, Inc.

3333 N. Torrey Pines Ct., Suite 200

La Jolla, CA 92037

ABSTRACT

Rather than design by arranging (and rearranging) components,

why not use fast-time mutation and selection to evolve the

required design? Simply generate a random set of alternative

designs. Suggestions/hints can be added at any time, but are not

required, for the process learns without instruction. Increasingly

appropriate designs are found through successive generations.

This evolutionary computation has been used to detect unknown

signals in noise (discovering new templates for later pattern

recognition), to design optimal neural networks (even when the

response surface is discontinuous), for forecasting

nonstationary time series given an arbitrary payoff function,

for determining the relationship among variables (modeling an unknown transducer/plant), for the control of that plant within

the limits of its controllability, and for gaming if that plant has

its own purpose. There are, indeed, a wide range of other

applications.

Of course, all this presumes the problem at hand is well defined,

that is, that a meaningful fitness/payoff function has been

specified. This requires more than simply measures of

effectiveness and related measures of performance. The problem

becomes well defined only if these measures are weighted in

relative importance and combined, taking into account their

degree of criticality. The Valuated State Space Approach

provides a convenient way to translate subjective judgment with

respect to intent into a concise specification of the purpose to be achieved. Top-down engineering can be realized by coupling

the Valuated State Space Approach with evolutionary

programming.

KEYWORDS:

top-down engineering, evolutionary programming,

stochastic optimization, evolutionary computation

1. INTRODUCTION

"en»gi»neer'ing, n. the planning, designing, construction,

or management of machinery," [1] begins with the recognition

of a need. The available resources/components/building blocks

are arranged within the imposed constraints. This construct is evaluated. The weak points/bottlenecks are identified. Adjustments are made to improve the design. This process

continues until further improvements are no longer cost

effective. The entire procedure is bottom-up.

But a much better design may exist . . . one that cannot be found

by continually improving on the original concept. Searching

the streets of Los Angeles for the quickest route may take you

away from a freeway entrance that might provide much faster

transit. Continually improving the gaslamp will never make it

into an electric light. Why not design top-down, that is, use

fast-time computation to directly search the domain of candidate

solutions/designs until one of sufficient worth has been found?

At first glance this might seem unreasonable, for the domain of

possible solutions is so immense. Exhaustive search is clearly

impossible. It becomes feasible only if an extremely efficient

search technique is available. Why not simulate the way nature evolves increasingly appropriate creatures/designs over

millennia? Each organism (design) faces the challenge posed by

its environment and is thus scored. Those that are sufficiently

fit produce offspring that are similarly tested. This optimization

process is extremely efficient and can be used to address welldefined engineering problems, that is, to find a good enough

solution fast enough for it to be useful.

2. DISCUSSION

Real-world problems are, indeed, extremely complex. The

constraints are nonlinear and the objective function may change

as the situation develops. To solve these, conventional

engineering relies on simplifying assumptions. For example, the

actual problem is often separated into components that can be more easily addressed. But locally optimal components do not

integrate to yield a globally optimal solution unless the

components are independent . . . and they rarely are. We call upon

linear programming even when the constraints are known to be

nonlinear. Steepest descent is used even when the response

surface may have multiple modes, be discontinuous, noisy or, in

the limit, have no gradient. Spectral analysis and Markov

processes are used to predict time series, even when the actual environment is known to be nonstationary. Such simplification

often yields the right answer, to the wrong problem!

Another way to simplify is to use expert systems. Here, the

design is based on using generally useful rules (heuristics)

derived from experience. But remembered rules may be in error. The sample size documenting the worth of individual heuristics

is likely to be insufficient. This is especially true when dealing

with a dynamic environment where the objective function is changing while the problem is being solved. And rules that are good "on the average," may not be good enough. In practice, we need an particularly appropriate way to solve the problem at

7
hand. Incidentally, when dealing with a nonstationary

environment, the rules that are best at any particular time are

likely to be far less than best at other times. To make matters

worse, obeying any set of rules is certainly not the best way to

operate in an environment that includes intelligently

interactive competitors.

Traditional engineering is, indeed, bottom-up. The design

process becomes increasingly complicated and cumbersome.

Computers are used to solve complex sets of differential equations . . . rather than to directly address the problem at hand. But we can now generate alternative solutions at negligible cost, and thus simulate the fundamental process of

evolution in order to design top-down. Alternative solutions are scored as separate entireties. No direct attempt is made to improve any of these individual designs. Those found inadequate

are simply discarded with no penalty. The solutions that are found to be worthy are varied to yield offspring, thereby

generating a new population (generation) that is similarly

scored. As in nature, the selection process is phenotypic.

Alternative designs/organisms are scored only in terms of their

expressed behavior, not their components or structure. The

mutation/selection process iterates until a sufficiently worthy

solution has been found (or the available computational

resources have been expended).

This fast-time neo-Darwinian evolution has a significant

history. There have been various approaches: evolution

strategies, evolutionary programming, genetic algorithms and

related efforts in genetic programming and classifier systems.

The first two of these are very similar, the primary distinction

being whether or not the parents are part of the next generation.

Genetic algorithms are quite different. They often use binary

string representations, even when this is not an intuitive

representation for the problem at hand. In contrast, in

evolutionary programming, the representation follows the

designer's intuition. Any suitable choice can be made. Genetic

algorithms strongly rely on crossing over to generate new

offspring, cutting and splicing existing solutions in the hopes

that such recombination will be useful. In evolutionary

programming, no emphasis is placed on any particular operator:

again the mode of variation can reflect the representation

chosen as well as the known interactivities between

components of the solutions. It may be wise to recombine ideas

from different solutions (for example, mix ice cream and root

beer), or it may not (for example, combining the first half of

Hamlet with the second half of Macbeth ... it is still Shakespear, but it doesn't make sense). Recent mathematical

proofs have indicated that crossover provides no general

advantage to solving problems [2], and so, in order to maximize

the practical use of evolutionary algorithms, the search

operators must be tailored to the task at hand. This requires

expertise.

Finally, with regard to the selection mechanisms, the

traditional genetic algorithm relies on proportional selection,

with the expected number of copies of each parent being made in

proportion to its relative fitness. In contrast, in evolutionary

programming, selection simply eliminates unfit solutions and

can also be made probabilistic such that there is a tunable

likelihood of accepting solutions with lower fitness. This

ability to adjust the selection pressure offers yet another

versatility to evolutionary programming. Note that it naturally

lends itself to parallel processing and can be operated in a

hierarchic manner, that is, with a higher level of evolution

adapting the variables of the lower level. This may involve

adjusting the population size, number of generations before

each decision, the selection pressure, the mutation noise

distribution, and so forth.

Indeed, evolutionary programming [3], [4], [5] is a most general

optimization technique. The only "rules" are iterative mutation

and selection. In its standard form, the basic evolutionary

program uses the four main components of all evolutionary

computation algorithms: initialization, variation, evaluation

(scoring), and selection [6], [7]. At the basis of this, as well as

other evolutionary computation algorithms, is the presumption

that, at least in a statistical sense, learning is encoded

phylogenically versus ontologically in each member of the

population. 'Learning' is a byproduct of the evolutionary

process as successful individuals are retained through stochastic

trial and error. Variation (such as mutation) provides the means

for moving solutions around on the search space, preventing

entrapment in local minima. The evaluation function directly measures fitness, or equivalently the behavioral error, of each

member in the population with regard to the environment.

Finally, the selection process probabilistically culls suboptimal solutions from the population, providing an

efficient method for searching the topography.

More specifically, evolutionary programming starts with a population of randomly chosen trial solutions (designs/plans of

action, that is, alternative ways of allocating the available

resources over time). These may include suggestions, but they

are not required. Each of these trial solutions is evaluated with

regard to the specified fitness function. Only some are retained

to serve as parents. Each parent is altered through application of

a mutation process. Mutations on the degrees of freedom are chosen with respect to a probability distribution, typically

uniform. The number of mutations per offspring is also chosen

with respect to a probability distribution or it may be fixed a

priori. These offspring solutions are then evaluated over the

existing environment in the same manner as their parents. After

the fitness or behavioral error is assessed for all offspring, the

selection process is performed in one of several ways,

depending on current knowledge of the response surface. In most applications, the size of the population remains constant,

but there is no restriction in the general case. The process is halted when either the solution reaches a predetermined quality, a specified number of iterations has been achieved, or some

other criteria (such as sufficient convergence) stops the

algorithm.

Evolutionary programming differs philosophically from other

evolutionary computational techniques such as genetic

algorithms in a crucial manner. It is purely top-down rather than

8
bottom-up optimization. It is important to note that (according

to neo-Darwinism) selection operates only on the phenotypic

expressions of a genotype; the underlying coding of the

phenotype is only affected indirectly. The realization that a sum

of optimal parts rarely leads to an optimal overall solution is key to this philosophical difference. Genetic algorithms rely on

the identification, combination, and survival of "good"

building blocks (schemata) iteratively combining these to form

larger "better" building blocks. In a genetic algorithm, the

coding structure (genotype) is of primary importance as it contains the set of optimal building blocks discovered through

successive iterations. The building block hypothesis is an

implicit assumption that the fitness is a separable function of

the parts of the genome. This successively iterated local

optimization process is fundamentally different from

evolutionary programming which is an entirely global

approach to optimization. Solutions/designs (or, by analogy,

organisms) in an evolutionary programming algorithm are judged solely on their fitness with respect to the given

environment. No attempt is made to partition credit to

individual components of the solutions. In evolutionary

programming (and in evolution strategies), the variation

operator allows for simultaneous modification of all variables at the same time. Fitness, described in terms of the behavior of

each population member, is evaluated direcdy, and is the sole

basis for survival of an individual in the population. A

crossover operation designed to recombine building blocks is not utilized in the general forms of evolutionary programming.

Evolutionary programming can be used to detect unknown

signals in noise (discovering templates for pattern

recognition), to design optimal neural networks (even when the

response surface is discontinuous), for forecasting

nonstationary time series given an arbitrary payoff function,

for discovering the relationship among variables (modeling an unknown transducer/plant), for the control of that plant within

the limits of its controllability, and for gaming if that plant has

its own purpose. It has been demonstrated for improving drug

design (Agouron Pharmaceuticals, Inc.), for adaptive control of

freeway ramp signals (CalTrans), for scheduling the production

of clothing (Levi Strauss & Company), for the distribution of

fuel (Chevron), for aiding the detection of breast cancer (U.S.

Army Medical Research and Materiel Command), and for various

other military programs that concern improved training and

real-time mission planning.

But all too often engineering problems as posed are ill-defined. Are the stated requirements hard or soft constraints? If soft, how

soft? What else should be measured? Are all these measures

equally important? Are some, or all of them, critical (that is,

failure in this regard nullifies the value of any other

achievement)? Are there degrees of criticality? We often simply

minimize the mean squared error rather than refer to the real payoff matrix wherein equally correct outcomes are not of equal

worth and equal, but opposite, errors have different costs.

Clearly, measures of effectiveness (MOEs) and the associated measures of performance (MOPs) do not tell the whole story.

Indeed, effective engineering begins with a clear understanding

of what must be achieved by when. But what if that outcome i s not realized? Surely some value is found in lesser degrees of

achievement. There are even times when our primary concern i s

to avoid a particularly undesirable situation. In other words, to be meaningful, we must identify each of the significantly

different futures, all the way from Utopia to catastrophe, for only

then can we measure the overall worth of any given situation.

Unfortunately, it is difficult to envision these significantly

different futures, no less their relative worth. The Valuated State Space Approach provides a convenient way to overcome this

difficulty. This method allows the responsible individual to

portray the significantly different futures in terms of

preferentially independent1 aspects of concern. These are the

dimensions of a hyperspace, each being attributed some relative

importance and made measurable by designating mutually

exclusive class intervals that indicate those differences that

make a difference in degree of achievement. The class intervals

exhaustively span the range of each parameter from the most to

the least desirable degree, each of these being attributed some

value. When parameters are not directly measurable, they are expressed in terms of subparameters that are measurable or extended to still lower levels in the hierarchy that include

directly measurable subparameters. Thus, the purpose to be

achieved takes the form of a hierarchic Valuated State Space

together with a normalizing function that can be used to combine contributions on the various parameters and

subparameters in a manner that reflects their degree of

criticality.

In many situations some overall worth is realized if there is some achievement in any regard. It is then appropriate to use

the weighted arithmetic mean. In other situations, all of the

parameters may be critical. Under these conditions, the

normalizing function takes the form of a weighted geometric

mean, that is, the overall worth is the product of the relative

degrees of achievement, each raised to the power of the

normalized importance of that parameter. If all the achievement

values are high, the weighted arithmetic mean can be used as an

optimistic estimate of the overall worth, for the difference

between these means becomes negligible at successively higher

values of achievement in every regard. [6J. Alternative "what

ifs" can then be scored in view of their corresponding futures. The best is selected and there is a list of the remaining

deficiencies, by priority. The worth of partially resolving any

of these remaining problems can easily be computed.

But organizations operate in a cooperative or competitive

environment. Our best move may not be best if it significantly

injures a friendly organization and/or greatly benefits an

adversary. The Valuated State Space Approach can also be used

to express the presumed purposes of the other players so that

1 wherein any change in the degree of achievement on a parameter does not alter the relative importance of the parameters.

9
their best moves and ours can be estimated in light of their

mutual attitudes and the state of the game.

Engineering decisions are improved when the purpose is made

clear and concise, for means have value only in terms of ends,

evolutionary programming can then be used to discover

increasingly appropriate designs and/or modes of behavior in

view of the presumed dynamics/constraints.

This capability has recently been demonstrated in gaming.

Effective training requires an interactive adversary. Having

qualified individuals simulate the opposing force is dangerous,

for it presumes an understanding of their culture and intent. Such

simulations are non-repeatable and cannot be calibrated. It is

equally dangerous to train against any rule-based enemy (expert

system), for the real enemy is intelligently interactive, learns,

may demonstrate initiative, and is likely to behave in a

generally unpredictable manner, by generating non-rule-based

intelligently interactive adversaries in tank platoon combat

simulation for the sake of improved training. Non-rule-based

intelligently interactive adversaries were generated for simulating tank platoon combat. Three series of experiments

were conducted using the Modular Semi Automated Forces

(ModSAF) simulation program that embodies the terrain,

platforms, and low-level deconfliction [8]. These tank warfare

experiments were performed using a Sparc 20 Work Station in

real-time. In the first series, opposing tank platoons were

situated arbitrarily, each given different missions in the form of

a Valuated State Space and normalizing function. These include

the weighted probabilities of kill and survival, as well as the

time and distance remaining to reach a specified goal-point. In one experiment, both platoons had unlimited visibility and

equal firing range of 1200 meters. The primary concern of both

platoons was survival. Realistic physical constraints were imposed, for example, the tanks could not move faster than 25

meters per second. Tactical decisions were made every 20

seconds after 30 generations of mutation and selection, the best

evolved behavior being implemented. In this manner, there was

learning across successive decision points.

The platoons moved toward their goal-points and, in this case, toward one another. They stopped just before reaching the firing

range. They behaved erratically until finding themselves in

synchrony. Then took a path toward its goal that remains

outside the firing range. In essence, both platoons discovered

"evasion" . . . without understanding this concept. In another

experiment a platoon trades-off the worth of continuing toward

its goal-point as opposed to pursuing the remaining enemy

tanks. Throughout these experiments, the exhibited behavior seems rational.

In the second series of experiments, one platoon was provided

information concerning the mission of the other platoon. This

resulted in improved performance. In the third series of

experiments, the same platoon was given misinformation about

the enemy's mission, this resulting in a measurable cost. Obviously, the decision points can be made a function of the

combat tempo. The less time between the decisions, the greater

the population and the larger the number of generations before

each decision, the greater the level of simulated intelligence.

Note that the level of intelligence and, indeed, the mission can

be changed at any time during the engagement. This combat

simulation can be extended to higher levels of command

wherein diverse platforms are interactively controlled in a coordinated manner. In essence, here is a simulation of co- evolution.

This non-rule-based simulation can also be used to provide

effective decision support, for evaluating alternative weapon

systems capabilities and the tactics/doctrine required for these

systems. In fact, it may be used on-line to generate particularly

worthwhile tactics/doctrine in light of the developing situation.

This simulation can also be used as a basis for measuring the

impact of soft intelligence factors on the outcome of combat.

To what extent does levels of training, loyalty, fatigue,

cohesiveness, and so forth modify force effectiveness?

3. CONCLUSION

Mathematics has long been the primary tool of engineering.

Linear approximations yield first cut solutions. Far more

complex representations are required to treat actual real-world

problems. This formalism requires significant computation. We

allocate extensive CPU time to solve differential equations that

portray time-dependent interactive dynamic systems.

But computers can be used more directly. There is no need for the

intervening mathematics. The machine itself becomes a fast- time model of natural evolution. Rather than yield a single best

design, it provides an evolved population of solutions, each of

measured worth. The engineer can review these, taking into

account concerns that were not directly stated in the payoff

function: this design scored well but may have undesireable side

effects or unintentional consequences, that design may prove

too costly, and so forth. The ultimate design is selected from

those that have survived extensive competition. If conventional designs are introduced as suggestions and are of

true worth they will be so recognized by having survived the

selection process, evolutionary computation is not in

competition with other methods of optimization, it simply

provides a way of improving on their results. In essence, it is a simulation of the scientific method and, therefore, an embodiment of creativity.

Of course, we must still recognize the need for a design and

express that need in concise terms for, to be effective, any

optimization technique must reference an explicit scoring

function. But ordinarily ends are stated in terms of means. The

contractor sees a new building in terms of brick and mortar

rather than the efficiency of layout, comfort, cost of

maintenance, longevity of service and, of course, ability to

withstand environmental extremes. This no longer need be the

case. We now have a convenient formalism for representing

purpose/intent/mission. We can now solve complex problems

10
using top-down engineering by coupling the Valuated State Space Approach with evolutionary programming.

But there is more to do. We need to determine the fundamental

capabilities and limitations of evolutionary computation. What

is the simplest way to generate useful heredity through

reproduction in a finite noisy environment? What form of

evolutionary computation should be used to treat which class of

problems? What are the trade-offs between population size,

number of generations, type of variation, and so forth? Are

there heuristics for selecting a most suitable representation for

any given problem? Are there ways to estimate the convergence

rate under different conditions? Under what conditions is it

better to evolve weighted rules rather than simply direct combinations of the available resources?

It might also prove worthwhile to examine the manner in which

evolutionary computation relates to natural evolution. Is it worthwhile to replicate the specific mutation/selection process

that takes place in nature? How should genetic variation be

combined with phenotypic selection? Is it worthwhile to

replicate natural evolution across the hierarchy from genes

through organisms (their organization and species)? What

theory of natural evolution (Lamarckian, Darwinian, and so

forth) is most appropriate for addressing certain kinds of

problems? Would it be advantageous to combine aspects of

these different theories?

How can evolutionary computation be made still more efficient

and effective? Is it worthwhile to use asynchronous evolution

to allow some of the better parents to reproduce across

generations and/or to artificially alter the response surface (the

adaptive landscape) to facilitate finding the global optimum?

How can evolutionary computation benefit from self-adaptation

(internally and/or through the use of meta-levels)? What are the

limits of evolving self-referential, self-modeling, self-aware,

conscious automata that, in an artificial social setting, may

even exhibit conscience?

How should evolutionary computation be realized under different

conditions/constraints? What is the most appropriate language

and coding procedure and why, given the circumstance? When

and how should distributed/parallel processing be used for

evolutionary computation? When is it advantageous to hardwire

evolutionary computation into a chip? These and other

questions are worthy of serious consideration.

In the meantime, there are diverse applications worthy of topdown engineering.

4. REFERENCES

[1] Websters New Twentieth Century Dictionary, 1983, Simon

and Schuster, New York, pp. 602.

[2] D.H. Wolpert and W.G. Macready (1997) "No free lunch

theorems for optimization," IEEE Trans, evolutionary

Computation, Vol. 1:1.

[3] Fogel, L.J., 1964, On The Organization of Intellect, Ph.D.

dissertation, University of California, Los Angeles.

[4] Fogel, L.J., Owens, A.J., and Walsh, M.J., 1966, Artificial

Intelligence through Simulated Evolution, New York, NY: John

Wiley.

[5] Fogel, D.B., 1995, Evolutionary Computation, Toward a New Philosophy of Machine Intelligence, Piscataway, NJ, IEEE

Press.

[6] Fogel, David B., Back, Thomas, and Michalewicz,

Zbigniew, 1997, Handbook of Evolutionary Computation,

Oxford University Press and Institute of Physics Publishing.

[7] Fogel, David B., 1997, An Introduction to Evolutionary

Computation (video presentation), Piscataway, NJ., IEEE Press.

[8] Fogel, L.J, Porto, V.W., and Owen, M., 1996, An

Intelligently Interactive Non-Rule-Based Computer Generated

Force, Proceedings of the Sixth Conference on Computer

Generated Forces and Behavioral Representation, Orlando, FL:

Institute for Simulation and Training, STRICOM-DMSO, pp.

265-270.

11
Ordinal Optimization and Soft Computing

Yu-Chi Ho

Division of Engineering and Applied Sciences

Harvard University

Cambridge, MA 02138

EXTENDED ABSTRACT

The world is full of large and complex engineering problems that we

do not know how to solve effectively or efficiently. Examples range from the design and operation of communication networks and

manufacturing plants, to traffic control on land, sea, and in the air, to

military C3I and logistic management. Such discrete event systems

permeate the modern human-made civilization. Typically they do

not possess simple analytical structures compared to the differential equation based physical systems; stochastic effects abound in such

systems; and finally their designs involve search in a huge

parameter/configuration space. While simulation is a general

purpose performance analysis tool of choice, fundamental theoretical

limitations on computation rule it out as an optimization tool for such problems. In this talk we advocate a strategic re-direction of

this general optimization problem and show that effective in-road can be made in practice. We will discuss the results that have been

achieved so far and the problems remain. Our thesis also advocates

the inclusion of this optimization tool as one elements of the computing intelligence arsenal. A live demonstration of the tool will be conducted during the talk to illustrate its generality and properties.

A separate session immediately following this talk also addressed more recent developments.

Additional details can be found in the author's web-site:

http://hrl.harvard.edu/people/faculty/ho/CRCD

and the following references.

REFERENCES

[l]Ho, Y.-C, R. Sreenivas, and P. Vakili, "Ordinal

Optimization of Discrete Event Dynamic Systems,", J. of

DEDS, vol. 2(2), pp. 61-88, 1992.

[2] Patsis, N., C.-H. Chen, and M. Larson, "Parallel

Simulation of DEDS," IEEE Trans, on Control Technology,

1996.

[3] Deng, M, Y.-C. Ho, and J.-Q. Hu, "Effect of Correlated

Estimation Error in Ordinal Optimization," Proceedings of the

Winter Simulation Conference, pp. 466-475, December 1992.

[4] Ho, Y.-C, "A New Paradigm for Stochastic Optimization

and Parallel Simulation," Proc. of 1993 DES Workshop in IMA/U. Minn. Lecture Notes Series, Springer-Verlag, 1994.

Presented at the IMA workshop 5/23/93 in Minneapolis and

the ORSA/TIMS/INRIA Conference on Applied Probability

in Paris 6/18/93.

[5] Ho, Y.-C, "Heuristics, Rules of Thumb, and the 80/20

Proposition," IEEE Trans, on Automatic Control, vol. 39(5),

pp. 1025-1027, May 1997.

[6] Ho, Y.-C, and M. Larson, "Ordinal Optimization and Rare

Event Probability Simulation," J. DEDS, vol. 5, #2-3, 1995.

[7] Wieseltheir, J. E., C. M. Barnhart, and A. Ephremides,

"Ordinal Optimization of Admission control in Wireless

Multihop Voice/Data Network via Standard Clock

Simulation," / DEDS, Vol.5, #2-3, 1995.

[8] Ganz, A., and X. Wang, "Efficient algorithm for virtual

topology design in multihop lightwave networks," IEEE/ACM

Transactions on Networking, vol. 2, June 1994.

[9] Xie, X.-L., "Dynamics and convergence rate of ordinal

comparison of stochastic discrete event systems," IEEE

Transactions on Automatic Control, to appear, 1997.

[10] Xie, X.-L., "An Ordinal Optimization Approach to a Token Partition Problem for Stochastic Timed Event Graphs,"

Proceedings of the 1994 Winter Simulation Conference,

Orlando, Florida, pp. 581-588, December 1994.

[11] Dai, L.-Y., "Convergence Properties of Ordinal

Comparison in the Simulation of Discrete Event Dynamic

Systems," JOTA, Vol. 91(2), pp. 363-388, 1996.

[12] Lau, T.-W. E., and Y.-C. Ho, "Universal Alignment

Probabilities and Subset Selection for Ordinal Optimization,"

JOTA , Vol. 39(3), pp. 455-490, June 1997.

[13] Deng, M., and Y.-C. Ho, "Sampling-Selection Method

For Stochastic Optimization Problem," submitted to AUTOMATICA, 1995.

[14] Lee, L.-H, T.-W. E. Lau, and Y.-C. Ho, "Explanation of

Goal Softening in Ordinal Optimization," IEEE Trans, on

Automatic Control, to appear, 1997.

[15] Ho, Y.-C, "An Explanation Of Ordinal Optimization,"

Proceedings of Joint Conference on Information Sciences,

Raleigh, NC, March 1997.

f The work in this paper is partially supported by NSF grants EID-9212122, EEC9402384, Army contracts DAAL03-92-G01 15,

DAAH04-95-0148 and Air Force contract F49620-95-1-0131.

12
[16] Tang, Z. B., and Y.-C. Ho, "Modification of Adaptive

Partitioned Random Search," Proc. of 1995 Conference on

Decision and Control, New Orleans, December 1995.

[17] Chen, C. H., and V. Kumar, "Motion Planning of

Walking Robots in Environments with Uncertainty," Proc. of

IEEE Conference on Robotics and Automation, 1996.

[18] Yang, M. S., L.-H. Lee, and Y.-C. Ho, "On Stochastic

Optimization and Its Applications to Manufacturing," Proc. of

AMS Conference on Stochastic Problems in Manufacturing, to appear in Lecture Notes in Applied Mathematics, 1997.

[19] Dai, L.-Y., and C.-H. Chen, "Rates of convergence of

ordinal comparison for dependent discrete event dynamic

systems," JOTA, Vol. 94(1), July 1997.

[20] Ho, Y.-C, "On the Numerical Solution of Stochastic

Optimization Problems," IEEE Trans, on Automatic Control,

Vol. 42(5), 1997.

13
Introduction to Quantum Theory of Open Systems

Yu. L. Klimontovich

Physics Faculty

Moscow State University

117234 Moscow Russia

E-mail: ylklim@hklim.phys.msu.su

Abstract

In this Lecture we are going to pave the way for

the quantum theory of open systems. The question

of completeness of description of physical phenomena

on the basis of quantum mechanics and other eter- nal questions of the quantum theory are considered.

Applications of the S-theorem and the conservation

law of Information and Entropy are demonstrated. In

this domain there are the intersections between the

Physics of Open Systems and Semiotics.

I. Introduction

As and in the classical kinetic theory, in the quantum one the simplest model is the one-component

rarefied gas of structureless particles (the Boltzmann

gas). This model it is possible to expand in two main

direction, and consider two more complicated models.

The first one is the rarefied electron-ion plasma,

which is a three-component system comprised of gases

of electron and ions, and electromagnetic field. The second is the system of atoms and field, which

in the simplest case consists of two components. The

gas component differs from Boltzmann gas in that the

structure of atoms or molecules is taken into account.

The second component is again the electromagnetic

field. A natural generalization of these two particular models is the so-called plasma-molecular system,

which of at least four components (KlimontovichWilhelmsson-Yakimenko-Zagorodnii 1989). An example of such system is provided by partially ionized

plasma. Foundation of the kinetic of systems of this

kind have been laid in (Klimontovich 1980 (1983);

1982 (1986) Klimontovich-Kremp-Kraeft 1981, 1987).

A consistent description of plasma-molecular systems is only possible within the framework of quantum theory; hence the need of bridging the gap between the classical theory of open systems to the appropriate quantum theory.

This is best done with the concrete examples of simple but real systems, such as the system of noninteracting hydrogen atoms or free electrons in electromagnetic field. We shall use these examples to illustrate

the transition from the reversible microscopic operator equations to irreversible quantum kinetic equations. Such transition may be interpreted as replacement of system of particles and field oscillators by a continuous medium.

In particular, this implies that Schroedinger equation of quantum mechanics for deterministic (not operator) wave functions describes the evolution of con- tinuous medium, but ignores the dissipative terms. In

this sense, there is an analogy between Schroedinger

equation in quantum mechanics and Euler equation

in hydrodynamics (Klimontovich 1993, 1995).

It would be natural to begin our study of quantum

system of atoms and field with the microscopic equations, which give complete quantum electrodynamic

description of atoms and electromagnetic field. Like in the case of Boltzmann gas, we again are faced with important questions. What are the smallest scales on which the initial equations of quantum

electrodynamics lose their reversibility? What is the cause of irreversibility?

Similar question arise at different levels of description. We might ask, for instance, what are the smallest scales which allow going over from operator equations of quantum electrodynamics to the corresponding Schroedinger equation for the deterministic distribution function of, let us say, the atom of hydrogen.

The fact is that quantum mechanical Schroedinger

equation is more coarse than the corresponding equation of quantum electrodynamics, since it only in- volves the mean field rather than the coordinates of

individual field oscillators.

The problem consists therefore in finding the start- ing point of transition towards irreversible equations.

In this connection we should mention simulating in- fluence of the work of Ilya Prigogine (Prigogine 1980;

Prigogine - Stengers 1984), who for many years has

been studying the possible generalization of the sec- ond law of thermodynamics to the microscopic level. The main role is assigned to the dynamic instability

14
of motion of microscopic objects. Dynamic instability

in quantum theory is manifested in significant change

of wave functions when the relevant initial conditions

are varied even slightly.

Recall that in case of Boltzmann gas the procedure

of smoothing over physically infinitesimal volume (the

"point" of continuous medium), which is necessary for

going over from the system of particles to the approximation of continuous medium, reflects the existence

of dynamic instability of motion. The smoothing over the physically infinitesimal scales in the construction

of irreversible equations of statistical theory is based on the existence of dynamic instability of motion of

particles of system. In this respect the dynamic instability of motion plays a constructive role in the

statistical theory.

Since the theory of dynamic instability in quantum

theory is still in its early stage, it will be expedient

to start with the evaluation of the smallest scales on

which smoothing is possible. This is necessary for

defining the limit of applicability of the initial microscopic equations of quantum electrodynamics.

The question of completeness of description of physical phenomena on the basis of quantum mechanics was the subject of the famous debate between Einstein and Bohr at the 5th Solvay Conference in 1927

(see Mehra 1975). Later this problem was discussed in

the paper entitled Can quantum-mechanical description of physical reality be considered complete? (Einstein - Podolski - Rosen 1935., and also in the papers

by de Broglie (1953) and Bohm (1952). The issue

of "deficiency of quantum-mechanical description" is closely related to the problem of the so-called hidden

parameters in quantum mechanics.

Most physicists argued that quantum mechanical

description is complete, and that the problem of hidden parameters does not exists. This view was based

for the most part on the book by John Neuman

(1932), in which he proved that hidden parameters are incompatible with the foundations of quantum theory.

It was not mentioned, however, that Schroedinger

equation of quantum mechanics is itself approximate.

Further theoretical and experimental studies were

simulated by the results of Bell (Bell 1965, 1966: Belinski, Klyshko 1993), who formulated the condition

of existence of hidden parameters as Bell's inequality. This was seen as a new possibility of experimental verification: if quantum mechanical description is complete, then Bell's inequality does not hold.

In a recent review (Belinskii - Klyshko 1993) we

read:

"The problem formulated many years ago by Einstein, Podolski and Rosen, by Bohm and Bell, still excite the new generation of physicists. To a large

extent this is due to the fact that the contradiction

between the prediction of quantum theory and the

theory of hidden parameters can be settled in a con- vincing way (in favor of quantum theory, of course)

by experimentum crucis, unlike most other quantum

paradoxes. The theory of hidden parameters is closely

related to the ensemble-statistical interpretation of

quantum theory, and this is the reason why such ex- periments (real or imaginary) add serious evidence to

the eternal debate between the advocates of statistical (Einstein) and orthodox (Bohr's or Copenhagen)

interpretations, and their numerous modifications."

And in the next paragraph:

"It is yet possible that in the future this debate

will be settled (perhaps in favor of a third way), and

historian of science will be see it as a vivid example

of fallacies which plagued even the brightest minds of

the past"

So the authors do note rule out possibility of a third

way.

Let us take advantage of this option. Our treatment

will be largely based on the ideas and methods described in detail in (Klimontovich 1993, 1995, 1997).

We would like to point the recent paper (Kadomtsev,

1994) in which the principle problems of quantum theory are discussed.

II. Microscopic and Macroscopic

Schroedinger Equations

Imagine a quantum system which consists of an

ideal gas of "particles" (hydrogen atoms, as example)

and fluctuation electromagnetic field. Microscopic description of quantum processes in

such system starts with the reversible dynamic equations for the particles and field. There two possible

approaches. On is based on the Schroedinger equation for the wave function of complete set of variables

of particles and field. The other relies on the equation for quantum (operator) wave function of particles

and electromagnetic field's oscillators. In both cases the initial dynamic equations give, in principle, an ex- haustive quantum mechanical description of time evolution of the system under consideration. Such level

of description corresponds to a pure ensemble.

For the sake of simplicity, we shall describe interaction with the electromagnetic field in the dipole approximation. So we have a closed set of equations

for operator wave function <3>(r, R,t) of electron in

hydrogen atom, and field operator E~(R,t). Instead

the ^(r, R, t) operator it is useful to use the quantum

operator f(r,p,t) which is corresponding to Wigner

quantum distribution function f(r,p,t) in the sixdimensional phase space.

However, owing to the nonlinearity of operator

equations, averaging over the Gibbs ensemble results

in a very sophisticated system of meshing equations in

15
the moments of different order. Accordingly, we once

again have to deal with the problem of closure, so as to obtain a closed system of approximate equations.

In quantum mechanics the equation for operator

wave function $(r, R,t) is replaced by Schroedinger

equation for the deterministic wave function ip(r, R, t) of the electron in a hydrogen atom (fy(r,R,t) —>

In quantum mechanics the equation for operator

wave function is replaced by Schroedinger equation

for deterministic wave function of the electron:

dip n

2 d

2

*p ih—— =

dt 2m dR2 + U(r)^ - dE(R,t)ip;

, drdR

1 (1)

This equation approximative but still reversible.

From (1) we can go over to the equation for deterministic "quantum distribution function" in Wigner's

form

f(r,p,R.t = (2)

(2

exp(— irp) ——dr

f ,/ ^ , drdpdR f , , „ . 0 drdR

(3)

Let us also write the corresponding kinetic equation:

df df „,„ .a/

(4)

U(r + -hr) U(r - -hr)

exp [it(p — p)] drdp = 0

which in the classical limit becomes

^L +V^L + E{R t )^l-—^l = 0 (5)

dt dr ' dp dr dp

We see that Schroedinger equation (1) for deterministic wave function corresponds in the classical limit

to the kinetic equation for the one-point distribution

function f(r,p,R.t). Like Schroedinger equation, this

equation is reversible since it does not take into ac- count the dissipation due to the interaction of electron

with fluctuation electromagnetic field. Now, to facilitate the transition to the irreversible

equations< let us refresh some points from Boltzmann's kinetic theory.

The kinetic Boltzmann equation differs from (5) in

that it includes the "collision integral" which take care

of the dissipation due to redistribution of the particle's velocities because of collisions between them. By

r and / we denote the relaxation parameters - the free

path time and length. We also introduce the characteristic parameters of the problem T and L.

As we know from gas kinetic theory, important

are two extreme cases, corresponding to the approximation of gas dynamics and of free molecular flow.

The gasdynamic approximation is used when r <C

T, I <Zi L. Then the kinetic Boltzmann equation

may be replaced by the simpler equation for the gasdynamic functions p(R, t),u(R, t),T(R, t). In the opposite extreme case, when t T, I 3>

L,the dissipative term (the "collision integral") in the

zero approximation may be dropped. This brings us

to the reversible kinetic equation which formally co- incide with (5).

It is possible to exploit this analogy?

Recall first of all that the nature of description is changed dramatically when we go over from the Liouville equation, which carries all information about the

motion of particles of system, to the Boltzmann equation. To wit, ^from the system of particles whose motion is described by the reversible Hamilton equations,

we go to a continuous medium in six-dimensional

space of coordinates and momenta. Naturally, the

transition to the approximation of continuous medium

is associated with restriction from the side of small

scales which define the size of the "point". Since the

information about the motion of particles within the

"point" is lost, the equation of continuous medium

must be dissipative and therefore irreversible.

This transition is necessitated by dynamic instability of motion of microscopic elements of the system.

It is the dynamic instability of motion combined with

uncontrollable small exertions form the surrounding

world, that makes the transition to irreversible equation inevitable. In this connection it is worthwhile to recall that dissipation is usually seen as damping of motion, scatter- ing of energy, loss of information. At nonequilibrium

phase transitions, however, which may result in the

appearance of new structure, the dissipation plays a

constructive role. This explains why the construction of dissipative

equations is of crucial importance for the statistical

theory of open systems. The first step in this direction

16
consists in the revision of the concept of continuous

medium. This requires given a concrete definition of

physically infinitesimal scales.

It is known how to do this for Boltzmann gas and for a plasma (Klimontovich 1983, 1985, 1987). How then

do we apply this knowledge to the quantum system

of atoms and electromagnetic field. Let us return to the classical kinetic equation (5).

For the Boltzman gas, for example it can be used

for describing free molecular flows. The approximation of continuous medium still holds, however, since

this equation does not carry information about the

motion of individual particles. This restrict the admissible values of T and L from below: they must be

much greater than the 6relevant physically infinitesimal scales:

r » T » Tph , I » L » I ph (6)

And yet, equation (5) is reversible, because it corre- sponds to the zero approximation in small parameter

L/l.

What is the situation in quantum theory?

III. Continuous medium approximation in

QUANTUM THEORY

To take care of the dissipation, we must include

into consideration the interaction of atoms with fluctuating electromagnetic field. This will result in dissipative kinetic equation for the quantum distribution

function (or density matrix) and the field. The appropriate "collision integrals" are determined by the small-scale fluctuations whose characteristic scales are much smaller than the characteristic scales of the kinetic equations. In this way, the

problem of the structure of "continuous medium" is brought up explicitly in the derivation of kinetic equations.

This problem is closely associated with the definition of kinetic equations.

In the pure ensemble, the operator density matrix

(for example, in Wigner's representation (Klimontovich,1958, 1995; Klimontovich, Silin, 1960; Brittin and Chapell, 1961; Hillery, O'Connell, Scully,

Wigner 1994) is expressed via product of operator

wave functions ty(r,R,t). Upon transition to the con- tinuous medium, when the kinetic equations become

irreversible, the pure ensemble is replaced by "mixed"

ensemble. Then there is no representation in which

the density matrix can be expressed exact via the

product of wave functions!

It might seem that the above formulas defy this

statement. Indeed, the quantum distribution function

(2)is defined as product of wave function which satisfy

Schroedinger equation (1). It is as if we returned to

the "pure ensemble" again.

Naturally, there is a fundamental difference between these two definition of pure ensemble. The

first exactly renders the statistical properties of quantum mechanical description, whereas the second definition of pure ensemble corresponds to approximation

of continuous medium. The approximation amounts

to neglecting the dissipation altogether.

For the system of N particles this approximation

corresponds to Hartree equation in quantum mechanics, or to self-consistent Vlasov approximation in

plasma theory, or, at last, to Euler approximation to

hydrodynamics which disregards the dissipation due

to viscous friction and heat conduction.

In order to define the structure of "continuous

medium" in quantum theory, we must first of all introduce the characteristic scales of the system in question. The characteristic length and frequency for hydrogen atom are:

ro =

ne2

' me e V0=

h-

(7)

The Bohr radius ro is the characteristic scales of the

ground state distribution |^(r)| 2

, the frequency luq

determines the energy of ground state. Additional parameters arise when we go over to the

dissipative kinetic equations. We divide them into two

classes.

The first class includes those parameters which

characterize the process of relaxation towards equilibrium. This time is defined by Einstein's coefficient

for spontaneous transitions:

1 4|d„ 2 , i 3 ml "•'n, 3mc3

2e2 u

2 ^ 71771 3mc3

(8)

Einstein's coefficient is proportional to the coefficient of radiation friction at the transition frequency.

The following estimate then holds good:

Am ~ n*ujnrn «; ujnm , where n =

he

(9)

is the "constant of fine structure".

At the zero temperature the atoms are in the

ground state, and the density of electron's position

in the atom is isotropic. The most probable distance

^from the nucleus is characterized by Bohr's radius

Now let us try to answer the following question:

does the distribution of electron's position in the

ground state display a finer structure? What are the

smallest times which the isotropic distribution takes

to become established in the ground state?

17
It is obvious that the structure of "continuous

medium" is defined by the scales smaller then those of

(8). In classical and quantum electrodynamics there

are two scales which are smaller than Bohr's radius

rore =

mc2

Ac = — ~ Mro < r0 , where /j = —

.

mc Tic(10)

The first is the "classical electron radius". The

main contribution to the effective cross section of scat- tering of photons by free electrons (the Tomson's scattering) is proportional to Tq . The second parameter is Compton's length, which defines the shift of

wavelength in case of scattering of x-rays by free electrons. Which of these characterizes the beginning of

irreversibility, and thus defines the finest structure of

"continuous medium" the size of "point" in quantum

mechanics?

Remark that the study of the structure of "contin- uous medium" in quantum mechanics is stimulated,

in particular, by those difficulties which is associated

with the attempts to calculate quantum fluctuations,

like fluctuations of velocity of free electron moving

in a fluctuation electromagnetic field (Klimontovich

1990(1991), 1993,1995). The solution of this problem

gives us possibility to define the smallest relaxation

time over which the irreversibility sets up. This smallest relaxation time is defined by the classical electron

radius r0 :

= ^ = 4; r

3mc3

2e2 (11)

m{v2

) - mu>l (x2) = kTWo = h^Tiioo coth

(13)

For atom-oscillators at room temperature the

coth huJo/2kT is close to one, and the amplitudes i>o,£o are therefore defined by the zero-point energy hu>o/2.

So we have the following expressions for the frequency

and amplitude of atom-oscillators which are in equilibrium with electromagnetic field:

mxr

mujQX2

) -huj0 . (14)

We find from them the expressions the amplitude, fre- quency and velocity of atom-oscillator (Klimontovich

1995)

TY me4 e

2 me2 h n

(15)

which are known in quantum mechanics as Bohr's

parameters. Now these parameters are not conse- quence of Schroedinger equation for atom-oscillators,

but they represent the condition of equilibrium between atom-oscillators and electromagnetic field. To describe the distribution in the space (x, v) for a gas of noninteracting atom-oscillators in equilibrium electromagnetic field, we can use the generalized Fokker-Planck equation (17.3.13) in (Klimontovich 1995) for the distribution function f(x,v,t):

Now we shall show that the scales re , re define the

fine structure of the atom's ground state.

IV. Establishment of ground state in

ATOM-OSCILLATORS

Consider a gas of noninteracting atoms in equilibrium electromagnetic field. Following to Tomson

model, we regard the atom as a sphere of radius ro which carries a uniformly distributed positive charge.

The electron vibrates with respect to the center of the

sphere. The frequency of oscillations is found from the

expression for the elastic force

eE = —-r = —mu0r; u0 mr"

(12)

For the sake of simplicity we consider one- dimensional oscillations of the atom-oscillators. In the equilibrium state the mean kinetic and potential

energies are defined by expressions:

dt dx

df

UJnX— =

dv

d_

dv

9f

dv

d r n

d_

dx

df ulx

1

f (16)

Here the diffusion and friction coefficients in velocity

space are given be expressions:

n — „, kTu0 V{v) = 7" 7

2e2 ujl

m 3mc3 T

The spatial diffusion and friction coefficients are

(17)

D{x) = J^k = Tx2 m7 0' = r (18)

The equilibrium solution of this equation is defined

by Planck's formula:

18
mv2 /2 + mu$x2 /2 \

f{x, v) - C exp ( — ) , kl Wll =

fcT„

0 ^cocoth^

(19)

Now we can show the that relaxation times T( V ),T( X ) differ very much.

Indeed, the corresponding diffusion times are defined by expressions

TW = ^7 = i; r(x) = 7^- = ^«r(u) . (20)

(„) D{x)

The "strength" of inequality <C can be expressed in

terms of "fine structure constant" fj, = e

2 /he :

After smoothing, the second dissipative term in

(E.15) drops out, and we arrive at the standard

Fokker-Planck equation commonly used for describing the Brownian motion of harmonic oscillator:

dt dx dv dv

I) (v)

dj_

dv

+

d_

dv

[ivf]

(23)

For quantum atom-oscillators the diffusion and fric- tion coefficients are defined by the expressions (17).

We see that in this equation the scale on which the

spatial diffusion takes place within the volume of a atom (in the volume of a ground state) is a "hidden

parameter" (or "hidden scales"!

^From the last relation (21) follows inequality

T(v) ^ l/^o allows us to further simplify equation

(23) by averaging over the period of oscillations. As

a result we have the following equation:

1 1 r

( x) ~ /i r(v) and r(l) ~ fi —; r(w) ~ -3—

(21)

We see that the spatial diffusion is much more

"faster" than the diffusion in velocity space. Thus,

are two stage ("fast" and 'slow") of the evolution to

equilibrium distribution (19).

The "fast" process of evolution characterizes by the

time of spatial diffusion t/ x ) = x

2 /D(x ) — 1/T. We

see that the quantum mechanical ground state is es- tablished during very short time interval ttx\ ~ re /c ~ /x3 (l/u;o) which much less of the period of Bohr

oscillations.

The diffusion time for "slow" process is defined by

the time spontaneous emission Tt v\ ~ 1/7(^0) • Thus, in within the atomic limits the spatial dif- fusion is the fastest process, As a result, Boltzmann

distribution with respect to x is established on this

scale within the time T( x ) ~ re /c and can be used

as the smoothing function for carrying out the transition to the smoother function f(x, v, t) (Klimontovich

1995).

Marking off the function which satisfies (16)with

tilde, we may define the operation of smoothing as

f{x,v,t)= / f{x-x\x,t)F(x')dx'-

F(x)

\/2ttxI

exp -

2x.q

(22)

We see that the scale x0 ("Bohr's radius") defines the

size of "point" of quantum continuous medium for

system is considered, and scale re defines the corre- sponding physically infinitesimal time.

dj_

dt

D(«)' d2 f , 1 d

2 f

dv2 dx2

(24)

This equation describes only the slowest process of

relaxation over the time of the order 1/7 3> 1/ uQ. We see that it is possible to describe Brownian

motion of quantum atom-oscillators with a varying

degree of finesse. The most detailed information is contained in the Fokker-Planck equation (16), where

the negligibly small ("hidden") scales are less than

re , re. The least detailed information is contained in

the Fokker-Planck equation (24)

Other example of Ground State Structure it is possible to find in the last chapter of the book (Klimontovich 1995).

V. About some eternal questions of

QUANTUM MECHANICS

We saw that the concept of "pure ensemble" is clear

defined only in the case of complete quantum mechanical description system of atoms and electromagnetic

field. In quantum mechanics, however, the term "pure

ensemble" is used also in those cases when the description is based on the Schroedinger equation (l)for

the deterministic wave function ijj(r,t) of only of the

variables of particles. This approach corresponds to

approximation of continuous medium and when the

dissipation is not taking into account. On this ground

it is impossible to describe transitions between sta- tionary levels accompanied by emission of radiation.

Since the description based on the Schroedinger

equation is not complete, there exist "hidden parameters" ("hidden scales") which are revealed the use of

19
a more realistic approach to problem under consideration.

We have illustrated this possibility with a concrete

example of the system of atom-oscillators and field. By introducing the scales of "continuous medium" we

were able to take into account the small-scale fluctuation in quantum Fokker-Planck equation.

The calculation of small-scale fluctuations is also

of interest by itself: these fluctuations, for instance, are definitive for the effective cross section of a scat- tering of photons by free electrons (Klimontovich

1993,1995).

It is important that the effective cross section in

the quantum domain (visible and x-ray ranges) does

not depend on Planck's constant, and can therefore be

found from classical calculations. The relevant scales re ,re are so small that Heisenberg's uncertainty relation does not hold. In this way, there are two "exits" from quantum

theory. One of these corresponds to the domain of

large scales and slow a spatial variations. The other

is associated withe the transition to the scales which

are much smaller than any of the quantum scales of

the system in question, which brings us into the realm

of "hidden parameters" ("hidden scales").

The second question of this section which was

the subject of the famous debate between Einstein

and Bohr is "Is Quantum Mechanical Description

Complete?"- the title of the famous paper (Einstein, Podolski, Rosen 1935). In the light of arguments

developed above, the answer to this question is negative. The fact is that quantum mechanical description

based on the reversible Schroedinger equation can al- ways supplemented by the inclusion of fluctuations.

Then, owing to the existence of fluctuation dissipation relations the dissipation is inevitable. Consequently, any kind of quantum mechanical description

is in practice incomplete, and the concept of "pure

ensemble" is just an abstraction.

The above arguments score in favor of Einstein's

standpoint. In this connection it would be interesting

to note that the problem of incompleteness of quantum mechanical description had been actually solved

by Einstein long before the emergence of quantum

mechanics as such.

As early as 1916 Einstein formulated the concept

of spontaneous emission for the case of two-level atom

interacting with the equilibrium electromagnetic field. This term emphasize the inevitability of energy loss

by radiation (Einstein 1916). The dissipation thus being inseparable from real processes. The Schroedinger

equations for hydrogen atom and other mechanical

systems can only be regarded as a useful idealization.

At this point we would like to quote Ilya Progogine,

who said (Prigogine 1980, p. 70):

"...Or, on the contrary, The should we argue that

nobody has ever seen an atom that would not decay when brought into an exited level? The physical

"reality then corresponds to systems with continuous

spectra< whereas standard quantum mechanics appears only as a useful idealization, as a simplified limiting case". Prigigine does not belong to the founding fathers of

quantum mechanics. His statement, however, closely

echoes the words of Louis de Broglie.

De Broglie expressed doubt in the completeness of

quantum mechanical description even at the heyday

of the quantum theory. His scepticism was not, however, shared by his contemporaries, and so he also

abandoned this attitude, becoming one of the most

brilliant advocates of the "Copenhagen" formulation

of quantum mechanics. He recalled this period in the

following words (de Broglie 1952):

"Some people, remembering that I abandoned my

first attempts and used the interpretation of Bohr

and Heisenberg in all my works for twenty-fifes years

thereafter, will accuse me of being inconsistent when

they see that I am again doubtful and ask myself

whether my initial orientation had been right after

all. Should I feel like joking, I can reply in Voltaire's

words, " Only foolish people never change their minds"

"The answer, however, can be more prudent.

"The progress of science is continually harassed by

the tiranic influence of certain concepts which in the course of time have become dogmas. Because of this,

the principles which have been recognized as final

must be subject to most thorough revision".

At that time these words were the voice of one crying in the wilderness. This can be illustrated with a

quotation from the article published in the influential

American newspaper;

"The principle of uncertainty has eventually made

all contemporary physicists (with the exception of

Dr. Einstein) recognize that there is no causality or determinism in nature. Dr. Einstein in majestic solitude

has held out against all these concepts of quantum

theory"

(The New York Times, 30 March 1952).

Yes another pertinent passage is taken from Dirac's

paper published shortly before his death (Dirac 1978):

"I think it might turn out that ultimately Einstein

will prove to be right, because the present form of

quantum mechanics should not be considered as the

final form. There are great difficulties (which I shall

mention later} in connection with the present quantum mechanics. It is the best that one can do up till now.

But, one should not suppose that it will survive

indefinitely into future. And I think that it is quite

likely that at some future time we may get an improve

20
quantum mechanics in which there will be a return

to determinism and which will, therefore, justify the

Einstein point of view.

But such return to determinism could only be made

at the expense of giving up some other basic idea

which we now assume without question. We would

have to pay for it some way which we yet cannot guess

at, if we are to reintroduce determinism."

We do not wish to comment on these statements: the

clarity and boldness of the classics can only be admired. Their words encourage further studies in the

quantum statistical theory of open systems, which will

be continued in the next part of this Lecture. We tried

to define the author's position with regard to the fundamental problems of quantum theory. I shall try go on by this way.

VI. Statistical presentation of Heisenberg

UNCERTAINTY PRINCIPLE

VI. A. The oscillatory form of Heisenberg relation

As well known from the text books on quantum mechanics, the Heisenberg uncertainty principle follows

from a inequality

/ L dx

dx

T* 0i 1, (25)

Here L is any length parameter.

Let us f(x,p,t) is a quantum distribution function

- Wigner function (2) then the last inequality we can

present in the following form:

xL2 h

+ 2 f(x,p,t)

dxdp

2nh

> 1. (26)

The left side of this inequality we can present as mean value of energy for harmonic oscillator with the

proper frequency is defined relation

h h

2 1

u>0 mL2 2mL2 2

-huiQ. (27)

Thus

f (mujkx2 p \ r , .dxdp L . , J {-h+k)"***TM

^

(28)

This means that the mean value of a harmonic oscillators can not be less than the corresponding zero energy

mul{x2

) (p

2

) l ~^2—

~2^n~ ~ 2

hU°- (29)

The inequality are presented here it is possible to

write in the followings forms:

h

and

uj.

7-2 , k

2 i^l

(P

2

) +

(P

2

)

(P

2

)

>0;

h

0 T12\'jJ0 m

^ 2~T~ \x*) {x ,2 /~2\ -> 0.

(30)

(31)

^From this inequality the Heisenberg uncertainty re- lation follows

<*W>>T- (32)

In a general case parameters L and uq have arbitrary

values. For the sign "=" these parameters are not -

there are some restrictions on its

L

2 = —=2(x2

) =

mu>o

or in other form

(P

2

) — mojQ (x2

) =

2(p2

)

1

(33)

= -huQ . (34) m 2mL2 2

VLB. The sign Distribution functions

For the sigh "=" the equation (25) has the following

solution

\1>(x)\' exp -

x 2(x2

) (35)

The corresponding solution of the equation (26)

it is possible to present as the Wigner distribution

for the harmonic oscillator with the proper frequency

Uq

f(x,p) = exp -

x p<

2(x2

) 2(p2)

. (36)

The dispersions (x2

) , (p

2

) are defined by relations

(34).

vii. s-theorem for quantum systems.

Relative ordering of states "=", "> "

VILA. S-theorem

Of all macroscopic functions, only entropy S possesses a combination of properties that allow it to be

used as a measure of uncertainty in the statistical description of processes in macroscopic systems.

Entropy being the sole function with properties of a measure of chaos, there is but one option. It is nec- essary to redefine entropy so that the average energy

remains constant in the course of evolution.

21
But evolution in time it is equally possible to consider the evolution of stationary states in open systems at slowly changing of control (governing) parameters. It is for this type of evolution , that criterion was introduced (Klimontovich 1983, 1984, 1988,1990

(1981), 1995). This criterion was for the first time formulated for specific cases (Klimontovich 1983, 1984)

and called "S-theorem". Later, its general formulation was suggested, to make possible to direct comparison between the relative degree of order from ex- perimental date (Klimontovich 1988).

Here we shall consider the evolution of quantum

states corresponding, accordingly, to the sigh "=" and

" > " in Heisenberg relation. In general case, the degree of order of the distinguished state differs, which account for one of them

being more chaotic than the other. Let us term it "physical chaos". As a rule, this state is nonequilibrium and more ordered than the equilibrium state. Let us, by assumption, the quantum state corre- sponding to the sign "=" is most chaotic. For this

state the quantum distribution function fo(x,p) is determined by the expression (36). The corresponding

entropy

To change the mean value of energy we introduce some

the non zero temperature T

m

— rnujQ (x2

) = kB TUJn — \hujQ coth

2k^f " 2^°-

(41)

Let us the quantum distribution function f(x,p,t)

characterizes any nonstationary state with the sign

"> " in the Heisenderg uncertainty relation. The

quantum distribution function f(x,p.t) may have and

negative values, but the corresponding distribution

functions separately for coordinates and momenta in

any cases are positive

f(x,p,t)^ = f{p,t) >0,

f dx

/ f(x,p,t)—=f(x,t) >0.

The corresponding entropy

S[x,p] = -J f0 (x,p)\nfo(x,p)

d"

1

(42)

2nh

SQ [x,p} = - / fo(x,p)\nf0 (x,p)

dxdp

2nh f(x)\nf(x)

dx

- I f0 (x)\nfQ (x)^-

/o(p)ln/0 (p)^ = S0 [x] + Sob]-

Zirn

(37)

The mean energy for this state is defined by the zero energy

_ mu2 (x2

) (p

2

) _ 1 {E) ~ 2 ~2^T ~ 2^ (38)

^From the inequality (29) the mean more then this.

But according the S-theorem to determine the relative

degree of order it is necessary to compare the states

at equal values of the mean energy To satisfy this

condition it is necessary to replace the distribution

function by the renormalized one

fo(x,p) -» fo(x,p). (39)

The renormalized distribution function is also Gaussian but with renormalized values (x2

) , (p

2

) for dispersions

fo{x,p) =

h

y/WTW)

exp

2 (x 2

) 2 (p

2

) > 0.

(40)

-J f(p)lnf(p)^ = S[x] + S\p}. (43)

To find the necessary value of temperature T we

must solve the equation

mJix2 p

2 \ -

, ^dxdp

//; . - ' p

2

JQ-J \ ,. . dxdp

,2„2 muinX" .dx

2 f{x) T

+ f_ , Ldp

2m J[P)

27rh'

The solution of this equation

T(t) > 0

(44)

(45)

therefore the choice of the state with the sign "="

in the Heisenberg uncertainty relation as the more

chaotic state is correct. In the (44) variable t for

nonequilibrium states plays the role of parameter.

Using the expression (40) for the renormalized distribution function fo(x,p) and the constancy condition (44) for the average energy , the expression for

22
the entropy difference of states with signs "=", "> "

can be present as inequality

S[x,p] - S[x,p] = S[x] - S[x] + Sp] - S[p] =

J fix) L J

JKF

> f(p) 27rh ~

(46)

Thus, the state with the sign "=" in the Heisenberg

relation is the most chaotic. The last expression serves

as the quantitative measure for relative degree of or- der any quantum state - stationary or nonstationary - and most chaotic state which corresponds to sign "="

in the Heisenderg uncertainty relation.

It is necessary remember that the oscillatory model

was exploited above only in the special case concern of

real physical oscillator. The model was considered in

much more general. The parameter L in the previous

formulas is some general length parameter. If L is the

size of the system then the relation L and ujo allows to use "as example" the oscillatory model for description

of a free particle motion Kadotsev 1994; Klimontovich

1995,1997 (in press)).

VIII. Information

There are to different statistical definition of Shannon information. The first one coincides with definition (by form) with Boltzmann definition of entropy.

If /(A') is any dimensionless distribution function of

dimensionless variable A, then the Shannon information (entropy or "5— information") is defined by ex- pression (Haken 1988; Kadomtsev, 1994)

I[X] = S[X] = - I

S(X)]nf(X)dX. (47)

or for discrete variables

I[n) = S[n] = -^Sn\nSn . (48)

n

Although in many cases the calculation of 5— in- formation is certainly useful, it does not reflect the existence of self-organization in open systems (Klimontovich 1990 (1991), 1995).

To define the changing of information in processes

in open systems it is better to use more general definition of information (Stratonovich 1975; Klimontovich

1982 (1986))

I[X\Y] = S[X] - S[X\Y]. (49)

Here is S[X] is ordinary Boltzmann - Shannon entropy

5[A] = - J

S(X)\nS(X)dX (50)

and 5[A|y] the conditional entropy. It is connected

with the conditional distribution function S[Ar |Y]

(S(X,Y) = S[X\Y]S(Y)) by relation

S[X\Y] = - J

S(X,Y)lnS(X\Y)dXdY. (51)

The expression for the information it is possible to

present in more symmetrical form

I[X\Y] = J

\n I^J^SiX^dXdY > 0. (52)

We see that is defined by such way the information

is positive. The equality corresponds to the case when

the quantities A, Y are statistically independent.

IX. Conservation law of entropy and

INFORMATION

Let us the distribution function is defined completely defined be the first moment

S(Y) = 5(Y-a). (53)

a is any characteristic parameter. In open systems

it can play the role of control (governing) parameter.

Introduce this function in the expressions (51), (50).

After integrating over Y we will obtained the following

expression for the information

I[X\a] = S[X] - S[X\a] = S[X}+

J

S(X\a)\nS(X\a)dX. (54)

If the nonconditional entropy S[X] does not depend

on values of the control parameter a, then, using the

last equality, it is possible obtain the corresponding

relationship between the information and the entropy

for any two values of control parameter

/[A>i] - I[X\a2 ] = S[X\a2 ] - 5[A| 0l ]. (55)

^From it follows the conservation law for the sum information and entropy

I[X\a] + S[X\a] = const. (56)

We see that for the cases, when the nonconditional

entropy S[X] does not depends on the value of the

control parameter.

23
In the paper (Kadomtsev 1994) represents the conservation law as sum of the nonconditional information and entropy

I[X] + S[X] = const (57)

but such presentation of the conservation law contradicts to the definition (47) of the nonconditional

information and entropy.

For the example we can use conservation law (56)

for quantum systems. Let us S[X] —> So[x,p] is the

nonconditional entropy for the state with the sigh "="

in the Heisenberg uncertainty relation. It corresponds

to the ground state of the system at the temperature

T = 0. Let us also S[x,p] is the renormalized entropy

for the state with the sigh " =" in the Heisenberg uncertainty relation, but for temperature T > 0,and, at

last, S[x,p,t] = S[x,t] + S\p,t] is the entropy of any

nonequilibrium of stationary states. The corresponding notation will be used and for conditional information. Then, in accordance with inequality (45) ([in

accordance with S— theorem), we have the relation

I[z,p,t] - I[x,p] = S[x,p] - S[x,p,t] > 0. (58)

Thus, at the transition from the more chaotic state to

the more ordered state the amount if the information

increase.

As and in the classical theory the 5—theorem it is possible now to use for the diagnostic of quantum systems and, thus, to solve one from the most important

problems of Semiotics (Meystel, 1995; Coombs,and

Sulcoski (Eds.) 1966).

X. References

[1] Belinski A.V.,Klyshko D.N. 1993: The Interfer- ence of Light and the Bell 's Theorem (in Russian)

Uspechi Fiz.Nauk, 163,1.

[2] Bell J.S.1965:On the Einstein-Podolski-Rosen.

Physics, 1,165.

[3] Bell J. S. 1965: On the Problem of Hidden Variable

in Quantum Mechanics. Rev. Mod.Phys. 38,447.

[4] Brittin W.E., Chapell W.R. 1961. The Wigner

Distribution Function and Second Quantization

in Phase Space. Rev of Mod. Physics 34 620.

[5] Bohm D. On the possible Interpretation of Quantum Mechanics on the Basis of Concept of "Hidden Parameters" , Phys. Rev. 85, 166, 180.

[6] Coombs M., Sulcoski M. (Eds.) 1996. Control

Mechanisms for Complex Systems. Las Cruces,

New Mexico.

[7] De Broglie L.1953: La Physik Quantique

Resterat-EUe Indeterministe? Paris.

[8] Dirac P.A.M. Directions in Physics. John Wiley

and Sons New York, 1978.

[9] Einstein A. 1916: Strahlung Emission und

Absorption naeh der Quantentheorie. Verhandl.Dtsch. Phys. Ges. 18,318.

[10]

[11

[12

[13

[14

[15

[16

[17

[18

[19

[20

[21

[22

[23

[24

[25

[26

[27

[28

Einstein A.,Podolski B., Rosen N.1935: Can

Quantum-Mechanical Description of Physical Reality Be Considered Complete?

Phys.Rev.47,777.

Haken H. Information and Selforganization.

Springer Heqdelberg, Berlin, New York, 1988.

Hillery M., O'Connell R.F., Scilly M.O., Wigner

E.P. 1994. Distribution functions in physics:

Fundamentals. Physics Reports 106 122167.

Kadomtsev B.B. 1994: Dynamics and Information. Uspechi Fiz. Nauk 164,449

Klimontovich Yu.L. 1958. On the Method of

"Second Quantization" in Phase Space. Soviet

Physics JETF 6 (33) 752.

Klimontovich Yu.L. and Silin V. P. 1960 (1962).

On the Spectra of Systems of Interacting Particles and he Collective Losses on Passage of Particles Through Matter. Uspechi Fiz. Nauk 70 247;

Fortschr. Physik, 10 389.

Klimontovich Yu.L. 1982 (1986) Statistical

Physics. Moscow "Nauka, 1982; Harwood Academic Publishers New York.

Klimontovich Yu.L. 1980 (1983) The Kinetic

Theory of Electromagnetic Processes. Nauka

Moscow; Springer Berlin, Heidelberg, New York.

Klimontovich Yu.L. 1983 Entropy Decrease in

the Processes of Self-Organization, (in Russian).

Pis'ma v ZhTF 9 1089.

Klimontovich Yu.L. 1984. Entropy and Entropy

Production in the Laminar and Turbulent Flows,

(in Russian).Pis'ma v ZhTF 10 80.

Klimontovich Yu.L. 1990, 1991 Turbulent Motion

and Structure of Chaos. Nauka, Moscow; Kluwer

Academic Publishers Dordrecht.

Klimontovich Yu.L. 1993: To the Statistical

Ground of Schroedinger Equation, (in Russian)

TMF, 97,3.1995:

Klimontovich Yu.L.1995:Statisticai Theory of

Open Systems. Nauka, Moscow; Kluwer Academic Publishers, Dordrecht, 1995.

Klimontovich Yu.L. 1996: Relative ordering criteria in open systems. Uspechi Fiz. Nauk 166 1231.

Klimontovich Yu.L. 1997: To Kinetic Theory of

Collisionless Plasma. Uspechi Fiz. Nauk, 167, 23.

Klimontovich Yu.L.,Kremp D.1981:Quantum Kinetic Equation with Bound States. Physica A,

109,512.

Klimontovich Yu.L.,Kremp D.,Kraeft W.1987:

Kinetic Theory for Chemically Reacting Gases and Partially Ionized Plasmas.

Adv.Chem.Phys.58, 175.

Klimontovich Yu.L., Wilhelmsson H.,Yakimenko

LP., Zagorodnii A.G. 1989: Statistical Theory of

Plasma Molecular Systems. Phys.Rev.175, 264.

Mehra J. 1875: The Solvay Conferences on

24
Physics. D.Reidel, Dordrecht, Boston.

[29] Meystel A. 1995 Semiotic Modeling and Situation

Analisis. AfRem, Inc.

[30] Neumann J. Mathematische Grundlagen der

Quantummrchanik. Springer, Berlin.

[31] Prigogine I.1980:From Being to Becoming. Freeman, San Francisco.

[32] Prigogine I., Stengers I. 1984: Order out of

Chaos. Heinemann, London.

[33] Stratonovich R.L.1975. Theory of Information,

(in Russian). Moscow "Sov. Radio".

25
Information Granulation and its Centrality in Human and

Machine Intelligence

Lotfi A. Zadeh

Abstract

In a general setting, granulation involves

a partitioning of a real or mental object into

granules, with a granule being a clump of points

(objects) drawn together by undistinguishability,

similarity, proximity or functionality.

Granulation is crisp or fuzzy depending on

whether the granules are crisp or fuzzy. In the case of age, for example, the time-intervals {1, 2, 3, ... ,130} are crisp, whereas the fuzzy time-intervals

{very young, young, middle-aged, old, very old}

are not. Granulation -- and especially information

granulation (IG) — are ubiquitous in human actions

and cognition. We employ granulation when we

speak, write, eat, walk and analyze an image; we

employ fuzzy information when we partition a human body into body parts: head, neck, chest, arms, legs, etc.; and more generally, we apply

granulation when we partition a complex problem

into simpler subproblems.

Modes of information granulation in which the granules are crisp (crisp IG) play

important roles in a wide variety of methods,

approaches and techniques. Among them are:

interval analysis, quantization, rough set theory,

diakoptics, divide and conquer, Dempster-Shafer

theory, machine learning from examples,

chunking, qualitative process theory, decision

trees, semantic networks, analog-to-digital

conversion, constraint programming, cluster

analysis and many others.

Important though it is, crisp IG has a major blind spot. More specifically, it fails to

reflect the fact that in much — perhaps most — of

human reasoning and concept formation the

granules are fuzzy rather than crisp. For example,

the fuzzy granules of a human head are the nose,

ears, forehead, hair, cheeks, etc. Each of the fuzzy

granules is associated with a set of fuzzy attributes,

e.g., in the case of the fuzzy granule hair, the fuzzy

attributes are color, length, texture, etc. In turn,

each of the fuzzy attributes is associated with a set of fuzzy values. Specifically, in the case of the

fuzzy attribute length(hair), the fuzzy values are long, short, not very long, etc. The fuzziness of

granules, their attributes and their values is

characteristic of the ways in which human concepts

are formed, organized and manipulated.

In human cognition, fuzziness of granules

is a direct consequence of fuzziness of the concepts

of indistinguishability, similarity and

functionality. Furthermore, it is entailed by the

finite capacity of the human mind to store information and resolve detail. In this perspective,

fuzzy information granulation (fuzzy IG) may be

viewed as a form of loose data compression.

Fuzzy information granulation underlies

the remarkable human ability to make rational

decisions in an environment of imprecision,

uncertainty and partial truth. And yet, despite its

intrinsic importance, fuzzy information granulation

has received scant attention except in the context of

fuzzy logic, in which fuzzy IG underlies the basic

concepts of linguistic variable, fuzzy rule-set and

fuzzy graph. In fact, the effectiveness and

successes of fuzzy logic in dealing with real-world

problems rest in large measure on the use of the

machinery of fuzzy information granulation. This

machinery is unique to fuzzy logic.

Recently fuzzy information granulation

has come to play a central role in the methodology

of computing with words (CW). More

specifically, in a natural language words play the

role of labels of fuzzy granules. In computing

with words, a proposition is viewed as an implicit

fuzzy constraint on an implicit variable. The

meaning of a proposition is the constraint which it

represents.

In CW, the initial data set (IDS) is assumed to consist of a collection of propositions

expressed in a natural language. The result of

computation — referred to as the terminal data set

26
(TDS) -- is likewise a collection of propositions

expressed in a natural language. To infer TDS

from IDS the rules of inference in fuzzy logic are used for constraint propagation from premises to conclusions.

There are two main rationales for computing with words. First, computing with

words is a necessity when the available

information is not precise enough to justify the use of numbers. And second, computing with

words is advantageous when there is a tolerance for imprecision, uncertainty and partial truth that can be exploited to achieve tractability, robustness,

low solution cost and better rapport with reality.

In coming years, computing with words is likely

to evolve into an important methodology in its own right with wide-ranging applications on both

basic and applied levels. Inspired by the ways in which humans

granulate human concepts, we can proceed to granulate conceptual structures in various fields of

science. In a sense, this is what motivates

computing with words. An intriguing possibility

is to granulate the conceptual structure of

mathematics. This would lead to what may be

called granular mathematics. Eventually, granular

mathematics may evolve into a distinct branch of

mathematics having close links to the real world.

A subset of granular mathematics and a superset of

computing with words is granular computing.

In the final analysis, fuzzy information

granulation is central to human reasoning and

concept formation. It is this aspect of fuzzy IG

that underlies its essential role in the conception

and design of intelligent systems. What is conclusive is that there are many, many tasks

which humans can perform with ease and that no machine could perform without the use of fuzzy

information granulation, This conclusion has a thought-provoking implication for AI: Without

the methodology of fuzzy IG in its armamentarium, AI cannot achieve its goals.

Professor in the Graduate School and Director,

Berkeley Initiative in Soft Computing (BISC),

Computer Science Division and the Electronics

Research Laboratory, Department of EECS,

University of California, Berkeley, CA 94720-1776;

Telephone: 510-642-4959; Fax: 510-642-1712;

E-mail: zadeh@cs.berkeley.edu.

Research supported in part by NASA Grant NCC 2-

275, ONR Grant N000 14-96- 1-0556, LLNL Grant

442427-26449, ARO Grant DAAH 04-961-0341 and

the BISC Program of UC Berkeley.

27

WORLD REPRESENTATION

The Role of Semiotic Descriptors in Relational Representation of Fuzzy

Granular Structures

Ladislav J. Kohout and Eunjin Kim

Department of Computer Science

Florida State University

Tallahassee, Florida 32306-4019, USA

kohoutQcs . f su. edu, ejkim@cs . f su. edu

Abstract

This paper describes the role of semiotic descriptors in

representation of knowledge by relational structures. Fuzzy relations can manipulate semantic information

that is carried by linguistic labels. The conditions imposed

on logic operations applied to fuzzy relational systems can

be strictly mathematically defined. But the logic semantic is not sufficient to deal satisfactorily with the meaning

of linguistic labels that carry the conceptual meaning of

applications. It has to be supplemented by the notion of

semiotic descriptors. These can be expressed as algebraic restrictions over the basic fuzzy relational system [5].

Semiotic Fuzzy Knowledge Representation Structure

consists of the pair of structures, namely < FRS, SD >. FRS is a Fuzzy Relational Structure consisting of a family

offuzzy relations, and SD is collection of semiotic descriptors [4].

After describing the general semiotic model, we shall

also show a specific application - use of Semiotic Fuzzy

Knowledge Representation approach in study of cost and

affordability in engineering design. Specific examples to be presented are taken form the domain of aeronautic industry. BK-products of relations [7] and fast fuzzy relational

algorithms [1] are the technical tools by which we extract meaning form the answers to specific questions presented

to engineers in our case study.

1 Introduction

This paper describes the role of semiotic descriptors

in representation of knowledge by relational structures. Fuzzy relations can manipulate semantic information that

is carried by linguistic labels. The conditions imposed on

logic operations applied to fuzzy relational systems are

strictly mathematically defined. But the logic semantic

is not sufficient to deal satisfactorily with the meaning of

linguistic labels that carry the conceptual meaning of applications. It has to be supplemented by some semiotic

notions that can be expressed as algebraic restrictions over the basic fuzzy relational system.

Semiotic Fuzzy Knowledge Representation Structure

consists of the pair of structures, namely < FRS, SD >. FRS is Fuzzy Relational Structure consisting of a family of

fuzzy relations, and SD is collection of semiotic descriptors

[4],{5].

Semiotic descriptors are obtained by exploratory knowledge elicitation [6]. We use repertory grids to elicit the

meaning as used by human experts [3] Once the relevant

semiotic descriptors are identified, relationships between

them can be captured by repertory grids using bi-polar

constructs, each construct consisting of a pair of semiotic

descriptors.

After the repertory grids are applied to a particular

problem, and the semantic relationship captured by the

grids, the grids are transformed into fuzzy relations which

relate the semiotic descriptors.

Relational methods of analysis are then applied in or- der to discover meaningful conceptual structures implicit

in these fuzzy relations. This is done by forming fuzzy

relational products and further processing thus obtained

composed relations by algorithms computing closures and

interiors of fuzzy relations.

Particularly useful structural relationships are equivalences, similarities and preorders between individual semiotic descriptors captured by the bi-polar repertory grids.

These structural properties relating the meaning of concepts intrinsically contained in the data captured by repertory grids must be made explicit by appropriate relational

computations. The computational algorithms for this purpose are based on BK-Products of fuzzy relations and Fast

Fuzzy Relational Algorithms [8] computational tools are used to identify relational structures and properties intrinsically contained in data.

After describing the general semiotic model, we shall

also show a specific application - use of Semiotic Fuzzy

Knowledge Representation approach in study of cost and

affordability in engineering design. Specific examples to

be presented are taken form the domain of aeronautic in31
dustry.

A specific example on which we demonstrate our methods will be knowledge elicited from human experts characterising an ingot process of the Lower Pressure Turbine

(LPT) Cover Plate. The data of this example is evaluated

by means of fuzzy relational subproducts with respect to the structural relationships of cost factors. Crucial to this

approach is the use of semiotic descriptors that allow for

linguistic interpretation of relational computations. These

descriptors potentially denote the technological and fiscal

entities and concepts that are relevant to the problem of

affordability.

2 Semiotic Descriptors, Granularity and

Meaning

2.1 Semiosis and Interpretation

The main goal of semiosis is interpretation of signs and

symbols - recognition of their meaning. The meaning interpretation unit is a very complicated one. The meaning of something can be different depending on the scale

which is used for representation. This makes the notion

of granularity a very important one. Levels of granularity

also referred to as levels of resolution are closely related to

generalization.

Interpretation and meaning depend on context. A process considered with all its details cannot be properly understood unless the details irrelevant within a particular

context or perspective are brushed away. But this interpretation will often be incomplete. With incompleteness

at work, there may be more than one interpretation. In- deed, a whole family of interpretations may be possible,

some of which may be conflicting. Fuzzy sets, relations

and logic can play an important role here: they allow us, through the theory of potentiality (or virtual plurality) to

deal with the whole family of virtual outcomes, and also

to measure the degree of conflict of individual members

of some possiblistic family of outcomes produced by the

meta-process of interpretation.

2.2 Object Emergence

The phenomenon of object emergence is linked with formation of crisp and fuzzy classes (generalized groupings).

Indeed, here we deal with the logic theory of fuzzy relations, which can be used to expose the inadequacy of

currently used logical structure of crisp (i.e. non-fuzzy objects). Logically, generalization is a process in which, by

means of grouping together relevant properties (intensional

specifications) of objects, we create new objects - struc- tures (given as such by extension) by new intensional specification. So OOP objects can be viewed as special cases of the pragmatics of groupings, the semantics of which is

given by many-valued logic based relations with special

meta-properties.

2.3 Triadic Distinction of Semiotics: Syntax, Semantics

and Pragmatics

One of the classic notions of semiotics is the triadic distinction: syntax - semantics - pragmatics coined by Morris

in late 1930s. That is the place where the duality Semiotics - Mathematics comes in. In logic methods of proofs, only

the "form", the syntactic composition plays the role. In

the so called logic theory of models, the primary goal is to interpret syntax in semantic meta-structures. But what we

need here is the fully fledged duality: syntax - semantics,

and the pragmatics of emergence of either of these. Here

the fuzzy logic can play an important role: we have the duality of linguistic descriptors and fuzzy structures to which

these descriptors apply. We also have the duality symbolic

vs. numerical that are both addressed by what Zadeh calls

"the fuzzy logic in wider sense". "Numerical" in our re- lational setting will be extended to the many-valued logic

valuation of relational structure, and "symbolic" will be

represented by semiotic descriptors, which are special instances of linguistic labels.

Now, we have to provide the link of Semiotic Fuzzy

Knowledge Representation Structure (SFKRS) with the

semiotic triangle. Semiotic Fuzzy Knowledge Representation Structure consists of the pair of structures, namely

< FRS, SD >. FRS is Fuzzy Relational Structure consisting of a family of fuzzy relations, and SD is collection of

semiotic descriptors [4], [5].. The semiotic triangle has three vertexes, namely name,

meaning and represented object. The vertex "name" of the

triangle maps into a semiotic descriptor SD, while the ver- tex "meaning" is represented by a Fuzzy Relational Structure (FRS). The vertex "object" maps into the object of

the real world characterisation of which is captured by the

pair <FRS, SD > of SFKRS. See Figure 1 for more further

details.

3 Semiotic Relational Model

3.1 Representing Activites in the Domain of Manufacturing in the Aeronautic Industry

In this second part of our paper, we look at a specific

relational model from the domain of manufacturing in the

aeronautic industry. First we give an overview of the global

relational structure in terms of semiotic descriptors SD.

This is followed by a section that shows how the Semiotic Fuzzy Knowledge Representation Structure SFKRS

(which consists of a pair of structures, namely < FRS, SD

>) 1 is further completed by eliciting the fuzzy member1 We have noted previously that FRS is a Fuzzy Relational Structure consisting of a family of fuzzy relations, and SD is collection of

32
[Name Space]

Semiotic Descriptor

Meaning

within a perspective

or a context

Object

with all its

relationships

[Conceptual Characterization] [Physical Reality]

Figure 1. Semiotic Triangle

ship values of FRS by repertory grids. Repertory grids are presented to human experts, in this case engineers who fill the grids. The grids are the turned into fuzzy relations

which are further processed by relational computations by

which the meaning within a context is extracted.

We have noted previously that FRS is Fuzzy Relational

Structure consisting of a family of fuzzy relations, and SD

is collection of semiotic descriptors.

3.2 Conceptual Categories of Semiotic Descriptors

The relational model presented in this case study is intended for the capturing and representing the features rele- vant to the affordability analysis and prediction. It cosists

of the following conceptual categories of relations :

• Objects,

• attributes,

• values,

• agents,

• perspectives,

• contexts,

• views.

Each conceptual category listed above represents a specific level of granularity. Each level of granularity may

posses conceptual refinements that are interlinked with

other granular structures. Each conceptual category has

specific meaning that can be understood and interpreted

by a domain expert.

Objects are, for example, either parts of a manufactures product, manufactured products or whole technologies, depending on the resolution level.

semiotic descriptors.

Attributes are characterised by linguistic descriptors. Examples of these are: low_raw_material_cost,

small-processing_windows, high_temperature,

goodJubricity, low_varianceJn_raw_material_costs, etc. But attributes can also be characterised by measurable

physical or fiscal parameters, such as: temperature, lubricity, cost_reducing_potential, potentialinvestment, cost, etc. Interactions (special kinds of relations), for example:

REL_1,5: low_variance_in_raw_material_costs —

low_cracking_probability

REL_2,3: good_processing_control —

-

low_raw_material_cost

REL_3,7: low_raw_material_cost —

common_standard_material_alloy.

Values. These are either linguistic variables or numerical variables determining the degree to which an object

possesses an attribute.

Agents. In the context of this project, agents are the observers (e.g. engineers or accountants) assessing the

degree to which an attribute is possessed by an object.

For example, in [R4], [R8], [RIO] describing the evaluation

of an LPT cover plate the observers were engineers evaluating to what degree various attributes can be assigned

to the LPT plate. Perspectives. An object or a family of objects can be evaluated within different perspectives. For example, an LPT cover plate can be evaluated

from the perspective of an engineer, or from the perspective of a business analyst performing value analysis of the

part, or from the perspective of an accountant. Each perspective may employ attributes that are different from the

attributes of a different perspective for the same object.

Some attributes may, however, be shared by different perspectives.

Contexts. Each object or family of objects can appear

in several different contexts. For example an LPT cover

plate may appear e.g. in context of ingot process, forging

process, extrusion process, or other processes.

Views. Even in one particular perspective or context,

different experts may assess the objects and situations in

which objects appear differently. These differences of views

of different experts can be captured by repertory grids and

compared by relational methods using algorithms provided

by TRYSIS.

4 A Case Study: Low Pressure Turbine

(LPT) Cover Plate

4-1 Semantics of the Relationships of the Relational

Model of LPT Cover Plate

4.1.1 Semiotic Descriptors of Relational Products

In representing knowledge structures, not only quantitative but also qualitative notions are involved. Productrelations formed by the relational products represent new

33
entities composed from the original data. Each relations

possesses meaning carried by its linguistic label. This

label, which is in fact an instance of semiotic descriptors carries a concrete interpretation within a particular

knowledge domain. This interpretation also determines

the meaning of the composed relation computed by the

relational product.

Our model relation M to be used in the sequel M £ 7Z(Y x 0 x P), relates the following three lists (sets) of entities:

• the set Y of process attributes;

• the set O of observers, assessors or measuring sensors; with the set G of process identifiers;

• the set of Parts or Components.

Applying the usual selection and projection operators

the ternary relation is decomposed into a family of 2-ary

relations in TZ(Y x O), indexed by the set P. The processes Pi and P2 are extrusion and forging, respectively.

The relation Rl and R2 are from the set of process at- tributes Y to the set O) is composed with its transpose

R

T by means of triangle subproduci and the local preorder

closure computed by the TRYSIS system. The result of

this computation is a relation from the process attributes

Y to y. This relation shows the dependencies of process

attributes represented as a preorder relation.

A sample result displaying dependences and equivalences of process attributes is shown in Figure 2. These

figures show the Hasse Diagram (HD) structures displaying the preorders of process attributes computed by the

fuzzy relational triangle subproduct over processes. The

object processed in both processes and evaluated by the

engineers is LPT cover plate made of gamma-titanium.

A number of evaluative schemes can be formulated,

showing inter-process dependences, inter-observer dependences, etc. Because the purpose of this paper is to show

basic techniques of relational analysis as applied to manufacturing processes, not to provide a detailed analysis of

engineering of LPT cover plate, further details of these

computations are not presented in this paper.

Three scenarios for using a repertory grid on LPT parts

have been used [3]. Here it will suffice to present just one

scenario, namely

SCENARIO A:

1 object (LPT cover plate) is rated by group of respondents

(engineers) where each of the respondents does assess the

object independently in a selected process. The aim is to

find the dependences between process characteristics and

the inter respondent consistency.

There may be several situations or processes in which the

object may appear. In our example these are extrusion

and forging.

4-2 Context Dependency of the Meaning of Semiotic Descriptors

In each context defined by a specific industrial process

(e.g. forging or extrusion) there is a set of semiotic descriptors that is relevant to the knowledge representation struc- ture that has been created for a specific purpose. Thus in our project [2], we study the question of affordability that

is related to the cost of production. This determines which

semiotic descriptors will appear in the SFKRS relevant to

each industrial process.

For example, looking at process of forging and extrusion for a particular part, i.e. LPT cover plate, we have

large/small process window bipolar semiotic descriptors for

extrusion and large/small process window bipolar semiotic

descriptors for forging (see the list of SD in Table 1). Out

of these, Large/small process window are identical and appear in both processes.

This however does not mean that a specific list of semiotic descriptors has the same meaning in two different contexts. A distinct difference in the meaning which a particular list of semiotic descriptors can acquire in different

contexts is clearly shown in Table 1. Fig. 2 shows that in the context of extrusion, semiotic descriptors large process window(CI) and long die

hfe(C9) are captured within the equivalence class of

FRS, hence they are equivalent in their meaning. In the context of forging on the other hand, it is different.

Large process window(C2) is equivalent with air furnace

atmosphere(Ch) in its meaning. The equivalence of large

process window(C2) and long die life(C9), however, does

not hold in the context forging despite of the fact that it holds for the process of extrusion.

Let us look at these results now in semiotic terms. As

can be seen from Table 1, the list of semiotic descriptors

used for evaluation of the process of forging is the same as the list of the semiotic descriptors used for the process of

extrusion. So in terms of Fig. 1, we use the same name

space for both processes. The Hasse diagram structure

of Fig. 2 for computed for extrusion is different from the

structure that was obtained for forging. In terms of Fig.

1, The Hasse diagram structures represent the third ver- tex (3) of the semiotic triangle, i.e. relational conceptual

characterisation. This characterisation has been elicited

experimentally from a group of human experts-engineers

by repertory grids. The fuzzy relation oftained from these

repertory grids was then tested for the relational property

of preorder that can be graphically presented as a Hasse

diagram.

We can also consider the SFKRS with the negative side

of bi-polar features of the semiotic descriptors. As shown

in Figures 3 and 4 the SFKRS can also be formed with the

negative semiotic descriptors. SFKRS depicted in Figure

3 shows the property of contrapositive symmetry2 while

2 A logic proposition is contrapositive if a — b = -ib — ->a.

34
SFKRS of Figure 4 does not show it. The implication operators used to compute the Hasse

diagrams displayed in Figure 2 of this paper are indicated

directly in the figures3

5 Conclusion

In this paper, we have shown by an experimental study,

that the semiotic triangle which is usually applied indiscriminately, is in fact context dependent. We have demonstrated that

• In one context, two different fragments of SFKRS

elicited by questioning engineers by the repertory grid

techniques may be equivalent in meaning. In another

context their equivalence may not hold.

• In two different contexts defined by two distinct industrial processes the meaning of a set of the identical

semiotic descriptors may be different in their meaning.

Our paper also shows that the use of basic semiotic notions such as a semiotic triangle, if properly applied may

add another dimension to enginnering. It is widespread

opinion, in particular in the US that semiotic is useful

only for literary studies. We hope that we have managed

to persuade our readers that semiotics enriched by fuzzy

relational techniques has important applications in technology.

[4] L.J. Kohout. A Perspective on Intelligent Systems: A

Framework for Analysis and Design. Chapman and Hall

& Van Nostrand, London New York, 1990. A Scientific Monograph, 255 pages.

[5] L.J. Kohout. Activity Structures: A methodology for design

of multi-environment and multi-context knowledge-based

systems. In [6].

[6] L.J. Kohout, J. Anderson, and W. et al. Bandler.

Knowledge-Based Systems for Multiple Environments. Ashgate Publ., Aldershot, U.K., 1992.

[7] L.J. Kohout and W. Bandler. Fuzzy relational products

in knowledge engineering. In V. Novak et al., eds, Fuzzy

Approach to Reasoning and Decision Making, pages 51-66.

Kluwer, Dordrecht, 1992.

[8] L.J. Kohout and W. Bandler. Use of fuzzy relations in knowledge representation, acquisition and processing. In L.A. Zadeh and J. Kacprzyk, editors, Fuzzy Logic for the

Management of Uncertainty, pages 415-435. John Wiley,

New York, 1992.

FRS of Extrusion

(S,H,harsh)= (S,(H,HU,M), mean) = (S*,(H,HU),harsh) = (S*,(H,HU),mean) = (G43,(H,HU),harsh) = (G43, H,mean) = (G43',(H,HU),harsh) = (C743',(H,HU),mean) = (L,(H,HU),harsh) = (L,(H,HU),mean)

ACKNOWLEDGEMENT: This work has been partially supported by the NSF grant DMI 9525991 entitled

Decision-Making with Incomplete Information in an Inte- grated Product and Process Development Enterprise: A

Management Decision Tool for Cost Modeling and Affordability Applications.

References

[1] W. Bandler and L.J. Kohout. Special properties, closures

and interiors of crisp an d fuzzy relations. Fuzzy Sets and

Systems, 26(3):317-332, June 1988.

[2] B. Dubrosky, L.J. Kohout, R.M. Walker, E. Kim, and

H.P. Wang. Use of fuzzy relations for advanced technology

cost modeling and affordability decisions. In 35th AIAA

Aerospace Sciences Meeting and Exhibit (Reno, Nevada,

January 6-9,1997), pages 1-12, Reno, NV, January 1997.

[3] E.. Kim, L.J. Kohout, B. Dubrosky, and W. Bandler. Use of

fuzzy relations for affordability decisions in high technology.

In R.A. Adey, et al. Applications of Artificial Intelligence

in Engineering XI. Computational Mechanics Publications,

Southampton, UK - Bilerica, MA, USA, 1996.

3 These are defined by formulas Lukasiewicz implication operator

5 a — b = mm(l,l — a + 6); Gaines-Goguen implication operator

4 a —* b = min(l,b/a) and S* (Heyting-Godel) implication operator

3 a—1-6=1 if a < b, b otherwise.

C4 C6 C7

FRS of Forging

(S,H,harsh) = (S,H,mean) = (S*,(H,HU,M),harsh) = (S*,(H,HU,M),mean) = (G43,(H,HU),harsh) = (G43,(H,HU),mean) = (G43',(H,HU),harsh) = (G43',(H,HU),mean) = (L,(H,HU),harsh) = (L,(H,HU),mean) = (KDL,HU,harsh)

C7 C9

C3

Figure 2. SFKRS(<FRS,SD>) with the positive bipolar fetures in the context of Extrusion

and Forging

35
Positive Semiotic Descriptors Negative Semiotic Descriptors

US vtti V inhnl uui IvT pa ninc SvmHol u v ill Ljyji IMpa ti i n CF IVlCCLXLlllg Pi v^apdijie jTviicLiy nc<ii iviociciiiig \y ± jjiiiiiieQ /\noiy iicai ivioaeiing

C2 Tiarep Prorpss Window C2 Small Prorp«j«! Window

C3 Low Temperature C3 High Temperature

C4 Good Lubricity Cl Low(or Difficult) Lubricity

C5 Air Furnace Atmosphere Cl Vacuum Furnace Atmosphere

C6 Good Process Control C6 Limited Process Control

C7 Available Tooling Cl New Tooling

C8 Flat Die Shape C8 Shaped Die Shape

C9 Long Die Life C9 Short Die Life

Table 1. SD both in the context of Extrusion

and Forging

FRS in Extrusion

(S,H,harsh)= (S,(H,HU,M), mean) = (S*,(H,HU),harsh) = (S*,(H,HU),mean) = (G43,(H,HU),harsh) = (G43, H,mean) = (G43',(H,HU),harsh) = (G43',(H,HU),mean) = (L,(H,HU),harsh) = (L,(H,HU),mean)

Cl C4 C6 C7 C3

FRS in Forging

(S,H,harsh) = (S,H,mean) = (S*,(H,HU,M),harsh) = (S*,(H,HU,M),mean) = (G43,(H,HU),harsh) = (G43,(H,HU,M),mean) = (G43',(H,HU),harsh) = (G43',(H,HU),mean) = (L,(H,HU),harsh) = (L,(H,HU),mean) = (KDL,HU,harsh)

Extrusion

(G43, M, mean)

( a) C6

C4

K

CI

l>

(^C2,C7,C9j

C3^\C5 C8

Forging

(G43, M, (harsh,mean) )

Cl C6

Figure 3. SFKRS(<FRS,SD>) with the negative bipolar fetures in the context of Extrusion

and Forging - holding the property of ContraPositive Symmetry

Figure 4. SFKRS(<FRS,SD>) with both positive and negative bipolar fetures in the context of Extrusion and Forging - withouth holding the property of ContraPositive Symmetry

36
AN INTEGRATED APPROACH TO FUZZY LEARNING AND REASONING

IN HIERARCHICAL KNOWLEDGE STRUCTURES

Jan C.A. van der Lubbe' & Emile Egbers2

1 Delft University of Technology, Dept. Electrical Engineering, Information Theory Group, P.O.

Box 5031, 2600 GA Delft, the Netherlands, E-mail: vdlubbe@it.et.tudelft.nl

2 Zappwerk, P.O. Box 3363, 2601 DJ Delft, the Netherlands, E-mail e.egbers@zappwerk.nl

Abstract

In this paper an integrated system is developed

which can perform the three inference methods

introduced by Peirce (1931-35) (abduction,

deduction and induction) and which is also suitable

for case-based reasoning. The hierarchical

representation of knowledge guarantees an optimal

strategy for inference.

1. Introduction

In Backer (1995) and Van der Lubbe & Backer

(1995) an expert system approach for fuzzy data

analysis was presented. By means of learning from

samples (i.e. data sets) implicit functional relations are transformed into explicit knowledge rules,

including the uncertainty associated with them. On

the basis of the knowledge rules which are ordered

hierarchically inference is made for new samples.

As such the system is capable for both inductive

learning and deductive reasoning. In addition to this

also case-based reasoning can be performed using

the exceptional samples which cannot be

generalized adequately to general knowledge rules.

In the present paper the system is extended to more general applications. Furthermore, the

induction part is enhanced by adapting the method

proposed by Ho et al. (1988). Specific attention is paid to the inference mechanism, where a membership function should be assigned to the

inferred conclusion(s). Situations whereby more

than one knowledge rule will fire are considered. In order to obtain a system which can deal with the

three semiotic inference types distinguished by the

American philosopher Charles Sanders Peirce

(1931-35) the problem of abduction in hierarchical

knowledge trees is studied. By means of so-called

pseudo-abduction the problem of abduction can be

solved in a deductive manner.

2: The reliable training set and inductive

learning

Let us assume that we have a set W of training

samples from the entire instance space supplied by

the expert. A member of the training set W is denoted by w. It corresponds to a specific sample.

It can be represented by an n-dimensional attribute

vector {a,(w),...,a] (w),...,an (w)}, expressing features

of that sample. The attributes can be quantitative or

qualitative. It is assumed that all qualitative

attributes do possess the same domain of possible

modalities { v,,....,v

p

}, like very low, low, medium,

high etc. For each attribute a,(w), the corresponding

modality is denoted by v: (w), whereby Vj(w) e

(v,,...,v

p

). And thus

w: (a,(w)=v,(w) an(w)=vn (w)}.

To each sample corresponds a decision or judgement with respect to some phenomenon. The

domain of modalities of a decision is denoted by D

= {d,,...,dj,...dm ). The learning problem now is to find the set {R} of rules that predict the correct

decision or domain modality for each training

sample if its attribute values given by the expert is taken into account. Rules have the form:

IF {a,(w)=v,(w),...,an(w)=vn (w)}

THEN {d=dj, fj(w)}.

This can be read as follows. If a sample has

attribute values according to the conditional part of

the rule, then dj is a correct decision with

membership function f,(w). Example: IF {al = high,

a3 = low}, THEN {d2 = very low, 0.8}. Remark

that not all attributes are per se part of the

conditional part of the rule. Clearly, from the expert point of view, the set D

= {d|,...,dj dm } can be associated with a

partitioning P of training set W in m classes

37
{P,,...,Pj,...,Pm }; the concept-driven partitioning. The

rule generation problem is to find for each class Pj a representative set of rules {Rj} = {Rj,,...,Rjh ,...}

that predicts dj for all the samples of Pj as good as

possible. There are two requirements on the

representative set of rules: the requirements of

covering and discrimination. The first says that for

each sample there should be a rule that can

recognize this sample. Thus, there should be no

samples that are not recognized. The discrimination

property implies that a rule which is aimed at a

specific decision is supposed not to recognize

samples related to other decisions. Key concept is coverage; the coverage of a rule Rjh is the number

of samples of Pj which is recognized by this rule. The coverage is denoted by Pj(Rjh

). The

membership function fj(w) of a representative rule

Rjh is considered to be equal to the relative

coverage OJRjh

) of that rule, expressed by

^(Rjh) = Pj (Rjh)/|P

j |.

I.e. the number of samples covered by the rule

relative to the total number |Pj of training

samples in the partition.

The quality of representative rule Rjh with respect to decision dj is defined as:

Q(RJh ) = P/Rj,,)/ Ej. Pj-CRjh),

which takes into account the number of samples

recognized by rule Rjh , which are not an element of

For the generation of representative rules the

method of Ho et al. (1988) can be used. One starts with the determination of the representative rule for

say sample Wj e Pj. Therefore, one begins with an

'empty' rule and ties an attribute that covers the

maximal number of samples of Pj. This is repeated

by adding other attributes until it is discriminative

and coverage cannot be improved. By doing so for

all samples of PJ5 a number of rules will be the

result. The first rule that belongs to the

representative set is the rule with the largest

coverage. The second rule is the rule that has the

largest coverage with respect to the samples of Pj

which were not covered by the first rule. Etcetera. Rules are added one after eachother, until all samples of Pj are covered.

Experiments were performed by modifying the

algorithm of Ho et al. (1988) in order to improve

its efficiency. First of all equally general and

equally parsimonious rules are all added to the rule

set. I.e. rules that cover the same training samples

and tie the same number of attributes in their

conditional part are thought to be equally

acceptable to represent a concept or decision as no

reasonable criterion exists to decide which one is the best.

Furthermore, on rules tying more than one

attribute in their conditional parts an extra

parsimonious check is carried out. This is necessary

by the way the attributes are tied to the rules by the

original algorithm. In this only the coverage of each

attribute is considered, under the expectation that

this will give the best chance on achieving a

general, discriminative rule in the fastest way. By

leaving out the tied attributes one by one from the

conditional part of the rule and checking for

disrimination, redundant attributes can be detected

and excluded from the rule resulting in a more

parsimonious (and therefore more general) rule. Sometimes, as in the case of equal rules as outlined

above, this will even cause rules to become

redundant.

Nevertheless, in general the result will be still poor, since the quality of the samples will differ. In order to rule out these effects, a data-driven

partitioning is performed, which is based on the

application of some numerical fuzzy clustering

technique leading to maximum intra-cluster similarity and minimum inter-cluster similarity. The result

of the data-driven partitioning is a hard partitioning

P' into clusters with for each sample the

membership value with which it belongs to each

cluster. By comparing the concept-driven partitioning and the data-driven partitioning poor

samples or exceptions can be found.

Figure 1. Reliable training set and exceptions.

38
This can be simply done by ruling out those

training samples that are not included in the

intersection of P and P' and those samples that

have no membership value to any of the clusters

above a certain threshold. These samples . are considered as exceptions. The corresponding set is denoted by E. The remaining samples of W form

together the reliable training set W = W/E. The

corresponding partitioning is P". See figure 1. The reliable training set W with its partitioning P"

is the proper training set on the basis of which

knowledge rules are determined. This is performed

according to the modified method of Ho et al. (1988), mentioned above. Once the rules are found

the system can be used for new samples for which

the decision should be inferred.

new representative set of rules is generated.

.w

system

rules/exceptions

add w' to

list exceptions

expert's judgement

updating no

rule set modification

3: Incremental inductive learning

If the rules are determined and new training

samples become available then it depends on the

situation whether the rule base should be modified

or not. Assume a new training data set/sample w',

for which a decision should be found. This sample

is characterized by its attribute values, as follows:

w': {a 1 (w')=v,(w'),...,an(w')=vn(w')}.

The corresponding decision according to the

expert's judgement is given by

J: {d=dk , fk(w')}.

However, the system predicts the concept d=dk

.

instead of dk with its corresponding membership

function:

S: {d=dk , fk .(w')}.

The following situations are distinguished. Compare

Figure 2.

a) If dk dk., then sample w' should be considered

as an exception, since system and expert come to different decisions.

b) If dk = dk

. and D(S,J) = |fk(w') - fk (w')| < 0.5,

then the difference between system and expert is small, and thus this new sample is covered by the

existing knowledge base and only the membership

function of the rule should be modified.

c) Modifications of the rules itselves are only

needed if dk=dk

. and D(S,J) = |fk(w') - fk (w')| >

0.5. The sample w' is then added to group Pk and a

Figure 2. Rule updating and identifying exceptions.

4: Hierarchical knowledge organization and

deductive reasoning

Now hierarchical knowledge organization in the

form of rule trees is considered. We assume that we

have been able to construct a nesting of

partitionings, P°, P

1

, P

2

, The null partition P°

contains all training samples. At level 1 we have a

partitioning P = {...,P

J

j ,...}, where Pj is one of the

subsets into which the sample space is divided. The

rule set which covers partitioning P is denoted by

{R1 } = {....Rj,...}, whereby R\ is the set of rules

related to subset Pj:

{Rj} = {Rj„ Rj*-.}.

At each level 1 it holds that:

- V i*j: P

1

, n Pj = 0.

- Ej |P'j| = total number of samples.

- If ^ is split up into P

1 ^ and P

+1

r then: P

l+1

, e P^.

and IP^J < IPJ, and similarly for P

+VIt can be shown, considering the rules for the

various partitions, that for increasing 1 the rules

become more specific. Thus at the top of the tree are the most general (and thus less discriminative)

rules, whereas at the bottom of the tree most

specific rules are. At the lowest level (1 large) we

have the rules corresponding to the individual

samples. However, the tree structure has also

another interesting property.

39
training sample (R3 i) P

3

>

Figure 3. Partitioning and knowledge tree.

If the hierarchical knowledge tree is used for

inference e.g. on sample w':

{a 1 (w')=v 1 (w'),...,an(w')=vn (w')} (whereby now the

decision is not known a priori), then in general one

has the following situation. Consider rule R'jh at level 1 and related to subset P^:

R'jh : IF {a1 (w)=v1 (w),..,an(w)=vn(w)}

THEN {d=d'

J

, fyw)}.

If this rule is applicable, i.e. the attributes (with

their modalities) of sample w' correspond to those

of the conditional part of the rule, the inferred

decision will be

{d = d\, fyw')},

whereby fyw') the relative coverage Q(R'jh) (=f\(w)) of the rule.

Since every partition in the tree is in general

represented by a rule set rather than by one single

rule, w' may be covered by more than one rule in

the rule set and therefore determination of the

membership of the inferred decision is not trivial anymore. Each applicable rule contributes to the

evidence for a new sample w' to belong to the

partition. I.e. the plausibility for a sample to belong

to the partition increases if more rules are firing at the same time.

Then simply adding all the relative coverages of

the applicable rules together is not correct, as it does not take into account possible overlap of the

coverages of the rule. Yet, as we have seen before a

rule will only be added to the rule set:

1 . If a rule covers at least (worst case) one currently uncovered training

sample, or

2. If rules are identical. I.e. they cover

the same training samples and tie an equal number of attributes

(equally parsimonious).

For that very reason, the effective relative coverage

is a more appropriate membership function.

Suppose a ruleset { R'j } for partition at level 1, containing n+m rules of which n rules {Rj„...,Rjn } are applicable to a new sample w' and the other m

rules {R1

j J)+1 ,...,R'j n+m } are non-applicable, and which

are ordered for decreasing coverage P"j(Rjh

). The

effective (relative) coverage Q(R\) then can be

calculated by the following two-step algorithm:

1- acR'j) = p'/Rj.);

for i=2 to n:

if P'/R'ji) < P'/R'j,.,) or pars(R'ji ) *

pars(R'jM ) (i.e. the # of tied

attributes of rule R^ and R'jM are unequal),

then ^(R'p = ^(R'j) + 1. 2- ^(R'j) = iP'jl - {P,

j (R1

j.n+ ,) ••+

•Pj(Rj.n+m)}-

The first step determines a worst case £>i(Rj)

according to all applicable rules. The second step

takes into account the maximum number of

trainingsamples that the non-applicable rules may

40
cover. Hence, the latter will result in a second

worst case Q9 (R'j).

Now the resulting worst case 0_(R';) can De found

as: Q(R\) = maxtQ^R'j), ^(R'j)]/ 1

| . As a worst

case 0_(R'j) is calculated, the membership can be

thought of as a pessimistic lower bound.

It can be shown that for increasing 1 the range of

uncertainty with respect to the inferred decision will

decrease. This implies that in practice making

inferences it is preferable when rules at the lower

levels of the knowledge tree can fire, since these ones give the smallest range of uncertainty.

However, starting at the lowest level leads to a computational complexity compatible with that of

usual case-based reasoning. Starting at the top of

the tree is more appropriate. One goes down to lower levels as long as there are rules that fire. If at a level where no rule fires than one stops. Although

the top-down approach is better than the bottom-up

one, a more adequate approach is searched for.

Considering the hierachical partitioning tree, not

all partitionings will be equally obvious. There

should be levels of which the partitioning

corresponds more to the internal test set structure than other levels. It may be expected that the rules

of the rule sets related to these levels have a higher

chance of firing than rules of other levels, since

these rules set are related to a more natural

underlying partitioning. Having found such levels

this can be used as starting point for making

efficient inferences in the hierarchical knowledge

tree.

In fact the problem is to find the most probable

partitioning as well as the 'true' number of clusters.

Based on the idea of core zones as discussed in

Bezdek et al. (1988), Jennes et al. (1994)

introduced the core zone index (CZI) for estimating

this true number of clusters. CZI is computed for

each level in the partitioning tree. That level with

the largest CZI is called the core zone index level

(see also Van der Lubbe, 1995). It is the starting

point for the inference process in the hierarchical

knowledge tree. Let the core zone index level be

indexed by 1, then in search for the most specific

rule the successive levels 1+1, 1+2 etcetera are considered until the level where no rule can fire. The last but one level is the level which generates

the ultimate decision(s). If more than one rule fires

at that level, i.e. in the same node, the membership

function with respect to the ultimate conclusion is according to the two-step algorithm mentioned

above. If the lower levels do not succeed, then the

higher levels 1-1, 1-2 etcetera are considered. If only

at a high level there are rules can fire with respect

to inference on a sample w', the conclusion should

be that the knowledge in the tree is not applicable

to the inference for that specific sample w', for the core zone index level is the most plausible level. The fact that only rules at higher levels succeed,

implies that a decision about a sample w' can only

be made if the optimal partitioning is neglected.

Then sample w' should be considered as an

exception.

In practice starting at the core zone index level

will lead to a faster solution than starting at the

bottom (or top).

5. Abductive reasoning

Whereas the methods described above are dealing

with induction and deduction, it is of interest to study the possibilities for abductive inference, since

in practice abduction is the most important of the

three Peircean inference forms. In literature many

methods for abduction are given. Compare Van der

Lubbe (1996). These methods are not applicable

here, taking into account the structure of the system

developped until now. Considering abduction as the

inverse of deduction, methods for abductive

inference should be compatible with the methods

followed for deduction. That means that also in the case of abduction a similar hierarchical knowledge

structure should be chosen as the basis. Clearly, the

hierarchical knowledge tree used in the foregoing

sections can not be applied for abduction, since the

conditional part of the rule is related to the

attributes and the concluding part to the decision or conclusion. In the case of abduction we are just

reasoning from decisions to attributes.

Let us assume that we have k decision domains

{D,,...,Dk } instead of just one decision domain. In the case of deductive reasoning we now have k

knowledge trees. For abductive reasoning there are n knowledge trees, if there are n attributes. The n abductive knowledge trees are generated in the

same way as the deductive knowledge trees are. I.e. by means of the modified method of Ho et al. (1988), taking into account possible exceptions.

Compare Figure 4. The final abductive result is achieved by

deductive inference in the n abductive knowledge

41
given: W = {a,(w') = v,(w') a^w') = v„(w')}

w' w' I »1

system inference: S(w') = {D, = u^w') [\ = um(w')}

system inference: w' ={(ai(w') = V|(w'), ... , a„(w') = v„(w')}

Figure 4. Deductive and abductive knowledge trees.

trees. Therefore, it can be considered as a form of

pseudo-abduction. For each of the attributes an

indication is given of its possible modalities on the

basis of the given decisions or conclusions.

Experiments were performed by first reasoning on the basis of the deductive knowledge trees - from attributes to decisions - followed by pseudoabductive reasoning on the basis of the abductive

knowledge trees: from decisions to attributes. In all cases the original attributes with their modalities were refound. This underlines the usefullness of

pseudo-abduction

.

Considering the overall system we may conclude

that instead of comparing the unknown sample with

all other samples of the training set, as is the case

in usual case-based reasoning, the hierarchical

knowledge organization enables a more efficient

inference; not in the least by determination of the core zone index level. By means of the hierarchical

structure there can be inferred to the most probable

decision step-by-step. If during the process

inference stops half-way by not further firing of

rules at the lower levels, more general decisions

will result than at the bottom of the tree. If the

knowledge tree is not applicable at all to the sample

to be judged, then it is considered as an exception.

Then, the only thing one can do is using case-based

reasoning and comparing it with earlier exceptions

in the hope that then some inference becomes

possible.

6. Conclusion

It has been shown that on the basis of a training

set an adequate hierarchical knowledge tree can be

generated by matching concept- and data-driven

partitionings of the sample space and by searching

for representative rules by means of induction.

These hierarchical knowledge trees are appropriate

42
for incremental learning and for handling

exceptions. Further, it enables inference for new

samples, by means of deductive as well as abductive reasoning, in an efficient way. This

efficiency is due to the fact that in general not all samples of the training set should be considered.

The core zone index and the determination of the core zone index level guarantee the optimal start

level. Usual case-based reasoning is only applied to exceptions.

References

- Backer, E. (J 995): Computer-assisted reasoning

in cluster analysis, Prentice Hall, New York.

- Bezdek, J.C. and Er-Woon Chiou (1988): A new

approach to feature extraction for visual displays,

In: Computer Vision, Graphics, and Image

Processing, Vol. 41, pp. 186-209.

- Davies, D.L. and D.W. Bouldin (1979): A cluster

separation measure, IEEE Trans. Pattern Anal.

Mach. Inteli, PAMl-1. pp. 224-227.

- Dubes, R.C. (1987): How many clusters are

best? - An experiment, In: Pattern Recognition, Vol.

20, no 6, pp. 645-663.

Egbers, E. (1996): Pseudo-abduction in

hierarchical knowledge structures (in Dutch), M.Sc.

Thesis, Delft University of Technology.

- Ho, T.B., Diday, E. and M. Gettler-Summa

(1988): Generating rules for expert systems from

observations, In: Pattern Recognition Letters, Vol.

7, pp. 265-271.

- Jennes, C, Jeedella, J.S.Y. and E.G. P. Bovenkamp

(1994): Finding the true number of clusters using a

core-zone-based index, Delft University of

Technology, unpublished report.

- Peirce, Ch.S. (1931-35): Collected papers of

Ch.S. Peirce, C. Hartshorne and P. Weiss (eds.),

Cambridge (Mass.)

- Van der Lubbe, J.C.A. and E. Backer (1995):

Hierarchical classification inference for fuzzy data

analysis, In: Proc. ISUMA-NAFIPS '95, College

Park (Maryland), September 17-20, 1995, pp. 402-

407.

- Van der Lubbe, J.C.A. (1996): A semiotical

approach to abduction in artificial intelligence.

Delft University of Technology, Technical Report

TUD-EE-IT 96101.

- Van der Lubbe, J.C.A. (1996): A Peircean

approach to artficial intelligence, In: Proc.

Intelligent Systems: A Semiotic Perspective, Vol. II, Gaithersburg (Maryland), October 20-23, 1996, pp.

7-13.

43
Conceptual Categories as Knowledge Structures

Christopher Landauer

National Systems Group, The Aerospace Corporation

The Hallmark Building, Suite 187, 13873 Park Center Rd., Herndon, Virginia 20171

Phone: (703) 318-1666, FAX: (703) 318-5409

E-mail: cal@aero.org

Abstract

This paper introduces an approach to knowledge representation as an active process. More than merely recording knowledge in some extractable form, we recognize that

representation must include the processes that perform the

activities of insertion as well as extraction. Our intention

is to develop a representational method that is powerful

enough and flexible enough that systems built using it can

represent, reason about, and change their own structure

and behavior.

The approach is based on recent work on knowledge representation for our "wrapping" integration infrastructures,

and on some comparative semiotics: studies of mathematical and linguistic reasoning.

The basic notion is a generalization of set theory in four directions: our collective objects have (1) indefinite boundaries and (2) indefinite elements; (3) the context is allowed

to leak into the interpretation of the objects; and (4) there

is a notion of multiplicity of structures that correspond

respectively to considering the same object or class from

different points of view, in different contexts. This notion

allows us to model the modeling decisions explicitly, and

to keep track of the modeling simplifications so we can relate them to each other and to the processes that create,

change and use them.

1 Introduction

The main goal of this work is to invent a more interesting and flexible mechanism for representing the knowledge

and information needed by, in, and for constructed complex systems in general, and computing systems based on wrappings in particular. We have written elsewhere

[5] about the barrier imposed by any well-founded sys- tem, and our problem is to try to build something that

does not have this same barrier (i.e., indefinitely refinable

knowledge structures) from something that is inherently

grounded in computer hardware (i.e., computer software).

The genesis of this work was thinking about the differences

between mathematical and linguistic reasoning [7].

In this section, we describe some of the background for our attitude, and introduce some of the concepts and ter- minology we use.

1.1 Background

In our research, we have considered two different mapping activities: modeling some phenomenon in the real

world (using simulation and modeling techniques we have

developed [8]), and implementing some abstract idea (using software engineering and software system development

techniques that we have developed [5]). In both cases,

there is a representation issue, and there are simplifications needed to make the representation. One of our goals

is to allow explicit treatment of the modeling process and

the representation issues.

We also want to get away from the use of sets as the only

model for categories of knowledge, since they artificially

limit the kinds of categories that can be considered [4]. Sets have both definite boundaries and specific elementary units. There are many models of "uncertainty" that

generalize the first constraint: probability distributions,

fuzzy sets, belief functions, rough sets, and many others.

As near as we can tell, there is no appropriate model that

generalizes the second constraint. This lack is mainly due

to the nature of mathematics as our most concrete form

of reasoning: the elementary units must be defined before

we can start mathematical reasoning. This constraint is not present in linguistic reasoning [7].

In addition, we want to generalize sets in two other directions: we want to allow context to leak into the de44
scriptions [1] [10], and we want to allow individuals to have different structures in different viewpoints. In many

cases, the indefinite boundaries of a category are made

more precise (though still somewhat indefinite) by specifying the context under which the category is being considered, thereby allowing the context to become part of

the specification of the category. For this reason, we make

context a part of viewpoint. We also note that the different viewpoints can give the category different structure, one of which can even be to take the category as an individual.

1.2 A First Look

In this subsection, we introduce the concepts that define our approach. Do not expect formal or precise definitions

here; they begin in the next section. Terms in italics in

this section are technical terms in our approach that are

defined in the next sections.

The most important source idea is the "thing" ness of all concepts: anything we can describe with language can be

"reified" , that is, viewed as a "thing" , and referred to as a

unit or viewed in a number of different, not wholly compatible, ways. That is, each viewpoint leads to a possibly different structure for the individual (and certainly to a different interpretation of the significance of the structure).

These "thing"s can be grouped naturally into categories.

We think of categories as including our notion of concepts

or classes. We call these "thing"s individuals, and think

of the categories as collections of them. It is this property that leads us to consider all concepts as individuals,

at least under certain viewpoints, and to recognize that

different viewpoints lead to different structures for the individuals. We can view a category as an individual under

certain viewpoints, and we can view an individual as an

assemblage under certain viewpoints. We can also view an

individual under a certain viewpoint to be a member of a

category under some viewpoint.

There are two ways to study grouping of individuals into

categories. We can begin with some individuals and try

to identify appropriate categories, or we can begin with

categories and try to examine individuals in them. Both

approaches are used here.

Categories also describe relationships among other categories. We want to generalize the notion that categories

contain other categories, which are separated by their distinctions into different roles. A relationship has roles that

may be filled by other categories, so we can talk about

roles without using the categories that might fill them. In

this sense, they are similar to frames with variable slots

for other objects.

A category can be divided partially by distinctions into

several other categories, and the distinctions become new

roles for the division (partially means not necessarily ei- ther disjoint or exhaustive, i.e., not only into subsets).

The "other" categories are called constituents. Distinctions are important only relative to a certain viewpoint, so

division of a category is defined only in terms of a viewpoint. Different viewpoints may divide the category in

different ways. The divisions include our notions of knowledge structures (including abstract datatypes such as "set of X" and other structures).

Constituent categories for different divisions of a category

generally have different viewpoints from each other. When

we write that a category "contains" another, it means that

there is a viewpoint according to which the second cate- gory is one of the constituents of the first one.

If we extend this decomposition further to many levels,

we get a kind of hierarchy of categories, related by various

divisions according to various viewpoints. This hierarchy

becomes a kind of "ontology" for the application domains

involved, and it allows us to make much more flexible use of the usual sorts of ontologies defined in knowledge representation languages.

1.3 Systems and Environments

A knowledge representation scheme makes no sense outside a context of use. The context we consider for this

paper is autonomous systems [2] [3] [9]. An autonomous

system must somehow classify its surroundings in ways

that allow appropriate responses, or have some way to recognize features of its surroundings that instigate appropriate responses. An autonomous system also needs to learn from its experience in the world, adjusting its internal "knowledge" structures to improve its knowledge of

the world, and therefore improve the effectiveness of its behavior.

This kind of system has internal structures that include

interpreter definitions in addition to the usual data and

explicit knowledge base structures, because the architecture of our systems (with their active integration activities

coordinated by wrapping processes) means that the interpreters are also defined by explicit data structures (e.g.,

45
wrex programs). The system also has four processes for

knowledge construction and use: "recording" experiences

(as traces) in processible structures; assessing it according

to different criteria; extracting knowledge (as models) in

processible structures; and using it for different purposes.

2 Organization Rules: Structures

We can organize knowledge either "top-down", from collectives to instances, or "bottom-up", from instances to

collectives. Our top-down approach to modeling knowledge depends on one notion of organizational entity and

one notion of organizational relation. The "categories"

refer to classes of real world phenomena, and the "divisions" represent them. Our bottom-up approach depends on these notions as if we were collecting "individuals" into

classes.

2.1 Category

Categories are descriptions of all phenomena. The fundamental organizational entity is the category, which represents anything that can be labeled by a symbol. In fact,

we want our notion of category to be co-extensive with the

notion of "concept" and the notion of something that we

can describe and reason about. That makes it the same

notion as the one we have considered before [7] for "symbols" : we can make up and use names for categories long

before we know everything (or anything!) that is in the

categories (e.g., black holes, phlogiston, public-key cryptosystems). This is the connection between our notion and

natural language processes: we are attempting to model

the effectiveness of language in referring to concepts, even though we expect there to be many more categories than

words or phrases [6].

2.2 Division

The fundamental organizational relation is division

of a category

into roles for other categories

according to a viewpoint.

This division is our replacement notion for the usual notion of set or structure. Our notion of division corresponds

to structural decomposition of categories, but it is much

more general; it allows all structuring methods to coexist.

We describe what a viewpoint is a little later on.

Divisions make some things about a category more definite. We make divisions because the more information

we have about a category, the more precisely we can use

it. We make multiple divisions because we think of cate- gories as being different in different contexts, or when we

consider them from different viewpoints.

One kind of division is to specify that the category plays a

particular role in some other division. This features allows

us to build up as well as down with the categories.

Another kind of division shows the structure of the cate- gory when considered from one viewpoint, with decomposition corresponding to subcategories of the category, and

constraints corresponding to distinguishing properties of

the subcategories.

We can also describe the structure of the individuals in a

category, at least according to a particular viewpoint, by

first defining a division that corresponds to considering the

category as a collection of individuals and thereby defining a category of those individuals. Then we can either use a

division of that category for the individual structure, using

architectures and roles for other categories, with "boxes

and lines" diagrams or hierarchies for structure, or we can imagine an abstract space containing (representations of)

the individuals as elements of the space, or as a subregion

in which they must lie, or as a mapping from some other

structure into the space.

We use a viewpoint to emphasize certain distinctions

among entities in a category. Distinctions can be differences in content, structure, available information, or intended use. They are often explicit, but sometimes un- known at first.

Distinctions define roles in the division of a category. For

example, a partition of a set is a division that has roles for

the various subsets, which may or may not be explicitly

distinguished. The different components of a structured

entity are roles in the division that defines that decomposition. The different steps of a structured process are

roles in the division of that process into parts. Some other

common ways to write about divisions are that a category

"contains" entities, or that a category "describes a relationship" among entities.

46
2.3 Individuals

Individuals are particular objects or agents or actions or

events or relationships, usually associated with one or more categories. The individuals are the "things" we referred to in our introduction. An individual is intended

to represent a real-world entity, the same way a category

does. In many cases, what we would normally consider to

be an individual is not uniquely specified, so we must make

do with a class of possibilities. In this case, we are using

the individual as a "typical" member of a category (which

derives from a particular viewpoint on the individual).

We talk about individuals as members of a category, even though membership requires a viewpoint, and therefore is

really only for divisions. That means that an individual

must be a member of a division, not a category. Every

individual is therefore an instance of one or more divisions,

and we consider the corresponding categories as "types"

of the individual (according to the viewpoint that leads to

the division).

Sometimes we are given an individual (including the current situation), and we try to form or understand the categories it may lie in. We may have to infer one or more

viewpoints, and consider different structures for the individual.

As we get deeper in the category hierarchy, the categories

become more and more concrete, and we eventually get to

sets and data structures, which in our scheme are divisions

of categories.

Divisions also apply to individuals, but we usually try to put the individual into a category first, so that the divisions apply to the category instead.

2.4 Viewpoint

We use viewpoints to distinguish different structures for our categories, either for the individuals in the category

or for the category itself. The viewpoint defines some of

the assumptions and modeling decisions that are reflected

in the presented division.

A viewpoint is a focus within a context. A focus is a presumed scope and level of detail, which defines the scope of

quantifiers, and the level of detail required to express the

viewpoint. A different focus means a different viewpoint,

which means a different division. Different viewpoints of a category often differ only in their focus. The scope defines the extent of the conceptual units, both structures

and processes, and the level of detail defines their conceptual "size". It is part of our ongoing research to develop

notations that express or define scope and level of detail.

There is something "compatible" about the "size" of the

conceptual units in a focus that makes it seem "natural".

It is important in this approach that the same category

may have many different divisions, each with a different

viewpoint, and that we can therefore easily imagine adding

new divisions as other viewpoints become interesting.

A viewpoint implies a choice of descriptive language for

the corresponding division, and a corresponding language

interpreter. The viewpoint is outside the division, but

refers to it.

One of the difficult outstanding research problems is to determine how and when viewpoints are related to each

other.

2.5 Context

We have long maintained that context provides all the

interpreters for symbols, and that semantics Js_ the interpretation of syntax. For this paper, it means that context

provides all the interpreters for categories, and that se- mantics is the interpretation of divisions in categories.

A context does not _do_ anything. It is a passive provider

of and reference to information and processes.

An interpreter is a mapping from elements to actions or

objects, and from constructs to patterns of action or structures. So just as focus is a collection of categories that are used as units, context is a collection of categories that are used as relationships (mappings) from some categories to

others.

There is a notion of specificity in context. There is a relation of "more concrete" among divisions, and interpretation is intended to map towards more concrete categories.

The simplest implementation of context is a collection of

mappings from attributes to values, but others are possible.

A context is a state of knowledge, which is a collection

of assumptions, specializations, relationships, and current

situation.

A context contains or refers to the domain-specific prior

information structures and interpreters. The environment

is the situation-specific current dynamic activity to which

47
the system must respond.

It is never the case that we know all of the context of a

division, so it is essential that we be able to augment the

context at any time. When we write of a category "in" a context, we actually mean the division of the category

according to the viewpoint given by the context and the

focus of the category.

3 Process Rules: Behaviors

Our knowledge representation defines more than just what

the concepts are and how they are related. It also defines

how things change and what can happen.

3.1 Activity and Action

Everything that happens is an activity. Every activity has an effect, which we may or may not be able to detect.

All activities take time, which may or may not be representable as instantaneous, according to the time scale in

use. An activity description includes all intermediate steps

or stages (we do not presume discrete steps). An activity

is a kind of category. An action is a kind of activity. An

activity can be made up of actions.

An action description is an indivisible activity. It is a kind of division that has the form of a collection of constraints among prior and posterior variables (i.e., roles for

individuals), and their times of occurrence. There is no intermediate "step" in an action; the values of the affected

variables can only be queried before the action or after

the action. During the action, the values are presumed

to be the same as at the starts of the action, but they

are also considered to be "in transit", so they cannot be

relied on to hold fixed for any positive amount of time.

An activity description allows querying of actions at all intermediate times. For example, a discrete sequence of

steps implements an activity as a set of actions, whereas

a continuous motion is an activity for which we know all the intermediate places as a function of time.

A division is a model in our usual sense, with component

roles for other models and interactions styles which distinguish different classes of divisions. Actions on a division

are converted into actions on the roles, the interactions or both. This conversion is part of the definition of a division. Different kinds of divisions correspond to different

collections of conversion processes.

Every action is a change of something. Action classes have

pre- and post- conditions, and descriptions of effects.

Every action has an effect, possibly an actor (which can be

an agency instead of an individual), and an actee, which

is usually one or more roles for categories (or individuals).

The difference between an event and an action is that

events are instantaneous; we don't use them. Actions can

take some amount of time.

3.2 Situations

Situations are particular parts of the environment (as if they were a component or aspect of the environment, ex- cept that we don't necessarily know anything else about

the environment). A situation describes part of the environment at a particular time, and in that sense is like a

context individual; the difference between the situations

and other parts of context is that situations are instances

of the environment in time.

There is some interesting new mathematics associated

with situations [1], and much work on situated planning

[10] and situated behavior [9], and we believe that our approach allows us to describe the situations, so that they

may be made explicit in the computations.

Computationally, the application of an action to a situation has three parts: the situation provides individuals,

the action roles match up to those individuals, and the

action effects change those individuals.

For these purposes, a situation can be thought of as a

time and a collection of individuals. It is not a set. It is a

partly determined category. Such a category is determined

by coincidence in time and space rather than coincidence

in defining properties.

3.3 Current Behaviors

We distinguish the rules of behavior, which are about

classes of situations and the appropriate corresponding

activities, from the actual behavior, which is about the

current situation and the current activities as time progresses. Classes of possible behaviors can be defined by

stringing together the rules according to classes of possible situations, but they must be specialized to represent

the actual (or presumed) situation.

What actually happens in a system (or, more properly,

within a system _and_ between it and its environment) is

48
a temporal pattern of instances of activities. We call them

"activities" instead of "events" because the latter term is used more often for instantaneous events, which we allow

only as a conceptual shorthand.

While the system is operating, the relevant part of the

"current" situation at any given time, or even the currently available knowledge about the current situation at

that time, is almost never enough to identify it uniquely.

There is therefore always a class of possible situations.

The class is organized not so much by its internal structure as it is by its component's coexistence in time.

4 Conclusions

The notions we have discussed here provide a different

approach to representing knowledge in a complex system.

We believe that they allow incorporation of most other

methods of representation, and that something along these

lines is necessary to allow the representation to take the

current context and environment into account.

We have provided a number of ideas for what a new representational approach would have to provide. Specifically,

we have stressed how "representing" must be changed from

static notions of the organization and definitions (data

dictionary style) to one that must include the active processes for interpreting the knowledge constructs. In this

processing plus the metaknowledge required for our soft- ware architecture approach [5] [9], we will begin to have

the necessary capabilities to handle and explicit contextual information which we consider essential.

The current research project is constructing a software system that implements this approach, and in which we can perform various studies of effective knowledge collection,

reorganization, and extraction.

References

[1] Jon Barwise, The Situation in Logic, CSLI Lecture

Notes No. 17, Center for the Study of Language and

Information, Stanford U. (1989)

[2] Kirstie L. Bellman, "When Intelligence is in Control", pp. 10-12 in Intelligent Systems: A Semtotic

Perspective, Proceedings of the 1996 International

Multidisciplinary Conference, Volume I: Theoretical

Semiotics, Workshop on Biologically Inspired Complex Systems, 20-23 October 1996, Gaithersburg,

Maryland (1996)

[3] Kirstie L. Bellman, Christopher Landauer, "A Note on Improving the Capabilities of Software Agents",

(poster summary) pp. 512-513 in Proceedings A A '97: The First International Conference on Autonomous

Agents, 5-8 February 1997, Marina Del Rey (1997)

[4] George Lakoff, Women, Fire, and Dangerous

Things, U. Chicago Press (1987)

[5] Christopher Landauer,

Kirstie L. Bellman, "Knowledge-Based Integration

Infrastructure for Complex Systems", International

Journal of Intelligent Control and Systems, Volume

1, No. 1, pp. 133-153 (1996)

[6] Christopher Landauer, Kirstie L. Bellman, "Semiotics of Constructed Complex Systems", pp. 35-40

in Intelligent Systems: A Semiotic Perspective, Proceedings of the 1996 International Multidisciplinary

Conference, Volume I: Theoretical Semiotics, Workshop on Intelligence in Constructed Complex Systems, 20-23 October 1996, Gaithersburg, Maryland

(1996)

[7] Christopher Landauer, Kirstie L. Bellman, "Mathematics and Linguistics", pp. 153-158 in Intelligent Systems: A Semiotic Perspective, Proceedings

of the 1996 International Multidisciplinary Conference, Volume I: Theoretical Semiotics, Workshop on New Mathematical Foundations for Computer Sci- ence, 20-23 October 1996, Gaithersburg, Maryland

(1996)

[8] Christopher Landauer, Kirstie L. Bellman, "ModelBased Simulation Design with Wrappings", pp. 169-

174 in Proceedings of OOS'97: Object Oriented Simulation Conference, WMC'97: 1997 SCS Western

Multi-Conference, 12-15 January, Phoenix, SCS In- ternational (1997)

[9] Christopher Landauer, Kirstie L. Bellman, "Computational Embodiment: Constructing Autonomous

Software Systems", pp. 42-54 in Judith A. Lombardi (ed.), Continuing the Conversation: Dialogues

in Cybernetics, Volume I, Proceedings of 1997 ASC

Conference, 8-12 March 1997, U. Illinois (1997)

[10] Lucy A. Suchman, Plans and Situated Actions: The

problem of human-machine communication, Cambridge U. Press (1987)

49
KNOWLEDGE REPRESENTATION LANGUAGE IN SEMIOTIC

SYSTEMS

Vagin V.N., E.Yu. Golovina

Moscow Power Engineering Institute, Applied Mathematics Department.

Krasnokazarmennaja, 14, 111250, Moscow, Russia.

Electronic mail: vagin@apmsun.mpei.ac.ru

gol@apmsun.mpei.ac.ru

ABSTRACT

A semiotic system is a multi-layer one, consisting of multilayer networks from signs-frames. One of the main components

of any semiotic system is a knowledge-based repository

(semiotic knowledge base). The difference of a semiotic

knowledge base from an ordinary one is in a structure of basic

units for knowledge representation (sign structure) and in operation set over these basic units. Multi-layer logic (MIX), developed by S. Ohsuga and H. Yamauchi, is proposed as knowledge representation language

m semiotic knowledge bases. MLL is appropriate apparatus for discription of knowledge structuring and aggregation.

We have been developed the extension of MLL syntax, which

allows to increase efficiency of the deductive inference. The

Scolemization algorithm and the unification algorithm for extented MLL syntax is developed. The system KM (Knowledge

Model), based on deductive inference in MLL, as a

modelling tool of complex-structured problem domains in semiotic knowledge bases is developed. The conceptual

language for modelling a complex-structured problem domain is researched. The translator of queries with conceptual language

into MLL is designed.

KEYWORDS: semiotic system, knowledge base, knowledge

representation language, problem domain, multi-layer logic.

1. INTRODUCTION

The widespread using of computer technology in different

spheres of human activity has made necessary to develop

semiotic systems.

A semiotic system is a multi-layer one, consisting of

multi-layer networks from signs-frames. The sign used in semiotic systems has three entities: a name, a concept and

representation which are interpreted as syntax, semantics

and pragmatics. A sign structure is matched with a frame

structure that also has similar entities: name, protoframe

and frame example. One of the main components of any

semiotic system is a knowledge-based repository (semiotic

knowledge base). The difference of a semiotic knowledge

base from an ordinary one is in a structure of basic units

for knowledge representation (sign structure) and in operation set over these basic units. The central problem of semiotic system development is problem domain modelling. To model the complexstructured problem domains, it is necessary to choice the

knowledge representation language, which is available for the description of such domains.

2. A FORMAL MODEL OF A COMPLEXSTRUCTURED PROBLEM DOMAIN IN

SEMIOTIC SYSTEMS

As a formal model of a complex-structured problem domain we have been proposed a hybrid model that combines the

"program engineering" paradigm [1,2,3,4] and the

"knowledge engineering" one [5,6], i.e. an object-oriented

approach [7,8] and procedures, and a model for representing knowledge about a problem domain, should be

used in order to represent a formal description of a problem

domain in semiotic systems [9,10,1 1,12].

We have been proposed that a logical model based on

multi-layer logic (briefly MLL) [13,14], should be used as a formalism for representing knowledge about a complexstrucrured problem domain. MLL is an integration of the

logical approach and of an approach based on semantic

networks. It may be considered as an object-oriented first- order predicate calculus that describes knowledge

structuring and aggregation.

By a slash we will mean a kind of delimiter used in prefix

of a formula. Thus, the simple slash (Qx/X) is used to denote that x is an element of the set X (x e X), yhe simple

"thick" slash (Qx/ X) denotes that x is defined on a set whose elements are the components of the object X

(X V x), while the double slash (Qx//X) denotes that x is defined on a set whose elements are part of the object X

(X x). We are developed the extension of MLL syntax, which

allows to increase efficiency of the deductive inference.

The extented MLL syntax is represented.

Alphabet

(1) constants: a,b,c,...,X,Y,Z (constant sets),...

(2) variables: x,y,z,...

(3) function symbols: f,g,h,...

(4) predicate symbols : P,Q,R,...

(5) quantifier: V, 3

(6) logic connectives: —i, &, V, -»

(7) auxilliary symbols: #,*,/, /,//,{,},(,)

50
Terms:

(1). Any constant and variable are terms.

(2) . If f is a n-ary function symbol and t

x ,t2 ,...,tn are

terms, then / (t

x , t

2

,

.

. . , t

n ) is a term.

(3) . All terms are obtained by applying the rules (1) and (2). The rules of designing well-formed formules (WFF) for

: extented MLL syntax is represented.

Fl. If P is a n-ary predicate symbol and f, , t

2

> . .

. , tn are

terms, then P(tx , t

2

,

.

.

. , tJ is WFF.

F2. If F and G are WFF, then -,F, F&G, FvG, F-*G are WFF.

F3 . If F is a WFF and x is an object variable, then

(1) . (Vx / y) F and (3x / y) F are WFF, where y is a

constant or variable (here / is an ordinary slash).

(2). (Vx / y)F and (3x / y)F are WFF, where y is a

constant or variable (here / is a fat slash).

(3) . (Vx // y) F and (3x // y) F are WFF, where y is a

constant or variable(here // is a double slash).

(4) . (V(x / Z)//y) Fand (3(x / Z)//y) F are WFF, where

y is a constant or variable, Z is a constant set.

F4. There are no other rules of designing WFF.

An inference algorithm for extented MLL syntax has been

developed.

At the present time the system KM (Knowledge Model)

based on deductive inference in MLL is designed.

3. THE MODELLING SYSTEM KM OF A

COMPLEX-STRUCTURED PROBLEM

DOMAIN

The system KM (Knowledge Model) as a modelling tool of

a complex-structured problem domains is developed. The

system KM allows :

to construct the ISA-hierarchy of object classes;

to define the object classes attributes and the

relations between object classes;

to construct the Part-of -hierarchy of object classes;

to define the class representatives;

to construct the representatives Part-of -hierarchy;

to browse the class objects and the hierarchies;

to describe the logic formulas;

to receive answer to queries.

The architecture of the KM system is represented in Fig.ure

1. The main components of the system KM are:

• subsystem of the problem domain model

controlling;

• subsystem of modelling;

• subsystem of browser;

• knowledge base;

• subsystem of the deductive inference.

The subsystem of deductive inference, based on inference in MLL, is served for:

• logical verification of information represented in a knowledge base;

obtaining attribute values and extensions of

relations what allows to "compress" the extensional

component of the knowledge base;

receiving the new knowledge from knowledge,

represented in the knowledge base;

obtaining answers to queries.

subsystem of

the problem

domain model

controlling

knowledge

base

subsystem of

browser

subsystem of the

deductive inference

Figure 1. The architecture of the KM system

Example 1. A program component x, including in the control

support system (CSS) #P, provides landing an

airplane y, assigned to the airport #A, if there are:

• PC t, in which x operates;

• a radiolocation station (RLS) s, connected with PC

t;

• information flow #11, containing message flow tl, accepted by RLS s and containing message class

rl, describing an airplane y and processing by a program component x;

• information flow #12, produced by a program

component x and accepted by an airplane y, containing message flow t2, transfering RLS s, in which there is a message class r2, containing

information about airplane landing y. The structures of the problem domain is represented in Figure 2. Formalization in MLL with extented syntax:

(3(x/program_component)//#P) (V(y/airplane)//#0)

(3 (s/RLS)//#A)(3 (t/PC)//#A) (3 (t 1 /message_flow)//#I 1

)

(3(rl/message_class)//tl) (3(t2/message_flow)//#I2)

(3(r2/message_class)//t2)

Operate(x,t) & Connect(s,t) & Accept_RLS(s,tl) &

Described l,y) &Process(x,rl) & Transfer_RLS(s,t2)

& Produce(x,r2) & Accept_airplane(y,r2) ->

Landing(x,y)

51
Message_Flow

MF11

Message_Flow

MF13

MF21

Message_Class

\

MF23

Message_Class

MC211 MC111 MC112 MC113 — MC212 MC213 — - "Component-of" relation ( V )

- "Element-of " relation ( e )

- "Part-of" relation ( )

Figure 2. The structures of the problem domain

52
The conceptual language for modelling a complexstructured problem domain is developed. The translator of

queries with conceptual language to MLL is designed.

The examples of queries

.

Example 2. Let us define the program components, which are part

of the developed system P, and the airplanes, which are part

of the controlling object O, between which the specific

relation "provideJly_upJo_ landing" is set up.

Formalization in MLL:

(3 (x/Program_component)//#P) (3 (y/airplane)//#0)

provide_fly_up_to_landing(x,y)-» .

Example 3. Let us define the program components, which are part

of the developed system P, and the computers, which are

part of the airport A, between which function relation is

set.

Formalization in MLL:

(3 (x/Program_component)//#P) (3 (t/computer)//#A)

function(x,t)-» .

The system KM supports "a free connection" [15] of KB and

DB under Paradox DBMS. Such implementation of the

system KM provides using all opportunities Paradox DBMS

such as distributed processing, high performance, complex

verification, supporting of integrity and safety of data,

failure and recovery of DB, supporting of very large DB.

The system KM is running under Windows'95. The

development language of the system KM is Borland C++.

4 . CONCLUSIONS

We have considered a new approach to desinging semiotic

systems. The knowledge representation language in semiotic systems is proposed. The system KM as a tool of

modelling a complex-structured problem domain is developed.

This work was supported by the Russian Fund of

Fundamental Researches (project code 96-01-00125).

5. REFERENCES

[1] Modern Software Engineering. Foundation and Current

Perspectives.- Edited by Peter A.Ng., Raymond T. Yeh. - VAN NOSTRAND REINHOLD, New York,-1990.- c.591.

[2] J.E. Cooling. Software Design for Real-time Systems. - CHAPMAN AND HALL (University and Professional

Division).- 1991, p. 505

[3] Harel D. and ets. Statemate: a Working Environment

for the Development of Complex Reactive Systems -IEEE

Transactions on Software Engineering, Vol. 16, No. 4,

April 1990, pp.403-413

[4] Robert V. Rubin, James Walker II, Eric J. Golin Early

Experience with the Visual Programmer's Workbench. - EEEE Transactions on Software Engineering, vol.16,

No. 10, 1990

[5] Andrew J.Symohds Creating a Software-Engineering

Knowledge Base.- Software Development Computer-Aided

Software engineerig (CASE).Edited by Chirofsky E.J.- EEEE Computer Society press technology series, 1989

[6] Marc Eisenstadt, J.Domingue, T.Rajan, E.Motta Visual

Knowledge Engineering,- IEEE Transactions on Software

Engineering, Vol.16, No. 10, October 1990

[7] Sally Shlaer and Stephen J. Mellor " Object

Lifecycles: Modeling the World in States",Prentice-Hall,

Englewood Cliffs, N.J., 1992

[8] E. Gibson Objects - Born and Bred- BYTE,

October, 1990

[9] M. Eisenstadt, M. Brayshaw A Knowledge

Engineering Toolkit - BYTE, vol.15, No. 10,12,1990

[10] Yokoyamat An object-oriented and constraint-based

knowledge representation system for design object

modeling.- Tokyo, Japan, ICOT Research Center, 1989

[11] V.N. Vagin, E.Yu. Golovina, N.O.Salapina. Intelligent

CASE for Decision Making Systems. Proceedings of

JCKBSE'96. Second Joint Conference on Knowledge-Based

Software Engeneering. Sozopol, Bulgaria. September 21-

22, 1996,-pp. 122-127.

[12] Vagin V.N., Viktorova N.P., Golovina E.Yu.

Multilayer Logic as a Knowledge Representation Model in the CASE System.- Journal of Computer and Systems

Sciencis International. -Vol.33, No.3, 1995, pp.72-83.

[13] Ohsuga S., Yamauchi H. Multi-layer logic - a

predicate logic including data structure as knowledge

representation language.- New generation computing,

Vol.3,-N0.4,-1985 -c.45 1-485.

[14] Ohsuga S. Toward inlelligent CAD systems.-

Computer Aided Desing, Vol.21,-N0.5,- 1989.-C.3 15-337.

[15] H. Yamauchi, S. Ohsuga Loose coupling of KAUS

with existing RDBMSs.- Data & Knowledge Engineering,

5, 1990,-pp.227-251.

53

Ill NN - MODELS

"Intelligence and Semiotics in Pattern Recognition and Neural Networks"

David Casasent

Carnegie Mellon University

Department of Electrical and Computer Engineering

Pittsburgh, PA 15213

Abstract

Pattern recognition is a vital part of many intelligent systems.

Various uses of intelligence in several new algorithms are described for a range of image processing problems: detection,

algorithm fusion, feature extraction, object representation,

optimal features for both representation and discrimination,

object classification and pose estimation. The techniques

employed include biologically motivated Gabor wavelet filters,

new neural nets, and nonlinear image processing. Test results on

IR, SAR, robotic and active vision data are presented.

/. Detection

This is the first step in general image processing or scene

analysis, locate all objects of interest in the scene independent

of object distortions and object class. These regions of interest

(ROIs) are then further processed to reduce false alarms and

determine the class and pose of the contents of each ROI. There

is no one magic detection filter or algorithm, similarly humans

do not use just one technique for detection. The best results we

have seen are obtained by applying several different detection

algorithms to a scene and then fusing the output results to obtain one detection plane with peaks at all ROI locations.

Algorithms

The best detection algorithms we have found are the

morphological wavelet transform (this applies morphological

and Gabor wavelet filters to the scene and fuses their outputs)

[1] and a Gabor basis function filter [3]. The morphological

processing removes spatially-varying background information

while the Gabor processing locates clutter regions of the scene where target detection confidence will be low; the Gabor basis

function filters detection objects. All results are distortioninvariant.

Algorithm Fusion

To combine the results from different detection filters, the

best algorithm fusion technique we found [1] was to use fuzzy

logic concepts to produce nonlinear membership mapping

functions to apply to each detection algorithm's analog output.

These map the outputs for the different algorithms to the same

range. We use different mapping functions for different ranges

of object contrast We then use pointwise minimum fusion (a

fuzzy logic AND) to fuse the different algorithm outputs.

These techniques thus use a variety of different image

processing techniques (morphology, distortion-invariant filters,

wavelets, fuzzy logic, fusion).

IR and SAR Results

For IR data (360° aspect distortions of 8 different object

classes in severe clutter, with poor object contrast) we achieved

excellent results (Table 1) for detection (PD) and false alarms

per scene (Pfa)- Algorithm fusion reduces Pfa by up to factor

10. Subsequent processor stages further reduce Pfa to below 0.

1

per km2 with Pc

= 95% correct recognition (Section 2).

Table 1: Algorithm fusion detection results (TRIM-2)

PD(%) PFA

90.6

80%

3.1

0.9

For SAR data [2], we designed a new set of distortioninvariant filters (about 3 per class). These are applied to an input scene and the WTA output if above a threshold indicates an ROI, the filter with the largest output above a threshold denotes

the class of the ROI data. This technique requires many fewer

templates than in model based methods. The filters are shift- invariant and hence easily implemented in DSP hardware. We

tested these filters on two different real SAR target databases

and a synthetic database of SAR target models. For clutter, we

used half of the man-made and natural clutter false alarms over 76 km2

that passed the first two stages of the Lincoln Labs SAR

processor. For four class data with 360° of distortion, we

obtained PD

= 99.8%, Pc = 96.6% and a superb PFA = 0.026/

km2

. We tested the filters at SNR = 0 dB and found a negligible

decrease in Pc of 0.5%. We tested the filters for 25% object

obscuration and achieved Pc = 80%. Thus, these intelligent

filters are robust.

New Intelligent Filter/fusion Design

We now advance a new neural net (NN) data driven concept

to use intelligence to automate the design of several different

Gabor wavelet detection filters (selection of their parameters)

AND the simultaneous design of the combination coefficients to be used to fuse different filter outputs [3]. This represents an automated data-driven intelligent image processing system. We

discuss this approach using Gabor wavelet filter functions

2 2 2 2

7i(x /a +y /b ) -j27trcocos(e-<|))

gn = e e

v/

(1)

When such a filter is applied to a scene, its analog output

denotes the amount of a given spatial frequency w at a given

orientation <)) present in each local scene region defined by a and

b. We consider Gabor wavelet (GW) functions with modulation

57
in 1-D only, we select co = l/2d (where d = a or b for horizontal

and vertical features respectively). We use filters formed from

the real and the imaginary parts of the Gabor function (GF); real Gabor filters are proven blob detectors and imaginary Gabor

filters are proven edge detectors.

We use 6 GFs, two real (these detect object height and width)

and four imaginary (these detect the left, right, top and bottom

object edges). We developed a separate algorithm to determine

the optimal parameters for each GF separately. These 6 GF

outputs or GF filters are the Pj inputs we consider to the neural

net processor of Figure 1. The Pj to P2 weights combine these

different GF functions into N2different macro GFs at P2. The

P2 outputs represent different detection correlation planes for

different macro GF filters. These outputs are then combined (P2

to P3 weights) into N3 fused output correlation planes at P3,

where a WTA determines if each local input scene region is an ROI or not (and the confidence of each estimate). The Pi to P2

weights are complex-valued and the P2 nonlinearity used is a

simple square law. These are radically new neural net concepts.

We have shown that this produces general quadratic nonlinear

decision surfaces of higher rank than other methods. The P2 inputs represent the N2 new macro GWfilters (combinations of

the basic 1-D GF input Pi functions), the P2

to P3 weights

represent the algorithm fusion of these N2 detection filters. Both

the filters and their outputfusion are automatically selected and

are data driven. This thus represents a very intelligent and

general distortion-invariant filter synthesis and algorithm

fusion concept. Initial results show better Pc and PpA on

distorted multi-class objects than any other Gabor filter method.

Pi

Fig. 1. Extended piecewise quadratic neural network

(E-PQNN) architecture.

2. Distorted Object Classification

Feature Space Trajectory (FST) Processor

Our distortion-invariant filters represent one method to drastically compress a model base of different aspect views etc. (distortions) of an object. When object class and pose are necessary, the FST representation is very novel and useful [4,5]. In this case, different aspect views of an object are represented

by different points in feature space. Points corresponding to

adjacent aspect views are connected by straight lines. This

produces an FST (piecewise linear trajectory). Different FSTs

are produced for different objects. This is an attractive semiotic

representation for all distorted views of an object To classify an unknown input, we plot it as a point in feature space. The

closest FST provides the class estimate; the closest line segment on that FST provides a pose estimate for the input. If an input

point is too far from an FST, it is rejected as clutter. This

representation overcomes many standard classifier problems

(training set size, generalization etc.) and requires very low online calculations.

IR and SAR Results. For our 8-class distorted IR database,

we used 11 aspect views of each object as a training set and

produced an FST for each object using shift-invariant wedge

magnitude Fourier features [5] (each FST has only 1 1 vertices).

We correcdy classified 95% = Pc of all test set aspect view

inputs. Of more importance, we input the 200 clutter region

false alarms (from our detection stage) to the FST processor. We

were able to reject all but one clutter input and reduce PFA

below 0.1/km2

. We also applied the FST to SAR data. For 2 classes of

objects in real SAR (with every other aspect view used for

training), we achieved Pc = 100%. With 0 dB SNR, we

achieved negligible loss (Pc = 99.77%). In both cases, (for 100

of the 200 clutter chips that passed the first two stages of the

Lincoln Labs processor), we achieved perfect PpA

= 0 false

alarm rejection. For a 4-class synthetic SAR object database, we

achieved Pc = 98.33% and PFA = 0.026/km2

. Thus, the FST is a

very attractive representation and allowsfor a unique processor

using semiotic concepts. It requires only 6.5 kbytes of storage

per object and only 6.5 kops per class. Object Representation. We have developed a technique to reduce the number of vertices (aspect views) necessary to represent an object and to determine which aspect views to use. We have used this to analyze the representation error in our 8-

class IR data (use of only 1 1 vertices (aspect views) per FST

produces a worst-case average representation error of only 3%).

We used it to reduce the number of training set images in our SAR data from 180 to 80 aspect views per class for a 2 class

real SAR database (we achieved Pc = 96% with PFA = 0 still).

Feature Spaces. Wedge or ring Fourier features are attractive

as they are shift-invariant. Another attractive semiotic

description of distorted object views are the dominant

eigenfeatures (KL); these perform better for SAR data. For

several object classes, we use FK eigenfeatures (they provide

better discrimination). We note that calculating FK features

from KL features rather than imagery is preferable (outliers are automatically removed), that use of more KL features is not best

(outlier data is included), and that we have developed eigen

techniques to determine if a training and test set are compatible

and to estimate Pcto be expected. We find these new

eigenspaces an new eigenanalysis methods to be new intelligent

semiotic data analysis tools.

58
Active Vision Uses

We have used a time sequence of views of an object over

several frames as input to the FST [5] and shown that by

matching an input sequence to FST sections that individual

errors in separate frames (as much as 50%) could be overcome

(Pc « 100%). This new semiotic representation and processor

thus also handles time sequences of data.

We recently [5] also considered various active vision

applications of the FST in robotics. In active vision, a sensor (or

robot) acquires a view of an object and then moves to another

location to better learn the object (or to grasp it, inspect it, etc.).

In such robotics case, the object or a model-based CAD

description of it is available and hence an infinite number of

distorted object aspect views are possible. The FST

representation and our adaptive algorithm are essential here to

select the number of aspect views needed and which aspect

views. We have shown that our algorithm yields better

representation than use of aspect views evenly-spaced in aspect

angle. We have also developed new analysis measures to determine which aspect view produces a pose estimate with the

best accuracy and which aspect view provides a class estimate

with the best confidence.

We use the FST to estimate the class and poise of the object

from a given view; we then use this to determine where to drive

the sensor or robot to look next to obtain: a better aspect pose

estimate, a better class estimation, a better view for inspection

or to grasp the object, etc.

Higher-order Features

Higher-order features can provide more information

regarding input data (higher-order correlations). Nonlinear PCA

has been applied to such cases, but all techniques are iterative

and have various problems (most notably the rank of the

decision surfaces produced). We have various new intelligent

semiotic ideas on how to extract preferable nonlinear features

(that provide both representation and discrimination) and how

to calculate such discriminant functions in closed form.

Standard KL features provide only representative, standard FK

(or Fisher etc.) features provide only discrimination. To select

features that are good for both representation and discrimination

we define a representative measure Er (using the covariance

matrix C of the data matrix) and a discrimination measure Ed

using the matrix

R

i2 = IX(*iP -V( *ip-V

T

' (2)

where ii and x.2 316 class 1 and 2 samples. For both good

representation and discrimination, we select the dominant

eigenvectors of £1 +£2+Ri2 (f°r me two-class case) as our

features. To produce nonlinear features, we describe each data

vector in a higher-dimensional space as (y^iih higher order

products included) and we use higher-order C and R matrices.

We solve for nonlinear higher-order features in the higher-order

H space (the solution has a closed form); the solutions are nonlinear in the original space.

Initial tests show that this approach yields decision surfaces

of higher rank (than nonlinear PCA can), that higher-order

correlations exist in real data, and that their use improves P^.

This is a very attractive, new (intelligent and automated)

semiotic method to nonlinearly represent and process data.

References

[1] D. Casasent and A. Ye, "Detection filters and algorithm

fusion for AlTR",IEEE Trans, on Image Processing, Vol. 6, no. l,pp. 114-125, January 1997.

[2] D. Casasent and S. Ashizawa, "SAR Detection, Recognition and Clutter Rejection with new MINACE filters", Optical

Engineering, accepted, October 1997.

[3] D. Casasent and D. Weber, "Quadratic Gabor correlation

filters for object detection", Proc. SPIE, Vol. 3078, April 1997.

[4] D. Casasent and R. Shenoy, "Feature space trajectory for

distorted-object classification and pose estimation in SAR",

Optical Engineering, accepted, October 1997.

[5] D. Casasent, L. Neiberg and M. Sipe, "FST distorted object

representation for classification and pose estimation", Optical

Engineering, submitted May 1997.

59
MORPHOLOGICAL PERCEPTRONS

Gerhard X. Ritter and Peter Sussner

University of Florida

Center for Computer Vision and Visualization

Room E301, CSE Building

Gainesville, Florida 3261

1

1. ABSTRACT

The theory of artificial neural networks has been successfully applied to a wide variety of pattern recognition

problems. In this theory, the first step in computing the

next state of a neuron or in performing the next layer neural network computation involves the linear operation of

multiplying neural values by their synaptic strengths and

adding the results. Application of a nonlinear activation

function usually follows the linear operation in order to provide for nonlinearity of the network. In this paper we

discuss a novel class of artificial neural networks, based on lattice algebra, in which the operations of multiplication

and addition are replaced by addition and maximum (or

minimum), respectively. By taking the maximum (or minimum) of sums instead of the sum of products, computation

is nonlinear before the application of a nonlinear activation function. As a consequence, the properties of these

networks, which are also known as morphological neural

networks, are drastically different than those of traditional

neural network models. The main emphasis of the results

presented here is on morphological perceptrons. Within the

constraints of this short paper, we define the basic computational model of a morphological neuron and examine some differences between morphological perceptrons and

traditional perceptron models.

Keywords; Artificial neural networks, perceptrons, morphological neural networks, morphological perceptrons.

2. INTRODUCTION

In recent years a novel theory of neural computing

based on lattice theory has emerged. Network models based on this theory have, in several cases, proven to be superior

to traditional models. Some references of the underlying

theory and applications of these networks can be found in

[5, 2, 1, 10, 3, 1 1, 8]. In this paper we restrict our attention

to morphological perceptrons.

Artificial neural network models are specified by the

network topology, node characteristics, and training or

learning rules. The basic equation governing the theory

of computation in the standard neural network model is:

Xj (i + i) = f\J2 xi(t) wn -e)j, (i)

where xj(i) denotes the value of the jth neuron at time

t, n represents the number of neurons in the network, Wij

the synaptic connectivity value between the z'th neuron and

the jth neuron, 9j a threshold, and / the next-state function which usually introduces a nonlinearity into the net- work. Although not all current network models can be pre- cisely described by this equation, they nevertheless can be

viewed as variations of this equation. In contrast, the basic equation governing neural computation based on lattice algebra is vastly different from the weighted sum of linear

algebra used in most neural computation. The next-state value of a neuron is obtained from an additively weighted

maximum (or minimum) of inputs from neighboring neurons connected to the neuron and the resultant value is then

passed through a hard-limiter. More precisely, computation

of the next state value of a particular neuron Nj assumes

the form

Xj (t + 1) = / (pj \/ Tij {Xi (t) + Wij)^ , (2)

where r,j = ±1 denotes the excitatory or inhibitory influ- ence of the /th neuron on the jth neuron, and pj = ±1

denotes the post-synaptic response of the jth neuron to the

total received input. The values +1 and —1 denote excitatory and inhibitory influences, respectively. In particular, if

tij = 1, then the tth neuron has an excitatory influence on

the jth neuron, and if r^- = —1, then the ith neuron tries

to inhibit the firing of the jth neuron. Similarly, if pj = 1,

then the post-synaptic response of the jth neuron is excitatory and if pj — —1, then the post-synaptic response of

the jth neuron is inhibitory. The function /is a hard-limiter

defined as f(x) = 1 if x > 0 and f(x) = 0 if x < 0. Neurons that compute their next state using Equation 2

are also called morphological neurons and neural networks

based on lattice theory computation are known as morphological neural networks [8]. Figure 1 illustrates the computational framework of neurons in a general morphological

60
neural net. An obvious advantage of this framework is that

it more aligned with the biological model and does not in- volve multiplication, thus providing for faster computation.

N,

Figure 1. Computational model of a morphological neuron.

The basic neural computations as expressed by Equations 1 and 2 are based on two fundamentally different al- gebraic systems. Observe that the computation represented

by Equation 1 is based on the operations of the algebraic

structure (R,+, x), where R denotes the set of real numbers. In particular, the computation J2 xi w* i s a linear operation involving multiplication and addition. In contrast,

the basic computation occurring in a morphological neuron, as expressed by Equation 2, is based on thesemi-ring

structure (R_oo , V, +) (or (Rqo , A, +) if we replace the operation of maximum by minimum). Here R_oo represents

the extended real number systems R_oo = Ru{—oo}.

The basic arithmetic and logic operations in the extended

real number systems are as follows. The symbol + denotes the usual addition with the additional stipulation that a + (—oo) = (—oo) + a = —oo Va (E R_oo» while the

symbol V denotes the binary operation of maximum with

the additional stipulation that a V (—oo) = (-oo) V a = a Va G R_oo- Note that the symbol —oo acts like a zero element in the system (R-ooiV,+) if one views V as addition and + as multiplication. Also, the role of the multiplicative identity in the structure (R,+, x) is played by

the number 1; i.e., 1 • a = a 1 = a Va € R. In the

structure (R_00> V,+) his role is played by the number 0

since 0 + a = a + 0 = a VaG R-ooSeveral advantages of morphological neural networks

over traditional neural networks models have been established in the area of associative memories. In [9] it was shown that morphological analogues of the Hopfield autoassociative memory have infinite storage capacity, provide

perfect output for perfect input patterns, and are more robust

in the presence of noise. It has also been proven that morphological bidirectional associative memories easily outperform traditional bidirectional associative memories in terms

of storage capacity, bidirectional recall, as well as recall under noisy conditions [6]. In this paper we discuss some

of the advantages of morphological perceptrons

3. MORPHOLOGICAL PERCEPTRONS

Due to page restrictions we shall concentrate our discussion mostly on single-layer morphological perceptrons

(SLMPs) and indicate how these can be used to construct

powerful multilayer perceptrons.

Some of the most successful associative memories

have been multilayer perceptrons. These are feedforward

nets that can be trained using such well-known algorithms

as back propagation. Some of the problems associated with

these nets are the selection of the number of hidden layers,

the choice of the number of neurons within a hidden layer,

very lengthy training procedures, and convergence problems

associated with training algorithms. In contrast, morphological perceptrons have very simple learning algorithms that

converge in two passes and these algorithms actually specify the number of neuron in a hidden layer necessary for a given classification problem [7].

The basic building blocks of morphological perceptions are single-layer morphological perceptrons. A singlelayer perception consists of an input layer of n neurons and an output layer consisting of a single neuron that computes a weighted sum of the input neuron values, subtracts a threshold, and passes the result through a binary-valued

non-linearity. Each of the two possible outputs corresponds

to a different classification response. Typically, a pattern

vector x = (xj, 12, . . .

, xn ) is presented to the input neurons, with each input neuron assuming the value (or state)

of the corresponding vector coordinate value. The pattern

x is said to belong to class Co or class C\ depending as to whether the output neuron's value is 0 or 1, respectively.

As shown in Figure 2, the topology of single-layer morphological perceptrons mimics that of the standard single-layer

perception. However, computation at the output neuron is based on the computational model given by Equation 2. In

particular, the result of the output neuron is given by

/(pyjiixi+wi)^, o)

where x,- denotes the value of the ith input neuron, if, the synaptic weight between the /th input neuron and the

output neuron, r,- indicates whether the input of the ith input

61
neuron to the output neuron is excitatory or inhibitory, and

p denotes the post-synaptic response of the output neuron.

output

input neurons

Figure 2. Single-layer morphological perception.

It is not difficult to ascertain that a single-layer morphological perception can provide solutions to problems that cannot be solved by traditional single-layer perceptions. We

provide a simple example of this.

Example 1. Suppose we want a single-layer morphological perception to classify pattern vectors (2,0), (0,2),

(2, 2) and close neighbors to belong to class C\, and pattern vectors (1, 0), (0, 1), (1, 1) and close neighboring points to belong to class Co. Simple computation will verify that the net shown in Figure 2 with n = 2, uii = tu2 = —1.5,

f\ = r2 = 1, and p = 1 will correctly solve this problem.

For example, using the inputs x = (0,1) and x = (2,2)

we obtain

/[(0-1.5)V(l-1.5)] = /(-.5) = 0

and (4)

/[(2-1.5)V(2-1.5)] = /(.5) = l,

respectively. Therefore, (0, 1) £ Co and (2,2) G C\.

An interesting observation is that the singlelayer perception of this example provides a solution

for a problem that cannot be solved by the traditional single-layer perception model since the two

classes of patterns are not linearly separable. This

observation follows from the fact that the equation

±Mxi + wx ) V r2 (x 2 + w2) V • • • V rn (xn + wn)] = 0

represents an (n — l)-dimensional surface, called the

perception's decision boundary, which divides Euclidean

n-space into two regions. The regions separated by the

decision boundary coirespond the output neuron's on-qff

regions as any input from one region will always result in an on state (value 1) of the neuron while any input from

the other region will result in an off state (value 0) of the neuron. For instance, the decision boundary generated by

the perceptron of Example 1 is the infinite step function

shown in Figure 3. Any point in the quarter-plane bounded

by the lines x = —w1 and y = —w2 will result in a O-state

value if used as input to the perception. Therefore, this perception could solve the two-class problem illustrated in Figure 3, where patterns of one class belong to the region

marked "class 0" and patterns of the other class belonging

to the region marked "class 1."

class 1

class 0

Figure 3. Decision boundary for the single-layer

morphological perception of Example 1.

Single-layer morphological perceptions are the basic

building blocks of multilayer morphological perceptions.

Thus, in oidei to construct multilayer morphological per- ceptions, it is necessary to have a thorough understanding

of SLMPs. The output neurons of SLMPs form the hidden neurons multilayer morphological perceptions. The decisions made by these hidden neuions depend on theii synaptic responses to inputs as well as the synaptic weights of

the input axons. These responses and weights determine

the decision boundaries for the neuron's on-off regions.

For a two-input nodes (n = 2) SLMP, the simplest decision boundary is obtained by setting one of the weights,

wi or W2, equal to —oo. If w\ = -co, then the decision boundary is the horizontal line y = —w2 , and if w2 = -co, then the decision boundary will be the vertical

line x = —w\. Figure 4 illustrates these two possibilities

for n = r2 '= 1 and p = 1. Changing the value of p

to p = —1 interchanges the two classes Co and C\ since

the on region becomes the off region and vice versa. If r 1 = 1 and w2 = —oo, then changing rj to ri = —1 will

also interchange the neuron's on-off regions. However, it

is important to note that if W{ = —oo, then we must have

r,- - 1 since —(x; — oo) = oo — x,- = oo, which is outside

the computational framework of the algebra (R_oo, V, +).

62
x2 J c, 11

-w.

^xf^;

x'

Figure 4. Decision boundaries for two-input,

single-layer morphological perceptron

having one synaptic weight equal to —oo.

The two SLMPs shown in Figure 4 can be combined to form a two-input multilayer morphological perceptron with one hidden layer as shown in Figure 5. The output neuron

of this multilayer perceptron computes the maximum of its two hidden layer input neurons. Hence, a pattern point will

belong to class Co if and only if it was classified by both

single-layer perceptrons as belonging to class Co. It is easy

to see that this multilayer perceptron is equivalent to the

single-layer perceptron shown on the bottom of Figure 5 if w\ — w\\ and u>2 = W22', a pattern vector x = (£1,22) is

classified by both perceptrons as belonging to class Co if and only if x\ < —wi and x-i < —w^-

The preceding discussion shows that a two-input

SLMP can have one of three distinct types of basic decision boundaries; a horizontal or vertical line, or an infinite step function formed by a vertical and horizontal half-line.

Figure 6 shows the four possible types of infinite step

functions for two-input SLMPs.

Figure 5. Two equivalent morphological

perceptrons. Here w\ = w\\ and u>2 = tx>22-

Figure 6. Decision boundaries for two-input,

single-layer morphological perceptrons

with real-valued synaptic weights.

The two algebras (R_oo,V,+) and (Roo,A,+) are dual algebras. The simple isomorphism h : R_oo — Roo

defined by h(r) = -r Vr G R-00 defines this duality.

Thus, it does not matter which of these two algebras we

use for the underlying mathematical foundation of morphological neural networks. This duality can be used for interchanging classes. For example, by negating neural inputs

(i.e., interchanging r,- with —r,) and interchanging the operation of maximum with minimum interchanges the classes

Co <-» Ci. This interchange of classes is illustrated in Fig- ure 7. Of course, as mentioned earlier, in order to inter- change the on-off regions we could have simply used an

inhibitory post-synaptic response for the output neuron of

63
the perception on the left side of Figure 7. This follows

from the fact that

f[-(-(x1 + w1 )Y(x2 + w2 ))]

(5) = /[(«!+ Wl) A -(x2 + w2 )].

Figure 3. Two SLMPs with identical decision

boundaries but reversed on-off regions.

In 3-dimensional space lines are replaced by planes

and half-lines by half-planes. For example, setting wi —

u>2 = —oo and ws G R yields the plane z — —w^ as

the decision boundary for the corresponding three-input,

single-layer morphological perception. Hence, by choosing Wi G R for some £ = 1, 2, or 3, and setting the re- maining two weights equal to -co, three basic types of

planar decision boundary can be obtained. In analogy to

the decision boundaries shown in Figure 4, each of these

2-dimensional decision boundaries will be a plane normal

to one of the coordinate axes and parallel to the remaining

two axes. Using two such decision surfaces (i.e., setting

only one of the weights equal to -co) a more complex

decision boundary can be formed. This decision boundary corresponds to a 2-dimensional step function. For instance, if w\ = —00 and u>2, ti>3 G R, the decision boundary divides 3-space into two regions, namely the region

{(x, y, z) : y < —102, z < —W3, x G R } and its complement if all pre- and post-synaptic influences are positive.

Since any two of the decision planes will intersect in a

line, 12 such basic 2-dimensional step functions can be

constructed, yielding 24 possible on-off regions.

An even more complex decision boundary is obtained

when all three weights are real-valued. In this case, the

decision boundary corresponds to the infinitely extended

boundary of a three-sided rectangular box. These analogies

carry over into higher dimensional spaces.

Two-layer morphological perceptions can solve any

class problem in which the classes are compact sets. This

is the case in basically all realistic pattern classification

problems, where the patterns of a given class belong to some bounded set. For instance, in the plane, any compact

set can be approximated arbitrary closely by rectangles.

Thus, decision surfaces can be obtained via horizontal and

vertical lines to form any set approximating rectangles. This

concept extrapolates to higher dimensional compact sets. For example, the two-input, 2-layer perception shown in Figure 8 will classify all patterns falling within the set bounded by the lines xi — —w\x, x\ = —w\ 2 , x\ — —u>i3, x 2 = —u>2i. x2 = —W22, and £ 2 — —^23 shown in the bottom half of Figure 8 as belonging to class Co.

It should be clear that any planar configuration can be

boxed in by such sequences of step functions. The number

of neurons in the hidden layer depends, of course, on

the number of step functions required to approximate a region. Another interesting obseivation is that the class C0 in this example is not convex, showing that a single hidden

layei is sufficient for both convex as well as non-convex

regions. This is in contrast to standaid perceptions that require two hidden layers for non-convex class decisions

[4]. Note also that if we eliminate the third neuron N3 in the hidden layer, then the new net would classify all points in the infinite, non-convex and non-compact region

R = {(xi,x 2 ): x 2 > -W23 if - wn < x x < -wi 2 or — W21 < x2 < —W22 if xi > —^12} as belonging to

class Co. Thus, multilayei morphological perceptrons can

also classify patterns belonging to unbounded regions.

x2

Figure 7. Non-convex decision boundary

of a 2-layer morphological perception.

Using the different decision surfaces that are provided

by the single-layer morphological perception discussed eailier, it will be an interesting and instructive exercise for

the reader to construct 2-layer morphological perceptrons

whose decision boundaries approximate the boundaries of

different geometric regions in the plane.

64
4. CONCLUSION

This paper introduces neural network computing based on lattice algebra, which provides a new paradigm for artificial neural networks. The resulting morphological networks

are radically different in behavior than traditional artificial neural network models. One advantage of using morphological neural networks over traditional artificial neural net- works is that the algebra (R_oo, V, +) does not involve the

operation of multiplication and thus provides for greatly

reduced computational overhead. Additionally, due to the

global maximum operation, the usual convergence problems

that exist in most of the traditional approaches do not occur

in the lattice algebraic approach. For example, in [7] we

showed that training algorithms for morphological perceptrons converge in at most two steps. Furthermore, these

training algorithms also add all necessary neurons in the

hidden layer. Our main emphasis this paper was on morphological perceptrons. We laid the foundations of single-layer

morphological perceptrons and indicated how these can be

used to construct multilayer morphological perceptrons

5. REFERENCES

[1] J.L. Davidson. Simulated annealing and morphological

neural networks. In Image Algebra and Morphological

Image Processing III, volume 1769 of Proceedings of

SPIE, pages 119-127, San Diego, CA, July 1992.

[2] J.L. Davidson and F. Hummer. Morphology neural

networks: An introduction with applications. IEEE

Systems Signal Processing, 12(2): 177-2 10, 1993.

[3] P.D. Gader, Y. Won, and M.A. Khabou. Image algebra

network for pattern recognition. In Image Algebra and

Morphological Image Processing V, volume 2300 of

Proceedings of SPIE, pages 157-168, July 1994.

[4] R.P. Lippmann. An introduction to computing with

neural nets. IEEE Transactions on Acoustics, Speech,

and Signal Processing, ASSP-4:4-22, 1987.

[5] G.X. Ritter and J. L. Davidson. Recursion and feedback

in image algebra. In SPIE's 19th AIPR Workshop on Image Understanding in the 90's, Proceedings of SPIE,

McLean, Va., October 1990.

[6] G.X. Ritter, J.L. Diaz de Leon, and P. Sussner. Morphological bidirectional associative memories. Preprint

available from authors. Submitted to Neural Networks.

[7] G.X. Ritter and P. Sussner. An introduction to morphological perceptrons. Preprint available from authors.

Submitted to IEEE Transactions on Neural Networks.

[8] G.X. Ritter and P. Sussner. An introduction to morphological neural networks. In Proceedings of the 13th In- ternational Conference on Pattern Recognition, pages

709-717, Vienna, Austria, 1996.

[9] G.X. Ritter, P. Sussner, and J.L. Diaz de Leon. Morphological associative memories. Preprint available

from authors. To appear in IEEE Transactions on Neural Networks.

[10] CP. Suarez-Araujo. Novel neural network models for

computing homothetic invariances: An image algebra

notation. Journal ofMathematical Imaging and Vision,

7(l):69-83, 1997.

[11] Y. Won and P.D. Gader. Morphological shared weight

neural network for pattern classification and automatic

target detection, volume 4 of Proceedings of the 1995

IEEE International Conference on Neural Networks,

pages 2134-2138, Perth, Australia, November 1995.

65
Traps and Tricks in Standard Benchmark Problems for

Neurocontrol

Ludmila M. Dolmatova

Scientific Cybernetics, Inc.

Arlington, VA 22201

dolm@juno.com

ABSTRACT

In the last few years neurocontrol has made

enormous progress, in terms of new engineering

applications, new mathematical designs and ideas, and new links to the brain. The success of real life applications depends on a vast variety of factors, from

general design ideas down to programming details. Sometimes it is not easy to find the real reason for success or failure in a particular application, because the usual approach to neural modeling is somewhere

between art and science. So, it's time to demystify the process of design, from idea to implementation to

interpretation of results. There exists a set of benchmark

problems described in [1] which became a de facto

standard for exploring the possibilities of new modeling

and control methods. However, most of these problems

(even though they were intentionally designed for instructive purposes) can be implemented them in

different ways, which complicates the comparison of

results. The goal of this paper is to demonstrate some

"underwater rocks" in the application of neurocontrol

methods using standard benchmark problems as a commonly available touchstone.

KEYWORDS: neurocontrol, benchmark

problems; model evaluation.

1. INTRODUCTION

Adaptive Critic Designs (ACD) [2,3], one of

the most powerful tools for solving

multidimensional optimization problems, are gaining growing popularity in research community

[4-8, etc]. It has been demonstrated that ACD

methods allow one to solve real-life problems with

large numbers of state variables with better

performance than traditional methods allow.

According to the definition of a "brain-like"

system, as suggested in [9,10], it should contain at

least three major general-purpose adaptive

components: (1) an Action or Motor system,

capable of outputting effective control signals to the plant or environment; (2) an "Emotional" or "Evaluation" system or "Critic," used to assess the

long-term costs and benefits of near-term

alternative outcomes; (3) an "Expectations" or "System Identification" component, which serves

Paul J. Werbos*

National Science Foundation, Room 675

Arlington, VA 22230

pwerbos(g)nsf. gov

as a model or emulator of the external environment

or of the plant to be controlled. Therefore, 3 separate but interacting subsystems are considered:

Critic, Model, and Action.

The implementation of these subsystems is always a matter of serious choice. In the most

general case, each of them may be implemented as some kind of function approximator. Of course, neural networks can be regarded as universal

approximators [11,12]; thus, in the majority of

applications the Model is chosen to be neural

network with straight feedforward or recurrent

architecture. However, in industrial processes some

kind of analytical model is usually available. So in

this paper we use analytical models to illustrate the

basic concepts of design. It is clear that such

models in real applications might be incomplete,

contradictory or ambiguous (sometimes they are such even in test cases), but end users most often

prefer to have first principles or empirical models

used directly in the development of an overall

control system, which is quite reasonable according

to the concept of utilization of all available

information.

The organization of the paper is as follows:

Section 2 briefly reviews the logic of dual heuristic

programming (DHP) used here as the example of

ACD design, and backpropagation through time.

These methods are applied in Section 3 which

describes ACD for 2 traditional benchmark

problems: pole balancing on a moving cart, and

aircraft autolander. Section 4 summarizes the

results of computer experiments with these

benchmark problems, and suggests directions for

further development. Finally, the conclusions are drawn.

* The views herein are those of the author, not

those ofNSF.

66
2. DHP AND BACKPROPAGATION

THROUGH TIME AS GENERAL

METHODS.

A complete description of backpropagation

through time (BTT) can be found in [13], and that

for various ACD including Dual Heuristic

Programming (DHP) in [3]. It is worth mentioning,

that the description in this source (Handbook of

Intelligent Control) is complete, but concise, as is determined by the nature of a Handbook.

Therefore, almost every subsequent publication has

added something from the author's understanding

of those methods. We review here the main ideas

of BTT and DHP just for the convenience of

readers.

CRITIC

R(t+1^ X(t+1)= cU(t+l)/ dR(t+l)

MODEL UTILITY

ACTION

R(t)

Target=^*(t)

Fig. 1. An outline of DHP.

DHP is a procedure for adapting that network

which approximates the derivatives of the

secondary, or strategic utility function J (Critic

network). The primary utility function U is supplied by the user. The process of network

adaptation is governed by dual subroutines which

backpropagate derivatives from the Model and the

Action as shown in Fig. 1 reproduced from [3] (the

forward flow of information is drawn in solid lines; the backward flow is in dotted lines).

The Backpropagation of utility, from the

other side, is an exact and straightforward method

for adaptation of the Action weights based on

explicit calculation of the utility function N steps

forward in time. Usually it is used for off-line

learning, but in the test example considered here

(aircraft autolander) it can be implemented as online method, because the control interval is only 10

times larger than the sampling interval, thus if the

system is able to calculate the utility function 10

steps forward reasonably quickly, it can adjust

weights in Action network between two

consecutive control moments.

3. COMPUTER EXPERIMENTS

WITH BENCHMARK PROBLEMS.

In both cases presented in Section 3, the

model of dynamical system is described as a set of

equations, not as a neural network or other

approximator. If the model is exact, it allows us to avoid prediction errors, and also to get exact

derivatives through the model, which are necessary

to adapt the Critic and Action networks.

3.1. Inverted pendulum on a moving cart: balancingforever.

The pole-balancing problem is one of the

simplest test problems in classical control theory

[14], reinforcement learning [15], and artificial intelligence [16]. The specific goals of researchers

have been different: from training the pole-and cart system so as to keep balance with only a fail signal

[15], to the demonstration of the optimal control

strategy [17]. Here we consider the intermediate

task, where learning of the Critic Network on-line

evaluation of selected utility function, so that the

resulting controller (trained Action network) is able

to balance the pole without evaluation of the

situation, using just the vector of state variables.

For our numerical experiments we have used

the equations from [15], and their finite difference

approximation with time step equal to 0.02.

gs'm&(t)+ cos 0(0

f(t)-mW1 (t) + fi

c sgn{x(t)) MP 8(0

9{t) = - m+m ml

^4 m cos 6(t)

3 m+m

*(/) =

f(t) + ml(9\t)sm 9(t) - d(t)cos 0(1)) - ju

c sgn(x(Q)

rn + m

x(t+\) = x(t)+ Sx(t)

x(t + 1) = x(t) + 5x(t)

9(t+\) = 8(t) + 6G(t)

8(t+\) = 6(t) + Se\t)

The control interval is equal to the sampling

interval, i.e. force can be applied each 0.02 sec, and

during this interval it is constant. A description of

model parameters and their default values is given

in Table 1.

67
Parameter Value Comments

g 9.81 m/s/s acceleration due to gravity

1.0 kg mass of cart m 0.1kg mass of pole

1 0.5 m half-pole length

0.0005 coefficient of

friction of cart on

track

* y 0.000002 coefficient of

friction of pole on

cart

fit) -ION

ION

force, applied to

cart's center of mass

at time t 8 0.02 sec sampling interval

Table 1. Description and c efault values of

parameters for pole balancing problem.

A principal difference from the previous

work consists in the choice of utility function U:

U = -/(r)(10sin# + sin 5+ xl 25) - O.50 2 - O.50

2 - Q.ix1 - 0.5x2

In contrast with learning by trials and errors

[15], we provide the possibility for the system to evaluate its state from the viewpoint of some

external observer. In this approach the system

should not fail at all if the utility function is defined correctly, if the system is evaluating its

state frequently to have time to respond, and if the

range of control signal is wide enough. In fact

under such conditions a dynamical system guided

by DHP should demonstrate one-trial learning ~

and it does.

With the pole starting in an upright position

of pole, after applying arbitrary force (about 2N)

the system actually converges to the neighborhood

of a stable state (zero angle from vertical, fixed

coordinate) after 3000 time intervals, i.e. in 60

seconds. That's what it costs to learn the balancing.

This process is shown at Fig. 2, where it can be

seen how the contradictory requirements of

stabilizing with respect to the angle and to the

coordinate are satisfied. The oscillations of utility

function certainly correspond to oscillations of

force (control action) when the system changes

priorities: after stabilizing the angle it comes to

stabilizing the coordinate of cart.

0.12

0.1

0.08

0.06

0.04

0.020

-0.02

-0.04

-0.06 -006

-0.1

(a)

2866 5731 8596/111461 14326 17191 20056 22921 25786 28

(b)

Fig. 2. Pole angle (a) and cart coordinate (b) during

training phase. Time interval is equal to 0.02 sec.

In this picture one can see a periodical

increase of angle and coordinate amplitude with

time. Sounds strange, but this is exactly what was

desired. Not to maintain the upright pole position,

because it is unrealistic for inherently unstable

system, but to maintain proper frequency of

oscillations, or combination of few frequencies,

because the system is optimizing several

parameters simultaneously ~ angle, angular

velocity, coordinate of cart, cart velocity. In training mode the controller was balancing

the pole at least 45 minutes without any growth of

oscillations. So, the initial goal - to keep balancing

forever having the possibility to evaluate system

state was reached in one trial.

Comments on choosing Ufunction.

A standard caveat in ACD description is that the utility function U is essentially problem

dependent, therefore the correct definition of U is crucial for the success of the application. There is also a source of possible danger, however.

Consider, for example, our expression for the U

function in the inverted pendulum problem (pole

balancing). It seems relatively simple and natural;

much more complicated expressions may be

derived when one attempts to incorporate human

experience [4]. However, this is false simplicity: in

fact, the major term in the utility function.

68
implicitly refers to a desired control law. Even

without learning, it would be enough to choose the

external force as

to push the system into the equilibrium state [18].

Though it's correct only when there are no

constraints on x coordinate (as in the cited

reference), this example clearly demonstrates that

the utility function should reflect general

optimization requirements like energy

minimization, being in the neighborhood of desired

point, and so on (as does the utility function

implemented here). As can be seen from data

analysis, at the beginning of training the derivative

of the utility function with respect to control

actually determines the direction of control

changes, then it becomes constant, and if the

dynamical system still followed such instructions it would move away from the neighborhood of

equilibrium point. Starting from approximately 50

sec of system time the influence of derivatives

through the model is more noticeable, and after that

moment those derivatives (and, in fact, other

components of utility function) determine the

changes of control action.

Generalizing abilities. When the system learned pole balancing

starting from the upright position, the problem was

a bit complicated. With the same arbitrary starting

control action it had to learn convergence to the

stable mode starting from a small angle. Using

Action and Critic networks trained for zero-starting

balancing, it was possible to train them further,

gradually increasing the starting angle to maintain

one-trial learning. At 0.6 rad training was stopped.

The Action network obtained at this step was later used as the control network for test examples. In

fact, trained Action network was able to stabilize

cart-and-pole system with starting angle up to 0.68

rad, which it was not trained for.

(a)

(b)

Fig. 3. Stabilizing the system staring from the

angle 0.6 rad. Time interval is equal to 0.02 sec

The results of a test for starting angle 0.6 rad

are shown in Fig. 3. After 20 sec of system time the

pole angle reached 0 (actually, small oscillations

around the zero point were maintained). Stabilizing

of the cart coordinate took about 1 min of system

time.

The next question was: is the controller truly

adaptive, i.e. what if we change the parameters of

pole and cart (mass, length of pole) or external

parameters (friction, gravity)? Yes, it was really

able to re-learn; moreover, this adaptation to new

conditions occurred instantly (Fig.4).

10

e

6

4

2

0

1

-2

2865 5769 8653 11537 14421 17305 1/ 189 23073 2iS67 2W1 3172

Fig. 4. Cart coordinate for training of the system

with variable parameters. Time interval is equal to 0.02 sec

Learning was started from the standard

parameter set defined in Table 1. After 2 min of

system time the mass of the pole was changed to 0.3 kg, and 2 min later it was changed to 0.05 kg

without interrupting of learning. As can be seen at the chart for cart coordinate, such changes (point

6000 and 12000) were hardly noticeable. Again

after 2 min of system time the length of the pole was changed to 3 m. and the mass of the pole was

set back to standard mass 0. 1 kg. This time it was

noticed (point 18000), and it coincides with human

experience ~ the easiness of balancing depends

more on pole length, than on its mass. At the point

24000 (next 2 minutes of system time) all parameters were reset to standard one; however

gravity was decreased 10 times. The general

structure of learning process remained the same,

69
but the frequency of oscillations decreased, which was entirely expected according to physical laws.

0 6

-0.6

(a)

(b)

Fig. 5. Action strategy for larger control interval.

Time interval is equal to 0.05 sec.

The last computer experiment that can be

done with our controller is to put it into really hard

conditions. It was trained for a control interval 0.02

sec; let us now assume that it is possible to apply

control actions only every 0.05 sec. It can be seen from Fig. 5 that even with such a restriction, the

Action network provides reasonable control

without retraining, though the control strategy is quite different: instead of small oscillation around

zero angle the system maintains a stable mode with

large amplitude of oscillations.

Comparing our results with those of

Balakrishnan [17] we can conclude that the

resulting controller shows behavior close to the

optimal control. It can be seen that choice of

different utility function does not influence the

nature of the stand-alone controller. The utility

function is important only during the training stage;

the resulting Action network should be close to optimal control law, whichever was the learning

method. Thus, the most general type of utility

function, derived, for example, from energy

conserving conditions (minimal intensity of

control) or desired set point description (minimal

square of all state variables) should be preferred over the fancy "problem-dependent" functions.

Shaping: an easy way to train the controller.

Now we come to the exploitation of scaleinvariance of the model. Since the system should

stabilize both pole angle and cart coordinate, the

simplest utility function is

u= -Q.se

1 -o.5(X/ Xmm y

where coefficients are chosen so as to simplify the

derivatives of utility function.

However, it is very difficult to train the

Action and Critic networks with such a general

utility function. With high learning rate the force

oscillates, but with low learning rate it is to slow to react properly. Note that now the system should

learn to react only to target variables, not to their

derivatives.

One technique, that is very efficient in such

situations is called "shaping" in [13]. In shaping, one first adapts a simpler controller to a simplified

version of the problem, one then uses the weights

of the resulting controller as the initial values of the

weights of the controller to solve the more complex

problem, and so on up to the required level of

complexity.

It is clear which is the critical parameter that

determines the complexity of pole-and-cart control:

gravity. So, the training was started from

g=0.0981m/sec2

; then, after convergence (about 60

sec of system time) this parameter was set to g=0.981 m/sec2

. This time training took a bit

longer, but still after 5 trials the system learned to keep its balance starting from zero position and

random (about 2N) initial force, as is shown in

Fig.6.

o e 06

04

Fig.6. Training phase for g=0.981m/sec2

, general

type of utility function: angle (a), x-coordinate (b). Time interval equal 0.01.

70
After that the system was able to stabilize the

pole with starting angle 0.5 rad without re-learning,

with the same high learning rates of Action and

Critic networks. Before, with a problem-dependent

utility function an increase of starting angle from

0.1 to 0.6 rad required a decrease of learning rate from 0.7 to 0.1. The essential point in the training process,

regardless of the utility function, (and mostly

regardless of the concrete example) was that there

be a difference between "convergence for training

with possibility of weights correction" and

"convergence for stand-alone action". In the first meaning, the system Action+Critic converged after

at most 12000 iterations (120 sec of system time,

see Fig.6). However, Action alone has been

converged, in the second meaning, only 30000

iterations later. Moreover, the controller for

g=0.981 m/sec

2 was able to control pole-and cart system up to the value of g=4.905 m/sec2

. Then the same shaping procedure was

repeated for the standard value of gravity. After

few trials it learned new external conditions, and at the end again Action network was able to control

pole-and-cart system autonomously. For the last case the utility function was slightly changed to gave more importance to the changes in x- coordinate.

None of the ACD pole balancer descriptions

cited here (except, possibly [8], which

implementation we had not possibility to evaluate

in details yet) was able to learn a stable stand-alone

controller working with simple general-type utility

function under the conditions of full gravity. Like

Balakrishnan [17] we were able to receive optimal

control strategy under reduced gravity (g=0.981),

however, then we scaled it up to real-life conditions. Shaping, as learning tactic was

extremely useful and time-efficient for this

purpose.

3.2. AIRCRAFT AUTOLANDER: THE

SIMPLEST DESIGN IS ENOUGH.

The Autolander problem described in [1] concerns the simulation of aircraft landing. This

linearized model of commercial aircraft and its environment includes such variables as longitudial

velocity, vertical angular velocity, pitch rate and

angle, altitude, horizontal position, autothrottle

state, and wind disturbance state. Pitch angle

command is used as control action. The equations,

parameters, and constraints are those from [1],

problem A. 3. The process of landing is guided by an

airport-based Instrumental Landing System (ILS),

which provides desired values of height and

vertical velocity of aircraft, and in this example

controller must track the prespecified trajectory. In

fact, it must learn the proper approach angle

relative to the runway threshold, which should be

maintained during the first phase of landing.

During the second phase, starting at 45 feet height,

the aircraft follows the exponential law, decreasing

both altitude and vertical velocity, and elevating

the nose. As was said before, almost every model

allows some undesirable freedom at the

implementation stage, which can be treated in

different ways. First, we re-defined the

intermediate variable aw=U0/h(t), where h(t) is the

height of aircraft at the moment t, to be aw=U0/10

for h<10 to avoid division by zero. The height

h=10 was rather arbitrary. Another modification was not so small, but it seemed to be reasonable in

the modeling context: during the flare phase in the

original model ILS provided the desired values for

height and vertical velocity starting from actual

height of aircraft (45 feet) at the beginning of the

flare regardless of what the desired height was just

before this moment.

(b)

Fig. 7. Broken desired trajectory for the original

model (a), and conunuos one for modified model

(b).

As a result, the desired trajectory had a break

at h=45 ft, and the process of learning during the

flare phase was biased. The difference between

original (a) and implemented here (b) desired

trajectory is shown in the Fig. 7.

71
The last modification was related to starting

conditions: the desired interception point calculated

from ILS data was at the end of the runway, so

instead of using real coordinate x to calculate the

desired (ILS) height we used x=x+500.

Under these conditions the utility function can be written as

U = -a, 0.5(h - hJ

2 - a2 0.5(/i - hc f

where h{h) is actual height (vertical speed) of the

aircraft, and hc {hc

) is the height (vertical speed)

value supplied by ILS. Coefficients ai and a2 varied

during the training phase: first, ai was much greater

than a2 , reflecting the priority of landing in the

target zone of runway; then a2 was increased to provide fine tuning of vertical speed.

The state vector comprised all aircraft and

environment variables, thus allowing us to avoid

including the information from previous time

intervals as additional input to Action and Critic

networks. Besides, using an analytical model we

can calculate exact derivatives with respect to control and input variables, and the accuracy of

simulation and evaluation of state essentially

increases, thus decreasing the number of iterations

necessary for convergence.

How it was really going

Training of the system was done with

backpropagation of utility [13] with calculation of

utility function 10 steps forward. Taking into

account that the sampling interval was 0.01 sec, and control interval 0.1 sec, it was almost real-time

learning. We include here some comments to

illustrate the concrete organization of this process.

First, input vector normalization of at least some

components of the input vector was necessary

(division of height (h) and horizontal coordinate (x)

by maximal values of these parameters, known in

advance).

Next, for this kind of modeling it is important

to simulate the noise vector outside the Model

itself, because when we use dual subroutine

DualModel for calculating the derivatives with

respect to control and state vectors at the backward

step, we need the same values of noise parameters

as were used during the forward step, so it should

be either the same input vector for Model and

DualModel or an external vectors available for

both. Another important point is already

commonplace: don't use the standard C random

number generator, which has extremely bad

statistical properties.

Wind shear, gusts, and generalization

abilities

Initially the system was trained in the absence

of wind gusts, with wind shear only. Learning was

fast, within 10 attempts the difference between

actual and desired trajectory decreased

significantly, and the Action network was able to land the aircraft starting from default conditions

subject to constraints on touchdown region, vertical

speed, horizontal speed and pitch value.

Then wind gusts were added, and learning was continued. Still the Action network was able to land the aircraft if control signals were generated

using the information about utility values 10 steps

forward. What really took time here, was the

training of the Action network to generate control

signals responding only to the state vector, without

dynamic weights correction. After a few hundred

iterations it was able to land the aircraft in wind

conditions in the majority of cases. As can be seen from Fig. 8(a), representing

test results for 200 landings with random noise,

most of the landings ended in the zone called

"shortened runway" in [5] (below 600 ft. The

distribution of vertical velocity is within a narrow

range, though it doesn't satisfy the constraints of

original model.

1000

900

700 600 -

500 i | 400 J

300 -| J 200 -

100 -

0

-

-100 -I 14 27 40 53 66 79 92 105 118 131 144 157 170 183 196

(a)

150 200

-1

-2

-3 .

(b)

Fig. 8. Test results for landings with random wind

gusts: x-coordinate (a), and vertical speed (b).

We can conclude that with a full and exact

analytical model of aircraft it is possible to achieve

a high rate of success even without guidance from

an Instrumental Landing System. What's more

important here, this rate has been achieved with

72
simplest system design possible - a feedforward

Action network and backpropagation of utility as learning method. This tells us that the autolander

problem in this formulation hardly can be

considered as suitable example for demonstrating

the advantages of more sophisticated designs.

DHP, for example, demonstrates approximately the same success rate, though with different

distribution of x-coordinate and vertical speed;

however DHP training took much more time for

this case. For examples of successful application of

HDP, BU, and DHP to this problem one may see

[5,7]. A brief description of successful application

of GDHP can be found in [6]. A lot of model

details are discussed in [19] where the problem was

originally posed.

4. FIRST OBSERVATIONS AND

FURTHER DEVELOPMENT

Though the examples described here are simply test problems, they allow us to make some

informal observations that may be helpful for reallife applications. First, these problems are not

complex enough to demonstrate the advantages of more sophisticated designs over simpler ones, like

BTT . Next, they allow multiple final formalization

that leads to different quality of models thus

reducing the compatibility of results. The last technical remark: usage of de facto standard test problems should be more formal than we can see now. None of the papers cited here deals with

exactly the same problem that any other paper

deals with. There are always small differences —

either the dimensions and components of input

vector, or different values of coefficients, or

slightly modified model. This complicates real

comparison and reproducibility of results. The same problems were recognized long ago

in supervised learning, and the benchmark set PROBEN1 appeared [20]. In summary, there is still a need for the creation of more challenging and more fully specified benchmark problems and

benchmarking rules for neurocontrol, which

(ideally) should be disseminated over the Web and

addressed in "challenge" sessions in major

conferences.

It is important to distinguish between the

complexity of ACD methods and the complexity of

the problem in hand. The application of these

methods can be straightforward, but the problem

may be underdetermined or contradictory. The

final formalization of a model may be done in

different ways; the details of its implementation are

also essential. Even the simplest examples

described in this paper demonstrate these

possibilities. Fortunately, ACD designs are powerful enough, and sometimes they can handle

ill-defined problems, but this is not always the

case. It is necessary, for instance, to provide proper

normalization, and the same range of calculated

and desired values of derivatives of utility function

before final judgement about modeling quality. The

optimal choice of parameters, like learning rate or network architectures is not an ACD-specific

problem. It's just an inner problem of

implementation modules that constitute the whole

system, and relationships between parameters of

different modules like those mentioned in [8] are most often the phantoms of more serious problems

inside the modules.

If we consider the "ladder of designs",

defined first in [2] then in greater detail in [21], an example clearly demonstrating the advantages of

higher-level designs over lower-level ones should

be something like this: — self-complete, not allowing to extend it using

commonsense or physical knowledge; — formalized up to the end, including input-output

parameters, integration scheme, list of adjusted

parameters, normalization procedures; ~ showing visible increase of some quality measure while climbing on the ladder of designs;

Besides, it should be physically interesting. To

develop such an example will be our next task. Another direction of further research is to

clarify some stability issues. As could be seen from more detailed analysis of the inverted pendulum

example, if the system is inherently unstable the

increase in calculated Critic value leads to greater

increase in target Critic value, and the system

quickly moves to or behind the accepted range of

parameters. This can be avoided by programming

tricks, like dynamic renormalization, but it would

be preferable and more reliable is to solve such

divergence problems at conceptual level.

5. CONCLUSIONS

When the problem at hand is solved, at least

to the degree acceptable to potential users, it seems

so easy that even the developer forgets the tricks he

applied and the traps he avoided. Yes, his abilities as a developer have increased, and at the

subconscious level he remembers the way to do

things right, but here the question of expertise

transfer arises. If something has been done, it would be useful to formalize a method of problem

solving, even if it is not the way the problem was

actually solved. First, it makes it possible to understand even one's own results more deeply.

Next, such "step-by-step" instructions allow

73
newcomers to the field to get their first results

easier, thus creating positive motivation, which in turn stimulates their productivity. Also, it provides

guidelines for future research. And finally, the

most ambitious though long-term claim: such

formalization of human experience leads to the

possibility of automating some routine procedures

and tactical decisions now reinvented again and

again.

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74
Neural Network Based Planner/Learner for Control

Systems

J. Albus* N. DeClariso A. Lacaze*o A. Meystel**

National Institute for Standard and Technology,

o University of Maryland, • Drexel University

lacazeQeng . umd . edu

Abstract

A neural network based planning/ learning system

that prunes its decision tree by generalizing upon results of previous experiences is proposed. The results

for the case of and inverted pendulum controller are demonstrated [1].

I. Introduction

Neural Networks (NN) for intelligent control as a

part of well known structures with "Adaptive Critic" are recommended [2, 3]. However, the advantages of

search are not fully used because the NN elements do

not have any capability for searching.

Real-time Control System (RCS) architecture of intelligent systems [4] determines the functionality of

Behavior Generation. The latter uses planning as a combination of job assignment and scheduling [4, 5]

which determines the need in a subset selection (focusing attention) and alternatives exploration (searching). Complexity of doing this can be substantially

reduced by forming a multi-resolutional system [6]

.

In this paper, we will follow the conceptual

paradigm of multi-resolutional planning/learning outlined in [7, 8]. We will build upon the learning algorithms used in Baby-Robot, [9, 10] but will implement

them with the planning algorithm.

Planning/learning as a joint process relies upon

simulation of multiple alternatives of the process,

Construction of decision trees is necessary in many areas where reactive strategies are insufficient to achieve

the desired performance (for example, manufacturing,

obstacle avoidance, control systems, medical interventions , etc). Most of these planning problems are solved in one of the following ways:

• Search techniques. These include Dijkstra, A*,

beam search and most of the AI techniques like

(genetic algorithms and expert systems). These

solutions are considered to be too slow for real

time operations and are in most cases nonlearning search techniques.

• Dispatching techniques. Frequently the designers decide that planning is altogether too expensive. Instead, they supply several general rules

of thumb that are supposed to reactively improve performance. Unfortunately, these rules

of thumb are very general (FIFO, LIFO, bidding) and usually under-perform most search al- gorithms. The dispatching techniques are equivalent to "greed" algorithms and generally, cannot

ensure the optimality of solutions.

The proposed NN-based Planner/learner has performance advantages over the dispatching algorithms

with adaptation. It plans (instead of reacting), and it learns rules (or rules of thumb) that allow it to search

only a reduced set of the decisions in the decision tree. The proposed NN Planner/learner learns rules of

actions for different lengths of strings of experiences,

and it learns to simulate the results of this actions.

Then, the NN-planner creates a look ahead search

where the different action rules are explored, and the

simulator predicts new states. This tree is explored

before any control is applied.

Before giving the details of the NN planner/learner,

we present its building blocks (NNs) and how are they

trained to learn both the action rules and the simulation rules.

II. The Neural Network Algorithm

In order to develop the NN based planner/learner.

Standard NNs were applied. The training algorithm

uses the Levenberg-Marquardt variation of Newton's

method to modify the NNs weights. The algorithm

approximates the Hessian matrix:

V

2 F(x)=2JT

(x)J(x) (1)

where J(x) is the Jacobian matrix. And Newton

method can be written as:

xfe+1 = xfe - Afc _1

gfc (2)

75
for (la«l;la<=iterations ;la++){ ext_al nncpyi(al,w3.rows)

;

ext_a2 = nncpyi(a2,w3.rows)

d3 funcPrime(func3,a3)

;

ext_d3 nncpyd(d3) .negO ; «xt.d2 f uncPriae(func2 ,w3.T() ,ext_a2,e:tt_d3) ; ext.dl funcPrime(funcl,w2.T() ,ext_al ,ext_d2)

;

ext_p « nncpyi(inp.TC) ,w3 .rovs)

;

jl nncpy(ext_dl .TO , ext.p.rows) .dotHul(nncpyi(ext_p.T() , ext.dl .rows) )

;

j2 * nncpy(ext_d2.T() , ext.al .rows) .dotKul (nncpyi (ext.al .TO , ext_d2 .rows) )

;

j3 = nncpy(ext_d3.T() , ext_a2 . rows) .dotHul Cnncpyi (ext_a2 -TO , ext_d3 . rows) )

;

jac = new MatrixCjl, ext.dl. TO, j2, ext_d2.TO , j3, axt_d3.T());

je = jac. TO .aultiply(e.TO) ; grad = je . normO ; if (grad < grad.ain) {la*la-l; break;}

// INNER LOOP, INCREASE HU UNTIL THE ERRORS ARE REDUCED

jj » jac. TO .multiply(jac) ; while (bu <* Bu_max){

dx » caldx(j j , je.nu) ; //calculates dx int aui count =0. transfer_dxs_to_dbs_and_dws(dx)

;

new.wl * wl.addCdwl);

new_w2 = w2.add(dv2);

new_w3 = w3.add(dw3);

new_bl bl.addCdbl)

;

new_b2 b2.add(db2); new_b3 = b3.add(db3); a=feedForward(inp, new.wl ,new_bl ,new_w2.new_b2,new_w3 ,new_b3)

;

new_e out .TO sub(a) ; for (k-0;k<new_e.cols;k++){ \calculates the new error new.error + new.e .data[0] [k] *new_e .data[0] [k]

;

>if (new.error < error) break; mu° mu*BU_inc; //changes mu

}if (nu > mu.naxH

la la-lj break;

}du mu * mu_dec;

// UPDATE NETWORK

wl = new.wl; bl » new.bl;

w2 = new_w2; b2 new_b2;

w3 = new_w3; b3 * new.b3;

e * new_e ; error * new.error;

System. out. println("Average error after "

la*" iterations "+ error* " bu""+bu ); if (error < press) la iterations + 10;

}

}

Figure 1: Levemberg-Marquardt JAVA implementation

where A, = V

2 F(x)|

x=Xfc

and gk = VF(x)| x=Xfc . Thus, by plugging in we get,

xfe+ i =xfc - [J

T

(xfc)J(xfc )]

_1

JT

(xfe)v(xfc ) (3)

the problem with the previous equation is that

JT (xfc )J(xfc) may not be invertible. Thus, LevenbergMarquardt algorithm warrants invertibility,

Xfc+i = Xfc - [J T

(xfc )J(xA: ) + fj,kl]

1 J

T

(xfc)v(xfc )(4)

by looking at the previous equation, we see that if

fik is large, then the algorithm approaches the steepest descent algorithm. If it is 0, it becomes the GaussNewton algorithm. In our implementation, different \i are tested, and the best one is selected at each epoch.

The core of the Java implementation shows how this was implemented is shown in Figure 1. The complete algorithm was successfully tested us- ing the standard problems (XOR, etc.). As far as

transfer functions the log sigmoid a = 1+

*_„ and the

hyperbolic tangent sigmoid a - were implemented. The hyperbolic tangent was used in the ex- amples for this paper.

reset levelcounter Assign the starting node to the list (level 0)

Do {

Find a node with level equal to levelcounter

if found a node {

Rebuild the schedule for this node

backtracking though the list

if (schedule is not complete) {

Create a new node for each possible

decision assigning as cost the simulated

results and marking the level. Put them in the list

}

} else increment level

} while (this level has a complete schedule and all the

nodes of the level are open)

Figure 2: Pseudocode for scheduling using dynamic

programming principle

III. The Planning Algorithm

This paper will go over the two most known planning algorithms. Most of the other algorithms are derived from these two, and they normally lose generality by doing so.

III. A. Dynamic Programming

The fundamentals of dynamic programming were

introduced in the 1950's by Bellman [11, 12] and thoroughly explained in [13, 14]. Dynamic Programming

interprets any optimization as a multi-stage decision

process. The results of dynamic programming can become known locally only after the total search for the

best trajectory is completed.

To calculate the optimal criterion value for any subset of size k, we first have to know the optimal value

for each subset k — 1. In this case, k represents the

level in the tree of search. Figure 2 shows the pseudocode dynamic programming process.

Dynamic programming originally was applied in cases where the branches of the tree cost the same. The space was intentionally discretized such that

moving to successors would generate exactly one unit

of cost. In these cases, dynamic programming opens

exactly the same amounts of nodes as Dijkstra Algorithm (next). In cases when the cost of the edges of

the graph are not the same, Dynamic programming

open significantly more nodes than Dijkstra. No matter which form is chosen, dynamic programming re- quires completion of the search to the goal .

III.B. Dijkstra Search

The average computational requirements are considerably less than those of the dynamic programming

76
Assign the starting node to the open list Do {

Find the node with the smallest cost in the open

list and move it to the closed list Rebuild the schedule for this node backtracking

through closed list

if (schedule is not complete) {

Create a new node for each possible decision

assigning as cost the simulated results. Put them in the open list

}

} while (schedule is not complete)

Figure 3: Pseudocode for scheduling using Dijkstra

algorithm

[15]. A pseudocode for Dijkstra algorithm applied to

scheduling is presented in Figure 3. The Dijkstra al- gorithm, in the same manner as dynamic programming warrants that the solution is optimal. The dif- ference between dynamic programming and Dijkstra

algorithm is that dynamic programming iterates in

the number of arcs in the graph while Dijkstra iterates on the length (or cost) of the arcs. An interesting

comparison between Dijkstra, dynamic programming

and Floyd-Warshall algorithm is presented in [15].

7/7. C. Using Neural Networks to Prune the Dijkstra

Tree

We can use NNs within the Dijkstra Planner in two

possible ways:

1. As simulators. NNs can be trained to predict

what will be the next state given the current state

and the decision. Of course there are some cases where the plant complexity itself will make this

mapping hard to train. In these cases (which may

be most) the system will have to be divided in dif- ferent hierarchical levels to handle its complexity.

This issue is outside of the scope of this paper.

For the examples given, one level is sufficient, and

this mapping can be learned with sufficient accu- racy to make the planning plausible.

2. As control rules. If information of the previous

working of a controller for the plant or results of

previous search with the same goal, this information can be used to train NNs to suggest patterns

of decisions that where successful in the past. We

propose to use abduction: search the tree of future decisions by exploring first paths that were

successful in the past. Of course, this technique

will not give better results than the full search,

but there are many cases where full search is not an option.

IV. An Example

For this example we have chosen the inverted pole.

The dynamical equations are as follows:

x2 (5)

(^+g.sin(*l) + ^)

1.(^ + 1 -(cosM)*.^) 1 ]

(U — Hr * sign{xi) — m.l.x\ * sin(:ri))

x2

'(l=dar + i-<«»(*i))a -]ifc)

, U — nr .sign{xi) xA = - + M + m

m.l.(x'2 . cos(a:i) - x\ * sin(a;i))

M + m

(7)

(8)

where

m = 1 Kg

I = 0.5 m

j m.l2

1 ~ 3

mass of pendulum

pivot of center of mass

inertia

pivot friction [ip = 2 * 1CT 6 *flpf

mass of cart M = 1 kg

rolling friction \iT = 5 * 1(T4 ^p.

gravity g = 9.81-ym

In order to simulate this equations, Runge-Kutta was

implemented in JAVA (see Figure 4).

The JAVA applet is shown in Figure 5

V. Learning the Control Rules

V.A. The Standard Way

The first step was to test the NN algorithm in the

pole simulation using the standard technique of learning the input-output mapping. The following experiment was performed:

1. A controller was built using the following parameters: U = (random(l) * 2 — 1) * error +400 * (x3 — goalpos)

+400 * xA -1089.172 *xi

-401.27* x2

To make it a little bit more realistic, a maximum

force of U was not allowed to get out of the interval [—300,300]. An error is introduced as function of error. The position of the goal goalpos is randomly placed at random intervals.

2. A string of 1000 states and actions were recorded

to simulate the normal working of the plant with

some error.

77
public void rk4 (double [] y, doubled dydx, int n, double x, double h, double [] yout){

int i

;

double xh,hh,h6;

double [] dym=new double [n+1]

;

double [] dyt=new double [n+1];

double [] yt=new double [n+1];

hh=h*0 . 5

;

h6=h/6 . 0

xh=x+hh

;

for (i=l;i<=n;i++) yt[i]=y[i]+hh*dydx[i] ; derivs (xh.yt , dyt)

;

for (i=l;i<=n;i++) yt [i] =y [i] +hh*dyt [i]

;

derivs (xh.yt ,dym)

;

for (i=l;i<=n;i++) {

yt[i]=y[i]+h*dym[i] ; dym[i] += dyt [i]

;

}

derivs (x+h,yt , dyt)

;

for (i=l;i<=n;i++)

yout[i]=y[i]+h6*

(dydx [i] +dyt [i] +2 . 0*dym [i] )

;

yt=null;

dyt=null

;

dym=null

}

Figure 4: Runge-Kutta Java implementation

\

Applet started. A

Figure 5: Pole. class applet of the inverted pole

A NN was trained by using the chosen control algorithm to learn the U given the states. The structure

of the net was a 6-6-1 net using the tangential logarithmic activation function. Figure 6 shows the error function of the network while training.

Figure 7 shows the error of the plant operating with

the trained NN and the error of the plant operating

with the original controller. This figure was created

by accumulating the er = abs(xi — goalpos) + abs(xz)

Sum-Squared Network Error for 39 Epochs

10 I

1 . , 1 ,

10

4

r

10

3

]S 1 ° r

f io°

;

E

10* r

io^I 1 1 1 1 1 1 —J- 0 5 10 15 20 25 30 35 Epoch

Figure 6: Learning error of the input-output function

Iteration

Figure 7: Similar cumulative error values for the NN

controller and the non-NN controller, for multiple

goals and compound cost function

during the normal operation of the plant. The goal is randomly changed, causing of the waves seen in the

figure. The error {error is not er) was not modified.

The results show similar error functions for the NN

and the original controller. Figures 8 and 9 show also

similar results using different cost functions: er —

abs(x\ — goalpos) and er = abs(x3 ) respectively. For

the last two examples, the goal was kept fixed, which

is why the function is not wavy.

Please note that these results where achieved without the planner and are only intended to show that

the NN is learning the control rule.

V.B. Learning for Planning

One of the biggest problems in learning is finding

the correct measure of goodness that allows the al78
Sum-Squared Network Error for 37 Epochs

1000 1200

Figure 8: Similar cumulative error values for the NN

controller (lighter curve) and the non-NN controller,

for one goal and position cost function.

Figure 10: Learning error of the state-action to new

state function

-10

-15

1

\

i

i

—''

1 1 1 1 -i———. ..!...:...

/

:j J

i

|

\v

\

i

i\

1

I /

i i i ;| 1 , , , 1_ , , , , 1 0 100 200 300 400 500 600 700 800 900 1000

Iteration

Figure 9: Similar cumulative error values for the NN

controller (lighter curve) and the non-NN controller,

for one goal and angular cost function

gorithm to separate the "good" examples from the

"bad" examples. This measure cannot be introduced

unless many circumstances of functioning are taken

into account. For example, if the cart is to the left of

the goal and the pole is angled to the left, one would

imagine that a force to the left could bring the cart

and the balanced pole to the left. If the force is high,

in the short term, the impression will be that the cart

has made good progress. But unfortunately this may

change as soon as the goal is achieved. The forces

of inertia will "over-regulate" the pole. On the other

hand, we can have long term measures of goodness

that are worthless in the short term.

Our planning system uses not a single one of these

heuristics but all of them in a planning system. In

this case, we can create control rules by training NNs

on experiences that are good at different length experiences (strings of state-action-state...). For example,

we can take all the SAS (state action state) triplets

that are above a certain measure of goodness. Goodness is calculated as the difference to the distance to

the goal before and after the string of actions. The

same can be repeated for SASAS quintuples and with

longer strings. The NNs trained with shorter strings

will have many experiences, since there is higher number of shorter strings than longer ones. The cost measure will give correct results only in the short term,

which may not be good. On the other hand NNs

trained with longer strings will have less strings, but

the cost measure is trustworthy in a longer term. In

this case we are interested in minimizing the cumulative error. The idea is to have these networks store behavior that was successful in the past at different string

lengths. The planner will start exploring the decision

space along this successful paths by creating tentative combinations of strings with different lengths. In

most plants behavior that was successful in the past

has a higher probability of future success. From the

errors that were introduced in the old plant controller

we want to learn behaviors that where successful not

because of the controller but by chance.

The NN for simulation was trained with the state

and action as input and the next state as output.

The Levemberg-Marquardt algorithm was used and

the structure of the net is 5-5-4 net. The evolution

of the training error can be seen in Figure 10, and

the output is compared to the Runge-Kutta value in

Figure 11.

79
Figure 11: Runge Kutta simulation output (top) and

NN output

The complete simulator can be trained using only one NN in very small problems. Where it becomes

computationally costly to train to increase the number of nodes to allow the network to properly model

the system, the problem can be divided into smaller

pieces. There could be a set of networks covering all or some of the space that we want to simulate. This

interesting topic is outside of the scope of the paper.

VI. The NN planner

The neural network planner learns two kinds of

rules from previous experiences: action rules , and

simulation rules. Action rules have the form

A,g (9)

where 5 is a situation vector, A is a action vector, g

is goodness estimate, and —> implies mapping. These

rules will be used by the planner to select the actions

that where good performers in the past.

Simulation rules are the second kind of rules that

are learned by this algorithm. They have the form

Sh Ai-+Ai+1 (10)

where Si is a situation vector, A{ is a action vector,

and 5i+i is an approximation of the state vector where

the system is likely to be after action Ai is applied at Sx

.The NN planner uses all the networks shown before.

The steps performed by the planner are as follows:

1 . The system runs using the previous controller introducing noise in its output to the plant. The

state (S) used by the old controller and the ac- tion (A) applied by the controller (with the noise)

will be stored in a database.

2. Experiences (SiAiSi+i) (Figure 12) are ordered

based on the goodness. Where goodness is the

difference of the distances to the goal before and

after A.

3. The "best" experiences are selected.

4. A neural network with St as input and Ai as output is trained. We will call these NNs control

rules.

s \ E

A /

El E

S E A E

S X E A /

63 E

S X E A E

S E

A /E5 E

S E

For SASASAS experience*

For SASAS expcrieocei

Good experiences

Tor (his goal

For SAS experiencci

Situation

vector

Action

Vector and

expected goodness

Situation and

Action

New

Situation

Figure 12: Proposed Approach

Figure 13: Decision tree

5. A neural network with Si and Ai as input and

Sl+ i as output trained. We call these NNs simulation elements.

6. The previous 4 steps are repeated for

SiAiSi+iAi+iSi+2,

SiAiSi+iAl+ \Si+2Ai+2Si+3, etc.

7. A lookahead search tree is generated using the

current state as the starting point and the control rules for SiAiSi+ i, SiAiSi+iAi+1 Si+2, etc

where Si match the current situation. Once these

actions are applied, we use the simulation ele- ments to simulate the next imaginary state (be- cause we have not applied the action yet). We

repeat this procedure again until we achieve the

desired imaginary state or we run out of time.

This lookahead planner is illustrated in Figure 13.

Please note that if enough time is allocated, paths

with actions that are not recommended by the

control rules can also be explored.

8. The first action in the best path through this

decision tree is chosen as the action to execute.

80
Figure 14: NN planner

Figure 14 shows a 3D visualization of the process

of developing a decision plan. As shown, only three

control rules exist in this example. The opening of

this decision tree follows the Dijkstra algorithm.

VII. Conclusions and Future Work

1. A planning/learning subsystem is constructed to use in control systems

2. The planner first explores the previously successful paths but it continues with the search if suffi- cient time is given. This planner will find optimal

trajectories.

3. The system incorporates both learning and

searching which makes it different and advantageous in comparison with the known systems

4. In the future, we are going to implement and

compare other NN engines: CMAC, conjugate

gradient, etc.

5. The approach seems to outline a constructive

model of brain-like intelligence.

REFERENCES

[1] A. Lacaze. A neural network planner that prunes

its own tree. Term Paper, Knowledge Engineering, Electrical Engineering Department, University of Maryland, May 1997.

[2] A. G. Barto. Neuronlike adaptive elements

that can solve difficult learning control problems.

IEEE Transactions on System, Man and Cybernetics, 13:834-846, 1983.

[3] D. A. White and D. A. Sofge, editors. Handbook

of Intelligent Control. VNR, New York, 1992.

[4] J. Albus. Outline for a theory of intelligence.

IEEE Transactions on Systems, Man, and Cybernetics, 21:473-509, 1991.

[5] J. Albus and A. Meystel. A reference model ar- chitecture for design and implementation of intelligent control in large and complex systems.

International journal of Intelligent control and

Systems, 1:15-30, 1996.

[6] J. Albus, A. Meystel, and A. Lacaze. Multiresolutional planning with minimum complexity, in

this volume.

[7] A. Meystel and A. Lacaze. Unified learning/planning automaton: generating and using

multigranural knowledge hierarchies, in this vol- ume.

[8] A. Meystel and A. Lacaze. Introduction to integrated/learning planning, in this volume.

[9] J. Albus, A. Lacaze, and M. Meystel. Evolution of knowledge structures during the process of learning. In Semiotics Workshop of the

10th IEEE International Symposium on Intelligent Control, Monterey ,CA, August 1995.

[10] J. Albus, A. Lacaze, and M. Meystel. Multiresolutional intelligent controller for baby robot. In

Proceedings of the 10th IEEE International Symposium on Intelligent Control, Monterey ,CA,

August 1995.

[11] R. Bellman. Dynamic Programming. Princeton

Univesity Press, 1957.

[12] R. Bellman and S. E. Dreyfus. Applied Dynamic

Programming. Princeton University Press, 1962.

[13] D. Bertsekas. Dynamic Programming. Prentice

Hall, 1987.

[14] R. Parker and R. Rardin. Discrete optimization.

Academic Press, 1988.

[15] D. Bertsekas and R. Gallager. Data Networks.

Prentice Hall, 1992.

81
A HYBRID HIERARCHICAL NEURAL-AI

MODEL OF MAMMAL-LIKE INTELLIGENCE

Paul J. Werbos

National Science Foundation, Room 675*

Arlington, Va. 22230

pwerbos@nsf.gov

Abstract

This paper briefly sumarizes and cites new work

which tries to bridge the gap between advanced

neural network designs and some of the known

capabilities of mammalian intelligence. The new

design draws heavily on concepts of hierarchy

and temporal chunking from AI, and on

relational representation of objects and space.

Overview

By 1995, several groups of researchers had

finally implemented neural network designs

which met certain basic criteria for what a brainlike intelligence should look likefl]. These

designs were intended to be able to learn "any

task" involving goal-directed behavior over time,

without prior knowledge of the task. In technical

terms, such designs have been called "modelbased adaptive critics" or model-based

approximate dynamic programming (ADP).

They have sometimes been classified as a type of

reinforcement learning system.

The engineering benefits of such

designs have become increasingly clear over the

past few years. By now ten groups have

successfully implemented such designs [2]. The

strengths and weaknesses relative to conventional

designs, in terms of stability, etc., are becoming

better understood [3]. In formal terms, these

designs provide a capability for optimization over

time

in uncertain noisy nonlinear environments; that,

in turn, permits systems to learn how to track a narrow desired trajectory or performance

envelope, which is especially useful when trying

to operate highly dynamical nonlinear plants.

In 1970 or so, when I first developed

the theory behind these designs, I hoped that they

would be enough to describe at least those

aspects of higher-order intelligence which exist

in the mammalian brain. This is not the same

thing as explaining consciousness in the minds of

humans. In order to understand consciusness in

the minds of humans, one must also address

issues such as symbolic reasoning, quantum

computaing and the soul, etc.; although I do have

ideas about those subjects [4], they are beyond

the scope of this paper. In my view, a scientific

understanding of the mammal-brain level of

intelligence is a prerequisite to a truly deep

understanding of those more advanced levels of

intelliegnce[2,4]. Indeed, the new design to be

mentioned here does begin to provide some ideas

about the deep structure underlying verbs,

nouns, and adverbs, at the very least. Nevertheless, by 1996 [1], it was

apparent that these advanced designs still had

two major deficiencies - major gaps between the

kinds of learning capability they provide, and the

kind which exists in the mammalian brain.

First of all, in order to learn many

difficult planning problems, such as generalized

spatial navigation, it would be necessary to "fill

in the boxes" in these designs with a certain type

of slow but powerful neural network, the"SRN."

[5,6]. To explain how the brain also achieves

* The views herein are those of the author, not those of NSF, but the paper was written on NSF time and

may therefore be freely copied subject to proper citation.

82
high-bandwidth control of muscle movements,

one then needs to assume a "two brains in one"

master-slave design described in [1].

Second, and more seriously, in order to

learn how to "see" far into the future, the

underlying learning rules have to be changed, to allow some sort of "temporal chunking." The

usual critic adaptation rules train a network at time t based on information about time t+1

.

One can do far better by allowing the use of t+T,

at times, where T is a larger time interval. But

how can one do this? My concerns about this wedre magnified by the growing evidence from

neuroscience that the basal ganglia are a crucial

part of higher-order intelligence, and that they

perform something very similar to task-based

planning in AI[1].

A careful analysis of the mathematics of

temporal chunking in ADP forced me into the

development of an hierarchical task-based

design, made up of "decision blocks." An

international patent disclosure was filed on this design on June 4, 1997, through Scientific

Cybernetics, courtesy of Sam Leven. The main

specification section of that disclosure is being

published in [7]. Of course, that paper mainly

deals with global implementation details. (The

disclosure also required 300 pages of additional

papers — mainly papers previously published —

in order to describe some of the subsystems.) In order to complement that discussion, another

paper is being published very soon [2] which

summarizes the preceding history and the

intellectual strategy here in great detail. It expands on the implications for neuroscience,

stressing the empirical data on the mammalian

brain.

I am very grateful to Alex Meystel for

drawing my attention to [8] , soon after the

publication of [2]. This paper made me

appreciate more seriously a third limitation of the

earlier model-based ADP systems — their

treatment of space. In a formal sense, this problem can be handled without changing the

higher-level architecture of the model [2,7]. It is a subsystem issue, at least for the mammalian

level of intelligence. (But mammals do not have

to coordinate 100 quasi-independent robotic

pieces of themselves spread out over an acre!)

Nevertheless, the required change in neural

network subsystems is very large, and has major

implications for neuroscience [2] and engineering

applications[7]. It is particularly relevant to tasks

like predicting the behavior of molecules or

controlling complex networks like heat

exchangers, precoolers, fuel processors, utility

grids, etc.

A Few Details

A BLOCK "A"

Internal Nets: J*> Critic {local U)

Modifiers J* Critic (p(A) result) local Action or Decision Net STOCHASTIC p(A) Predictor

9o. 9l £*

Info From

e(A) f Blocks

entry states p(A)

Nets: J*-, g* (i) post-exist states

Net: J

A*

Figure 1. Structure of a Decision Block

Figure 1 is a reduced version of a figure which

appears in [2]. It summarizes the structure of a

"decision block." In this theory, the upper level

of the mammalian brain (excluding the higher

motivational systems) is essentially made up of a

library of such decision blocks. The blocks are formally distinct, but in practice (as in the brain)

they may share hidden nodes, and must share a common estimated state vector R.

The task of each decision block is to decide which lower-level decision blocks to

activate. This is a crisp, discrete decision. (In [1],

I speculated that the activation might be fuzzy

instead of crisp; however, because of the problem

of local minima, and the need for rational

learning, this did not turn out to be promising.)

For the lowest level block, the decisions are

really just actions u sent to the lower brain.

Decision blocaks may be thought of as "active

verbs." The arrangement is strictly sequential in nature, with only one decision block activated at any time on any level of the hierarchy.

When a decision block is activated,

three kinds of additional information are also

needed, to guide the actions taken nside the

block: "adverb" modifiers, a fuzzy goal object g, and compressed information about the goals

inherited from higher levels of the hierarchy. In

[7], mechanisms for adapting all of these

structures or networks are provided.

The fuzzy goal object mainly consists of

an image of a desired state r* plus a vector of

weights (indicating which components of that

image vector are most important). In effect, this object provides a kind of explicit quadratic

representation of a value function. The need for

83
this kind of representation became clear only

after considerable analysis of the problem of

communication between decision blocks.

Within each decision block, neural

networks must be adapted which are very similar

to those in the usual model-based adaptive critics — local critic networks, a local Model or prediction network, and a local Decion or action

network. In this case, however, it is especially

critical that the latter two networks be stochastic

networks, rather than the usual sorts of

deterministic neural network[2,7]. Two

additional networks are needed in order to optimize the interface with other decsiion blocks.

A key aspect of using stochastic

networks is that one can replicate such

phenomena as "imagination" or "dreaming" or novelty-seeking behavior which is crucial to

effective higher-order problem-solving and

mammalian behavior [4,9].

nets planned for circa December 1996. See

also www.glue.umd.edu/~pangxz.

7.P.Werbos, A Brain-Like Design To

Learn Optimal Decision Strategies in Complex

Environments, in M.Karny, K.Warwick and

V.Kurkova, eds, Dealing with Complexity: A

Neural Networks Approach. Springer, London,

1997.

8. J.Albus, Outline of Intelligence,

IEEE Trans. Systems, Man and Cybernetics,

Vol.21, No.2, 1991.

9. . D.S.Levine and S.J.Leven,

eds, Motivation, Emotion, and Goal

Directio n in Neural Networks, Erlbaum,

1992.

References

1. P.Werbos, Learning in the Brain: An

Engineering Interpretation, in K.Pribram and

J.King, eds, Learning as Self-Organization,

Erlbaum, 1996.

2. P.Werbos, Values, goals and utility in an engineering-basxed theory of mammalisn

intelligence, in K.Pribram, ed, Values (tentative

title), Erlbaum 1997.

3. P.Werbos, Neurocontrollers, in J.Webster, ed., Encyclopedia of Electronics and

Electrical Engineering, Wiley, forthcoming.

4. P.Werbos, Optimization: A

Foundation for understanding

consciousness. In D.Levine & W. Elsberry

(eds) Optimality in Biological and Artificial

Networks?, Erlbaum, 1996.

5. P.Werbos & X.Z.Pang,

Generalized maze navigation: SRN critics

solve what feedforward or Hebbian nets

cannot.Proc. Conf. Systems, Man and

Cybernetics (SMC) (Beijing), IEEE, 1996.

(An earlier version appeared in WCNN96.)

6. X.Z.Pang & P.Werbos, Neural

network design for J function approximation

in dynamic programming, Math. Modelling

and Scientific Computing (a Principia

Scientia journal), special issue on neural

84
LOGICAL CALCULI FOR SEMIOSIS

Plausible Reasoning and Its Logics

Oleg M. Anshakov, Victor K. Finn, Dmitry P. Skvortsov

VINITI - All-Russian Institute of Scientific and Technical Information

Usievitcha St. 20a, Moscow, Russia, 125219

Phone: +7 095 152-5447, Fax: +7 095 152-5447

email: lis@viniti.msk.su

ABSTRACT: The paper deals with some formal

models of plausible reasoning. The so-called JSMmethod of automatic hypothesis generation is one of

these models. Some important notions of JSMreasoning and its logical basis are informally

introduced in this paper.

1 INTRODUCTION

Reasoning can be considered as synthesis of cognitive

procedures. These procedures include valuating of

elements of our knowledge such as facts, hypotheses,

and arguments. General scheme of plausible reasoning

is represented by the notion of Quasi-Axiomatic

Theory (QAT). [Finn 1991], [Finn 1995].

Let Z be the set of axioms that are known to provide an

incomplete characterization of the application domain,

let Z' be an open set of elementary (protocol)

propositions representing facts (we simply call these

propositions facts), where S'=une(i)5^, and En is the set of facts corresponding to the n-th state of the QAT. Let

9? be the set of inference rules such that 9?=SR'u9to>

where 9?' is the set of plausible inference rules (PIR)

and 9to is the set of reliable (deductive) inference rules. Then r'=<I,I',SR>, r=<Z,9*> and Tn =<Z,Zn,9?>will

be called QAT, QAT carcass, and n-th state of QAT,

respectively.

Computer analogs of these concepts are obvious: 2^, is

the state of the data base (the fact base) and T is the

knowledge base containing declarative knowledge (Z)

and procedural knowledge (91). The QAT itself is the

limiting (ideal) notion that all the states of the carcass T

are attainable in the limit, e.g., we have

ZicE2c:...cXn

c:....

Particular realization of QAT is JSM-method of

automatic hypothesis generation. The paper discuss this apparatus and its logical foundation.

Applications of JSM-method are considered in

[Zabezhailo et al. 1995], [Mikheyenkova 1995]

2 INFINITE-VALUED LOGIC WITH

FINITE NUMBER OF TRUTH VALUE

TYPES

We use a logic with the following types of truth values:

empirically true (denoted by +1), empirically false

(denoted by -1), empirically contradictory (denoted by

0), uncertain (denoted by x), logically true (denoted by

t), logically false (denoted by f), other (they can be

added in some special versions of JSM-method). By £

denote the set of all types of truth values. Thus, £={+1,

-1, 0, t, t, f}. In some special cases, £ can be extended.

An informal interpretation of the truth value types is as follows:

• the truth value of predicate P is a value of type +

1

(empirically true) iff it is known that P (possibly)

holds;

• the truth value of predicate P is a value of type -1

(empirically false) iff it is known that P (possibly)

does not hold;

• the truth value of predicate P is a value of type 0

(empirically contradictory) iff there are arguments

both for P and against it;

• the truth value of predicate P is a value of type T (uncertain) iff there are neither arguments for P

nor against it. The types +1, -1, 0, and x are called internal. The

types t and f are called external. We denote by Ve the

set of all truth values of type e. By V we denote the set of all truth values.

We say that e is a non-split type if Ve is a one-element

set. We say that e is a (denumerable) split type if Ve is

a denumerable set. The types +1, -1, and 0 are split

types. The types t, f, and x are non-split types.

By £'nl denote the set of all internal types of truth

values. £

int ={+l, -1, 0, x}. By £ext denote the set which consists of two external types of truth

values. £

ext ={t, f}. By £w

denote the set of all

(denumerably) split types of truth values. £w ={+1, -1,

0}. By £0 denote the set of all non-split types of truth

values. EQ ={x, t, f}. If it is necessary, we can extend

the set £ by adding a finite set of non-split internal

types of truth values. We denote this set by £o

nt

.

For any non-split type e there exists a unique truth

value in Ve denoted by <e, 0> (or by £). If e is a split

type, then Ve = {(e, k)\ k e co'}, where

(o' = {0, 1, co} = (oU{co}, i.e., co' is a successor

87
of the first limit ordinal co. In other words, co' is obtained from the set of all natural numbers by adding

the item co, which is greater than any natural number.

Suppose we have a procedure of hypothesis generation

such that, using it for an arbitrary predicate P, we can

look for the truth value type of this predicate. Assume

that the truth value of the predicate P is (e, k) , where e

is a split type of truth values. Then k is the number of

the step, where the truth value type of this predicate was found. We can use k as a measure of plausibility.

The more k the less plausible is a hypothesis. If k=0,

then the truth value type of the predicate is known

before the beginning of the above procedure.

In the standard JSM-method, the truth value (0, 0) is

not considered. In other words, in the standard JSMmethod the empirically contradiction cannot be a fact,

but it can be a hypothesis.

By definition, put V(x

» = {t}U U{(e, k)\ k > n}. If

J e (e e E), J/F B\, (e e E^) where J E and can be

ee£m £e£ffl (i.e., e is a split type), then by definition we put

% n) =

{(e> k - "} Intuitively, the fact that the

truth value of the predicate P belongs to VL n^ means

that we did not find the truth value type of this predicate within n steps. The fact that the truth value

of the predicate P belongs to Vj

e

\ , where £ is a split

type, means that we found truth value type of this predicate within n steps.

We will use shorter notation for Vj

e n j and VjT n

^

,

namely: (e, n) and (x, n) respectively. Note that

(x, n)=(z, « + l)u{(+l, n), (-1, n), (O, «)}=(t, « + l)U \](e, n)

In our logic we use the following connectives:

j (a) = i

t if a =

v

6 ' ")'

( e> ") |f otherwise,

j (a) _ j* if a 6 (T ' n)>

^ T '"^ If otherwise,

>(e.») (a) =

j

t if a e (e, «),

f otherwise,

where e is a split type (ee{+l, -1, 0});

-i, & , v, —», <->, V, 3 ; the latter are the classical

logical connectives and quantifiers over {t, f}.

We can describe the syntax of this infinite-valued logic

and define terms and formulas in a general way. Both

infinite-valued and two-valued (external) predicates can be considered in this logic. We can take the

following connectives as basic symbols: —i, &, v, —>, <->, V, 3 (the classical two-valued

connectives and the quantifiers; it is sufficient to take

only -i, v, 3 );

•<e,B

> defined as follows:

Je(«)=

f

t if cxeVe ,

otherwise,

( e '"^ ^ {f otherwise.

Then by definition, we put

J(£.«)( p) = VJ(e,fe)(/>

)' where ee£M , and

k<n

J(x. n)(P) = Jx(P) V V(J. (P) & -J(e, n)(P))

The above logic is an example of the J-definable J- compact logics considered in [Anshakov, Finn,

Skvortsov 1989]. In this paper it is proved that every J- definable J-compact logic is strongly axiomatizible,

i.e., for any J-definable J-compact logic L one can

construct a calculus / such that the strong completeness

theorem holds: r \-

{ A iff r \= L A , where

r \-j A means that the formula A is deducible from

the set of formulas T in the calculus /, r \=L A means

that the formula A is a semantic consequent of the set of formulas T in the logic L.

3 SIMPLIFIED FORMULATION OF JSMRULES

We consider items of three types. The items of the first

type are objects of arbitrary nature. The items of the

second type are fragments (parts) of these objects.

Assume that we can find the common part (fragment)

of any set of objects. The fragments may be objects,

but they are not neccesarily objects. The items of the

third type are sets of properties of objects. We can

imagine the objects as sets, the fragments as subsets,

the common part of several objects as their

intersection.

Suppose X is an object, x is a fragment (part) of an

object, A is a set of some properties of the objects.

Consider two many-valued binary predicates denoted

by and > 2

: X =>] A means that the object X

(possibly) has all the properties from A; x => 2 ^

means that the fragment x is a (possible) cause of any

property from A.. In the simplest case A = {a}. In this

case we write X =>, a and x =>2 a instead of

X =>j {a} and x =>2 {a }

respectively.

For the sake of simplicity, assume that our objects are represented by sets; their fragments are subsets of

objects; the common part of several objects is their set- theoretic intersection. Moreover, suppose that all sets ofproperties of the objects are one-element

.

88
We write J^T „)(*=> 2 a ) if we do not yet know

whether the fragment x is a (possible) cause of the

property a, after n steps of Hypothesis Generation

Procedure. We write J^+1 n^(x =>2 a ) if we discovered

that x is a (possible) cause of the property a just at step

n. Similarly, we write J^_, ^(x => 2 a ) if at steP n we

found arguments for x to be a cause of absence of a, and we write J^0 ^(jc=> 2 a ) if at steP n we f°und

arguments for x to be a (possible) cause of both

presence and absence of a The Fist-type JSM-rules are formulated as follows:

J(t,n)(j:=> 2 4 M»(*. a), ^M^x, a)

'(+1, n+l)

("+"-rw/e)

("-"-rw/e)

J(x, n )(

x=>2 a)- Mn(** a), ^M+(x, a)

("0"-rule)

J(_,,„ + l)(*=*2 «)

J(0. n+ l)("r ^2«)

("x"-rule)

J(t,*)(*^2 4 "-M^x, a), -,M~n (x, a)

J(U+1)(^2«)

We write J^+1 n ^(X =>] a) if we discovered that the

object X (possibly) had the property a within n steps of

Hypothesis Generation Procedure. Similarly we write

J(_i „)(X =>i if we discovered that X do not had

the property a within n steps.

Suppose S + (a) = {x\ 3 {+ln] (X =>, a)},

5„"(a) = {xi J

(_1>n) (X =>! a)j. M+(y, a) means that

there exists X cS„+ (a) such that the following

conditions hold:

(1) xcs;(a);

(2) y= I X;

XeX

(3) y*0.

M~(y, a) means that there exists X cS~(a) such

that the following conditions hold:

(1) |X|>2;

(2) y= I X;

XeX

(3) y * 0 ;

Suppose J(+i,„)(X; =>i a),

(i = l, 2, 3); Jc+l^CF! ==>! a),

(see Fig. 3-1). Using first-type JSM-rules, we obtain,

J(-l,n)(Zi =>] a )>

J(+ l,„ + l)(*=>2 a). J(0,n + 1)(^ => 2 «)- J(-i,„ + i)(z=>2 a).

We write J(T n ^(X =>, a) if we Jo not yet know

whether the object X has the property a after n steps of

Hypothesis Generation Procedure. We write

n){^ ^1 a )

if we discovered that X has f/ie

property a just at ste/? n. Similarly, we can describe the

conditions J^_j n ^[X =>, a) and J^0 n^(X =>j a).

Tfce Fist-type JSM-rules are formulated as follows:

("+"-rule)

("-"-rule)

J(+l,n+l)(X=>l fl )

J(_,,„ +1 )(X =»i a)

("0"-rule)

J(m)(x=*i4 n°(x, a )

J(0,n +l)( X =*l fl )

(V-ruZe)

*(x.n)( x =>i 4 ~'n»(X ' 4 4- ^n°( X ' 4

j(+i,»+i)(X=>i fl )

n*(X, a) holds iff the following conditions are

satisfied:

0) J(+1 n) (y =>2 a) for some yc X;

(2) J(_, ^(z=>2 a) for not any zc X.

U~(X, a) and Tl +

n (X, a) are defined dually.

Tl

0

n (X, a) holds iff the following conditions are

satisfied:

(!) J(+i, n)(> ^2 a ) for some ^X;

(2) J(_,_ „)(z=>2 Q) for some zcl.

For example, let J(+1 ^(x =>2 a) , J(_, n ^(y =>2 a)

(see Fig. 3-2). Then using the second-type JSM-rules,

we obtain J(+1> n+1)(X =>2 a) , J (o n+ ^(Y =*2 a) ,

J(_i( „+1)(Z=>2 a) J(t, „+i)<w =>2 «)•

89
Figure 3-1: First-Type Rules

4 JSM-THEORY

The JSM-theory T(M) imitating system M of rules of

the JSM-inference is constructed on the base of the J- logic V with finite number of types of truth values. This

theory is constructed in some many-sorted language L

containing individual variables of three sorts: for

objects, subobjects and properties (or sets of

properties).

The JSM-theory consists of three families of axioms.

Procedural axioms imitate hypothesis generation

procedures of the JSM-method. Namely, the plausible

rules of the first and second type are rewritten in the

form of implications (so-called axioms of step-by-step

inference):

(e,r,n)

WX =>i A)& IT^X, A)^J(e „ +l) (X A),

(0),r,n)

where r=l,2 and ee Ea

.

Similarly, the axioms imitating the first-type rules can

be formulated.

Then the axioms ofstabilization are added:

V^(j(x, n )(^^. A)^J(t,n+i)(*=*i A))->

-*VXVa(jm(X =>, A)^JT (X =>, A))

Similarly, the axiom of stabilization with respect to the

predicate =>2 can be formulated.

W

Figure 3-2: Second-Type Rules

(namely, if on the

step n no one new

value <e,n+l> is attributed then all remained subdefined up to their

moment acquires

the ultimate value

CO). Remark. For each

axiom of step-bystep inference, the converse holds.,

i.e. the

correspondence

equivalencies are provable in the

JSM-logic. These equivalencies correspond to the

constructivity of generation of truth values in the JSMinference.

The generating condition are expressible by the

formulas of the language L. These formulas involve the

notions of similarity and difference of the objects

considered. More precisely, the operations (e.g. set- theoretical intersection or the corresponding operation on graphs etc.).

!Algebraic a^wmsTa describe the properties of these

operations, e.g. semilattices or Boolean conditions on & (namely, axioms of atomic Boolean algebras)

Some means of description of finite families of objects

(and subobjects) are necessary too. Namely, one can

use quantifiers on sequences of an arbitrary finite length (i.e. finite functions on natural numbers) or

quantifiers over finite sets of objects (and the

corresponding axioms of weak monadic second order

logic are included in Ta ). Hence, algebraic part Ta describes the structure of

domains (of our three sorts) and corresponds to the

structure of data in database with incomplete

information involved.

Finally, the JSM-theory can conclude some declarative

axioms Td corresponding to procedures of verification

and falsification of results of the JSM-reasoning, in

particular:

(i) axioms of formal correctness representing the

interrelation between the predicates (e.g. axioms of

monotonicity and additivity),

(ii) axioms of control of JSM-inference (axioms of

causal completeness, consistency etc.)

(iii) descriptive axioms characterizing peculiarities of a

subject domain (e.g., some principles of sociology or another field to which the JSM-method is applied).

REFERENCES

Anshakov, O.M., Finn, V.K., Skvortsov, D.P. 1989. On

axiomatization of many-valued logics associated with

90
formalization of plausible reasoning. Studia Logica,

vol. XLVm, N 4, pp. 423-447.

Finn, V.K. 1991. Plausible inferences and plausible

reasoning. Jour. Soviet Math., Plenum Publ. Cor., Vol.

56, N l,pp. 2201 -2248.

Finn, V.K. 1995. JSM-reasoning for control problem in open (+)-worlds. Proceedings of the 1995 ISIC

Workshop. 10th IEEE International Symposium on

Intelligent Control, Monterey, CA, USA. pp. 75 - 79.

Josephson, J.R., Josephson, S.G. 1994. Abductive

Inference: Computation, Philosophy, Technology.

Cambridge University Press. Mikheyenkova, M.A. 1995. Applications of JSMmethod to problem of sociology. Proceedings of the

1995 ISIC Workshop. 10th IEEE International

Symposium on Intelligent Control, Monterey, CA,

USA. pp. 429 - 433.

Zabezhailo, M.I. et al. 1995. Reasoning Models for

Decision Making: Application of the JSM-method in

Intelligent Control System. Proceedings of the 1995

ISIC Workshop. 10th IEEE International Symposium

on Intelligent Control, Monterey, CA, USA. pp. 99 -

108.

91
Application of JSM-Theory of Plausible Reasoning to Social

Data Analysis and Social Actions Prediction

V.K.Finn and M.A.Mikheyenkova

All-Russian Institute for Scientific and Technical Information (VINITI)

Usievitcha 20, Moscow, Russia, 125219

Phone/Fax: +(7-095)- 152 54 47

e-mail: lis@viniti.msk.su

ABSTRACT

The present report continues the series of papers, devoted to attempts to describe formal frames of

theory of reasoning for sociological investigation and

to apply it to real sociological problems. Logicalcombinatorial JSM-method of automatic hypotheses

generation is chosen to be the basis of our approach.

The method realizes special class of plausible

reasoning in open subject domains with large amount

of empirical material and ill-formalized knowledge.

KEYWORDS: plausible reasoning, quasiaxiomatic theory, modelling in the humanities

1. INTRODUCTION

The present report continues series of papers,

devoted to attempts to describe formal frames of

theory of reasoning for sociological investigation

and to apply it to real sociological problems [1-

3]. Logical-combinatorial JSM-method of

automatic hypotheses generation is chosen to be

the basis of our approach. The method realizes

special class of plausible reasoning in open

subject domains with large amount of empirical

material and ill-formalized knowledge [4, 5].

Informally the method can be considered as a reasoning scheme "similarity - cause - analogy":

the reasons of events (phenomena) are searched

by the analysis of their structural similarity and

then these reasons are employed to forecast new

events (phenomena) by structural analogy. This

scheme corresponds to the principle "similarity

of objects involves similarity of their properties".

Here similarity (or it's n-ary generalization) is considered to be reflexive and symmetric

relation.

2. APPLICATION OF JSMMETHOD IN SOCIOLOGY

Thus, sociology as the humanity investigating

social phenomena' similarity, the humanity with

ill-formalized knowledge generated on the basis

of huge empirical data, can be supposed to be a

field for JSM-method application. However,

certain condition must be fulfilled for success of

92

JSM-method' s application (see, for example [2,

6]), in particular, empirical data must really

contain causal relations.

The possibility of JSM-application in sociology

is based on consideration of social systems as systems with multi-factor (^-influences. 1

Consequently, we speak about studying the

relation "subject (individual) => behaviour" in supposition that the individuality of the person is responsible for his behaviour. Comparison of

individuals' behaviour, similarity and difference

revealing is necessary to use proposed tools for

analysis of the involved relation.

For this analysis we need structural description of

the subject (individual) by the system of

differential indications. Part of them is to describe social characteristics (in accordance

with idea of E.Fromm about social character).

Another part defines the characteristics of

individual irrelatively to social interactions. And

the last part represents features of person's

biography, essential for the problem involved. By

another words, proposed approach gives the

possibility of individual behaviour prediction,

when combinatorial analysis is inaccessible

(because of substantial amount of information)

for human's brain. Let's underline, that the relation "subject

(individual) => behaviour" is the micro-level

representation of the macro-level (macrosociology) relation "situation behaviour". The

latter relation to be investigated "situation"

concept must be specified and formalized.

General scheme of JSM-reasoning (see [4, 5]) in application to problem involved is interpreted as followes.

(1). Creation of statements about reasons of

objects' properties (by observing of facts (examples) from the initial data base with

incomplete information - DBII)

application of plausible inference rules of

first kind (PIR-I). Determinants of

behaviour are defined on this stage.

We are aware that more objective picture of social

reality must include a description of irregular

disturbances [7], treated by statistical methods.
(2) . Prediction of unknown properties of objects

in DBII (the first-step hypotheses about

reasons are used in this prediction),

inference by analogy - application of

plausible inference rules of second kind

(PIR-II). Forecast of individual behaviour is carried out on this stage. Forecast control is realized experimentally (in corresponding

period of time).

(3) . Explanation of facts and results and inference

control on the base of sufficient-basis-forconclusion criterion (CSBC). We generate

falsificators for DBII automatically by

CSBC use.

3. JSM-METHOD WITH SCALES

Let U

(1) = {dx ,...,d

rx }, U

<2) = {a x ,...,a h

} be

two sets, on which we define two Boolean

algebras, (E\ = {2

U

, -, n, u} - algebra of

objects, (E2 = {2

U

, -, n, u} - algebra of

properties. Consider 2 partially defined relations:

=»i* and =>2 * • 2-place predicate symbol =>i

corresponds to =>i* , 2-place predicate symbol

=>2- to =>2 * • X=>]Y means, that the object X

possesses the set of properties Y; the predicate

describes data base with incomplete information

(DBII). V=>2\V means, that the subobject V

causes the set of properties W; the predicate

describes automatically generated fragments of

knowledge base (KB). Inner truth values (for real

facts and semi-facts representation) have the form

V = ( V, n) , n - number of step of PIR using.

Traditionally four types of inner truth values v in JSM-logic are used: +1 - factual true, -1 - factual

false, 0 - empirical contradiction and x

-

uncertainty. Types of external truth values (for

facts' with valuation and PIRs' representation): t

- "logical true",/- "logical false". Let 7v O be the

operator, 7v O = true, if v(O) = v , 7v O = false, if v(O) * v , where v[<t>] - valuation.

We suppose the knowledge in empirical theories

(that deal with the open world, progressively

replenished with new facts) to be represented in

the form of quasiaxiomatic theory (QAT) [4, 5] 3

= (I, I', R), where I is an open axiom set, describing a subject domain (SD) incompletely;

If is an open set of empirical elementary

statements about subjects from SD (I

corresponds to knowledge base KB, I' corresponds to data base DB). R is an inference

rules set, R = Rd u Rp

, where Rd is a set of

deductive rules, Rpis a set of plausible inference

rules (PIR).

In QAT for JSM I' - set of empirical facts

^(X^Y) (ve { 1, -1, x}) of the considered SD.

7(v>0>(X=»iY) means, that the statement "object X

possesses set of properties Y" has the valuation v

(true, false or uncertainty) in the initial state (on

the 0-th step of reasoning). Plausible inference

rules Rp in the JSM-QAT are PIR-I and PIR-II. Let's turn to our problem.

Let U

(1) = { U],..., ur } be a set of differential

indications, describing individual personalities'

qualities, several social features and biographical

data (sociological data are collected by methods

of formalized interview and psychological tests in our investigation). X, (i* = 1,.., k) - objects

(persons, subjects of sociological investigation,

X, e 2

U<1>

. U

(2) = {b,,..., bs } - a set of

behaviouristic readinesses, Y, (i = 1,..., k) - a set of /-subject's behaviouristic readinesses, Y, e 2

U°\

The relation =>i* is formed on the basis of expert

analysis (which is fulfilled by sociologists and

psychologists) of questions complexes. Since answers of "possibly, yes" and "possibly, no" -

types are very often in sociopsychological

practice (side by side with "yes" (+1) and "no" (-

1) - answers), we introduce two new types of

truth values - +1/2 and -1/2 - to characterize the

degree of properties presence or absence. Logical

connectives & and v are defined in a standard manner - see, for example, [4].

Three strategies of empirical data investigation

with different degrees of properties' presence or absence (different scales) are possible.

(a) . The difference between degrees is supposed

to be unimportant, only direction (+ or -) is essential. Then types of truth values +1/2 and

+1 (as far as -1/2 and -1) merge,

VXVY(y(1 , 0) (X^1 Y)^y^ ,o>(X=hY)), and

we return to traditional four types of truth

values (see above).

(b). Mechanisms of different degrees of

properties presence or absence exposing are

different. Then

VXVY^(7(1 , 0) (X^1 Y)^y( i-,o

> (X^1 Y)), ~ +1

special predicates Ma \ (V,W,k) for treating

facts J( -j fy(X=>iY) (n - number of calculation

step) are introduced (analogous to M* n (V,W,k) for treating facts

y(

i i0>(X=*iY); for -1/2 and -1 - symmetrically)

and then usual scheme of JSM-reasoning is applied.

(c) . ±1/2 is considered to be "weak" (expressed

insufficiently) ±1 correspondingly (see also
[1]), VXVYC/^X^YWi.o^iY))- In

this case we take into account examples with

both types of truth values (+1/2 and +1) to discover the reasons of relation's =>j*

exposing with the truth value +1/2. This

process is formally described by the predicate

Ma \ (V,W,k) (which differs from section

(b) predicate). This predicate reveals local

similarity on (+1/2)- and (+l)-examples

y( ^-,n)(Z1 ^1 U/ ) and J(1 , n) (Z,- =>, XJj)

correspondingly, i = 1,.., p, j = p+l,..., k, where k is variable (1 < p < k, k > 2). (For -

1/2 - symmetrically.)

Analogously, the predicate Ti

+

B

2 (V,W,k) for 2-nd

kind rules PIR-II (rules for prediction) includes

the subformula, expressing the statement, that V

contains positive (+1/2)- and (+1) reasons

Xi,...,Xp and Xp+1 ,...,Xlt of properties Yh ...,Yk correspondingly, W being covered by these sets of properties. (For -1/2 - symmetrically.)

PIR-I gets the form.

4_n)(V=*2W),

M+

a, n (V,W)&^M"a, n (v,w)&-,M 7n (v,w)

d

(+)

) /(i^i,(V=>2W)

4.n)(V^2W),

-M+

a,n(v,w)&^M"a, n(V,W)&

M ^n (v,W)&-.M ^(V.W)

(I

( +T))

^< T.n+l

> (V^2W)

(V=>2W) gets truth value +1/2, only if it does not

simultaneously gets truth value +1. (For -1/2 and

-1 - symmetrically.)

4fl)(v=>2w),

M

+

a, n(V,W)&M"a, n (V,W)v

lVr^(V,W)&M ^n(V,W)v

M"a, n (v,w)&M *J,(V,W)v

M ^n (v,W)&-,M 7n (V,w)

(I

( 0))

V+i>(v=*2W)

^.n)(V^2W),

^M+

a, n (V,W)&^M"a, n(V,W)&

-.M ^n (v,W)&-,M 7n (V,W)

dw)

94

In comparison with [4, 5] representation of rules

for PIR-n is changed only for ±1/2.

/

( „n)(v^,w), n

+

2

n(v,w)&^n+

n(v,w)

(H(+T)

) /(-^(V^W)

(V=>iW) gets truth value +1/2, only if it does not

simultaneously gets truth value +1. (For -1/2 and

-1 - symmetrically.)

The former consideration involves two degrees of

properties presence or absence - +1/2 and ±1.

This scheme can be generalized to the case of n

degrees.

4. CONTEXTUAL METHOD

But the simple (binary) model of causal relation

"cause - effect" appears to be quite insufficient

for many empirical fields. More profound -

contextual - analysis of causal relation is provided by the so-called "generalized" JSMmethod. We shall try to develop an idea of

contextual analysis in application to the problem

involved.

Let us introduce new sorts of variables.

Variables of the 5

th sort - for set of attendant

(promoting or deterrent) factors, U

(5> = {cj,..., c

p

}, constants and variables of the 5

th sort, Ze 2 . Variables of the 4 sort for sets Z, Zu —, 2

ul5) Zm...(and corresponding constants), Ze2

Alongside with Boolean algebras (i= 1, 2) (see

above) Boolean algebras (E4 = { 2 , —, n, u} - 2

U

algebra of attendant factors - and (E3 = {2 —, n, u} - algebra of external circumstances -

are considered.

Let's consider ternary predicate F(X Z,Y) -

"objects X under the circumstances Z possesses

the set of properties Y" - instead of binary

predicate X=>jY - "object X possesses (does not

possess) the set of properties Y". Binary

predicate V =>2 W - "the subobject V causes the

set of properties W" is substituted by 2 ternary

predicates: Tpr(V,Z,W) - "the subobject V under

the circumstances (promoting factors) from the

set Z causes (does not cause) the set of properties

W" - and Td(V,Z,W) - "the subobject V, if circumstances (deterrent factors) from the set Z

are absent, causes (does not cause) the set of

properties W".

There is not enough place here to present the

complete description of formula for predicates

Mapr,n (V,Z,W) and M^ n (V,Z,W). We can
only say, that first one describes a set of examples

(this set being a base for plausible inference),

expresses the exaustability condition - demand to consider all appropriate examples from initial DB. Empirical regularity, that describes

predicted causal relation in M^pr n (V,Z,W) ,

is expressed by subformula

VXVZVY(((7(I>n)F(X,Z,Y)&VY'VZ/(7(i,n)F(X,Z

',Y')-*Z'cZ&Y'cY)&VcX)&(V,prcZv...vVr

pr cZ))->W*0&WcY)

("V causes set of properties W under the

condition that elements V^,..., Vr

pr from the set of attendant (promoting) factors Z are present").

Other fragments of the predicate

M^pr n (V,Z,W) describe local similarity of

the situations, where promoting factors Z act,

exaustability condition - taking into account all these situations, - condition of Vi

pr minimality (i = 1,..., r) and condition, that their set is unique.

The predicate M^j n (V,Z,W) is formulated

analogously to generalized predicate of

agreement Mj5>n (V,X,W) from [8]. The only

difference is in sorts of elements from Z and X. The elements of the set of obstacles X from

Mj^ n (V,X,W) are subobjects (from 2

U<1>

)

whereas the elements of the set of attendant

factors Z from M^ n (V,Z,W) represent

U
 external circumstances (from 2 ), under which

causal relation exists. Empirical regularity, that describes predicted causal relation in

j n (V,Z,W), is expressed by subformula

VXVZVY(((7(1 , n)F(X,Z,Y)&VY'VZ,(7(i,n)F(X,Z

',Y')->Z'cZ&Y'cY)&VcX)&-,(V ,

prcZv.. . vV

r

prcZ))->W*0&WcY)

("V causes set of properties W under the

condition that elements Vi

pr

,..., Vr

pr from the set of attendant (deterrent) factors Z are absent").

It is obvious, that context consideration is

essential in investigation of individual

(collective) behaviour. The proposed approach to context consideration does not, of cause, rule out

the necessity to formalize "situation" concept and

to investigate "situation => behaviour" relation,

the latter problems being the problems of

macrosociology.

5. PRESENT STATUS

We have just begun to study the particular case of behaviour - predisposition to one or another

social identification and solidary actions. We

collaborate with the group of researchers from

Institute of sociology, Russian Academy of

Sciences - E.N.Danilova, S.G.Klimova,

O.N.Dudchenko - headed by Director of Institute

professor V.A.Yadov. First results of JSManalysis of solidary behaviour have been

received. They are in accordance with theoretical

models of sociological investigation. The results

give the possibility to represent the totality of

social actions' determinants reflecting different

types of consciousness.

6. ACKNOWLEDGEMENTS

Most part of computer work has been carried out

by S.S.Moscovsky with participation of

N.I.Melnicov. The authors are grateful to D.W.Vinogradov for fruitful discussions.

7. REFERENCES

[l]Finn, V.K., Mikheyenkova, M.A. "On the

application of JSM-method of automatic

hypotheses generation in sociological

investigations", Artificial Intelligence News,

special issue, pp.91-98, 1993.

[2] Mikheyenkova, M.A. "Application of JSMreasoning to problems of sociology", in Proceedings of the 1995 ISIC Workshop, 1995,

pp.429-433.

[3] Mikheyenkova, M.A., Danilova, E.N., Finn,

V.K., Ivashko, V.G., Yadov, V.A. "Application

of JSM-method of automatic hypotheses

generation to some problems of sociology", in

Proceedings of Workshop on Applied Semiotics,

European Conference on Artificial Intelligence96, 1996, p.22-25

[4] Finn, V.K. "Plausible Inferences and

Plausible Reasoning", Journal of Soviet

Mathematics, Plenum Publ.Cor., vol.56, N 1, 1991.

[5] Finn, V.K. "Plausible Inferences in Intellectual Systems of JSM-type", Itogi Nauki i Tekhniki, ser. Informatica., V.15, pp.54- 101,

1991 (in Russian).

[6] Finn, V.K. "JSM-reasoning for control in open (±)-worlds", in Proceedings of the 1995

ISIC Workshop, 1995, pp.75-79.

[7] Finn, V.K. "On intelligent systems of

automated support of scientific research",

Nauchno-tekhnicheskaya informatsiya, ser.2, N

5-6, p. 1-2, 1996 (in Russian).

[8] Finn, V.K. "On generalized JSM-method of

automatic hypotheses generation", Semiotics and

Informatics, Issue 29, pp.93- 123, 1989 (in

Russian).
Algorithmic Complexity of Generating Hypotheses and Forecasts

in Version Spaces Formed by Concept Lattices

S.O. Kuznetsov

Intelligent Systems Laboratory,

Moscow, RUSSIA

serge @viniti. msk. su

ABSTRACT

A survey of results concerning algorithmic complexity of

learning in the version space formed by Galois (concept) lattices is given. The results are related to some work in machine

learning and abductive reasoning.

KEYWORDS: concept lattices, machine learning, classification, abductive reasoning

1. INTRODUCTION

Recent studies [12], [3] show that formal concept analysis

based on Galois (or concept) lattices is a good means for

learning of concepts. However, this approach faces much

computational difficulties, since the number of concepts can be

exponential in the number of examples. Therefore, the problem of computational complexity is crucial here. Algorithm

reported in [3] is quadratic in the number of concepts generated. In this paper, we present some results concerning the

complexity of generating the set of all hypotheses in the ver- sion space formed by Galois lattices. We describe an algorithm

which is linear in the number of hypotheses (and, therefore, in

the number of concepts), and can work both in batch and in- cremental modes. Unlike the model of concept clustering

method from [3], the JSM-method from [4, 5] uses both positive and negative examples. This allows us to relate the model

presented to a generalization of version spaces [8] known as disjunctive version space approach [10], [9]. We discuss some

extensions of the approach to more general data structures

(e.g., to graphs).

2. MAIN DEFINITIONS: HYPOTHESES AND FORECASTS (CLASSIFICATIONS)

The model presented here was first proposed in [4] as JSMmethod of automatic hypothesis generation and described in more detail in [5]. Let be a set of positive examples and E be a set of

negative examples of a class (defined by a property W, in the

sequel, we do not mention the name of the property when possible), and U be a set of attributes, t and f be relations defined on E* xf/and E xU, respectively. The triples (E+.U.t) and (E

,U,r) are called positive and negative contexts, respectively.

Definition 1. Let A c U, B c E*. The Galois connections on

the set E*xU are given in the following way:

s(A) ={e e E

+

\ et a for all ae A),

t(B)={ae U I at e for all ee B).

As in [11], instead of s(A) and t(B) we write A' and B'. We

will use the notation A

'

' and B" as abbreviations for t(s(A))

and s(t(B)).

A pair (A,B) such that A ' = B, B = A ' is called a (positive)

concept, A is called the intent, and B is called the extent of the

concept [11]. The set of all concepts forms a lattice (for properly defined sup and inf operations) called Galois lattice [3] or concept lattice [11].

Definition 2. Let (E*,U,t) and (E,U,r)be positive and negative contexts. A positive concept (H,H'), Hcz U is a positive

hypothesis generated for these contexts if H c e for no negative example ee E.

Analogs of this definition are used in various paradigms of

machine learning. It says, that a hypothesis (concept, description, etc.) should cover some positive examples and should not cover any negative example.

A positive hypothesis (H,H') is called minimal by inclusion if there is no positive hypothesis

(Hi H, ') such that Hi qH (minimality of a hypothesis means

that it is most general among the set of all hypotheses).

Galois connections for negative examples and (minimal) negative hypotheses are defined similarly.

The following definition gives the rule of forecast

(classification).

Definition 3. Let (E', U,r) and (E, U,I~) be positive and negative contexts, and Q be an object that belongs neither to E* nor

to E (i.e., we do not know whether it has or does not have the

property W). A positive hypothesis (H+ ,H+') is called a hypothesis in favor of Q if H*czQ. A negative hypothesis (H. ,H.

') is called a hypothesis against Q 'xiH.czQ is called a positive forecast if there is a positive hypothesis in favor of it and

there is no negative hypothesis against it. Negative forecasts are defined dually.

96
The relation "be in favor of corresponds to the relation

"cover" (when the talk is about descriptions covering examples). We avoid using this word here, since "covering" has the

opposite order-theoretic connotation.

3. COMPLEXITY RESULTS

3.1. Theoretical Limitations

It is easily shown that the number of hypotheses can be exponential. Moreover, this number is hard to compute and esti- mate (which could have been useful for resources allocation).

The following result is a testimony to this statement.

Theorem 1. The problem of determining the number of all

positive (negative) hypotheses is #P-complete.

Theorem 2. The problem of determining the number of all

positive (negative) hypotheses minimal by inclusion is #Pcomplete.

Theorem 3. The following problem is NP-complete:

INSTANCE Positive context (E*,U,f), negative context

(E-,U,n, query Q.

QUESTION Does there exist a positive hypothesis in favor of

w

The theorem is proved by considering a combinatorial interpretation of the problem: a problem related to a quadripartite

graphs [6].

The following particular cases of the problem from Theorem 4

where polynomial-time algorithms are possible were indicated

in [6]: • The set of negative examples is empty,

• The number of attributes from U that correspond to the

query Q (i.e., \Q\) is bounded from above by a constant. This case is very important for applications, for example,

in computer drug design, where the size of a chemical

compound is limited, but the number of compounds in- volved as positive and negative examples is large. The al- gorithm used in this case is linear w.r.t. the number of

positive hypotheses in favor the query.

In the following table, we present results from [6] about the

complexity of decision problems concerning hypotheses with

restrictions on the sizes of their intents and extents.

< >

Iff! NP P

Iff'l P NP

Iffl+lff'l NP NP

As above, \H\ and \H'\ denote the sizes of intents and the extents of hypotheses, respectively; P denotes that there exists a polynomial algorithm for solving the problem, NP denotes

NP-completeness of the problem. For instance, the upper left

element of the table means that the problem "does there exist a hypothesis such that lffl< kV (k is a parameter) can be solved

by a polynomial time algorithm. The element in the bottom

line and right column is indicative of the fact that the problem

"does there exist a hypothesis such that Iffl + lff 'l> k?" is NPcomplete.

3.2. Close-by-One (CbO) Algorithm for Computing Hypotheses and Its Complexity

We assume that all objects from E* are numbered, and so a

set X qE* can be represented by a respectively ordered tuple.

The numbering of objects from E

+ induces lexicographic or- dering of sets from the powerset of E*. For the sake of convenience, we can represent the process of computing hypotheses as a top-down one, which generates some tree whose verti- ces correspond to hypotheses. During this process, the examples from E* can be labeled or remain unlabeled in each vertex independently. The following algorithm is based upon the

depth-first strategy, though other strategies are possible as

well. Y denotes the extent of a current hypothesis.

Close-by-One (CbO) Algorithm

Step 0. There is only one root vertex where all examples are unlabeled, Y:= 0.

Step 1. The current vertex corresponds to the concept with

the extent Y. The first unlabeled element of E*, say X, , is

taken, (Yu/X,/)'and (Y<j{Xj))"aie computed. A new vertex

that corresponds to (Tu/X, }) "is generated and connected by

an edge to the vertex associated with Y. Step 2. Check conditions (a) and (b):

(a) (Y^j{X, J) "contains objects with numbers less than those of

the objects from Y or the number of X„ (i.e., the concept with

the extent (yu/X, /)"has already been generated).

(b) (Tu/X, /J 'is contained as a subset in a negative example

from E

If either of these cases holds, all elements of E* are labeled at

the vertex (Ku/X, })"(thus, the branch will not be extended). If neither of conditions (a) and (b) holds, we label additionally

the element X, at the vertex Y and all elements of (Y(j{Xj }) "at

the vertex (Ku/X })"

Step 3. If all elements of E* are labeled at (Ku/X, }Y\ we go

to Step 4. Otherwise,

Y: = (YvfXi))", we return to Step 1. Step 4. We backtrack the tree upwards to the nearest vertex with unlabeled elements of E*. If such a vertex exists and cor- responds, say, to the object Z, then Y:= Z and we have to go

to step 1 . If there is no such vertex, this means that all concepts

have been generated and the algorithm halts.

Theorem 4. Let (E*,V,t) and (E,UJ) be positive and negative contexts, respectively. Then the set of all positive hypotheses can be generated in time 0(\E+ \\E\\U\K) and space

97
0((\E*\+\U \ + \E\)K). by the algorithm CbO, where K is the

number of resulting hypotheses. The same estimate holds for

negative examples.

Thus, the resources required are linear w.r.t. to the number

of hypotheses generated, which is better than results reported

in [3], where an algorithm is proposed that has quadratic complexity w.r.t. to the number of hypotheses.

Algorithm CbO can work in purely incremental way without recomputing old hypotheses: new examples are given se- quential numbers greater than those of the existing examples

and the generation of hypotheses continues. The principle of

canonical ordering of hypotheses used in the algorithm enables

the parallelization of the algorithm: all hypotheses are generated with the use of local operations and tests, which does not

require the interaction of processors, the use of a supervisor,

and shared memory.

The CbO algorithm can be applied to more general type of

data than contexts from Definition 1, e.g., in the case where

examples are represented by sets of graphs. In this case, we do

not use Galois connections, but define operation G' on a set of

graphs G as the set of all maximal by inclusion common subgraphs of the graphs from G. Though the problem of computing such operation is NP-hard, the algorithm remains linear

with respect to the number of hypotheses generated. More

generally, the algorithm can be used for arbitrary data that al- lows the definition of an idempotent, commutative and associative operation n (i.e., of inf type) on pairs of objects. The

expression. (Yu{Xj})'in the formulation of the CbO algorithm

is replaced by Y, U . Jl Yk U Xh where { Y, ...,Yk } = Y and

expression (Y<u{Xj))" is replaced by the operation of taking

the set of all objects S that contain Z (i.e., S TiZ - Z) In the

case of contexts the operation II corresponds to the settheoretic intersection n. The time complexity of the algorithm

in the general case is 0(\E*\K)a + 0(\E*\2

1 E I AT)p\ where m

is the number of positive examples, K is the number of resulting hypotheses, a is the complexity of computing operation

II, P is the complexity of testing the order relation corre- sponding to the operation 11.

4. RELATION TO OTHER WORK AND DISCUSSION

As mentioned above, our algorithm constructs Galois or concept lattices as their version spaces. Machine learning

method reported in [3] uses the same version spaces, but the

algorithms used therein are less efficient and do not take into

account negative examples (concept is a particular case of a hypothesis when E = 0). The version space used in this work

is similar to the disjunction version space proposed in [9, 10] as the extension of Mitchell's version spaces [8]: examples

must be covered by a disjunction of concepts, not by a single

concept as in the work by Mitchell. Hypotheses defined in this paper correspond to the set S of the lower boundary of the

disjunctive version space. The work [10] reports on the quadratic algorithm for the generation of S, which is outperformed

by our algorithm. Definition 3 presents a way of plausible

reasoning similar to abduction [2]. Moreover, this definition uses a method for generating hypotheses (Definition 2),

whereas in abduction models they appear like deus ex machina. Computational results concerning forecasts are similar

both in pessimistic (related to #P-completeness) and optimistic

(linear complexity in the number of hypotheses) aspects to those obtained in [2]. A more close look on the connection of

JSM-method with the formal concept analysis along the lines

of [1 1] is presented in [7].

The CbO Algorithm was used in an applied system for computer drug design [1]. By means of this algorithm the system

detects structural causes of biological acitivity and classifies

unstudied compounds w.r.t. biological activity under study.

Chemical compounds can be presented both in descriptor form

(as sets of descriptors) and as molecular graphs. Though the

latter case is more preferable from the point of view of applications (better forecasts are obtained), computing all hypotheses on average Pentium PC computer is feasible only for small

samples (20-30 examples), as it was in the case of octane series [1]. The use of CbO algorithm drastically reduced the

computation time (60% on average) as compared with the time

needed for previous algorithms used in the system, which, like

those in [3] and [10] had quadratic time complexity in the

number of hypotheses.

4. REFERENCES

[1] Blinova, V.G. On Results of Applying JSM-method of

Hypothesis Generation to the Problem "Structure of Chemical

Compound - Biological Activity," Automat. Document. Math.

Linguist., No. 5, 1995.

[2] Bylander, T., Allemang, D., Tanner, M. C, and Josephson,

J. R., "The Computational Complexity of Abduction," Artif.

Intell., 49, No. 1,25-60, 1991.

[3] Carpineto, C. and Romano, G. "A Lattice Conceptual

Clustering System and Its Application to Browsing Retrieval,"

Mach. Learn., 24, 95-122, 1996.

[4] Finn, V. K. Data bases with incomplete information and a new method of automatic hypothesis generation, in: "Dialog

and Factographic Information Systems" [in Russian], Moscow, (1981), pp.153-156.

[5] Finn, V. K. "Plausible Inference and Plausible Reasoning",

J. Sov. Math. , 56, No.l, 1991.

[6] Kuznetsov, S. O. "Algorithmic Complexity of the Generation of Hypotheses and Classification Based on the Search for

Set Intersection", Doklady Akad. Nauk, 335, No. 3, 300-303,

1994 (Physics-Doklady), 39, No. 3, 142-145, 1994.

[7] Kuznetsov, S. O. "Mathematical Aspects of Concept

Analysis," J. Math. Sci., ser. Sovremennaya Matematika i ee

Prilozheniya, 18,27-71, 1995.

[8] Mitchell, T. "Generalization as Search," Artificial Intelli- gence, 18, 203-226, 1982.

98
[9] Nikolaev, N. Land Smirnov, E. N. "Analytical Learning

Guided by Empirical Technology: An Approach to Integration," in: N. Lavrac and S. Wrobel, Eds., Proc. European

Conference on Machine Learning, Lecture Notes on Artificial Intelligence, 912, Springer Verlag, 327-330, 1995.

[10] Smirnov, E. N. "Space Fragmenting - A Method for Disjunctive Concept Acquisition," in: B. Du Boulay and V.

Sgurev, Eds., Artificial Intelligence V: Methodology, Systems,

Applications, Elsevier, 97-104, 1992.

[11] Wille, R. "Restructuring lattice theory: an approach based on hierarchies of concepts," in: I. Rival, Ed., Ordered Sets,

Dordrecht-Boston (1982), pp.445-470.

[12] Wille, R. "Concept Lattices and Conceptual Knowledge

Systems," Comput. Math. Appl. , 23, No. 6-9, 493-515, 1992.

99
To the Scaleable Technology of Automated Document Understanding

based on Quasi-Axiomatic Theories.

M.I. Zabezhailo

Intelligent Systems Laboratory,

Moscow, RUSSIA

lis@viniti.msk.su

ABSTRACT

A new approach to full-text processing is presented. The discussed

text-processing technique is based on the logical formalism of quasiaxiomatic theories (QAT). A core element of the described approach

is in use of original machine learning technique - so-called JSMmethod of automated hypotheses formation. The described QATbased technique is used as a tool for analysis of similarities in contents of full-text documents. Finally, possible applications of the presented tools as a practical instrument for automated message understanding are discussed.

KEYWORDSJ quasi-axiomatic theories, plausible reasoning,

machine learning, automated document understan ding.

1. INTRODUCTION

To design a semiotic model of open system in many cases means to provide an ability to process data of different types

describing open (unclosed, partially described, etc.) subject

area. In more details it means to support the following two

characteristic features:

• to provide the ability (for the system controller and for the

model under design) to learn by experience (e.g., by examples^);

• to provide the ability to process (by "unified" data OLAP2

and decision making instruments applied in a "unified" decision making environment) data of different types (e.g.,

symbolic and numeric, structured and unstructured, textual

and graphical, etc.).

Our approach to design the presented type mechanisms

of modeling is based [1] on the so called Quasi Axiomatic

Theories (QAT). Every QAT may be characterized (for more

details see, for example [1] and [4]) by a tuple

r = <z,z\R>

where

• Z is an axiom set (describing a "current state" of the subject area under investigation and the controlled system.

1 I.e. to base current decision making process on the experi- ence of both "good" (i.e. "positive") and "bad" (i.e. "negative") previously made decisions.

2 OLAP - OnLine Analytical Processing.

Roughly speaking it's a set of "empirical dependencies" -

invariant lows3 - describing a situation under analysis); • Z' is a set of empirical statements (i.e., elementary "facts")

characterizing empirical knowledge (e.g., examples of pre- viously made decision, etc.);

• R is a set of reasoning rules consisting of two parts

R = Rr u Rp where

- Rr is a set of reliable inference rules (e.g., rules of deductive inference);

- Rp

is a set of plausible reasoning rules (e.g., formalized

variants of reasoning by analogy rules, "common sense"

reasoning rules, rules of abductive reasoning, etc.).

From our viewpoint the challenge is to provide the designed

semiotic model of the analyzed open system by the following

two features:

• to be able to learn (by use of reasoning rules from

R = Rr u Rp

) new empirical dependencies from

"examples" (i.e. from elements of Z') and

• to be able to use this new dependencies (i.e., procedural

extension of Z processed from Z' by R) in "understanding"

and "processing" of new situations (i.e. control activities in new situations) for open system under analysis.

2. AN APPROACH.

We start from the methodological hypothesis characterizing a formal model of natural language as a set of local dependencies (i.e. grammatical rules, axioms) and a set of exclusions

(i.e. facts, that can not be described by the mentioned axioms).

Our aim is to learn by examples of facts and to extend (where

it's possible) some known rules on new cases (new facts). We

use the JSM-method (see [1]) as the tool of machine learning

and reasoning formalization realized by means of QAT. This

technology may be introduced as a methodological platform

for machine intelligence systems that implement a synthesis of

cognitive procedures. The technology is based on the original

and sophisticated mathematical formalism of inductive learning. The described mathematical formalism provides an effective co-operation of the following reasoning techniques:

3 Providing only partial (i.e. - uncomplete) description of the

situation under analysis.

100
• constructive formalization of abductive reasoning (in the sense of C.S.Peirce);

• constructive formalization of inductive reasoning (in the sense of J. S. Mill);

• automated deduction;

• formalized reasoning by analogy.

The presented tools are oriented on the processing of large

volumes of information in full-text data bases. The discussed

tools provide sufficiently "flexible" and effective search of

documents that are "relevant" to fixed themes. Using this type

tools it's possible to implement NL-text-processing based on

"understanding" documents by computer (this "understanding"

is provided by original instruments that model NL-text semantics by special syntactic structures).

The key characteristic of our text-processing tools is in auto- matic (i.e. implemented by computer) "understanding" of a

target set of full-text documents. This "understanding" is provided in the process of co-analysis of the target texts and

automatically extracted from the semantic structures (so-called

concepts). The discussed concepts are designed in the process

of machine learning by analyzed texts. We use QuasiAxiomatic Theories (QAT) as an original methodological platform for automated text understanding: the techniques used for

machine learning is formalized by means of QAT.

Basic elements of our approach are the following:

• automatic extraction and analysis of the "semantic similarity" classes for processed documents;

• an ability to use, in the process of machine learning, both

positive and negative text-precedents;

• a flexible structure of logical inference rules for document

classification (i.e. for similarity classes generation);

• an ability to combine logical and statistical methods of data

analysis.

The most important features that differs our approach from

other solutions used in the discussed problem area may be

characterized by the following:

• we are able to provide effective machine learning from

small samples of texts-precedents;

• we are able to process automated text "understanding"

based on both positive (i.e. examples of texts that are rele- vant to the analyzed theme) and negative information (i.e. examples of texts that are not relevant to the analyzed

theme);

• we are able to design non-monotonic (i.e. dynamically re- structured in accordance with the extension of text corpora

under analysis) structure of the "semantic similarity"

classes for processed documents.

3. APPLICATIONS

We suppose that QAT-based techniques may be used as a background for a qualitative break and effective spurt in the area of automated text understanding. JSM-style document

processing tools can provide NL-document processing which

realize an automated document clustering (e.g., "natural kind"4

clustering of theme vectors extracted from documents by lin- guistic analysis tools of the ORACLE ConText type [2]). In opposite to the approach based on the analysis of statistical

correlations5 (and realized, for example, in PATHFINDER

[3]) the JSM-style document processing and "understanding"

technique can provide an exhaustive deterministic analysis and

"context-dependent" computational document understanding

We suppose that the most important applications of our theoretical approach and software tools might be designed in the

following problems:

• the improvement of effective and rapid information

searches on the INTERNET;

• automated message understanding;

• automated classification of full-text documents;

• improvement of the text-processing effectiveness for stan- dard document management systems;

• improvement (based on the use of machine learning technique) of effectiveness for information search tools in stan- dard text based information retrieval systems;

• an analysis of "semantic analogy" for sets of full-text documents (e.g., an analysis of how closely connected, in the sense of their content, two sets of texts are);

• automatic diagnostics for the existence of "many aspects"

(multi-dimensional semantics) in the content of the text corpora under analysis;

• automatic diagnostics of a "new content" occurrence caused by an extension of analyzed text corpora by new

elements (i.e. by new texts);

and some other fields, characterizing applications of intelligent

information systems (see for example [5]).

4. REFERENCES

[1] Finn V. K. "Plausible inferences and plausible reasoning".

- Journ. Soviet Mathematics. Plenum Publ. Corp., vol. 56, N 1, 1991.

[2] "CONTEXT: Introduction to Oracle ConTexf - ORACLE

White Paper.- ORACLE Corp., September, 1993.- Pp.1-17.

4

I.e. clustering based on machine learning by examples of

documents that relevant to the processed query (i.e., by so

called positive examples) and by examples of documents that are not relevant to the processed query (i.e., by so called negative examples).

5 More correctly: it is based on the analysis of "distances"

between "lexical units" - e.g., words, themes, ... - and on the

analysis of there "coexistence" in analyzed documents.

101
[3] "PATHFINDER (Version 7.0)".- User's Guide. - Pre- August 1995, Monterey, CA. - AdRem, Inc., 1995. - Pp. 99-

search Inc., Fairfax, VA. - 1994. 108.

[4] Zabezhailo M.I. et al. "Reasoning Models for Decision

Making: Applications of JSM-Method for Intelligent Control

Systems". - Architectures for Semiotic Modeling and Situa

[5] Zabezhailo M.I., Finn V.K. 'Intelligent information sys- tems". - International Forum on Information and Documentation (FID, The Hague, Netherlands).- 1996. - Vol.21. - N2. - Pp.2 1-31

Hon Analysis in Large Complex Systems.- Proc. of the Workshop of 10th (1995) IEEE Symp. on Intelligent Control

(Eds.: J.Albus, A.Meystel, D.Pospelov, T.Reader). - 27 -29

102
NonMonotonic Reasoning in the Modal Quantificational Logic Z

Frank M. Brown

Artificial Intelligence Laboratory

University of Kansas

Lawrence, Kansas, 66045

brown@eecs.ukans.edu

Abstract

Nonmonotonic reasoning can be recursively

axiomatized as a formal axiomatic theory which is monotonic. This paper describes how this is done

beginning with an axiomatization of logical truth with

the modal quantificational logic Z which builds on

previous works of Leibniz, Carnap, Prior, and

especially Bressan. It explains how to form default

statements in terms of modal possibility with respect

to a theory, how to reduce possibility with respect to a theory to logical possibility, how to determine when

something is logically possible, how to form

reflective equations where the default is formed using

the theory containing the default itself, how to solve

various types of reflective equations in

quantificational logic to obtain their "fixed points",

and how to deal with multiple solutions by taking

their commonalty. In a broader sense this work

supports Lewis's original claim that modal logic is a missing part of classical logic in that it illustrates how

classical logic extended with modal logic accounts

for nonmonotonic reasoning.

1. Introduction

NonMonotonic Reasoning is a form of deductive

reasoning that allows general laws to be asserted and

general conclusions to be drawn from them without

contradiction in the presence of numerous exceptions.

For example, in a nonmonotonic system one may

assert the general law that birds fly even though we

also know that penguins are birds which do not fly. In a nonmonotonic system the assumption that there

are such penguins will not be contradictory. This is achieved by representing general laws as defaults

rather than merely as universally quantified

implications. Thus instead of writing "birds fly" as

for all x if x is a bird then x flies: Vx((bird x) -»(fly x))

it is written as for all x if x is a bird and if it is logically possible with respect to a theory T for x to

fly then x flies: (Vx((bird x WoCrWflv xV)) ^>ffly x))))

The underlined phrase speaks of logical possibility

thereby implying a reduction of nonmonotonic

reasoning to modal logic There are of course many

different modal logics, but there is one that is particularly relevant, namely the modal

quantificational logic Z [Brown90] whose possibility

operator is analogous to the semantical concept of

satisfiability in classical first order logic. For all sentences T of first order logic,

(Satisfiable (kwote Y)) if and only if (<> T)

where (kwote V) is the name of T in the metatheory.

The remainder of this paper describes nonmonotonic

reasoning in terms of the Z modal logic. Z is axiomatized in Section 2. Proof techniques for

determining what is logically possible are given in

Section 3. Section 4 introduces reflective equations

and describes an approach to solving them. Section 5

describes the propositional quantifier disjunction

idiom, which is used to represent the disjunction of

solutions to a reflective equation. Some conclusions

are drawn in section 6.

2. Axiomatization of Z Modal Logic

The modal quantificational logic Z is an eight tuple:

(—>, #f, V, =, [], vars, predicates, functions) where —>, #f, V, =, and [] are logical symbols, vars is a set of variable symbols, predicates is a finite set of

predicate symbols each of which has an implicit arity

specifying the number of terms to be associated with

that predicate, and functions is a finite set of function

symbols each of which has an implicit arity

specifying the number of terms to be associated with

that function. The set of logical symbols, the set of

variables, and the set of predicate and function

symbols are pairwise disjoint. The set of terms is the

smallest set which includes the variables and is closed under the process of forming new terms from

other terms using the functions symbols of the

language. The set of sentences is the smallest set which includes #f, the variables, and each of the

predicates followed by an appropriate number of

terms, and is closed under the process of forming new

sentences from other sentences using the logical

symbols of the language, provided that no variable in any subexpression of a sentence has free occurrences both as a sentence and as a term. Variables which

occur only in term positions are called object

variables. Variables which occur only in sentence

positions are called propositional variables. Roman

letters possibly indexed with digits are used as

variables of Z; for example: p, q, r, w, v, xi...xn,

yi...y n. Greek letters are used as syntactic

metavariables, y ranges over the variables, k, 7ii...7tn range over the predicate symbols, °°, °°i...°°n range

103
over function symbols, 8, 5i...8 n range over terms,

and a, ai...an , P, Pl-Pn. r, and Ti ...rn range over

sentences. Thus, the terms are of the forms y and (°°

81. ..6n), and the sentences are of the forms (a —>P),

#f, (Vy a), (Qa); (tc 8 i...8n), (5i=82 ), and y. A

nullary predicate n or function °° is written as a

sentence or term without parentheses, i.e., k instead

of (ji) and °° instead of («>).

The primitive symbols of Z are shown in figure 1 Symbol Meaning

a—> P if a then 3- #f falsity

Vy a for all y, a. 81=82 81 is (contingently) equal to 82. n a a is logically necessary

Figure 1: Primitive Symbols of Z

The defined symbols of Z are listed in figure 2 below

Symbol Definition Meaning

—.a a->#f not a

#t -, #f truth avP (-i a)-> 0 a or P

aA3 ^a-*.-.B) a and 3

cc<h> P (a-> P) a (p-» a) a if and only

if 3

3y a -iVy-ia some p is a

<> a -.[]-.« a is logically

possible

a^p [](a^P) a and 3 are synonymous

[PI a (ri(B->a)) 3 entails a

<P> a (<>( Pacx)) a is possible

in 3

81[=]82 (<8i=«2)) 81 necessarily

equals 82

(world a) (<>a)A

(Vy(([a]y)v([a]^y)))

where y is not in a

a is a world

(gen a) (v(3yn...ymi (a= ("1 Yll-Yml)))) - (3Yln-Ymn

(as(7tn Yln-Ymn)))))

where all the

predicates are 7ii ...7T n and the arity of 7ri is mj and for each i and

j, Tij is a distinct

variable not in a

a is a generator

Figure 2: Defined Symbols of Z

are recursive. The classical (i.e., non-modal) axioms

and inference rules of Z include those of

quantificational logic [Mendelson] given in figure 3. The laws MR1, MR2, MAI, MA2, MA3, MA4,

MA5, MA6, and MA7 are a standard set of axioms

and inference rules for first order quantificational

logic except for the following two points: First,

because y in laws MR2 and MA4 may be a

propositional variable these two laws constitute an

additional fragment of 2nd order logic beyond first order logic. Propositional quantification in modal

logics has been investigated by [Fine 70]. A

conceptual interpretation of quantification [Garson

84] is at the heart of this logic, although this will not

be noticed until one deals with necessity, because all the normal laws of first order logic hold otherwise.

MR1: from a and (a—> P) infer p

MR2: from a infer (Vy a)

MAl:a->(p-> a)

MA2: (a-» ( p-> p)) -> ((a-> P)-» (a-> p))

MA3: ((-n a)-> (-n P))-> (((-, a)-> P)->a)

MA4: (Vya)-> P

where Pis the result of substituting an

expression (which is free for the free positions

of y in a) for all the free occurrences of y in a. MA5:((Vy(a^P))^ (a->(Vyp)))

where y does not occur in a. MA6: ((x=y)->

((Ai, n (On zii...x...zmi)^(7ti zi j...y...zmi))) A(Ai, n2((ooj zii...x...zm0=(ooi zii...y...zmi))))

where 7ti ...7Cn are all the predicates

and °°\...°°r\2 are all the functions.

MA7: x=x

Figure 3: The Classical Rules and Axioms of Z

Z is effectively axiomatized with a recursively

enumerable set of theorems as the set of axioms is

itself recursively enumerable and its inference rules

The modal inference rule and axioms of Z which are about logical necessity (i.e., []) are given in figure 4. The laws R0, Al, A2 and A3 constitute an S5 modal

logic[Hughes&Cresswell 68] which, with the

nonmodal laws, is similar to [Carnap46,Carnap56]

and a first order logic version of [Bressan 72]. A4

says that a proposition is logically necessary if it is entailed by every world proposition. This law was

implied in [Leibniz] and has been used by a number

of authors including [Prior&Fine 77, Fine 70]. Laws

A5, A6, and A7 axiomatize the predicates. A5 is the

key axiom which says that any exhaustive

conjunction of negated or unnegated distinct

generators is a world, provided that there is a sentence a expressible in the formal language of Z

which holds when p is an unnegated generator of that conjunction. Like the A5 axiom in [Brown87] it handles quantifiers over arbitrary domains. The A5

axiom is far stronger than the trivial modality axioms

such as 3pq((-.[p]q)A(-i[p]-.q)) assumed in [Lewis

36] and 3p((op)A(<>—.p)) assumed in [Bressan 72].

It also extends certain axiom schemas used in

propositional logic S5c [Hendry&Pokriefka 85] and

104
propositional logic S13 [Cocchiarella]. Laws A6 and

A7 axiomatize the intensionality of predicate

arguments and are compatible with Bressan's

[Bressan 72] view that predicates map tuples of

concepts into propositions. Laws A8 and A9

axiomatize the functions which may be viewed as

(world(Vp((3x3y(p=(loves x y)))

v(3x(p=(happy x))))

->(p<->[](p=(happy John)))))

By S5 modal logic this becomes:

(world

((VxVy((loves x y) <-> ((loves x y)s(happy John))))

a(Vx((happy x)<->((happy x)=(happy John))))))

By Axioms A6 and A7 this becomes:

(world((Vx((loves x y)<-» #f>)

A(Vx((happy x)f->(x[=]John)))))

Since, by definition, worlds are logically possible it follows that: <>((Vx((loves x y)<^ #f))

A(Vx((happy x)<-»(x[=]John))))

Since (<>(oa(3)) implies (<>(3) in S5 it follows that: <>Vx((happy x)<-> (x[=]John)

The main problem with using axiom scheme A5 to prove that something is logically possible lies in

finding the appropriate substitution for the parameter

a. The theorem ZP1 given below is the basis of a

heuristic for finding such instances. Intuitively, we

know that the conjunction of instances of a predicate

and the conjunction of instances of the negation of a predicate are logically possible whenever the two do

not coincide on any instance. For example: ((p a)A(p

b)A(-i(p c))) is logically possible but ((p a)A(p

b)A(-i(p a))) is not. Thus if a sentence can be written

in the form: (rA(Vx(a^(p x)))a(Vx(P->(-.(p x)))))

where p does not occur in a, (3, and T, then it is logically possible if and only if {x:a}n{x:P) is empty, which is to say that 3x(ccaP) does not follow

from T or to say that V and —i3x(oa|3) is logically

possible. In this manner determining whether a sentence with n predicates is logically possible can sometimes be reduced to determining whether a sentence with n-1 predicates is logically possible

without having to guess any instances of the A5.

Theorem ZP1: The possibility of a disjoint predicate

definition: If r , a , and P

are sentences of Z

containing no unmodalized occurrence of the

predicate n, =, or a propositional variable, k is of

arity n, and x=xl...xn is a tuple of n variables then:

(<>(rA(Vx(<x-»(rc x)))a(Vx(P->^(tt x)))))

<-^(<>(rA(-i3x(aAp))))

Proof

Assume: n is not in T, a, nor p then

(<>(rA(Vx(CC-K7T x)))A(Vx(P-^-n(7T x)))))

<-K<>(rA(-dx(aAp))))

divides into two cases: Case 1: (<>(rA(Vx(a->(7c x)))a(Vx(P->-.(7c *)))))

^(<>(rA(-n3x(oAp))))

resolving on the implications with n and —iTt gives:

(<>(rA(Vx((X^(7l X)))A(VX(P-MJC X))))

A(Vx(-.av-,p))) -»(<>(rA(-ax(ciAp))))

which may be rewritten as:

mappings of tuples of concepts into concepts.

RO: from a infer ([] a)

Al: ([]p)-»p

A2: ([p]q) -> (([]p)-» (Dq))

A3: ([]p)v([]-,[]p))

A4: (Vw((WORLD w)->([w]p))) -> []p

A5: WORLD(Vp((GEN p)-)(pH[]a)))

for every expression a. A6: -,(= (jci xi„.xn)(JC2 yi-ym))

where k\ and K2 are different predicate symbols.

A7: ((TCXi...xn)=(7c yi.,.yn))

<-> ((xi[=]yi)A....A(x n [=]y n)) A8: -.((*»! xi...x n)[=](<~2 yi-Ym))

where <»i and °°2 arc different function symbols.

A9: ((°° xi...x n)[=](°° yi...y n ))

<-> ((xi[=]yi)A..A(xn[=]yn))

Figure 4: The Modal Rule and Axioms of Z

Example : A parucular Z language contains the binary

predicate: loves and the unary predicate: happy, the

unary function father-of, and the 0-ary function John.

The definitions and axioms depending on the this

language are as follows. First, the generators are defined to be those propositions beginning with the

loves and happy properties:

(gen a) =df(3x3y(a=(loves x y)))v(3x(a=(happy x)))

The equality axiom MA6 becomes:

MA6: x=y -> (((loves x z)<->(loves y z))

A((loves zx)b (loves z y))

A((happy x)<-» (happy y))

A((father-of x)=(father-of y)))

Using the above definition of generators, the axiom

scheme A5 becomes:

A5: (world(Vp((3x3y(ps (loves x y)))

v(3x(p= (happy x))))

->(p<->[]ct)))

for every expression a. Finally, axiom schemas A6,A7,A8, and A9 become:

A6: -.((loves xl x2)=(happy yl))

A7a: ((loves xl x2)=(loves yl y2))

^((xl[=]yl)A(x2[=]y2))

A7b ((happy xl)=(happy yl)) xl[=]yl)

A8: -.((father-of xl)[=ljohn)

A9: ((father-of xl)[=](father-of yl))<-> (xl[=]yl)

3. What is Logically Possible?

Axiom scheme A5, which has a recursively

enumerable number of instances, expresses what is logically possible to the extent that it can be so

expressed. In the previous example, instantiating a

in A5 to (p=(happy John) produces:

105
(o(rA(Vx(oc->(jc x)))a(Vx(P-Mtc x))))

a(-,(3x(oaP)))) -^(<>(rA(^3x(aAP))))

which holds by the laws of S5 modal logic.

Case 2: (o(TA(-n3x(OAP))))

-»(o(TA(Vx(a-»(jc x)))a(Vx(P-*-.(jc x)))))

Using axiom A4 twice we get:

(3 w((world w)a([w] (rA(-^3x(OAp)))))) —>(3w((world w)

A([w](rA(Vx(a->(7tx)))A(Vx(p-»-,(7Cx)))))))

Let (h w) represent the world in which (it x) holds if and only if a holds in w and every other generator

holds if and only if it holds in w:

(h w):= Vg(Gen g)->(g<->((3x((gs(7c x))a([w]cc)))

v(K3x(g<rcx))))A([w]g))))

By A5 (h w) is a world. From this assignment it follows that: ([(h w)](Vx((7C x)*->([w]a)))). The w in the conclusion is instantiated to (h w) giving:

((world w)A([w](rA(-3x(tXAP)))))

->([(h w)](Ta(Vx((x->(7C x)))a(Vx(P^(tt x)))))

Since ([(h w)](Vx((tc x)<->([w]a)))), (it x) may be

replaced by ([w]a) giving:

((world w)A([w](rA(-n3x(OAp)))))

->([(h w)](TA(Vx(a^([w]a)))A(Vx(P^([w]a)))))

Pushing -1 through the the world w entailment gives:

((world w)A([w](rA(-n3x(OAp)))))

->([(h w)](rA(Vx(a-^([w]a)))A(Vx(P->([w]-,a)))))

The hypothesis may be rewritten giving:

((world w)A([w]rA(Vx(p-*-.a))))

->([(h w)](rA(Vx(a->([w]a)))A(Vx(P->([w]-,a)))))

Reducing the scope of [w] in the hypothesis gives

((world w)A([w]r)A(Vx(([w]p)->([wHa))))

->([(h w)](rA(Vx(a^([w]a)))A(Vx(p->([w]-na)))))

Since [w]-.a is implied by [w]P if it is entailed by

[w]p, it suffices to prove:

((world w)a([w]Da(Vx(([w]P)-K[w]-.cO)))

->([(h w)](rA(Vx(a^([w]a)))A(Vx(P->([w]P)))))

Reducing (h w) to lower scope gives:

((world w)a([w]Oa(Vx(([w]P)-K[w]-iOO)))

->(([(h w)]r)A(Vx(([(h w)]a)->([w]a)))

A(Vx(([(h w)]P)^([w]P))))

Since it, =, nor any propositional variable occur unmodalized in F, a, or p, (h w) entails these

sentences if and only if w does, thus (h w) in the

conclusion may be replaced by w giving:

((world w)A([w]r) A(Vx(([w]p)-K[w] -«))))

-K([w]r)A(Vx(([w]a)-+([w]a)))

a(Vx(([w]P)->([w]P))))

which is a tautology. QED.

ZP1 is applicable to any theory (such as propositional

logic, monadic predicate logic, and the case of a finite theory) which can be put into a prenix conjunctive

normal form such that no disjunct contains more than one unmodalized occurrence of it, since by the laws

of classical logic such theories are equivalent to a

disjunction of expressions of the form: (Fa(Vx(o:—Ktt x)))a(Vx(P-Mtc *))))•

Example: The database K contains the following

facts: Tweety and Chilly-Willy are birds, but (being a penguin) Chilly-Willy does not fly. By default birds

fly. That is, for all x, if it is possible (with respect to the theory that Tweety and Chilly-Willy are birds,

and Chilly-Willy does not fly) for x to fly, then x

does fly:

K=((bird cw)A(bird tw)A(-,(fly cw))

A(Vx((bird x)

A«bird cw)A(bird tw)A(-i(fly cw))>(fly x))

-Kflyx))))

The possibility may be rewritten by the laws of Z so

as to divide the positive and negative occurrences of

the predicate fly as follows:

<>((bird cw)A(bird tw) AVz((z[=]x)->(fly z))

AVz((z[=]cw)->(-<fly z))))

Using ZP1 with r:=(bird cw)A(bird tw), x:=z, 7c:=fly, oc:= (z[=]x), and P:= (z[=]cw) gives the equivalent

possibility:

<>((bird cw)A(bird tw)

a(^(3z((z[=]x)a(z[=]cw)))))

Since [=] is transitive, symmetric and reflexive the 3z

quantifier may be eliminated giving:

<>((bird cw)A(bird tw)A-!(cw[=]x))

The same process is now applied to the Bird

predicate. First it is rewritten as: <>Hcw[=]x))

AVz(((z[=]cw)v(z[=]tw))->(bird z))

AVz(#f-K^(bird cw))))

Using ZP1 with T: =-n(cw[=]x), x:=z, 7t:=bird,

a:=(z[=]cw)v(z[=]tw), and p:=#f gives the equivalent

possibility:

<>(-,(cw[=]x))A(^(3z(((z[=]cw)v(z[=]tw))A#f)))

which by classical logic is just: <>(—i(cw[=]x)) which

by Z is just: (->(cw[=]x)). Therefore, the original

expression then becomes:

Ks((bird cw)A(bird tw)A(-,(fly cw))

A(Vx(((bird xK-(cw[=]x))-Kfly x))))

which is equivalent in Z to: K=((bird tw)A(bird cw)

A(Vx((bird x)->((fly x)<->-.(x[=]cw)))))

The sentence: Vx((bird x)->((fly x)^-> ->(x[=]cw)))

which contains a necessary equality entails the non- modal sentence: Vx((bird x)—>((fly x)«-1 (x=cw))).

ZP1 implies that contingent definitions added to a

theory are conservative extensions:

Theorem ZP2: Definability of a predicate: If T,a are sentences of Z containing no unmodalized occurrence of a predicate it, =, or propositional variable then:

(<>(rA(Vx((rr x)m))))f)(or)

proof: Let P be -ia in ZP1 and simplify. QED.

4. Reflective Reasoning in Z

One problem with computing defaults with respect to a theory T is that the default itself is not part of the

theory T. When T essentially contains a disjunction

106
this often causes the resulting theory to be

inconsistent. For example, if r were the statement

that either Tweety does not fly or Chilly-Willy does

not fly then the proposition that Chilly-Willy does

not fly is possible with T and likewise the proposition

that Tweety does not fly is also possible with T. Thus both propositions would be true by default.

Unfortunately, their conjunction contradicts T if it were also asserted. Thus, the following is #f:

((bird cw)A(bird tw)A((-i(fly cw))v(-.(fly tw)))

A(Vx((bird x)A(<(bird cw)A(bird tw)

A((-,(fly cw))v(-,(fly tw)))>(fly x))

-Kflyx))))

For this reason, the expression is reformulated so that

the default itself becomes a proposition within the

possibility expression. This is done by writing a

reflective (i.e. fixed point) equation in K where the

variable K is made synonymous to the theory and the

default and where K replaces T in the default itself: K=((bird tw)A(bird cw)A((-i(fly cw))v(-.(fly tw)))

AVx(((bird x)A(<K>(fly x)))-Kfly x)))

A reflective equation has the form K=(0 K) where K

is a propositional constant (i.e. a globally scoped

universally quantified variable such as a Skolem

function). The goal is to transform the initial

equation into a disjunction, ((K= Pi)v...v(K= pn)) with each pi free of K. If K= Pi implies the original

equation then Pi is a solution to the original equation.

We call the process of finding solutions to a reflective

equation reflective reasoning.

Example: A Reflective Equation: Tweety and ChillyWilly are birds. At least one of them does not fly.

By default Birds Fly.

(K=((bird tw)A(bird cw)A(-,fly tw)v(-,fly cw))

A(Vx(bird x)A(<K>(fly x))-»(fly x))) )) where bird and fly are lary predicates. To solve this equation we divide the default into three instances:

(Ks((bird tw)A(bird cw)A(-ifly tw)v(—,fly cw))

A(<K>(fly tw))-Kfly tw))) )) A(<K>(fly cw))-»(fly cw))) )) A(Vx(birdx)A(-,((x[=]tw)v(x[=]cw)))

A(<K>(fly x)) -K^fly x))) )) Splitting into 4 cases we then get:

((<K>(fly tw)) a (<K>(fly cw))

A(K=((bird tw)A(bird cw)A((-,fly tw)v(fly cw)

A(fly tw)A(fly cw)

A(Vx((bird x)A(-.((x[=]tw)v(x[=]cw)))

A(<K>(fly x)) H(flyx)))

v((<K>(fly tw)) A(^<K>(fly cw)))

A(K=((bird tw)A(bird cw)a((—,fly tw)v(-ifly cw))

A(fly tw)

A(Vx(birdx)A(-.((x[=]tw)v(x[=]cw)))

A(<K>(flyx)) ^(flyx)))))

v((-,<K>(fly tw))A (<K>(fly cw))

A(Ks((bird tw)A(bird cw)A((-ifly tw)v(-ifly cw)

A(fly cw)

A(Vx(bird x)a(-,((x [=] tw)v(x[=]cw)))

A(<K>(flyx)) -Kflyx)))))

v((-,<K>(fly tw))A(-,<K>(fly cw)))

A(Ks((bird tw)A(bird cw)A((-,fly tw)v(-,fly cw))

A(Vx(bird x)A(-.((x[=]tw)v(x[=]cw)))

A(<K>(flyx)) -»(flyx))))))

which simplifies to:

( (<K>(fly tw)) a (<K>(fly cw))a(Ks#0) easel

v((<K>(fly tw)) A(-n<K>(fly cw))) case2

A(K=((bird tw)A(bird cw)A(-ifly cw)A(fly tw)

A(Vx(birdx)A(-.((x[=]tw)v(x[=]cw)))

A(<K>(flyx))->(flyx)))))

v((-,<K>(fly tw))A (<K>(flycw)) case 3

A(K=((bird tw)A(bird cw)A(-.fly tw)A(fly cw)

A(Vx(birdx)A(-i((x[=]tw)v(x[=]cw)))

A(<K>(fly x)) -Kfly x)))))

v((-i<K>(fly tw))A(-i<K>(fly cw))) case 4

A(Ks((bird tw)A(bird cw)A((-1 fly tw)v(-ifly cw))

A(Vx(birdx)A(-n((x[=]tw)v(x[=]cw)))

A(<K>(fly x)) ->(fly x)))))) In case 1, since K is #f, which cannot be possible,

that case is eliminated. In case 4, the negated

possibilities say that [K](-,fly tw)A[K](-ifly cw), but

since the equation implies that: [((bird tw)A(bird cw)A((-ifly tw)v(-ifly cw))

A(Vx(birdx)A(-.((x[=]tw)v(x[=]cw)))

A(<K>(fly x)) ^(fly x))))))]K

it could only hold if: [((bird tw)A(bird cw)A((-,fly tw)v(-,fly cw))

A(Vx((birdx)A(-.((x[=]tw)v(x[=]cw)))

A(<K>(flyx)) -»(fly x))))]

((-ifly tw)A(-,fly cw))

but the negation of this is o((bird tw)A(bird cw)A((-.fly tw)v(-ifly cw))

A(Vx((birdx)A(-.((x[=]tw)v(x[=]cw)))

A(<K>(fly x)) ->(fly x))))))

A((fly tw)v(fly cw))

which is implied by:

<>((bird tw)A(bird cw)A((-ifly tw)v(-.fly cw))

A(Vx((bird x)A(-,((x[=]tw)v(x[=]cw)))-*(fly x))))

A((fly tw)v(fly cw))

which is true by ZP1. So this case is also false and

may be eliminated. For the remaining two cases the

inequalities are repeated inside the possibilities:

(((<K>(fly tw))A(-,<K>(fly cw))) case2

A(K=((bird tw)A(bird cw)A(-.fly cw)A(fly tw)

A(Vx((birdx)A-,((x[=]tw)v(x[=]cw))

A(<K>((-,((x[=]tw)v(x[=]cw)))->(fly x)))

->(flyx)))))

v((^<K>(fly tw))A(<K>(fly cw)) case 3

A(Ks((bird tw)A(bird cw)A(-nfly tw)A(fly cw)

A(Vx(birdx)A(-i((x[=]tw)v(x[=]cw)))

A(<K>((-n((x[=]tw)v(x[=]cw)))->(fly x)))

-Kflyx)))))

Since the parts inside the <> of the following two

sentences entail K for cases 2 and 3 respectively, and

since they are #t by ZP1:

<(bird tw)A(bird cw)A(-,fly cw)A(fly tw) for 2

A(Vx((bird x)A(-,((x[=]tw)v(x[=]cw)))-Kfly x)))>

107
A((-.((x[=]tw)v(x[=]cw)))-Kfly x)))

<(bird tw)A(bird cw)A(-.fly tw)A(fly cw) for 3

A(Vx((bird x)A(-,((x[=]tw)v(x[=]cw)))-Kfly x)))>

A((-.((x[=]tw)v(x[=]cw)))-Kfly x)))

the above cases 2 and 3 simplify to just:

(((<K>(fly tw))A(-.<K>(fly cw))) case2

A(K=((bird tw)A(bird cw)A(-,fly cw)A(fly tw)

A(Vx((birdx)A-.((x[=]tw)v(x[=]cw))A#tA

^(fly x)))))

v((-,<K>(fly tw))A(<K>(fly cw)) case 3

A(K=((bird tw)A(bird cw)A(-ifly tw)A(fly cw)

A(Vx(birdx)AK(x[=]tw)v(x[=]cw)))A#tA

-Kfly x)))))

Substituting the solution for K in each case into the

remaining possibility statements and using ZP1 gives:

((#tA#tA(K=((bird tw)A(bird cw)A(-,fly cw)A(fly tw)

A(Vx((bird x)A-.((x[=]tw)v(x[=]cw))A-<fly x)))))

v(#tA#tA(K=((bird tw)A(bird cw)A(-ifly tw)A(fly cw)

A(Vx(bird x)A(-,((x[=]tw)v(x[=]cw)))A^(fly x)))))

By the laws of classical logic this simplifies to: ((Ks((bird tw)A(bird cw)

A(Vx((bird x)->((fly x)h->(x[=]cw))))

v(K=((bird tw)A(bird cw)

A(Vx((bird xH(fly x)<-Mx[=]tw)))))

which results in a disjunction of two solutions; one where cw is the only bird which does not fly and one where tw is the only bird which does not fly.

5. Propositional Quantifier Idiom

When a reflective equation has more than one

solution there arises the question as to which solution

is to be used. One way of avoiding this question is to adopt the conservative approach of only accepting

what is common to all the solutions. This is achieved

with the idiom: K=3k(kA(ksa)) which may be read

as the database K is the (possibly uncountably

infinite) disjunction of all the solutions k to the

reflective equation k=a. When there are a finite

number of solutions Pi-.-Pn to such an equation:

(k=Pi)v...v (k=pn), the expression 3k(kA(k=a)) is equivalent to 3k(kA((k=Pi)v...v(kspn))) which by

the distribution properties of a and v and by the fact that 3 associates through v gives the equivalent

expression: (3k(kA(ksp1 )))v...v(3k(kA(kspn))). Since 3k(kA(k=P})) is logically equivalent to just Pi

K will be equivalent to the disjunction of solutions:

Piv...vpn . For example, the disjunction of solutions

from section 4 gives:

K=((bird tw)A(bird cw)A(-ifly cw)*->(fly tw)

A(Vx(((bird x)A-n((x[=]tw)v(x[=]cw)))->(fly x)))

6. Conclusion

Nonmonotonic reasoning captures a deep and

important aspect of human reasoning. Essentially it allows us to express laws and to reason without

cluttering up our laws with numerous exceptions.

The Modal Quantificational Logic Z provides an

effective (i.e. recursively enumerable) method for

automatically deducing nonmonotonic consequences

for many interesting problems. Z improves upon

previous methods of defining nonmonotonic

reasoning via complicated metatheories by allowing

for quantification through modal scopes and by

eliminating those theories' inherent ineffective

processes for computing consistency. In a broader

sense, Z supports Lewis's [Lewis 36] original claim

that modal logic is a missing part of classical logic in that this modal logic also accounts for nonmonotonic

reasoning.

Acknowledgments

This research was supported by the National Science

Foundation Grant No. MIP9526532. I thank Guy

Jacobs for his help.

References

Bressan.Aldo, A General Interpreted Modal

Calculas, Yale University Press, 1972.

Brown87a,F.M. "The Modal Logic Z", The Frame

Problem in AI: Proceedings of the 1987 AAA!

Workshop, Morgan Kaufmann, LosAltos.CA 1987.

Brown91,Frank M., "The Modal Quantificational

Logic Z Applied to the Frame Problem",

International Journal of Expert Systems Research

and Applicatiions, Special Issue: The Frame

Problem. Part A. eds. Keneth Ford and Pattrick

Hayes, vol. 3 number 3, ppl69-206 JAI Press

1990. Reprinted in Reasoning Agents in a Dynamic World: The Frame problem, editors:

Kenneth M. Ford, Patrick J. Hayes, JAI Press 1991.

Carnap46, Rudolf, "Modalities and Quantification"

Journal of Symbolic Logic, vol. 1 1 , number 2, 1946.

Carnap56, Rudolf, Meaning and Necessity: A Study

in the Semantics ofModal Logic, The University of

Chicago Press, 1956.

Cocchiarella,N.B., "Philosophical Perspectives on

Quantification in Tense and Modal Logic",

Handbook of Philosophical Logic, D. Reidel,1984

Fine, K., "Propositional Quantifiers in Modal Logic"

Theoria 36, 1970.

GarsonJ.W. "Quantification in Modal Logic",

Handbook of Philosophical Logic, Volume II, Extensions of Classical Logic, 1984.

Herbert E. Hendry and M. L. Pokriefka, "Carnapian

Extensions of S5", Journal ofPhil. Logic 14, 1985.

Hughes,G.E. and Creswell,M.J., An Introduction to Modal Logic, Methuen & Co. Ltd., London, 1968.

Leibniz.G. "Necessary and Contingent Truths" 1686,

Leibniz Philosophical Writings, Dent&Sons. 1973.

Lewis.C.I. Strict Implication, Journal of Symbolic

Logic, vol I. 1936.

Mendelson.E. Introduction to Mathematical Logic,

Van Norstrand, Reinhold Co., New York, 1964.

Prior.A.N. & Fine,K., Worlds, Times, and Selves,

Gerald Duckworth, 1977.

108
V LEARNING

INDUCTIVE THEORY OF SEMIOTIC SYSTEMS

Lev Goldfarb

Faculty of Computer Science

University of New Brunswick

Fredericton, N.B., E3B 5A3, Canada

goldfarb@unb.ca

Induction, which has been called the "scandal of philosophy", has become the

scandal of psychology and artificial intelligence as well.

J. H. Holland et al., Induction (1986)

ABSTRACT — In light of the ongoing discussion about

the name of the emerging field, I propose and partly motivate the name Inductive Semiotic Systems as an appropriate one. The three postulates given in section 5 capture the essence of the justification for the proposed name. They can

be further reduced to the following. Since all objects, in the

universe have emergent compositional structure, the term

"object structure" (and therefore the term "meaning" ) can- not be properly understood, defined, and captured outside

the inductive learning process. Such a process, based on the

appropriate formal mathematical structure, try to capture

the object-class structure by constructing the "inductive

sign" that represents in the given context both the object

and the corresponding class of objects. Moreover, I conjecture that all other representations and semiotic processes

have evolved around these, inductive, representations. The

main link with the classical sciences is outlined: the working hypothesis (which we currently pursue) that the proper

sensors for all intelligent systems are symbolic, or inductive,

measurement devices, a far-reaching generalization of the

classical, or numeric, measurement devices. In this connection, I briefly review the inductive nature of the cognitive

processes responsible for the emergence of numbers.

Keywords: intelligent systems, symbolic representations,

numbers, inductive learning, inductive class representation,

evolving transformation system, symbolic (inductive) measurement devices.

1. INTRODUCTION

This paper was motivated by a number of developments

all originating from my work on the foundation of pattern recognition began 20 years ago and intended to

This work is partially supported by the NSERC research

grant number OGP0002686.

unify the two basic but incompatible approaches: vector space, or the classical statistical, approach, and formal grammar, or the syntactic, approach. The work

gradually culminated in a fundamentally new mathematical model, Evolving Transformation System (ETS),

that attempts to capture formally the nature of "symbolic" representations [1, 2, 3, 4, 5]. The model eventually led to the outline of the inductive theory of vision

[6], which, in turn, prompted the re-examination and

generalization of the classical, or numeric, measure- ment processes [7]. What, basically, motivated a se- rious re-examination of the classical measurement processes is not, as one might expect, the well-documented

problematic state of the quantum measurement problem, but the realization that ETS embodies a fundamental generalization of the classical mathematical concept of (measurement) space [8, 9] such that the former

cannot be reduced to the latter. In other words, it became clear that most processes in a symbolic representation space are not reducible to those in a numeric

space, the fact whose importance cannot be overes- timated. In particular, ETS suggested that the currently accepted understanding of biological information

processing (inevitably dictated by our current state of

measurement and instrumentation) as proceeding from

numeric to symbolic representations is not correct: all stage of biological information processing, including the

initial stage of transduction, can properly be understood using the appropriate symbolic representations

only [10].

Thus, with the understanding of fundamental irreducibility of the symbolic, or semiotic, processes to the

numeric ones, the question of the structure of intelligent

semiotic systems could be addressed in a more appro111
priate and satisfactory manner, i.e. the basic formal

language should be that of a formally specified "symbolic" mathematical model, or ETS. Since the latter was developed to capture the nature of inductive learning processes, it is quite natural to call the emerging

theory the inductive theory of semiotic systems. Moreover, the name is also (and mainly) justified on the

basis of the fact that, according to the ETS, the modification of "geometry" of the symbolic representation

space, and, as it turns out, of the very representation

itself, is actually accomplished during inductive learning processes, which thus emerges as the central intelligent processes. It appears also that the concept of

emergent representation cannot be adequately understanding outside inductive learning processes.

The exposition in the paper is as informal as possible in order to be accessible to a wider range of re- searchers, and therefore no technical details of the ETS

model, which led to all the considerations, are given.

2. THE CENTRAL ROLE OF INDUCTIVE

LEARNING PROCESSES

The pre-eminent role of inductive processes in epistemology and science has been recognized almost from

the very beginning and increasingly so as science matured. Thus, passing Bacon, Hume, Mill and confining

ourselves to the latest period, this century, we find, for

example, B. Russell devoting to induction a chapter in

his book "Problems of Philosophy" (1912). In "Outline

of Philosophy" (1927) he states:

Induction raises perhaps the most diffi- cult problem in the whole theory of knowledge. Every scientific law is established by

its means, and yet it is difficult to see why

we should believe it to be a valid logical

process. . . . When mankind took to sci- ence, they tried to formulate logical principles justifying this kind of inference. I will

only say that they seem to me very unsuccessful. I am convinced that induction must

have validity of some kind in some degree,

but the problem of showing how or why it can be valid remains unsolved.

Another leading philosopher, A.N. Whitehead, in spite

of the basic philosophical differences with his important collaborator B. Russell, in "Science and the Modern World" (1925) also agrees with the latter on the

important role of induction: "The theory of induction

is the despair of philosophy—and yet all our activities are based upon it"

.

Before proceeding further, a "fresh" model-independent

definition of inductive learning process proposed by me

might be useful.

Definition: Given a small finite set C+ of positive

objects that are randomly chosen from a (possibly infinite) class C—class to be learned—and a small finite set C~ of negative objects, i.e. not from C, the inductive learning process has to construct an inductive class

representation (ICR) of C such that

• ICR can generate an approximation Capp of C,

and

• if C*

pp

is a noisy perturbation of Capp and C*

is a noisy perturbation of C, then the ratio of

cardinalities

\C*\

is close to 1.

Note both the generative (and, therefore, mainly discrete) nature of the ICR, as well as a fuzzy boundary

of the "generated" class (and, therefore, the presence

of continuous element in the ICR, which is not obvious

from the definition). These two features, combined in a

natural way, make the above definition unique among

the other definitions of inductive learning processes.

Furthermore, both of them are supported by psychological experiments ([11], pp. 33-38; [12], pp. 97-102).

The uniqueness of the definition is further clarified by

our recent experiments, which strongly suggests that

the well known "inductive learning" models, including

connectionist models, are, in fact, not inductive learning models at all. What does make the inductive learning process a prime candidate for the central cognitive process? The

answer, I believe, is strongly suggested by the ubiquitous fact that any object/event representation is guided,

to a considerable extent, by the finite number of the

agent's encounters, direct and indirect, with that object/event. In fact, it is not difficult to see how the

construction of practically all cherished concepts in cognitive psychology, including frames and mental models, can be accomplished based on the concept of ICR.

Moreover, H. Plotkin in [13] makes a book-length ar- gument that only inductive mechanisms can allow each

biological species to convert the "Humean uncertainty

. . . into a pragmatic issue of dividing the world into

band width of frequencies of change and fluctuation,

and [to employ these] . . . mechanisms that are able to

match the rates of perturbation of the world with or- ganic structures ... to alter their own states at equivalent rates" (see also [14]).

3. INDUCTIVE ORIGIN OF NUMBERS

Remarkably, it appears that the decisive and irreplaceable role of the inductive axiom in the well known

112
Peano axiomatization of natural numbers is a reflec- tion of the inductive cognitive origin of numbers.

Following [15], sect. 1.2, I first summarize the 4

stages in the emergence of numbers. The presence

of the first stage (which has evolved in many animals

many millions of years ago) is indicated by the ability to reasonably accurately compare the sizes of some

temporal and spatial sets of events or objects (see, for

example [16, 17, 18, 19]).

The second stage is manifested in the primitive cultures in the form of the choice of very few selected

reference, or standard, sets of objects mainly for the

purpose of explicit storage of various set sizes (see, for

example [16, 17, 18]).

The third stage is achieved when a single reference

set of object is selected, and the fourth stage is characterized by the emergence of the abstract concept of

number, independent of any particular set of reference

objects. One should note that the last stage is quite

recent (4000-2000 B.C.) and it is reflected in many of our measures of length: the height of a horse is measured in "hands" and length generally in "feet" (from

foot) and earlier also in "ells" (from elbow, 1 ell = 45

inches). Also, the word "digit" means not only the

numbers 1, 2, 3, ... but a finger or a toe as well. Similar phenomenon is observed in practically all languages

[16, 17, 18].

One point to observe in the progression of the four

stages—and this has actually became perfectly clear

only at the end of the last century—is that a number is, in fact, a sign representing the (infinite) class of

all finite sets whose sizes are all equal to this number.

This, plus the other point, which will be discussed next,

lead quite naturally, as we shall see, to the hypothesis

proposed in the title of this section that the concept of

number has been acquired by means of the evolutionary

inductive learning processes, when the evolving agent

gradually acquires the concept of number via embedded in the agent (and therefore also evolving) cognitive

inductive learning processes interacting with the environment.

Let us next look at this process from a little more

formal perspective. The definition of inductive learning

process given in section 2 is model-independent, i.e. no

concrete mathematical model is specified to account,

first, for the generativity and, second, for the measure

of proximity of elements in the set. Thus, to continue,

we shall need to choose some concrete mathematical

model satisfying the two general and absolutely essential conditions of the definition. Since at present no model except ETS satisfies the requirements of the definitions, the latter is quite naturally my choice. Hence,

in what follows I simply adopt the ETS as the model of

inductive learning (see, for example, my paper in the

last year proceedings of this conference [5] or [2, 3, 4]). In a few words, ETS can be described as a formal

mathematical explication of the idea of the "symbolic"

object space as opposed to the idea of "numeric" object space. The latter is captured, for instance, by concept of Euclidean vector space. It turns out that there

is a profound difference in the nature of the (metric)

geometry for the two classes of spaces, numeric object

spaces forming a very special, "degenerate" , subclass of

the class of symbolic object spaces. (The distance between two symbolic objects—or, more precisely , object

representations—is defined as the "shortest" sequence

of weighted symbolic transformations connecting the

two objects, e.g. deletions, insertions and substitutions.) The important new idea here is that the distance function is defined by the fixed set of weighted

symbolic operations, each of which can transform one

object into the other. In other words, the new idea is that the concept of distance is introduced via the fixed

set of symbolic operations, which in a numeric case, e.g. vector space, becomes "trivial". Moreover, the representation itself is not fully determined by the "struc- ture" of the object itself but also by the latter set of

operations, specifying the emergent multi-resolutional

structure that can only be discovered during various

inductive learning processes. For example, in case of

strings, to indicate such an emergent structure, the

usual string representation aacdbaacdcabba is not

sufficient, and more adequate form of representation

might be, for example, a.acd.ba.acd.ca.b.ba reflect- ing the corresponding symbolic operations that are constructed during the learning stage from the basic singleletter operations with the help of several fixed composition forming operators [3]. In ETS, the inductive class representation (ICR),

constructed during the learning process, consists of a

small selected subset of the positive training set plus

the learned set of weighted operations (that can act on the selected training set to generate the approximation Capp of the class C to be learned (see Definition in

section 2). The very simple nature of numeric object

representation space manifests itself in the simplicity of

the ICR for the set N of natural numbers: 1 & the successor operation. The latter can be seen, for example,

from the Peano axiomatization of N, which is now universally accepted as the standard one. This symbolic,

or compositional, simplicity becomes perhaps more apparent when we view natural numbers as the set of

strings over a single letter alphabet {a}:

N = {a, ao, aaa, aaaa, . . . }.

Thus, looking at N as the result of application of the

corresponding ICR (e.g. string aaa plus the deletioninsertion of a), it is not difficult at all to connect this

113
ICR with the actual learning process as reflected in the

above four stages: the positive training set may consist

of several strings of a's, for example, a, aaa, aaaaaa,

and the negative training set is simply empty. Since

the final set of operation consists of just one singleletter deletion-insertion operation, no multiresolutional

structure enters the "picture" . In this manner a very

natural connection is established between the emergence of natural numbers and the central intelligent

processes—inductive learning processes.

4. GENERALIZED MEASUREMENT

PROCESS AS INDUCTIVE LEARNING

PROCESS

In the last section we have connected the structure of

natural numbers—and therefore of most of our presentday mathematics—to the simplest form of inductive

class representation (ICR), consisting of a single object

plus a single operation. It is not difficult to see now the

gradual development of the classical scientific paradigm

as application of this (Peano) ICR to the representation of various important "numeric" features of reality:

mass, distance, time, speed, etc. etc.. I want to emphasize the fact that in spite of apparent multitude of

"variables" introduced in basic sciences, the structure

of the representation space for all these variables—e.g. Euclidean vector space—is essentially determined (via

the real numbers) by the structure of the ICR of natural numbers.

Given the above, one can propose to view more general, i.e. "symbolic, or semiotic", measurement processes simply as various concrete implementations of

general inductive learning processes. (We were lead to these general measurement processes [7] after the investigation of the foundations of computational vision

processes [6].) To better understand the meaning of "symbolic measurement process", let us first look from the new perspective at a concrete example of the classical, or numeric, measurement process—length measurement. It goes without saying that the emergence of numbers has

preceded the idea of the ruler. Hence, the idea of length

measurement should be looked at as a quite natural

application of the above view of natural numbers (via

Peano ICR) to the concept of length, i.e. the above a becomes (linear) unit of measurement.

We have recently proposed [7] to generalize the classical idea of length measurement to the idea of plane

shape "measurement" . The basic idea is to expand the

"measurement alphabet" from A = {a} to, for example, A' — {a, b, c}, where the nonlinear units b and c are the oriented concave and convex corners, as in the

example in [1]. In other words, if the idea of the classical linear ruler is to assemble successively identical

copies of a single linear unit of measurement, the basic

idea of the above "plane ruler" is to allow one to as- semble dynamically several, including nonlinear, units

of measurement and to apply the inductive learning

process to discover the corresponding symbolic operations that specify the multiresolutional structure of the

shape representation as a member of a certain class of

shapes. For a more detailed exposition of this example see the companion paper [7], where, in particular,

it is illustrated how the noise in the symbolic representation can also be eliminated during the inductive

learning process by discovering the corresponding symbolic operation of weight zero.

5. INDUCTIVE SEMIOTIC SYSTEMS

In the tradition of these conferences, I propose to address both the "computational semiotics" ([20], p. 155)

and the semiotics understood by Metz as "the formalization of the natural sciences" ([21], p. 30) in one framework—Inductive Semiotic Systems (ISS). The cor- responding new science can then be defined as the sci- ence concerned with the study and modeling of au- tonomous (including biological) systems that can symbolically encode a functionally necessary (but possibly

unbounded) class of events/objects in the environment

after an exposure to a very small number of events from

the class. As was partly outlined in the last section, the questions related to "the problem of how signals from sensors can be reliably transformed into symbolic data

structures that are suitable for logical reasoning" [22] are also addressed by the proposed framework but in a manner much more radical than implied by that state- ment: the sensors themselves must embody inductive

(symbolic) measurement devices. Such intelligent devices

contrary to the classical sensors based on the very simple form of the ICR—would be modeled in accordance

with the new mathematical structure, ETS, that al- lows the measurement device to capture in a much less

restrictive, symbolic, form the structure of the corre- sponding class of events in the environment. The outputs of such measurement devices, as in the case of

biological systems, would be the current multiresolutional symbolic representations of events, or objects.

Hence no transduction of the numeric input into symbolic representation is necessary. Moreover, as became

gradually clear to us, such a transduction appears to be

meaningless, since, as was mentioned above, the class

of numeric spaces forms a degenerate subclass of the

class of symbolic spaces, so that in this case the very

rational for symbolic representation collapses.

Semiotics is often defined as a field "involved in

114
analyses of trilateral unity: object-sign-meaning" ([23],

p. 45). The latter view goes back to C. Peirce, who

introduced semiotics as "the doctrine of the essential

nature and fundamental varieties of possible semiosis" , where "by the semiotics I [he] mean[s] an action, an

influence, which is, or involves, a cooperation of three

subjects, such as a sign, its object and its interpretant,

this tri-relative influence not being in anyway resolvable into actions between pairs" ([21], p. 15). In accordance with the above (ISS) view of semiotics, one can introduce a somewhat more precise perspective on the "analysis of the trilateral unity" , as the

the study and modeling of the following triad: combinative, or compositional, object structure, the cor- responding sign (i.e. object representation) structure,

and the mathematical structure that captures the for- mer. And it is the inductive learning processes, through

the discovery of the object-class structure, that relate

the members of the triad. This interpretation, as well

as the following postulates, are adopted from the similar view of the computational vision given in [6]. The

following three postulates may be viewed as a more detailed description of the relation between the members

of the triad.

Postulate 1. All objects in the universe have emergent compositional structure. Moreover, the term "object structure" , and therefore the term "meaning" , can- not be properly understood and defined outside the inductive learning process.

Postulate 2. The inductive learning process is an evolving process that tries to capture the emergent

compositional object-class structure mentioned in Postulate 1. The mathematical structure on which the

inductive learning model is based should have the intrinsic capability to capture the evolving compositional

object structure.

(As discussed in section 3, the appropriate mathematical structure is fundamentally different from the classical mathematical structures.)

Postulate 3. All basic representations, i.e. signs, are constructed on the basis of the "inductive signs"

,

which, in turn, are constructed by the inductive learning processes (see Postulate 2). Thus, the inductive

learning processes form the core around which all other

semiotic processes have evolved.

6. CONCLUSION

I have proposed to put the inductive object-class representation constructed during the inductive learning

process at the basis of the semiotic "analysis of the tri- lateral unity [of] object-sign-meaning" [23]. There is considerable evidence (mainly not discussed in this paper) to suggest that the inductive learning processes

are the central intelligent processes responsible for the

construction of the current basic object representations

( "signs" ) . The emergent symbolic operations constructed

during learning and inducing on the symbolic space

the "optimal (metric) geometry" clarify the meaning

of "meaning" as well as the meaning of the multiresolutional representation.

As discussed in section 3, the emergence of numbers appears to be a result of application of the perceptual inductive learning processes to the representation of the set size only, the latter being a very re- stricted, numeric, form of inductive object-class representation. Moreover, the application of the general

inductive learning processes to a less trivial, symbolic,

form of object-class representation suggests, in particular, the future, qualitatively quite different, line of

development of mathematics, as was also suggested,

for example, in ([24], p. 36). Such "symbolic" rather

than "numeric" mathematics would be about the entities that are compositionally structured in a manner

less "trivial", or more general, than the "numeric" entities. In connection with this, it is interesting to note

the considerable (non-technical) similarity of Fodor and

Pylyshyn's important argument [25] in favor of symbolic representations as opposed to numeric ones on

the basis of thoughts having non-trivial compositional

structure and directed against the connectionist cognitive models.

The real possibility of development and the nature

of symbolic, or inductive, measurement devices are also

briefly discussed, in order to suggest the essential scientific link between the classical sciences and that of

the inductive semiotic systems.

Thus, the present paper can be considered as an

attempt to fundamentally address the great recurring

"scandal" mentioned in the epigraph.

7. REFERENCES

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Knowledge: Concerning Adaptations, Instinct and

the Evolution of Intelligence, Penguin, 1994.

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Knowledge: Essays on the Methodology of Mathematics, Mysl' Publ., Moscow, 1968 (in Russian).

[16] J. McLeish, The Story of Numbers: How Mathematics Has Shaped Civilization, Ballantine, New

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Meystel, R. Quintero, Vol. 1, 153-158.

[21] U. Eco, A Theory of Semiotics, Indiana University

Press, Bloomington, Indiana, 1979.

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control, Preface in [23].

[23] A. Meystel, Semiotic Modeling and Situation

Analysis: An Introduction, AdRem Inc., Bala

Cynwyd, Pennsylvania, 1995.

[24] C. Landauer and K.L. Bellman, Semiotics of constructed complex systems, Proc. 1996 Conf. on Intelligent Systems: A Semiotic Perspective, eds. J. Albus, A. Meystel, R. Quintero, Vol. 1, 35-40.

[25] J. A. Fodor and Z.W. Pylyshyn, Connectionism

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symbols, MIT Press, Cambridge, Massachusetts,

1988.

116
Unified Learning/Planning Automaton:

Generating and Using Multigranular Knowledge Hierarchies

AlexMeystel and Alberto Lacaze T

National Institute of Standards and Technology

o Drexel University

v

University of Maryland

Abstract. This paper introduces an approach for

analysis of systems employing unity of learning and

planning processes. An architecture of an automaton with

joint learning and planning (LPA) is presented which

determines a class of learning algorithms. An algorithm of

learning that employs grouping, focusing attention and

combinatorial search is described. LPA searches for an

appropriate set of rules, and then, for a preferable motion

trajectory. It creates top down planning/control processes

which are based on multigranular hierarchies of knowledge

and lead to the temporal evolution of the system.

Key words: complexity, control, evolution in biology,

experiences, focusing attention, generalization, granularity,

grouping, intelligence, multigranular knowledge hierarchies,

multiresolutional architecture, planning.

1. Introduction

In 1986 the concept of "baby-robot" was introduced in

[1]. This concept emphasizes processes of unsupervised

learning and is associated with the joint evolution of

behavior and knowledge incorporated within a system. It seems plausible that learning from multiple experiences is inseparable from the architecture of applying the acquired

knowledge for shaping the desirable behavior.

We introduce a formal system—a learning automaton

which has the faculties required to obtain and use knowledge:

sensors, subsystems for storing and organizing information,

subsystems for generating commands, actuators for changing

the world, but initially it has no world model and no rules to achieve a goal. This knowledge should be learned and our

goal is to understand how.

The concepts of experience as a part of behavior, as well

as desirability of behavior and its components-experiences,

will be introduced and explored (Section 3). Behavior is shaped by the actions which emerge as a result of planning

the goal-states, actions that lead to goal-states, and strings of

them. The process of finding the string of desirable states and actions leading to them is called planning. The

latter would be impossible unless the ability to judge the

degree of desirability of states and actions would not be

acquired in advance. Generating and applying proper

commands to execute the planned trajectory and compensate

for errors is called execution. Both planning and execution

are a part of control. The process of acquiring the relevant

information and processing it so that a proper behavior could

be generated is called learning. Planning/control and learning

are complementary procedures of intelligent computation.

The process of planning starts with focusing

attention which selects the initial representation of the world

or the map with its boundaries. The space is discretized into

tessellata which determine the space resolution, or

granularity. Combinatorial search is performed as a procedure

of choosing one string (the minimum cost string) out of the

multiplicity of all possible strings formed out of the space

tessellata at this particular level of resolution.

Grouping the tessellata in a variety of feasible strings

allows selection of one of them. This determines an envelope of focusing attention around the vicinity of the

minimum cost string. All information within the envelope

is being transformed to the higher level of resolution and

grouping of behavior units starts again. Focusing attention

presumes proper distribution of nodes in the state space so

that no unnecessary search be performed. Combinatorial

search forms the alternatives. All of these three procedures

together can be considered as a process of generalization.

Generalization is a generation of the representation at the

lower level of resolution.

Figure 1. Multiresolutional Consecutive Knowledge

Acquisition by the virtue of Generalization

An example of joint functioning of these three

operations is shown in Figure 1. The operations work

jointly as a triplet, which can be considered an elementary

117
unit of intelligence [2]. The process is shown in Figure 1

for learning. It presumes generalization of high resolution

units of information into lower resolution clusters. This

process can proceed in the opposite direction, from a lower

resolution to a higher resolution, i. e. counterclockwise.

Then it will demonstrate planning and presume instantiation

via decomposition of low resolution units into higher

resolution. Both generalization and instantiation are the key

processes of intelligence.

All of these phenomena presume that the system under

consideration can "behave" as a result of its perceiving the

states, planning the decisions and acting by using the

actuators. The overall system can be represented using the

concept of elementary loop of functioning [2-4].

This paper demonstrates that learning leads to emergence of a multiresolutional representation and a hierarchy of planning/control.

2. Algorithms of Unsupervised Learning

with Combinatorial Enhancement and

Generalization

2.1 Learning Automata. An automaton is a state machine which generates outputs by using its transition

function and state-output function tabulated in advance for

all possible states. Conventional automata are capable of

demonstrating "reactive behaviors" according to the

prescriptions stored in their transition and output functions

[21, 22]. In this paper, a class of learning automata is outlined which are state machines whose transition and state- output functions are updated and modified based upon prior

experiences which are stored in the memory and transformed

into sets of rules. The transition and output functions of

these automata have open lists of rules. New rules can be

added to these lists. This concept is similar to the one described in [5]. In

this paper, we will equip learning automaton with a new

capability: to synthesize their output by combining together

previously stored rules in search of the most appropriate

behavior. In addition to reactive responses, our learning

automata demonstrate the skill of deliberation, or planning.

This new type of automata will be called Learning and

Planning Automata (LPA). LPA are presumed to have a learning system L which allows for enriching both the

transition and the output functions and a planning system,

as a part of the mechanism of behavior generation BG.

As the system of rules develops it becomes a

hierarchical one. This is equivalent to formation of the

hierarchy of automata as a result of the evolution of a single

learning automaton and affects the corresponding input and

output vocabularies. Operators of L are equipped by

minimum initial set of tools including the ability to form

strings, to construct hypotheses, and to infer tautologies.

Learning system L can be defined as a system of

acquisition of experiences, transformation of these

experiences into rules of action, derivation of new concepts,

and organization of these concepts into enhanced knowledge

base (entity-relational network similar for the long term

knowledge called ontology, base of hypotheses, concept base,

etc.) This improves decision-making for achieving the goal.

In order to support processes of learning, each learning

automaton is equipped by the set of actuators that follow

commands at the output of learning automaton. Changes in the world are measured by the sensors. A set of sensors is the

only source of information for the learning system about the

state of the World (state.) The automaton is also equipped by

subsystems of Sensory Processing and World Model which

allow for interpreting the input from sensors. The Learning System can judge upon truthfulness of

this information only by the results of actions (behavior)

which are undertaken to achieve the goal. The subsystem of

Behavior Generation (BG) contains transition function and

output function [2, 3, 6]. Other devices of BG are described

in Section 5. This approach is presented earlier in [7, 8]. The state of the world is understood as a set of n

sensors' outputs which arrive at a particular moment of time.

Action is a set of m action outputs which are generated by

the system between two consecutive states. States can be

represented as sets (lists), or as vectors within a particular

system of coordinates. Actions are understood as causes of

changes that are sensed after the actions are applied.

Goal is a state which must be achieved as a result of the

behavior. The goal is often presumed to be given to a system. From [2-6] we know that goals can emerge also as a

result of planning. From [3,4] we know that the process of

learning generates subgoals.

It is presumed that any valued experience is associated

with a certain measure of "goodness". It can be interpreted as

a reward for the pursuit of the goal G. The value of reward

will be used for the subsequent process of hypotheses

generation and selection. Ultimately, it determines the rules

necessary for "survival." A rule can be obtained as a result of

transforming the cause-effect relations discovered within

repetitive experiences.

After the rules are confirmed, some of their parts which

emerged as a result of generalization, may not belong to the

initial vocabularies. These parts are to be treated as new

concepts. Concept is a label for the entity which can be

obtained recursively as a cluster or group of higher resolution

concepts. All new concepts are obtained from two available

classes of rules (see Figure 2.) states and actions are concepts

and so are clusters of states and actions, as well as their

components.

I s l A 12 S 2

J 12) EXPERIENCES (G)

RULE [lF(Si,G) —> THEN A 12] RULE [IF (Si , A12) —> THEN S 2]

CANDIDATES FOR CONCEPT BASE

Figure 2. Experiences—>Rules—>Concepts

(S-state, A-action, J-reward, G-goal)

The new concept obtained from the generalized

experiences as a result of their transformation into rules are

118
novel words which are not present in the lists of previously

defined input and output vocabularies. These novel words are words of the new vocabularies: at the lower level of

resolution. They describe the phenomena related to groups of

units of experiences.

2.2 The Algorithm of Inductive

Generalization. The following sequence of activities can

be explicated from the definition of learning:

1 . Experiences are collected and stored in memory.

2. Experiences are compared, resemblances are determined,

and clusters are formed by the virtue of resemblance.

Clusters of experiences which already have cause-effect

relationships, are transformed into rules, and control rules and

events rules are separated.

3. Search for the meaningful cause-effect relationships can

be done not only among the stored set of experiences but

among the synthesized experiences too.

4. The clusters of states and actions that are parts of the

newly created rules are stored as concepts of lower resolution;

then the growth of the concept base begins. New concepts

emerge as a result of clustering: the new clusters are labeled

and receive a status of a new word.

5. Each of the clusters of similar enhanced experiences is considered to be a candidate for becoming a rule hypothesis.

6. The hypotheses are stored. Subsequently, the new

experiences are stored in parallel in two new vocabularies: the

original and the one formed by the newly created concepts.

7. The process of consecutive operations

{collection of experience—>hypothesis formation—

>

—>generation of rules—>concepts emergence}

is repeated each time as a new experience arrives.

8. Hypotheses are validated by statistics of their use and

then enter the base of hypotheses. As vocabularies grow,

they allow to represent and control functioning of the system

by using their new words. The sequence of steps 1-6 can be

repeated which forms a lower level of representation.

The algorithm (Figure 3) describes a recursive process

which leads to a multiresolutional (MR) system of world

representation and an MR systems of rules of actions, both

acquired as a result of learning. Inductive generalization

claims that multiple occurrences of similar experiences

testify for existence of a particular rule, if most of these occurrences have the same (or similar) explanation of causes

[14]. If the number of occurrences is not statistically

persuasive, then we can talk about the case of hypotheses

generation by means of abductive generalization: In both

cases, it is important to account for the list of

attributes/variables and for the relations among them [15].

Learning employs the algorithm of generalization which

presumes a multiple iteration of the triplet from Figure 1: focusing attention on the subset of experiences and

searching among them and their combinations until a grouping can be performed, i.e. a cluster of similar units

could be substituted by a single generalized hypothesis [10].

If the subsequent experiences confirm the hypothesis, it becomes stronger. Automata with generalization have not

been previously discussed in the literature on learning.

Since the algorithm of generalization as applied

recursively to its own results, each two adjacent levels of

resolution use generalization applied to the initial information which can be considered experiences and to generalized information which is called hypotheses. Thus, we

can distinguish two kinds of generalization pertaining to the

level to which they are applied: generalization from

experiences before any hypothesis is available and

generalization from hypotheses.

STORING EXPERIENCES

r

C/J UJ

C/J UJX

\

>•X

O

Z

o.

PL, <

FOCUSING ATTANTION.

SELECTION OF ADMISSIBLE

EXPERIENCE

COMBINATORIAL ENHANCEMENT

OF ADMISSIBLE EXPERIENCES

CONSTRUCTING SIMILARITY

CLUSTERS

Gl

SEARCH FOR HYPOTHESES

AMONG SIMILARITY CLUSTERS

STORING HYPOTHESES

ASSIGNING A STATUS OF RULE

TO SELECTED HYPOTHESES

ALGORITHM

OF

GENERALIZATION

Figure 3. The Generalization Algorithm

Learning with generalization allows for using

experiences in a very efficient way: it is a tool of reducing

complexity. In order to receive innovations, some

combinatorics should be introduced for generating words

beyond the existing experiences. Similar mechanism has

been proven to be very useful for design purposes [10].

2.3 Combinatorial Enhancement: Searching

for Hidden Implications. Each experience can testify

only about some part of the overall state. The available sensor information not necessarily can be a good basis for

generating a hypothesis. Consider an example with

autonomous mobile robot which must learn how to act in a

particular environment. In a particular state, a single actuator command cannot be a proper response. Frequently, a combined command (steering + propulsion) must be

assigned. Just value of the sensor reading of angle of

"heading", Zee, or value of "angle to the goal", Zo~, cannot

119
be an antecedent in a rule what to do. However, their

difference (Za - Za) is a perfect variable of control.

The enhancing creates a new set containing the initial

set and all possible combinations of its elements.

RELATIONAL

DATABASES

CONCEPTS

RELATIONAL

DATABASES EXPERIENCES RULES

CONCEPTS

1

EXPERIENCES RULES

Figure 4. Evolution of Acquired Knowledge

The enhanced states is a set formed by a state, all possible combination of its components, and all possible

combinations between components of the action A and the

state S. Such two persuasive examples of learning as the

evolution of living creatures and the evolution of knowledge

would be substantially impaired if no combinatorial

enhancement would be possible.

The following factors are considered critical for

stimulating evolution of living creatures: reproduction,

mutation, competition, selection [9]. These factors are applied to knowledge in a similar way.

The algorithm of generalization creates new hypotheses,

rules, and concepts which become new words in vocabularies.

The same algorithm is applied to its own results. Now the

previously generalized experiences are generalized again, and

the hypotheses and rules of "lower resolution" are obtained.

Evolution of acquired knowledge is illustrated in Figure 4. This diagram shows that the joint system of knowledge

representation and behavior generation converges to a multiresolutional one. 2.4 Searching for Valid Hypotheses among

Clusters. The reason behind the creation of clusters is our

belief that each of these clusters is a candidate to become a hypothesis of a rule of a different behavior [7, 8]. The hypotheses are then stored in the database of

hypotheses as a tree where each hypothesis is related to its "parent" by the goal. If no hypothesis was found for a certain

state, then the state in the hypothesis with closest state to ours becomes a subgoal. This is one more source for the

emerging hierarchies of acquired knowledge.

2.5 Combinatorics of refinement. When

hypotheses are sought for within the level of higher

resolution, the objects and experiences are supposed to be

"enhanced" combinatorially in the way similar to one used at

a level. This enhancement is used for the problems of design.

It is a part of the process of "task decomposition [3, 6]."

3. Behavior Generation as a

Multiresolutional Search for a Motion

Trajectory in the State Space

The second process characteristic for the learning

automaton is Behavior Generation (BG) (see [4,16-20].) This

process is understood as a sequence of top-down planning

activities which end with receiving a set of control

commands. The purpose of learning is to enable the

subsequent process of planning. Conventional automata are only capable of reactive decisions; they are not capable of

"look-ahead" decision making processes which are typical for

deliberative planning.

Behavior generation consists of two components: goal

refinement and trajectory generation. The goal is given from

the upper level at a particular resolution. In order to plan the

trajectory, this representation of goal should be refined ("job

assignment".) Then, "each member of the team" can plan its trajectory ("scheduling.") Unlike learning, which develops

bottom-up and works via generalization (or coarsening), the

process of planning develops top-down and works via

instantiation (or refinement.) The process of planning is determined as choosing the desirable behavior by anticipating

admissible alternatives among possible behaviors and

selecting the best of them.

From Section 2, we conclude that all experiences

acquired and hypotheses generated contain some knowledge of

some reactive rules. For example, "if it is necessary to get to S2 from S j, apply Aj2-" This rule reacts by evoking A^ to

the need of getting into S2 from S j at i level of resolution.

Trajectory is a string of adjacent admissible elementary

subdomains (or tessellata, tiles of the discretized space).

Any well posed problem of planning should start with

assigning the initial point and the final point of the

trajectory which should be determined at the higher resolution

within the tessellatum of the resolution under consideration.

The feasible trajectory is determined at the lower level of

resolution.

PT is called a feasible trajectory if it has an initial and a

final points, and all tiles of the string are contained in the

feasible trajectory at the lower level of resolution. Thus, a

feasible trajectory for the level i is always represented as a

string of tiles for the i+1 level of resolution and is a subspace of the i level of resolution. Clearly, the needs in and the algorithms of finding a feasible trajectory are tools of

focusing attention. We determine the subspace in which the

wpp of planning should be resolved, and the optimum

trajectory should be found. Indeed, the feasible trajectory

determined at the i+1 level of resolution becomes an

"envelope," a bound domain of space at the i level of

resolution. Search in the state space or S -search, (see [8, 14-

20]) is done by synthesizing the feasible trajectories for a

particular level of resolution and then building the

alternatives of possible motion trajectories for the lower

120
resolution level within the envelope cost space.

Figure 5. Illustration to the MSJ -algorithm.

Some particular volume of the state spaces designated

for a subsequent search for a solution, Operation of

contraction puts constraints on this volume and should be

properly justified. We need to reduce the probability that contraction eliminates some or all of the opportunities to

find the optimum path trajectory. The following heuristic

strategy of contraction is chosen. After the search at the

lowest resolution level is performed, the optimum

trajectory is surrounded by an envelope. It is a convex hull which has a width w determined by the context of the

problem. Then, the random points generation at the next

level of resolution is performed only within this envelope

of search. The problem of consistency of representation

under the contraction heuristic has to be addressed in the

future.The Behavior Generation part of LPA functioning is

illustrated in Figures 5 and 6.

4. Conclusions: The Issues of Further

Research

The results presented in this paper has been

confirmed by the experimental results [1,7,8]. "Baby-Robot" was able to learn how to reach the arbitrary situated goal

only after implementing the algorithm of generalization with

combinatorial enhancement. Before this algorithm was

implemented, Baby-Robot was able to learn how to reach the

particular located goal. If the location of the goal was

changed, the successful learning process for the previous

goal could not help to find a new one. Generalization n with

combinatorial enhancement has enabled the robot to make

the discovery, and initiate the process of hierarchical

learning. Other positive results are recorded in [19,20].

1 . In this paper, we introduce and analyze an algorithm

of MR unsupervised learning with inductive generalization

and a search for hidden implications. This algorithm is applied recursively to its own results at the output. Thus,

LPA develops an evolving MR system of representation. It enables the system of behavior generation (BG) also to evolve. LPA provides for an evolution of the automata

equipped with such systems. LPA becomes an MR

automaton, and its levels of resolution can change as the

evolution of knowledge and behavior proceeds. This

evolution can be illustrated by Figure 7.

2. From Figure 8, one can see the behavior evolves.

This producing different plans and motion trajectories as shown as a horizontally developing tree. At the same time,

its knowledge evolves as shown in the vertical hierarchical

structures. This process seems to be even more important to analyze of the evolution of living creatures. We believe that LPA allows for analysis of the processes of evolution of its systems as species. It is possible to equip the automaton by

the system of reproduction. It would be possible to analyze

how the process of knowledge evolution is affected by

different mechanisms of reproduction.

3. This line of research takes advantage of the

uniqueness of LPA among other known systems of automata

with learning. The mechanism of unsupervised learning

allows for the ultimate freedom in the way the learning

process organizes the acquired knowledge. It is possible to

anticipate that as the knowledge base evolves, the knowledge

becomes utterly diversified. Rules concerning the external

world will emerge, and the rules concerning processes of

inner knowledge organization and procedures of processing

will follow.

4. LPA can be used to analyze all stages of learning

including the "early learning" stage. Certainly, some initial knowledge ("bootstrap knowledge") is presumed. This

bootstrap organization of knowledge can strongly affect the

subsequent processes of knowledge evolution. On the other

hand, the learning system is presumed to be free of a building

up of all subsequent knowledge organization. How it will

organize the knowledge acquired and why?— this is the

research issue for LPA.

5. The processes of knowledge acquisition are affected

by the knowledge stored. They start creating some bias in the

subsequent knowledge acquisition since the results of

automaton functioning will be induced by the knowledge

previously stored. So, if the results of functioning were "good" or led to a "better" behavior, the system might assume that its goodness is due to the knowledge used. It might happen that the experiences the system acquires are limited by its predisposition.

6. Since the system has been developed to demonstrate

some particular behavior, the evaluation of this behavior

should be the ultimate measure for the process and results of

knowledge organization as well as the processes and results of the ways knowledge is acquired from the external world

and knowledge used for behavior generation. This determines

an interesting interconnection between further developing the

hierarchy of functions for evaluation of goodness which

precipitate at different levels of resolution. The

121
122
interconnection between learning, behavior, and emerging

"system of values" in LPA is an important research issue.

TIME

Figure 7. Evolution of Knowledge and Behavior of LPA

7. All these three processes: acquisition, organization

and use affect the overall system functioning. Therefore,

other systems of learning can modify and alter the system of

LPA. At the present time the following mechanisms of

knowledge acquisition are known from the literature:

a) . Learning by transfer. In this case all knowledge

which subsequently is required for behavior generation is

transferred from another source where it was stored and

organized in advance based upon existing design decisions and

experiences of functioning. This method of knowledge

acquisition presumes that the structure of the system of

interest and its functioning in required circumstances are previously known.

b) . Learning by examples. In this case, we

presume a "Teacher" which has substantial knowledge about

my cases of possible functioning, stores knowledge of

previous experiences and spells out a set of possible

scenarios in which the functioning of the system is expected.

Undoubtedly, a set of tests can be developed in which a behavior of system is entertained and after each case of

behavior the system receives the teacher's evaluation

whether it was good, and how good it was. The difference between these systems and LPA can be

easily seen. 8. Learning and Behavior Generation produce

structural and behavioral hierarchies. It is possible to state

that using LPA reduces computational complexity by

increasing the structural complexity.

7. References

1 . Meystel A. Baby-robot: On the analysis of cognitive

controllers for robotics, Proc. IEEE Int'l Conf. on Man &

Cybernetics, Tucson, AZ, Nov. 11-15, 1985, pp. 327-222

2. Meystel A., Intelligent Systems: A Semiotic Perspective,

International Journal of Intelligent Control and Systems, Vol.1,

No.l, 1996, pp. 31-57

3. Albus J., Meystel A., A Reference Model Architecture for

Design and Implementation of Semiotic Control in Large and

Complex Systems, Proc. of the 1995 IEEE ISIC Workshop,

Architectures for Semiotic Modeling and Analysis in Large

Complex Systems, Monterey, CA 1995, pp. 33-45

123

4. Meystel A., Nested Hierarchical Control, in Eds. P. Antsaklis, K. Passino, An Introduction to Intelligent and

Autonomous Control, Kluwer Academic, Boston, MA 1992

5. Rajaraman K.,Sastry P.S., Finite Time Analysis of the

Pursuit Algorithm for Learning Automata, IEEE Transactions on

Systems, Man & Cybernetics, Part B: Cybernetics, Vol.26,

No.4, August 1996, pp. 590-598.

6. Albus J., Outline for a Theory of Intelligence, IEEE

Transactions on Systems, Man and Cybernetics, ol. 21, No. 3, May/June I99\, pp. 473-509

7. Albus J., Lacaze A., Meystel A., Autonomous Learning

Via Nested Clustering, Proc. of the 34th IEEE Conference on

Decision and Control, New Orleans LA, 1995, pp. 3034-3039

8. Albus J., Lacaze A., Meystel A., Theory and Experimental

Analysis of Cognitive Processes in Early Learning, Proc. of the

1995 IEEE International Conference on Systems, Man and

Cybernetics, vol. 4, Vancouver, BC, Canada, 1995, pp. 4404-

4409

9. Fogel D.B., Evolutionary Computation: Toward a New

Philosophy of Machine Intelligence, IEEE Press, NY, 1995

10. Meystel A. .Thomas M. Computer aided conceptual design

in robotics, Proc. IEEE Int'l Conf. in Robotics, Atlanta, GA,

March 13-151984, pp. 220-229

11. Mirkin B., Mathematical Classification and Clustering,

Kluwer Academic, Dordrecht, 1996

12. Mirkin B., The Method of Principal Clusters, Automation

and Remote Control, 1988, pp. 1379-1388

13. Mirkin B., Method of Fuzzy Additive Types for Analysis of

Multidimensional Data, Automation and Remote Control, 1990,

pp. 683-821

14. Michalski R.S, A Theory and Methodology of Inductive

Learning, Artificial Intelligence, Vol. 20, No. 2, Elsevier,

Amsterdam

15. Goldfarb L.,Abela J., Bhavsar V.C., Kamat V.H. Can a

Vector Space Based Learning Model Discover Inductive Class

Generalization in a Symbol Environment, Pattern Recognition

Letters, V. 16, 1995, pp.7 19-726

16. Meystel A., Planning in a hierarchical nested controller

for autonomous robots, Proc. IEEE 25th Conf. on Decision and

Control, Athens, Greece, 1986

17. Meystel A., Planning in a Hierarchical Nested Control

System, in Eds. W. Wolfe, N. Marquina, Mobile Robots, Proc. of SPIE, Vol. 727, Cambridge, MA 1986, p.p.42-76

1 8. Saridis G., An Integrated Theory of Intelligent Machines

by Expressing the Control Performance as Entropy, Control:

Theory and Advanced Technology, Vol. 1, No. 2, p.p. 125-

138, MITA-Press, Tokyo, Japan, 1985

19. Meystel A., Uzzaman S., Landa G., Wahi S., Navathe R., Cleveland B., State Space Search For An Optimal Trajectory

Proc. of the IEEE Symposium on Intelligent Control, Vol. II, Philadelphia, PA, 1990

20. Grevera G., Meystel A., Searching for a path through

Pasadena, Proc. of the IEEE Symposium on Intelligent

Control, Arlington, VA,1989

21. K. Nairn, A. S. Poznyak, Learning Automata: Theory

and Applications, Pergamon, 1994

22. S. Lakshmivarahan, Learning Algorithms Theory and

Applications, Springer- Verlag, New York, 1981
Structural Learning for Classification of High Dimensional Data

Dr. Paul M. Baggenstoss

Naval Undersea Warfare Center

Newport RI, 02841

401-841-7505 x 38240 (TEL)

401-841-7453 (FAX)

p.m.baggenstoss@ieee.org (EMAIL)

EDICS 6.1.6 / 3.5 / 6.17

July 1, 1997

Abstract

This paper is concerned with probability density estimation in high-dimensional settings. A breakthrough

in classifier performance has been achieved by as- suming that the multidimensional feature vector is composed of statistically independent "groups" . The

method, which we call independence grouping, determines a mapping of features into separate lowdimensional feature groups, which are regarded as independent. The optimal size of the groups and the

best mapping is determined either by large numbers

of random trials, or by pairwise test for mutual independence of features. The bias associated with the

independence assumption is traded off with large improvements in PDF estimation from the dimensionality reduction.

1 Introduction

In many classification problems of current interest, no concise statistical model is available the competing hypotheses. Example: a microphone is placed at a busy street intersection, the noises received at the

microphone are to be classified. There are two choices

for such difficult problems:

1. Employ a single general model with a large number of unknown parameters (such as Neural Net

or Kernel-based PDF estimator).

2. Employ several low-dimensional models, each

specific to a hypothesis.

Either way, a large number of parameters (features)

must be estimated and used jointly for classification. In such problems, the curse of dimensionality strikes

causing the amount of data required to train the classifier to rise exponentially, far outstripping the ability

to collect, store or process.

Many researchers hypothesize that many natural phenomana are inherently low-dimensional, but

in some unknown subspace or manifold of the

high-dimensional feature space. Learning this lowdimensional structure we call structural learing.

In this paper, we expose a novel method of struc- tural learning that has achieved a breakthrough in

classifier performance. The method, which we call independence grouping, determines a mapping of features into separate low-dimensional feature groups,

which are regarded as independent. The best mapping is determined either empirically by large numbers of trials, or by direct determination of the degree of independence. The bias associated with the

independence assumption is offset with large improvements from the dimensionality reduction.

Because of practical considerations (computer and

time resources) many of the results presented in this

paper were obtained from different data sets. However, the results are presented in the order in which

they were obtained along with the thinking that led

to them. The author hopes that this style this will

result in a very readable presentation.

2 Independence Grouping

Let there be N features organized into a vector x =

{xi,X2, . . . ,xn}- The full-dimensional (FD) classifier

for M hypotheses,

max p(x\Hj) p(Hj)

j=l,.,.,M

v JJ v J/

makes use of the FD PDF estimate p(x\Hj) which

is derived from some training data. We use K to

124
denote sample size and superscripts to denote sample

number:, {x1

,

. . . ,XK

}.

Let the N features be divided into G groups, each

group having Kj features, thus N = ^2j=1 Kj. The

feature mapping are denoted by Pi G [l,G], i =

1,...N which maps each feature Xi into a group.

Note that that G = 1, Pi = 1 for i = 1, . .

. , N is the

mapping for the FD PDF.

For each mapping (3 = {Pi, . . . ,Pn}, the

independence-grouped (IG) PDF for x is constructed

as a product of group-PDF's.

p(x\P,Hj) = p({xi : Pi = l}\Hj)

p({Xi : Pi = 2}\Hj) (1)

...p({xi :pi = G}\Hj )

The above expression carries with it an implication

that the groups are statistically independent of one

another. Note that (1) must be trained on a training

data set for each j. Training requires a double maximization/optimization: optimize jointly over (3 and

the parameters of the PDF estimator for the data

set available. When training the lower-dimensional

PDF's, less data is required. Or, with a fixed training data size, they will be more accurate than the FD

counterpart. But, is the increase in accuracy enough

to counter the bias associated with the assumption

of independence? In the cases we have studied, the

implicit assumption of independence among groups

simply is not true - there always seems to be statistical dependence between any two features. We now

argue that the goodness this assumption can be directly tested.

Note that (1) is a PDF in its own right on the same

feature space and may be directly compared with the

FD classifier using likelihood value. The apropriate- ness of the independence assumption will be reflected

in the total log-likelihood of the PDF estimate obtained

under the assumption. There is no need for guesswork

(note that we assume here that the total log-likelihood

"score" of the PDF estimate must be obtained from

a statistically independent set of data as was used for

training or else "overtraining" occurs).

We claim that the high dimensional PDF, when

optimized to fit a limited set of training data may

be making far worse compromises in the process of

training, although these compromises are hidden from

view in the vast reaches of TZN . Should (1) provide

better performance than the FD counterpart, then

there is no sane reason to not accept it. After all, recall that the FD classifier is contained in the set of

all groupings.

3 PDF Estimation

In this paper, estimates of PDF's for FD or IG PDF's

are derived from training data using a standard multivariate PDF estimation approach called heteroscedastic Gaussian mixture (GM) modeling. A widely ac- cepted technique for estimating the parameters of the

GM model is the EM algorithm [1],[2]. The EM al- gorithm suffers from numerical problems when there

is insufficient data leading some researchers to avoid

it [3] or constrain the covariances of the kernels to

be identical [4], or of uniform size with variable rotation [5] . Adding to the covariance estimates based on

a Bayesian prior density argument is the preferred

method of dealing with the problem [6], [7]. We

have obtained excellent results using Bayesian priors

to represent an implied assumption of measurement

noise. Measurement noise may represent quantization

noise or subjectively determined error variances.

4 Optimum Group Size

We have not mentioned how G or kj are determined.

We start by selecting G and kj empirically. We will

shortly see that for a given problem, algorithm performance has a broad peak at a certain group-size,

say k*

.

In the following experiment, a data set of time series "snapshots" from M = 6 signal types was available. The data was divided into 5 sets containing

different amounts of additive noise to artificially produce a variation of SNR in 3 dB increments. A total

of N = 44 features were extracted from each time series. An average of about 150 samples was available

from each class at each SNR for training and testing.

The group sizes were fixed and (3 was common

across hypotheses. For each /3, PDF's were estimated on the groups from training data, the combined PDF

(1) was formed, and classification performance (probability of correct classification, Pcc ) was measured us- ing a separate testing data set. This was repeated for a range of group sizes. When we speak of trials, we

refer to independent random data splits into training and testing halves. The Pcc was averaged across

trials. Pcc was measured by counting the number of

correct decisions as a fraction of the total number of

data samples used in testing.

The 44 features were grouped into sets of

2, 3,4, 5,6, 7, 9, 11, 17, and 21 features. The last group

contained the remainder number of features when 44 was perfectly divisible. A total of 16 statistical trials were run at each SNR and for each group size. In

each trial, not only was the data randomly split, but

the features were randomly assigned to groups.

125
It was expected that using very small groups would

induce poor performance due to the (incorrect) as- sumption of independence between groups. For larger

groups, the dimensionality issues would dominate.

The net result would be an optimal dimension. The

experiment was repeated for various levels of additive

Gaussian noise (SNR reductions) in 3 dB steps. This

expectation is very clearly supported in Figure 1. The

group size (dimension P) is plotted on the abscissa.

Pec vs. P at various SNRS (in 3 dB steps)

0.95

0 85

, ' 1—1——1

• •

•

! !!—

. i i i i_i i i i—i—i—;

l_ 10° to' io!

Figure 1: Classification performance as a function of

feature group size, average of 16 random trials.

The importance of Figure 1 cannot be overstated.

Conventional thinking in classification has been to in- crease N using the FD classifier until a collapse in peformance is noted due to dimensionality issues. Here,

we keep TV fixed but are able to adjust the dimension nevertheless by adjusting group size. The performance peak at P ~ 5 shown in Figure 1 cannot be

found by existing methods of model order selection

which do not utilize all the features at once.

5 Best Grouping

The limitations of the previous experiment are that no attempt was made to find an optimal gouping,

which should be different for each class hypothesis.

However, it still clearly indicates the existence of a broad maximum for group size around k* = 5. The following experiment is a variation of the previous M = 6 experiment. A total of N = 64 features were used in the random grouping scheme. Random

group sizes in the range of 3 to 6 in length were used.

As before, the groupings were held constant across hypotheses. For each grouping, Pcc was averaged

across SNR. A total of 1800 groupings were tested on the CRAY T3D at NUWC in Newport, RI. The

best grouping of the 1800 was selected. Multiple trials were then run using this "best grouping" to more

accurately measure its performance.

When measuring Pcc , it was necessary to add a constant to each log-PDF (equivalent to adjusting prior

probabilities of the hypotheses in a Bayesian framework). The 6 constants were adjusted to minimize

the total number of errors. This optimization was re- peated for each trial. The grouping with the best av- erage performance was then used in 16 trials at each

SNR step. In Figure 2, the resulting performance

of the best grouping is plotted in which RG stands

for random grouping. This graph shows the Pcc per0.6 -SBF(GM1) o

0.55 1 1 1 1 1 1 1 1 -35 -30 -25 -20 -15 -10 -5 0

Relative SNR, dB

Figure 2: Classification performance vs. SNR of the

best grouping out of 1800 trials for IG PDF (denoted

RG) vs. three other classifiers (see text).

formance as a function of SNR for the best random

grouping as compared with three other classifiers:

1. GM48: Full-dimensional classifier for 44 features

using 48 mixture components.

2. KNN(A; = 3): K-nearest neighbor classifier (A; =

3).

3. GM1: Full-dimensional classifier for 44 features using 1 mixture components, essentially a

quadratic Bayesian classifier.

For each data point on the graph represents an aver- age of 16 trials, each using a different random data

split of the same overall data set. The IG classifier

clarly outperforms the other classifiers.

5.1 Measure of Fit (MOF)

Up to now, we have optimized the feature grouping

by maximizing estimated Pcc . This has two disadvantages:

1. It requires a lot of computation each time Pcc is estimated. This limits the number of combinations that can be tried.

126
2. It constrains each class to have the same grouping

(it would not be practical otherwise).

In an attempt to avoid these problems, alternative

ways were sought to optimize the groupings.

Consider an algorithm for training a Gaussian Mixture estimate of p(x\Hj). Such an algorithm operates

my maximizing the average or total log-likelihood of

the data \ogp(xk

). But, as mentioned earlier, (1)

is a PDF on TZN in its own right. There is no reason

not to jointly optimize the groupings at the same time

as the parameters of the Gaussian Mixture based on

total likelihood. This incorporates grouping selection

(structure learning) directly in the PDF estimation of a given class. Thus, grouping selection is separated

from classification performance. More grouping trials could be tested per class for a given amount of

computer resources. In addition, differences in the

data structure of different classes could be taken into

account.

In Figure 3, we show 32 histograms. Each histogram is created from 37 random groupings for a

given random data split. It may be seen that the distribution of the average likelihood depends greatly on

the data split. It is theorized that some data splits

contain data points that are likely to be "alone" , without neighbors and not likely to be "covered" by PDF

mixture kernels, which tends to bias the likelihood

value down. Thus, the determination of the "best

grouping" overall had to factor in the bias of each

random data split.

The best grouping overall for each class hypothesis was selected. An improvement in classification

performance was noted, however, it was not significant. The author believes that this is due to the

high-dimensional space in which to search for the best

/3. In the following, we break through this barrier.

5.2 Independence Measure

If the implied assumption of independence groupings

is the statistical independence between groups, then

it makes sense to obtain a measure of feature interdependence. Unfortunately, for practical reasons, we

must limit ourselves to pair-wise tests. We are not

interested is simple correlation coefficients since this

is not descriptive enough. Uncorrelated random variables can be statistically dependent. The scheme we

use is based on a hypothesis test for independence

vs. dependence. More specifically, the independence

hypothesis says that

p{Xi,Xj) =p(Xi)p{Xj)

The procedure is then to estimate the three PDF's

p(xi,Xj), p(xi), p(xj) from available data, then form

350

.300

250

"§200 c

S2.

1 150 E

o

CO

°100-

50

-120 -110 -100 -90 -80 -70

Average likelihood

-60 -50 -40

Figure 3: Histograms of random Groupings for 32

different random splits

the empirical independence measure

Q(i,j)

1 K

fc=i

P(sf)p(*?)

'

where K is the number of available training samples

and the superscript indicates the sample index.

This measure was computed for all feature pairs

in a 70-feature example. The results are provided in

Figure 4. In the graphic, feature dependence measure

is scaled and quantized to a number between 0 and

15, represented as a hexadecimal character. Anything

below 3 is shown as These types of graphics are then used to manually or automatically determine the

best feature groupings.

The following procedure was found to be satisfactory: .

1. Determine what the largest group size that can be accepted.

2. Any two features with a dependence measure

greater than a threshold r are placed in the same

group.

3. Begin with r equal to some large value.

4. Lower r until the largest group size has been

reached.

5. Continue to lower r, grouping together features,

but do not add to groups that have exceeded the

maximum group size.

127
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Figure 4: Graphic of feature interdependence

6. Terminate when r reaches some minimum limit.

This procedure can be automated. The graphic in

Figure 4 produced the grouping in Table 1. The

reader may notice that the largest group size is

11. Many of the features in the largest group were

highly dependent and could not be justifiably separated. Furthermore, highly dependent (or correlated) features could be grouped together without

greatly increasing the ultimate voulme of the space.

Thus, groups with highly dependent features could be

larger.

5.3 Results of Groupings based on

Independence-Measure

Consider the second (from top) histogram in Figure

3 (trial number 31 of 32). We expand this histogram

in Figure 5. In addition, a single point is added at the far right. This point is the likelihood value of the

PDF using the grouping determined from pair-wise

independence measures and tested with exactly the

same data split as the rest. The fact that this point

is far outside the population of the randomly selected

groupings graphically illustrates how significant the

independence measure method is with respect to ran- dom grouping selection.

Group Features

1 13 14 15 23 25 27 28 43 46 24 29

2 5 8 40 21 22

3 19 20 34 18 31

4 55 56 57 58 59

5 67 68 69

6 4 45 3

7 6 10 44

8 26 30 17

9 37 38

10 41 42

11 7

12 11

13 12

14 16

15 32

16 33

17 36

18 39

19 47

20 48

21 49

22 51

23 52

Table 1: Feature grouping corresponding to Figure 4

5.4 Genetic Algorithm for Grouping

Optimization

Neither random search nor search based on pair-wise

independence measure are expected to locate the best

grouping. Since the search is on a discrete space,

gradient-based methods cannot be employed. However, a genetic algorithm is well suited for the task.

In the preliminary implementation, the following approach was employed. A starting point was selected

based on random search or independence measure. Then, a mutatiuon was performed by applying one of

three possible changes:

• Swap 2 features.

• Move 1 feature.

• Merge 2 groups.

All operations used a uniformly distributed random

variable to select the group or feature. If a feature was moved outside the range of existing groups, a new

group was created. Approximatelty 1000 single mutations were performed and the MOF was determined.

The 8 mutations which produced the largest change in

MOF with respect to the original parent for the same

random split were selected. These 8 children were

then used as parents (asexually) for the next generation. The MOF was always calculated on testing data,

i.e. unseen by the PDF training algorithm. A graphic

128
Average likelihood

Figure 5: Histogram of 37 random Groupings using

same data split

showing a histogram of the MOF of each generation

is shown in Figure 6. Beginning from the bottom, the

Full-Dim ^I^A^^

Gen 6 e L.

Gen5 |

i:.Jj\ : Gen1 \

: Hand-Selected A -J 1 -50 -45 -40 -35 -30 -25 -20

log-likelihood

Figure 6: Five generations of Genetic Algorithm

MOF histogram for the parent "hand-seleted" grouping determined from pair-wise independence is shown

along with a single data point on the right indicating the MOF for the training data. Loosely speaking,

this represents an upper limit of achievable MOF for

testing data. Next, the MOF histograms of generations 1 through 5 are shown. The smoothness of

these histograms reflects a large number of groupings

included in contrast to the single parent grouping.

Note a shift to the right with each generation. The

best grouping of generation 5 was seleted. The next

histogram, dennoted "Gen 6" is its MOF histogram.

Note that again we include the "uppper limit" point,

the average MOF for training data. The final histogram of the FD PDF (at top) provides a contrast

that clearly illustrates the characteristic of IG PDF's.

Note that the average likelihood for the training data

(single points at right) is higher for FD vs. IG. This

is expected since it reflects the fact that the IG PDF

is more constrained than the FD PDF and cannot fit the training data as well. However, when testing data

is used, the more robust IG PDF's far outperform the

FD PDF.

6 Conclusions and Future Work

An entirely new dimension has been added to the

PDF training phase of classifiers (or any PDF-based

algorithm). Structural learning finds the best structure upon which to train the PDF. While PDF es- timation must be performed by matching the PDF

parameters to best fit the given training data, structural learning must be performed by fitting to the

testing data, unseen by the PDF estimator. This en- courages the combined structure-PDF estimate to be

robust while at the same time optimizing the measure

of fit.

References

[1] R. L. Streit, "A neural network for optimum

Neyman-Pearson classification," IEEE Trans.

Neural Nets, vol. 5, no. 5, pp. 764-783, 1994.

[2] L. I. Perlovsky, "A model-based neural network

for transient signal processing," Neural Networks,

vol. 7, no. 3, pp. 565-572, 1994.

[3] J.N.Hwang, S.R.Lay, and A. Lippman, "Nonparametric multivariate density estimation: A

comparative study," IEEE Trans SP, vol. 42,

pp. 2795-2810, October 1994.

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129
LEARNING FROM LARGE DIMENSIONAL, SMALL SAMPLE DATA BY A

POTENTIAL FUNCTION METHOD WITH NONLINEAR TRANSFORMATION: A

CANCER DIAGNOSTIC STUDY

Mark Modell

MediSpectra, Inc., Cambridge, MA

Victor Kamensky

Albert Einstein College of Medicine,

Department of Epidemiology

and Social Medicine, Bronx, N.Y.

1 Introduction

Machine learning methods are especially well suited

to medical diagnostic applications. One of the application is the screening and diagnosis of cancerous and pre-cancerous conditions. In the present paper we discuss novel techniques of machine learning

applied to the analysis of data from a new optical biopsy device where the dimensionality of each

original observation of the data is very large (60, 000

items) and where the number of observations is very

small (approximately one hundred).

We have analyzed data collected by the

ColpoProbe device (MediSpectra, Inc., Cambridge,

MA) at the colposcopy clinic of the Beth Israel Hospital, Boston [L.Burke et al, 1996]. It is widely ac- cepted that Pap Smear testing has been successful in reducing cervical cancer in the U.S. by more

than 70%. It is, however, also recognized that the

methods are far from ideal and not cost effective.

Each year, 50 million women in the U.S. receive a Pap Smear test and of those, approximately 6% are returned with a finding of ASCUS (Atypical Squamous Cells of Undetermined Significance). This diagnosis represents minor Pap Smear abnormalities

that are not sufficiently clear-cut to permit a more

specific diagnosis. Because of obvious prognostic

concerns, this population requires thorough evaluation to determine whether benign or malignant processes are more likely.

The triage of patients with ASCUS results from

Pap smears is a growing problem. Currently, patients are either referred for repeat Pap smears or

directly to colposcopy. There have been several

studies in the literature on the use of Pap smears

for triaging non-negative Pap smears. These show

that the sensitivity of the Pap smear when used as a follow-up is typically between 40 and 62% (Slawson, D.C., et. al., 1994; Slawson, D.C., et. al., 1993;

Casimir Kulikowski and Ilya Muchnik

Rutgers University, Piscataway, NJ

Louis Burke and Jonathan Niloff

Department of Obstetrics, Gynecology

Reproductive Biology, and Pathology

Harvard Medical School

and Beth Israel Hospital, Boston, MA

Xiao-Wei Sun, et. al., 1995). This results in a significant number of patients with ASCUS Pap smears

not being referred to colposcopy. Additionally, the

relatively high false positive rates of the repeated

Pap smear implies that many women would be inappropriately referred to colposcopy [MF. Mitchell,

1994].

MediSpectra has developed the ColpoProbe device, an optical biopsy instrument, as a triage tool

for following an ASCUS Pap Smear result in order

to select those women most likely to require colposcopy. Increasing the sensitivity of the procedure

will result in more patients receiving the required

treatment, while increasing the specificity will re- sult in fewer unneeded colposcopies. In order to

quantify the accuracy of the ColpoProbe device,

MediSpectra has completed a feasibility study of

the instrument. We have analyzed the data collected by the ColpoProbe to assess its performance.

The present paper evaluates the diagnostic power

of the method using a novel machine learning strat- egy to efficiently process the large amount of data

produced. It also emphasizes methodological questions surrounding the application of these machine

learning techniques.

2 Data description

A single observation from the original data set comprises 300 spectrograms of fluorescence emission.

These emissions were less or equal 200 nsc. of each.

Each emission spectrum is divided into 185 spectral components. Usually the fluorescence emission

spectra have high noise. Therefore, it is necessary to aggregate the observations to increase reliability in

the processing. We used the following aggregation

before analysis:

1. The average spectrum, i.e. mean spectrogram, was computed from the 300 individual observa130
tions;

2. The average spectrum was filtered to decrease

the noise;

3. The filtered average spectrum was aggregated

in the following way: the original 185 components were separated in a small number of

groups. Each group was represented by the

mean and the standard deviation of original

spectral components in the group.

These steps of "pre-analysis" yield an efficient

data representation. Thus, after the preparation

each spectrum was represented by 51 variables. Finally, we got the set of the vectors in 51-dimensional

space. We will call them below also records or

cases. The set consisted of 81 cases classified by

histophathologist into five biopsy result categories,

denoted as CC, Metapl, NED, SILHI and SILLO

with the distribution indicated in the table 1 below:

Table 1: BIOPSY

CC Metapl NED SILHI SILLO Total

7 26 19 21 8 81

In this paper we present results of discrimination

of these 81 records when they were combined into

two groups of biopsy categories namely, "precancerous" (denoted as SIL and including SILHI and

SILLO categories) and "non-precancerous" (nonSIL, consisting of the other three categories of CC,

Metapl and NED). Thus there are 29 SIL and 52

nonSIL records.

3 A New Machine Learning Algorithm

based on the Potential Function Method

and on a Nonlinear Transformation for

Extracting Discriminating Features

3.1 Overview of Method

Most machine learning methods build objectclassification functions in a space of features. In- put objects are represented as vectors of features

and can be interpreted geometrically as points in

the feature space. Thus, any surface which splits

the space into regions associated with the different

classes can serve as an object classification function.

The main problem with machine learning is to derive or learn a classification surface from a limited number of cases of known classification. In other words, the goal of learning is to generalize the

knowledge from a limited set of samples. In geometrical terms, the goal is to construct a discriminating

surface using the limited set of labeled points in the

feature space so that it will be able to identify any

new set of input vectors (points) of unknown classifi- cation. This surface is called a discriminant surface,

and the mathematical function which describes it in

the feature space is called a recognition function, or a recognizer [Debroye et al., 1996].

The potential function method is an universal machine learning method [0. Bashkirov, E.Braverman

and I. Muchnik, 1964, Aizerman et al., 1974, E.

Braverman and Muchnik, 1983]. Recently it took on renewed importance because the support vector machine approach [V. Vapnik, 1995] has demonstrated

great efficiency in applying integral kernels as a system of functions for building discriminants. Learning procedures based on this method allow practitioners to incorporate and test a wide variety of al- ternative sub-methods that can be adapted or cus- tomized to specific problems. The principal idea is to identify a similarity function between a vector

and a class represented by a collection of vectors

of known classification (known as the training set).

Each class will be identified by its particular similarity function. This function is constructed as a

linear combination of integral kernels (the potential

functions), each of which is associated with one vector from the training set. A discriminant is defined as the maximum of the

similarity functions. Thus, for each vector, the val- ues of the similarity functions are calculated and the

largest of these determines the class associated with

the vector. To learn the class identification is to determine the coefficients of the similarity functions.

As in all machine learning methods, the potential

function method has free parameters that must be

learned from the training data. Also, in addition, it allows to choose an integral kernel types to corre- spond to the implicit structure of similarity or dissimilarity in the training data. The disadvantage of

this additional freedom is the fact that the search

for the best kernel and its parameters can be quite

expensive and time-consuming.

Over 30 years ago, a two-stage recognizer design was proposed to transform original variables

into "informative" in a particular sense [Sebestyen,

1962]. The simple rationale here was that the fit

131
between learning procedure and training samples

is expected to be better in the new space than in

that of the original one. Mostly, the mentioned

transformation was linear [W. Weiss and C.A. Kulikowski, 1991; S. Watanabe, 1969]. Further development of this approach for recogner design using a

non-linear transformation model was originally suggested by Fukunaga [K. Fukunaga, 1992]. However,

this method does not lend itself to wide practice

because, for example, it does not explore combining

potential function method at all.

In this paper, we describe and test a new nonlinear procedure for transforming a space of original variables into one that is more discriminating . The result of applying this technique is a set of new

features with approximately the equal degrees of information content. The potential function method

can work better with these features since they can

be then combined directly without the need for separate weights. The potential functions, then, corre- spond to simple distance functions.

The new nonlinear transformation is based on

three simple steps:

1. Extend the set of original variables by adding to them non-linear transformations such as their

products, ratios, etc.

2. Build Boolean variables based on applying cut- points derived from the training data to yield

the best predictive performance for the given

classifications based on a statistical similarity

criterion. Generally, the idea of using Boolean

space for a recognizer was very popular in the

60's [Bongard, 1968] and are implemented now

when the machine learning area is integrated

with Al-approach [P. Hammer et all., 1995].

Our realization of the idea is based on a particular systematical approach using of the Exact

Fisher Test.

3. keep a part of generated Boolean variables

which are not correlated.

The result of the first two steps of the procedure

is a set of Boolean variables instead of the original

numerical ones. A third step suppresses redundant

information from these derived boolean variables.

It keeps as a final set only those informative features which are correlated no higher than some cho- sen threshold. Because the procedure produces a

Boolean space instead of a numerical one, it is natural to use the potential function method with kernels based on a Hamming distance function. Next

we concentrate on the specific implementation of the

described combined algorithm for our problem. One

can easily change the algorithm by varying the described procedure.

Note, in order to maximize the use of a data set it

is common to derive a feature space transformation

such as the above based on the entire data set (i.e. training and testing sets combined). However, we

determine the weights of the kernels for the potential function algorithm only from the training data

set alone.

3.2 Principal Steps of the Learning Procedure

Below we give a formal description of the main procedures for the presented method.

Transformation from numerical data into

boolean data. Three procedures are described

here which require the following notation and definitions. Let us denote by X — \\xij\\ y

i —

1, 2, N; j = 1, 2, n any given matrix of N rows

{x,-.} which presents objects characterized by n nu- merical variables.

The first procedure extends X to Y =< X, X' >

where new variables from X' are, as mentioned

above, the products and ratios for all possible pairs

of n variables from X. Every pair of original variables [xk, Xfc'] determines three new numerical variables, - (xk * Xk', Xk/xk>, Xk'/xk). The total number

variables in Y becomes (n * (n — 1) + n(n + l)/2).

The second procedure analyzes all possible cut- points on every y-variable (y is a column of the matrix Y; a cut-point is a value of y which splits all given in the matrix Y y-values into 2 groups: which

are smaller then the cut-point and which are higher

it). This analysis permits us to evaluate how well

the associated boolean variable correlates with the

output-classification, which is also is a boolean variable. We will denote the output variable as C: if for an i-th record the corresponded value C,- = 1 it means the i-th record belongs into the class A and

if C, = 0 it belongs into the class B.

One determines one boolean variable z,k by conditions

zsk = 1 if yk > y*

k and z>k = 0 if yk < y*sk where y*

k

is the 5-th cut-point on the corresponding

numerical variable yk- One evaluates the variable

132
zs k by calculating the 2*2 table

a b

c d

where a = #i(zi3k = lkd = l),b = #i(zis {k) = ltd = 0),c = #«(«,-,(*) = O&C- = l),d =

#<(*,-.(*) = O&C* = 0).

In the above equalities were used the following

notation:

a) a number of observation in a given data which

matches conditions definded by the content

The table allows to use a statistical measure to

estimate the probability P of the event n

Zi t (k) =

lkyi. = A and zis (k) = O&y;. = S". After the

evaluation one chooses a threshold P* for the probability P: if P > P* (or, 1 - P > P*) then zt (k)

is LepA as a candidate significant boolean variable.

Mai"'r different statistics can be used for this purpose, of which the simplest is to directly use the

ratio p = (a + d)/(a + b + c + d) : if for example P* = .7 then z, is significant if p > .7 or if

(1 — p) —> .7. In our concrete research we used so

called the Exact Fisher Test [Fleiss,1982; Hays,1978;

Woolson,1987]. The quantities a,fe,c, and d are the

numbers of cases in the 2X2 confusion matrix where

the biopsy classes nonSIL and SIL denote the true

classification and VBOOLi = 0 denotes a negative

screening result from using the i-th Boolean variable

related to a significant variable, while VBOOLi = 1 would correspond to a positive result for the same

variable.

Fmin = m\nFishert

. (2)

BIOPSY

VBOOLi nonSIL SIL Total

0 a b a+b

1 c d c+d

Total a+c b+d a+b+c+d

For this table the calculation of Fisher's exact (2-

tailed) test was carried out. The probability of measuring a,b c and d in the table under the assumption

that the percentages 1-s and s for the two classes

(nonSIL and SIL ) are the same is then given by the

following formula:

Fishert =

(a + b)\(c + d)\(a + c)l(b + d)\

(a + b + c + d)\a\b\c\d\

(1)

Variables are evaluated and selected by using the

values of

This procedure screens all n yk-th for all the cor- responded cut-points s(k) and collects a complete

set of the candidates for significant boolean variables. We denote the set as S and let the module of

S be M. This completes the second procedure.

Significant variable extraction. The final step

is to extract a set S' of highly significant boolean

variables which we define as the smallest subset of

5 which has a high enough level of correlation with

the variables from the complementary subset (5 —

5'). One can apply different heuristic procedures to obtain this type of the core set. We used one of the

simplest:

1) building a matrix of correlations on the defined

set of all M candidates for the significant variables;

2) for every candidate calculate the sum of the

moduli of coefficients of its correlations with all other variables;

3) to extract a set S' with cardinality corresponding to a prior chosen value M' with the largest val- ues of the sums. Potential function procedure. We chose

to use the potential function method in its non- parametric form modeled by a parametric family of

integral kernels [Aizerman et al. 1976]:

K(u,v) = l/{a + brq (u,v)), (3)

where u and v are vectors with components which

are extracted significant boolean variables (vectors

in the M'-dimensional space); r(u,v) is a distance

function defined on an arbitrary pair of vectors and

{a, 6, q} are three scalar free parameters. Because

K is a monotonically decreasing function of the distance function we can interpret it as a similarity measure. The method introduces a similarity function K(u, G) with values that are average similarities between a vector u and a class of vectors G.

The function is the mean of the above described el- ementary similarity measure K(u, v):

K(u, G) = W\ ^2 c{v)K{u,v), (4)

where | •| is the notation for a modulus, and c(v) is a

function of weights defined on all elements of G. Let

us assume that the training set for class A contains

iV"i vectors and the training set for class contains

iV2 vectors then the discriminant rule is given by

the function:

133
F(u) = K(u, A) - K(u, B). (5)

The rule is simple: if F(u) > 0 then u belongs in

class A and vice versa. The function of weights c(v)

is defined on the training set by a standard algorithm of the potential function method: the training set is observed iteratively, - an observed element u is recognized by the above rule based on current

values of the function c(v), and if it is recognized incorrectly the corresponding weight c(u) is increased

to [c(u) + 1]; if it is recognized correctly no weights

change. The procedure is stopped when a cycle of

observations of all elements in the training set don't

yield changes in the value of the function c(v).

4 Procedures for performance evaluation

Two types of tests have been used for the performance evaluation. The first is a computationally

inexpensive single test procedure, while the second

is a form of cross-validation:

A) Single Test Procedure:

1. Randomly divide each class (nonSIL and SIL)

into approximately equal subsets

2. Perform the procedure described in section 3.5

twice. First let SUBSET 1 be the learning

sample, and SUBSET 2 be the testing sample. Then reverse this, using SUBSET 2 as the

learning sample, and SUBSET 1 as the testing

sample.

Recognition results for both applications of the

method are then combined into the following standard performance table (or confusion matrix):

DISCR. DECISION CLASS BY BIOPSY

nonSIL(N)

SIL(P)

nonSIL(N) SIL(P)

Tn Fp

Fn Tp

where: Tp - True Positives:the number of SIL

cases correctly recognized as SIL;

Fp - False Positives:the number of SIL cases incorrectly recognized as nonSIL;

Tn - True Negatives: the number of nonSIL correctly recognized as nonSIL

Fn - False Negatives: the number of nonSIL incorrectly recognized as SIL

Their percentages with respect to the correct cat- egorization (based on biopsy results) can then be

used to evaluate the performance of the discriminant method in terms of true positive and true negative frequencies (Tp% ,Tn%

respectively), and their

percentages with respect to the classifier decision

provides the predictive power of a positive result

vs. that of a negative result (Pp% and Pjv%) respectively).

B) Multiple test procedure:

The test described in A) above is performed 100

times - for 100 random splits of the data set into two

parts. Summary statistics for frequencies of true

positives, false positives, true negatives and false

negatives will provide the appropriate performance

results for the discriminant method. This is a type

of cross-validation.

5 Results of ColpoProbe Data Analysis

All the results described below were obtained by applying the potential function method on significant

boolean variables derived from the entire set of 81

observations. While from an application perspective

statistically it would have been more appropriate to have derived these Boolean variables from the learning set data alone, the present analysis suits the

purpose of providing an evaluation of the potential

function learning method. The application of the

cut-point procedure produces 20 significant boolean

variables generate from the set of 81 observations.

For the selected variables we performed 100 tests of the discriminant function using 100 random

splits, yielding the performance Table 2(in the first,

fourth and seventh line of the table are numbers of

observations were tested, - because every original

observation was tested 100 times the total number

of tests was 8,100; respectively, second and fifth line

of the table present results in rows; finally, the third

and sixth line present for columns of the table).

Statistics for percents is the table 3.

The best performance is given by a split with the

results shown in the table 4.

134
Table 2: 100 Tests result

6 REFERENCES

Decision BIOPSY 1 T T> - 1_ t XT:i~XT Tilt V. . 1. .. 1 : - . /"* A I T J 1

,

1. L. Burke, J. JNilott, M. Jvobelin, (j. Abu-Jawaen,

nonSIL SIL lotal a. z<eiencnuK ana jvi. lvioaeii^iyyDj

nonSIL 4766 507 5273

90.38 9.62 Use of Autofiuorescence of Cells to Evaluate Cer91.65 17.48 vical Neoplasia Journal of Gynecologic Techniques,

SIL 434 2393 2827 Vol. 2, No.4:187-190.

15.35 84.65

8.35 82.52 2. M. F. Mitchell(1994)

Total 5200 2900 8100

Table 3: Average results

Variable N Min Max Mean Std Dev

100 65.5 93.1 82.5 6.7

100 70.4 92.9 84.8 4.9

TN%

100 82.7 96.2 91.7 3.0

100 81.5 96.1 90.5 3.4

There are nine splits that yield the minimum

number of two false negatives (Fn, where SIL is mistaken for nonSIL) like in the above best performance table.

From examining the statistics of these results we

can see that, for a preliminary data set with a rel- atively small amount of data of large dimensionality, the performance provides excellent results with

tight bounds for controlling (expensive) false positives, while keeping the number of false negatives

within reasonable bounds. Its negative predictive

power is remarkably high (96% with a standard er- ror of 3%) for a first analysis of the data.

Further analyses and refinements of the preprocessing and the method are being carried out with

the goal of tightening the bounds and further improving the false negative performance of the test - and hence its positive predictive power.

The accuracy of colposcopy Clinical Consultations in Obstetrics and Gynecology, No. 6:70-73.

3. Slawson, D.C., et al.(1994)

Should all women with cervical atypia be referred

for colposcopy: a HARNET study J. of Family Practice, 38:4, 387-392.

4. Slawson, D.C., et al.(1993)

Follow-up Papillomavirus Smear for Cervical

Atypia: Are we missing Significant Disease? J. of

Family Practice, 36:289-293.

5. Xiao-Wei Sun, et. al.(1995)

Evaluation of the Hybrid Capture Human Papillomavirus Deoxyrbonuckeic acid detection test Am.

J. Obstetrics and Gynecology, 173:1432-1437.

6. Devroye, Gyorfi and Lugosi(1996)

A Probabilistic Theory of Pattern Recognition.

Springer, p. 654

7. Bashkirov, O.A., Braverman,E.M. and Muchnik,I.B. (1964),

Potential Function Algorithms for Pattern Recognition Learning Machines, Automation and Remote

Control,25, n 5, 629-631.

Table 4: The best result

DECISION BIOPSY

nonSIL SIL

nonSIL

SIL

49 2

3 27

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Potential Function Method in Machine Learning

Theory Nauka, Moscow, 384 p. (in Russian)

9. Braverman, E.M. and Muchnik, I.B.(1983)

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Structural Methods for Analysis of Empirical

Data, Moscow: Nauka , 464p.(in Russian)

10. V. Vapnik(1995)

The nature of statistical learning theory Springer,

London, 267p.

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Computer Syttems that learn: Classification and

Prediction Methods from Statistics, Neural Net,

Machine Learning, and Expert Systems, Morgan

Kaufmann, Palo Alto, 233p.

12. Sebastyen(1962)

Decision Making Processes in Pattern Recognition Macmillan, New York, 1962, 162p.

13. S. Watanabe(1969)

Knowing and Guessing Wiley, New York,

14. M. Bongard(1968)

Problem of recognition

15. P.L. Hammer, E. Boros, V. Kamensky, A.

Kogan and Ilya Muchnik(1995)

Logical analysis of data(LAD): an implementation in SAS(R) language, Proceedings of the Eighth

Annual NorthEast SAS Users Group Conference,

Washington, DC,PP 683-688.

16. K. Fukunaga(1992)

Introduction to Statistical Pattern Recognition

Academic Press, London, 591 p.

17. Fleiss Joseph L.(1982),

Statistical Methods for Rates and Proportions,

Second Edition, John Wiley and Sons, New York.

p.25-26.

18. Hays, William L.(1988)

Statistics. Fourth Edition, Holt, Rinehart and

Winston, New York. p. 783-787.

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Statistical Methods for the Analysis of Biomedical

Data, John Wiley and Sons,New York, p.215-221.

136
Incremental Learning of Inheritance

Jose Neves, Evgueni Smirnov and Cesar Analide

Department of Informatics

The University ofMinho

Largo do Pago

4719 BRAGA CODEX-PORTUGAL

e-mail: {jneves, smirnov, analide} @di-ia.uminho.pt

Abstract. This paper proposes a cycled system for learning of the hierarchical models of inheritance of

Multiagent Systems (MAS), using a logical framework. The system acquires the appropriate models

from the descriptions of the most informative models

with respect to the learning process. The determination of the most informative models is accomplished

by analysing hypothetical space of the models and

evaluating the problem solving capabilities of the MAS, based on these models. The system presents

two advantages: its components are symbolic, and it requires significantly small number of the "training"

models. This allows learning of "understandable"

symbolic descriptions of the hierarchical models of

inheritance in reasonable time.

Keywords: Machine Learning, Multiagent Systems,

Logic Programming.

1 Introduction

Learning in MAS is on the intersection between the multiagent paradigm and the machine learning one [3,

8]. It is motivated by the insight that it is not possible

to determine a-priori the complete knowledge that must exist within each component of a distributed

system, in order to allow for a satisfactory perform- ance of such a system. It is therefore broadly agreed in both the Distributed Artificial Intelligence and Machine Learning communities, that there is need to pro- vide these systems with the ability to learn, i.e. to self- improve their future behaviour.

Learning in MAS consists of two types of learning.

First, single-agent learning; i.e. learning that is done

by a single agent as a result of its interaction with the environment or a set of other agents. This type of

learning presupposes the application of the traditional machine learning techniques. Second, distributed

learning, that is defined as learning what is possible,

only because several agents are presented. This type

of learning comprises learning in teams, learning to

act in teams, learning to coordinate agents, learning of

the organisational structure of MAS, etc. The main

techniques used in distributed learning are borrowed

from Reinforcement Learning and Neural Networks

[6,8], which ensure perceptiveness, correctness and

reactiveness of the MAS, but at the same time retain the main shortcomings of the non-symbolic ap- proaches to Artificial Intelligence, namely:

• incomprehensibility of the knowledge and behaviour of the systems;

• high time complexity as a result of exploring a

sufficient number of environmental states. The research considered in this paper aims at overcoming these problems in the learning organisational structure of MAS, endorsed via the disjunctive

logic programming paradigm facing inheritance [1]. That is why the learning organisational structure is reduced to the task of learning of the hierarchical

models of inheritance. Solving this task is proposed to be done in a closed cycle:

WHILE there is no acceptable description of the

models of inheritance DO

Determine the satisfactory performance of the MAS

with respect to their current models of inheritance;

Consider the descriptions of the models, as their

examples with positive or negative classification in respect to the performance;

Learn the general descriptions of the "good" models with the new examples;

Determine the most informative (examples) models

with respect to learning;

Change the model of the systems with the most in- formative ones. END

The steps 1-2 and 4-5 are completely symbolic

sub-processes, that require explicit descriptions of the

inheritance models. That is why the learning step

obeys this requirement, and the communication within

the cycle is accomplished on a symbolic level. This means that the intermediate results of the learning

process are symbolic descriptions of the models of

inheritance. Their complete acquisition is accomplished when the determination of the most informative models is not possible, or when the designers of

the MAS agree on some of the acquired descriptions

of the "good" models, as satisfactory. Therefore, the

process of learning is completely autonomous, and

requires only the most informative models, in contrast with existing algorithms [8]. The final results are the symbolic descriptions of the models of inheritance,

that guarantee a satisfactory performance and understandable behaviour of the corresponding MAS.

This paper sketches the logical knowledge representation scheme in section 2. Section 3 considers a system for learning of the models of inheritance,

based on the proposed cycle. Section 4 analyses the system and proposes future directions for research.

137
2 Knowledge Representation with Inheritance

This work considers knowledge representation by means of a hierarchical model, with inheritance, that endorse the treatment of incomplete information, al- lowing for commonsense reasoning.

The system structure is supported by two kinds of

entities: agents, that represent specific entities such as objects or their individual classes or instances; and

links, which are used as a way of formalising relation- ships among those entities (Figure 1). One link may

represent a hierarchical relation between agents, or the association of a set of data to an agent (the agent's

theory).

Figure 1. A Hierarchical Model of Inheritance

In terms of a logic program, this kind of relation between two agents can be described by a predicate of

the type ISA links, that are found in most of the works

about hierarchical structures, namely:

isa: Agent, Class, Cancelled

where the first argument labels the agent on a hierar- chical structure, linked to the class given by the sec- ond parameter. The last argument presents the set of

information that must be cancelled in the inheritance process. One may say that Tweety is a bird, where the knowledge about whether it may or may not fly, is not

inherited, but represented in terms of the production:

isa( tweety, bird, [fly])

About the agents knowledge, a predicate is defined, being the first argument the identification of the agent, and the second its theory:

agent: Agent, Theory

The fact that birds can fly, that have wings, but do

not have wheels, can be declared as:

agent(bird, [fly, wings, —(wheels])

Note that the classical negation, '-.', is being used

in a way that permits one to denote what kind of

knowledge must be interpreted as known to be false, distinguishing from other situations where one does

not have information about the truth of knowledge.

In this system the agent's data is represented at the

level that it appears on the hierarchy. For those agents

which are subclasses of other entities, its knowledge

may be inherited from the hierarchy, where the proof

mechanism to provide the system with this kind of

flavour may be stated as follows:

• a question may be proved at the agent's level; or

• the solution to a question may be found at a level on the hierarchy that is meta to the agent to which

the question was initially for. This type of reasoning will be performed by a proof

predicate, defined as:

proof: Agent, Question

where Agent identifies the agent questioned and

Question represents the question itself. The first bullet above can be declared, as:

proof(Agent, Question) <—

agent(Agent, Theory)

,

process(Question, Theory)

where " names "if and the proof for a question

stated for a specific agent is found if it is possible to process that question in the agent's theory.

The second bullet, states that the solution to one's

question must be searched up to the hierarchy, through

those branches with permission to inherit knowledge:

prooflAgent, Question) <—

isa(Agent, Class, Cancel)

,

not exists( Question, Cancel) , proof{ Class, Question

)

3 Learning Hierarchical Models of Inheritance

Learning hierarchical models of inheritance, based on

the proposed knowledge representation scheme, are needed, because it is not possible to determine a-priori the models, such that a satisfactory performance of the systems is guaranteed. This presupposes that the hier- archical models of the systems have to be refined

(learned), using the feedback from their decision

making processes. The definition of the learning task,

and proposition of a system for its solving, are the subjects of this section.

3.1 The Definition of the Task

A system based on the knowledge representation

scheme from section 2, can be considered as a MAS.

The system consists of a set of agents and classes,

whose relationships are determined by a given hierarchical model of inheritance. The task for learning of

the models is a task of acquiring new models, that ensures the system effectiveness with respect to a given criterion of performance.

The Task of Learning the Hierarchical Models of

Inheritance

Given:

• A multiagent system:

• A set of agents and agent's classes;

• A hierarchical model of inheritance.

• A criterion of performance of the system;

• A set of the tasks of the system.

Find

• The hierarchical models of inheritance of the sys- tem that maximise its performance criterion. The task of learning the models of inheritance is a

task of learning the relationships among the agents

and their classes. It is motivated by the fact that the

138
The Hierarchical Model of Inheritance The correspondence between the ISA

predicates and the attributes in DNF language

isa(ag2, ag,,[Y])<->A,= 0

isa(ag2, ag,,[]) <->At= 1

isa(ag3,ag,,[Y])<->A2 =0

isa(ag3, agj,[]) <->A2 = 1

isa(ag3, ag2,[Y]) <->A3 =0

isa(ag3, ag2,[]) <->A3 = 1

isa(ag<, ag2,[V]) <->A4 =0

isa(ag4, ag2,[]) *->A4 = I

Figure 2. An Example of a Multiagent Logic Programming System, its Hierarchical Model of In- heritance, and Corresponding Description Languages

model of inheritance is formed by such relationships,

and therefore is described by a conjunction of the cor- responding ISA predicates. As different hierarchical

models can have "positive or negative classification"

with respect to the performance criterion of the sys- tem, their "ISA" descriptions can be considered as

training examples of these models. Forming the ex- amples is a gradual process of transition, of a system's

model to another, by means of an association of the models with the classification determined by the crite- rion of performance. This means that the task of

learning models of inheritance is an incremental one. The result of the learning process has to be a set of

the most important models with respect to the high

quality performance of the system. The set is defined

as a set of models, such that does not exist any other

set with smaller number of models, which lead to the

satisfactory performance of the system.

3.2 The Choice of the Description Language of the

Hierarchical Models of Inheritance

The description of models of inheritance has to be

made within languages that ensure solvability of the incremental learning task in real time. Therefore the DNF attributive languages are chosen, because the corresponding learning algorithms are very simple,

and lead to suitable average complexity for both batch

and incremental learning.

Encoding the descriptions of models of inheritance

in DNF attributive languages is possible by the fol- lowing scheme: every ISA link corresponds to an attribute, and every cancelled list corresponds to an in- teger (Figure 2). The integer number represents a vector with N binary digits, where N is the number of

the possible predicates, whose extensions can be inherited. Therefore a position in the vector corresponds

to a predicate, and the value 1 (0) of the digit means,

that the extension of the predicate can(not) be inherited. The integer belongs to the closed interval [0,2N

] which boundaries mean forbidden and full inheritance.

This scheme of representation aims at decreasing

the description complexity of the learning task, and at the same time preserving the exactness of the model

descriptions. In this way the task can be solved in rea- sonable time by the incremental decision tree learning.

3.3 Incremental Decision Tree Learning

The requirements: i) the task of learning the models of

inheritance is incremental; ii) the learning has to identify the important models; and Hi) the representative

scheme of the models is attributive, determine ITI algorithm as the most suitable one [7]. ITI is an algorithm for incremental concept learning by induction on decision trees, that handles both numeric and symbolic values of attributes of the examples in DNF at- tributive languages. Algorithm understanding presupposes the consideration of the notion of the decision

tree and the method of learning.

3.3.1 Decision Trees

A decision tree with respect to a set of pre-classified

examples, that are presented in a conjunctive attributive language, is a tree whose nodes correspond to different attributes of the language, and the branches

(arcs) correspond to different values of the attributes, so that every example from the set can be coded by

simple traversing from the root of the tree to the cor- responding example's leaf (Figure 3). The use of the decision tree in induction is due to the natural fact,

that the process of learning consists of finding the

nodes within the tree, corresponding to examples with

the same classification. The descriptions of the paths

from the root of the tree to these nodes are represented

in the conjunctive attributive language. Each of these

descriptions is discriminant; i.e. it contains only those

attributes which values discriminate examples from

the corresponding node with respect to other examples. Therefore the disjunction of the conjunctive descriptions with the same classification form the dis- junctive discriminant description (in DNF attributive languages) of a concept, that is associated with the

classification. This is a natural result in decision tree learning, that can be re-interpreted as acquiring the maximal descriptions of the concepts in the partially

ordered DNF attributive languages.

The main problem in decision tree learning is the

fact that the number of possible decision trees is equal

139
A pre-classified set of examples

of the model of inheritance

The Corresponding Decision Tree

Training Data Classification Ai A2 A3 A4 of the examples 0 0 0 1 0 0 11 +

0 10 1 0 111 1111 +

-0101

-0111

The resulted description of the "good" hierarchical models of inheritance derived by traversing the paths in the tree:

( (A2 = 0aA3 =1) v(A,= 1 a A2 = !))<->

<->((isa(ag3, ag,,[Y]) a isa(ag}, ag2,U) ) W isa(ag2, agi.O) a isa(ag). ag,,[]) ))

Figure 3. A Decision Tree from the Training Examples of the Inheritance Model

to the possible combinations of the attributes in the languages. That is why the problem of finding the most minimal decision tree is very important, and at the same time unsolvable in the general case. In spite

of this negative fact there exists a general decision tree algorithm [4], that builds decision trees using a topdown, divide-and-conquer approach: select an attribute; divide the example set into subsets, characterised

by the possible values of the attribute; and follows the same procedure recursively with each subset until no

subset contains examples with different classification. The algorithm is able to construct near-optimal decision trees when the choice of the attribute on every

step is made by the use of the following information

theoretic method: suppose that the training example

set contains p

positive and n negative examples; at the same time any attribute A divides the training set E

into the subsets El....Er, according to its r distinct values; each subset Ei has pi positive and ni negative

examples; so the information gain from the test of the

attribute A is:

r Gain(A) = I(-^, -£-)- XtHt ^T^T' 7^ 1=1 where / is the informative formula.

In this way on every step the algorithm calculates the information gain of the attributes, and chooses the one that has the best gain. This guarantees the building of near-optimal decision trees in batch manner, whose validity has been shown in [4].

3.3.2 Incremental Algorithm

ITI algorithm builds incrementally Decision Trees (DT) in contrast with the general decision tree algorithm (Figure 4). It uses the following scheme: the

initial tree is the empty tree (NIL). When an example

is to be incorporated into a tree, if the tree is NIL then

the tree is replaced by a leaf that indicates the class of

the leaf, and the example is attached to the leaf. Whenever an example is to be incorporated, the branches of the tree are followed according to the val- ues in the example until a leaf is reached. If the example has the same classification as the leaf, the example

is simply added to the set of examples, saved at the node. If the example has a different classification from

the leaf, the algorithm attempts to turn the leaf into a decision node by the choice of the proper attribute. Immediately after an example incorporation, the tree

is balanced according to the gain's expression.

ITI(D7V decision tree, E: training example set)

FOR every example e e E DO

IF DT is NIL

THEN

Replace DT by leaf node L with classification

equal to the classification ofe;

ELSE

Classify e in DT andfind a leafL in DT,

that corresponds to e; IF e has the same classification as the corresponded leafL

THEN

Add e to the example set ofL;

ELSE

Convert the leaf L into a decision node

DN and determine the partition attribute

of DN;

Extend DT with a sub-tree ofDN;

Balance DT.

END.

Figure 4. ITI 's Algorithm

3.3.3 The Most Informative Learning

The incremental learning can be speed up, if it is carried out by the most informative training examples,

which are defined as examples that correspond to a

half of the descriptions in the hypothesised space of

the concepts to be learned. In this way, regardless of

their classification, the learning is dramatically speed

up, because a half of the currently plausible concept

descriptions is rejected.

Applying this idea to decision tree learning pre- supposes the determination of the DNF hypothetical

spaces of the concepts, presented in decision trees (Figure 5). These hypothetical spaces are determined

by two boundaries in the partial ordered structure of

DNF attributive languages [2]. The first, upper

boundaries, are disjunctive discriminant descriptions

140
The structure of DNF hypothetical space

Ai=?a A2=Oa A3 =l a A<=? Ai=1a A2=l a A3=?a A*=?

Ai=0a A2=0 a A3 =1a A4=? A,=?a A2=0a A3=1aA4=1 Ai=1 a A2 =1a A3=1a A4=? Ai=1a A2=l a A3=?a A«=l

A,=0a A2 ^0"a'A3=1a A4=l Ai=1a A2=1a A3=l a A4=l

The upper boundary:

(A2 = 0aA3 = l)v(Ai = l aa2 =

The lower boundary:

(A,= 0 aA2 = 0 aA3 = 1 aA4= 1) v(A/= 1 aA2 = 1 aAj= 1 aA<= 1)

Both conjunctive hypothetical spaces in DNF space are shown with and lines.

The upper and lower boundaries of the first conjunctive hypothetical space are,

respectively: (A 2 = 0 aAj= /) and (A/= 0 aA2 = 0 aAj= 1 aA<= I)

The upper and lower boundaries of the second conjunctive hypothetical space are,

respectively: (Ai= 1 aA2 = 1) and (Ai= 1 aA2 = / aAj= 1 aA<= 1)

Figure 5. The Hypothetical Spaces of the "Good" Models of Inheritance

of the concepts, that according to the properties of

decision trees are the maximal descriptions of the concepts in the DNF attributive languages. The sec- ond, lower boundaries, are disjunctions of examples

of the concepts, which ensure their minimality in these

languages [5].

The most informative examples with respect to the

first conjunctive hypothetical space:

(A,= 1 a A2 = 0 aA3 = 1 aA4 = I) and

(A/= 0aA2 =0aA3 = I a A<= 0);

These examples are near misses examples with respect

to (A t = 0 a A2 = 0 a A3 = 1a A4 = 1) and correspond to (A2 =0aA3 =1).

Figure 6. Determining the Most Informative Examples

with respect to the First Conjunctive Hypothetical

Space (presented in Figure 5).

The DNF hypothetical spaces can be considered as unions of conjunctive hypothetical sub-spaces (Figure

5). These sub-spaces are determined by the conjunctive discriminant descriptions of the concepts (upper

boundaries) and corresponding concepts examples

(lower boundaries), which are mutually disjointed

with respect to examples, once their upper boundaries

are discriminant. Therefore it is not possible to deter- mine the most informative examples for DNF hypothetical spaces. However that is possible for the conjunctive hypothetical sub-spaces, once they are con- vex and definite (for the chosen coding scheme), and

there exists a simple near-optimal heuristic procedure

for determining the most informative examples with

respect to them. It determines the most informative

examples, as near-misses examples; i.e. the examples

whose descriptions are different with respect to the descriptions from the lower boundaries only with the value of one attribute (Figure 6) [2]. The simplicity of

the procedure makes possible the development of oracle for support of most informative incremental

learning of decision trees (Figure 7). The oracle gets, as an input a decision tree and acquires the most in- formative training examples with respect to the tree and the concepts to be learned. In order to do that, the oracle determines conjunctive hypothetical spaces of

the concepts by acquiring their boundaries from the decision tree. The lower boundaries serve to deter- mine the most informative examples by the use of the

heuristic procedure, and the upper boundaries for

sifting out those of them, that do not correspond to the spaces.

Oracle(Z)r : decision tree; { Eq }' set from sets of

the most informative examples of the concepts)

Determine the upper (U) and lower (L) boundary

sets of the conjunctive hypothetical spaces of the concepts C encoded in DT;

FOR every concept C DO

FOR every boundary set of concept C DO

Determine the set of near-misses examples E'c

with respect to L;

Removefrom E'c those examples that do not correspond to U;

Eq — Eq kjE c END

Figure 7. The Oracle for Determining The Most In- formative Examples

3.4 A System for Learning of the Hierarchical

Model of Inheritance

The system for learning of the hierarchical models of

inheritance consists of a set of embedded (six) subsystems, that form a closed cycle (Figure 8). The first one is a MAS, which models of inheritance have to be

determined. This system tries to solve a particular task from a given task set, as its initial model of inheri- tance is preliminarily determined. The results of the

141
problem solving process are analysed by the second

sub-system, that identifies their quality by a given

criterion of performance of the MAS. The logic description of the current hierarchical model is trans- lated to DNF attributive language by the third subsystem, that uses the coding scheme, proposed in the sub-section 3.2. The resulted attributive description is considered, as a training example with positive or negative classification, depending on the quality of the current solution. The fourth sub-system ITI algorithm

updates the decision tree of the concept corresponding

to the models of inheritance with the new example.

The new decision tree is used by the fifth sub-system

of oracle, that determines an ordered set of the most new informative examples. This set of examples is translated by the sixth sub-system from DNF attributive language to the initial logic language. The first example of the set represents the description of the new most suitable model of inheritance with respect to the learning process. That is why the MAS changes its model of inheritance according to the new description

and continues to solve its tasks. This closed process of

learning of the hierarchical models of inheritance goes on till the moment when the oracle is not able to generate new examples, or the designers of the MAS determine some of the models, as satisfactory. In both

cases the final result is a symbolic description of the "good" inheritance models of the MAS.

4 Conclusion

This article proposes a system for learning the hierar- chical models of inheritance of MAS, that are repre- sented under the logical knowledge representation

scheme, presented in section 2. The main advantages

of the system are the following:

• The system acquires the symbolic descriptions of

the most important symbolic models of inheri- tance, that ensures satisfactory and understandable

performance of the corresponding MAS.

• The system learns the models of inheritance in reasonable time, because the most informative ex- amples of the models are only used, that leads to rejection of a half of the hypothetical spaces of

models in the average case. This property contrasts

the proposed system with the existing system for refinement of the agent relationships, that use arbitrary examples [6,8]. • The system is completely autonomous; i.e. it does

not require external help.

• The system can be applied to different MAS with

inheritance models.

The main shortcomings of the system pointed the directions for future research:

• Impossibility to learn, when the criterion of per- formance of the MAS is not well-defined, that leads to the presence of noise in the training descriptions of the models;

• Impossibility to learn, when the agent's theories are changed. In this case some of the models of in- heritance change their performance classification

Figure 8. The System for Learning of the Models of

Inheritance

and the learned "good" models became invalid. Both shortcomings correspond to learning in the presence of noise and concept drift. They can be easily avoided for the learning sub-system, but not for the oracle one. That is why the main efforts for improvements have to be made in the oracle based decision

tree learning, that is a completely new area of research

in machine learning, ensuring the extension of the

capabilities of the system.

References

[1] Analide, C, and Neves, J., Hierarchical Structures with Inheritance, Technical Report, Department of

Informatics, University of Minho, April 1997.

[2] Mitchell, T., Generalisation as Search, in: Dietterich, T. and Shavlik, J., (eds.) "Readings in Machine

Learning", Morgan Kaufmann, 96-107, 1991.

[3] Kaiser, M., Dillman, R., and Rogalla, O., Communication as the Basis for Learning, in: Proceedings on Workshop on Multiagent Learning, ECAI, 1996.

[4] Quinlan, R., C4.5: Programs for Machine Learning, Morgan Kaufmann, 1993.

[5] Smirnov, E.N. and Neves, J., Example Order In- dependent Learning of Disjunctive Concepts, AIDRI97 Conference, Switzerland, 1997, (in print).

[6] Stone, P., and Veloso, M., Multiagent Systems: A

Survey from a Machine Learning Perspective, (in

print).

[7] Utgoff, P., An Improved Algorithm for Incre- mental Induction of Decision Trees, in Proc. on Inter- national Conference on Machine Learning, 1994.

[8] Weiss, G. and Sen, S., Adaptation and Learning in Multiagent Systems, Springer-Verlag, 1996.

142
MULTIRESOLUTIONAL METHODS

Multi- Resolution Data Processing:

It is Necessary, It is Possible, It is Fundamental

S. A. Starks1

, V. Kreinovich 1

, and A. Meystel2 *NASA Pan-American Center for

Environmental and Earth Studies (PACES)

University of Texas at El Paso, El Paso, TX 79968

emails {sstarks,vladik}@utep.edu

2 National Institute of Standards and Technology

Gaithersburg, MD 20899

ABSTRACT

Experience shows that many data processing problems are

difficult to solve, and some of these problems have even been proven to be computationally intractable. Human

experts successfully solve many such problems by using

a hierarchical, multi-resolution approach. These multiresolution methods are, in several cases, provably optimal. However, due to the computational intractability of

the problem itself, the multi-resolution approach can only

work if the systems that we are analyzing are themselves

hierarchical. We show that, first, due to (inevitable) measurement inaccuracies, an arbitrary input data is consistent with the hierarchical model, and second, that in many

cases, the actual physical world is indeed fundamentally

hierarchical.

Since traditional statistical methods have been designed

primarily for non-hierarchical models, their direct application to multi-resolution data processing can lead to biased

estimates. On a simple example, we show how these methods can be corrected to avoid this bias. Surprisingly, the

analysis of this problem leads to new unexpected symmetries. KEYWORDS: multi-resolution data processing, granularity, computational intractability, wavelets, fractals, satellite image, semiotics, environmental studies,

Schroedinger's paradox

1. DATA PROCESSING IS DIFFICULT

Data processing is difficult: an empirical fact. From

the engineering viewpoint, the main problem with data ac- quisition and processing is to manage to acquire the data.

To launch a successful space mission to other planets is indeed an extraordinary engineering achievement. However,

even for such missions, the pure volume of acquired data

is so huge that processing all this data becomes a very

difficult task.

Computers become faster and faster, new algorithms are designed, and therefore, data processing becomes faster

and faster; however, at the same time, this same progress

leads to better data acquisition devices that drastically in- crease the amount of raw data, and to new ideas of what

additional information we can extract from the old data. A

typical NASA-related example: the University of Texas at El Paso, together with Jet Propulsion Lab, is currently analyzing the data from Mariner missions to find relativistic

effects on the spaceships' trajectories.

The complexity of data processing is a difficult problem for

many different application areas, but is especially difficult

for areas in which it is relatively easy to get new data.

Environmental and earth studies are one of such areas: lots

of relatively easily accessible data come from satellites, and

processing this data becomes more and more difficult.

This problem is going to become even more acute in the

nearest future: Indeed, currently, environmental-related

satellites use a few frequencies (no more than 10). From

the resulting measurement results, we only get a small sample of the spectrum, and from this small portion, it is often

difficult to tell one type of terrain from another (or even from a cloud formation). To get a better understanding

of Earth features, NASA is currently planning to launch a

series of new multi-spectral satellites that, for each point,

will measure up to several hundred intensities instead of

the usual few. This increase in data flow is definitely advantageous, but it makes data processing even more more

complicated.

Data processing is difficult: theoretical results. Every once in a while, new algorithms appear that drastically

decrease the computation time of different data processing

problems. This continuous progress in algorithm design

may lead to an (over)optimistic viewpoint that sooner or

145
later, ideal algorithms will emerge that will perform all the

data processing tasks in real time (i.e., the current data will

be processed by the time when new data will arrive).

Alas, this optimism is unfounded: numerous theoretical

results show that in the general case, data processing problems are computationally intractable (or, to use the precise

term from the theory of computing, NP-hard). This is true

for general data processing (see [8] and references therein),

for the problems of reconstructing the past [1,2], for problems of quantum mechanics [10] and space-time geometry

[7], etc. Crudely speaking, these results mean that for any algorithm that solves a data processing problem, there exist

possible data on which this algorithm takes exponentially

long time, i.e., time that grows as 2", where n is the length

of the input (measured, e.g., in bits). Already for reason- ably small n (e.g, for n « 300), the required time exceeds

the lifetime of the Universe. In short, such problems are indeed intractable.

The problem. The problem is: how to process real-life data?

2. MULTI-RESOLUTION DATA PROCESSING IS NECESSARY

How do we humans solve this problem? Enter the

idea of multi-resolution data processing. There are many data processing problems in which human experts

are much better than computers, image processing one of

them. To be more precise:

• If we have a small amount of data, e.g., a blurry noisy

image, a human eye will only see the noise, while a computer can perfectly well filter this noise out and

get, e.g., all these nice pictures that we see coming

from the Hubble telescope.

• On the other hand, if we have a huge amount of data,

e.g., if we need to identify a face on a photo or a

geological pattern on satellite image, then a trained

human eye does it in no time, while supercomputers

often take forever or even sometimes fail.

How do we humans do it? Definitely not because our brain

is faster than a computer: its main processing elements

(neurons) have a processing time of 10-100 milliseconds.

The main reason why we can do this job is because we do

not store and we do not process the pixel-by-pixel image

as a computer would normally do. Instead, we store and

remember image in a very compressed form, usually, as a small collection of standard images described, usually, in

semiotic form, i.e., by words and symbols (mental or real).

Moreover, this description is usually hierarchical, multiscale: first, we remember and describe the "big picture"

146

(main features), then we go into more details (i.e., into a ! somewhat smaller scale), etc. Since we humans use this idea, and use it successfully, it j is desirable to make computer programs use this idea as i well.

Wavelets: a mathematical representation of the I idea of multi-resolution data processing. One of the

most practically successful formalizations of the idea of

multi-resolution data processing is the wavelet technique

j (see, e.g., [13]). Crudely speaking, a wavelet transform decomposes the original image into "sub-images" that corre-

' spond to the large-scale details, medium-scale details, etc. So, we can store and process these sub-images instead of

the entire original image.

Multi-resolution methods are indeed optimal.

Many people have heard about wavelets, and it is rea- 1 sonably well known that in many application areas (e.g.,

in data compression) wavelet-based methods are often in- . deed better than more traditional techniques. What is less known is that wavelet-based methods are not simply bio- i

logically motivated and empirically good: there are mathematical results that show that in many problems, wavelet1 based methods are indeed optimal. We will mention two , such results:

• The first result is closer related to human way of , data processing: it tells that among all possible neural networks, neural networks that use wavelet-type I activation functions have (asymptotically) the best

approximation property [9].

• The second result is directly related to data process- ! ing, namely, to image processing: it shows that in a

j certain class of problems (like the problem of automatically detecting whether a surface mounted device is correctly mounted on a chip) wavelets are in- deed the best data compression method [6]. This

second result is not just an asymptotic optimality result: it has actually led to successfully wavelet-based

image processing results [3,5].

Multi-resolution methods may be the best of the

possible ones, but how come they are good? The

very fact that multi-resolution methods are the best (i.e., the fastest) of all possible methods of solving data processing problems does not invalidate the above-cited pessimistic result that this problem is computationally in- tractable. In other words, theoretically, one can describe

possible combinations of data for which these methods will

not work.

However, both our own experience (as human experts we

use multi-resolution methods) and the experience of data
processing algorithms that use multi-resolution techniques

show that these methods are practically very feasible, in

other words, that these horror worst-cases practically do

not happen in real life. The question is: why? Is nature

designed in such a way that these methods always work, or simply we were lucky so far and bad cases will still appear

in the future?

Our answer is optimistic: yes, nature is designed in this manner.

3. MULTI-RESOLUTION DATA PROCESSING IS POSSIBLE AND IS FUNDAMENTAL

Two explanations. We will give two explanations why

nature is designed in this way:

• Our first explanation will say, crudely speaking, that even when nature can form arbitrarily complicated

images and data strings, the inevitable presence of

noise and measurement errors makes every observation compatible with a hierarchical model (i.e.,

with a model that can be handled by multi-resolution

techniques).

• Our second explanation is that not only the approximate image of nature is hierarchical, but the nature

itself is granular and hierarchical.

First explanation: Tsirelson's theorem. [15]

Tsirelson noticed that in many cases, when we reconstruct

the signal from the noisy data, and we assume that the re- sulting signal belongs to a certain class, the reconstructed

signal is often an extreme point from this class. For ex- ample, when we assume that the reconstructed signal is monotonic, the reconstructed function is often (piece- wise)

constant; if we additional assume that the signal is smooth

(one time differentiable, from the class C

1 ), the result is usually one time differentiable but rarely twice differentiable, etc. Tsirelson provides an elegant geometric explanation to this

fact: namely, when we reconstruct a signal from a mixture

of a signal and a Gaussian noise, then the maximum likeli- Aoot/estimation (a traditional statistical techniques) means

that we look for a signal that belongs to the priori class,

and that is the closest (in the L

2 —metric) to the observed

"signal+noise" . In particular, if the signal is determined

by finitely many (say, d) parameters, we must look for a

signal s = (s\, .

.

., Sd) from the a priori set A C R

d that is the closest (in the usual Euclidean sense) to the observed

values 6 - (o l5 . .

. , Od) = («i + ni, . . . ,s d + n d ), where n, denotes the (unknown) values of the noise.

Since the noise is Gaussian, we can usually apply the central limit theorem and conclude that the average value

of (rii)

2 is close to a

2

, where a is the standard deviation of the noise. In other words, we can conclude that

(«i)

2 + . . . + (rid)

2 » da2

. In geometric terms, this means

that the distance \/£2(oj — S{) 2 = y/^nf between s and

o is « cr\/d. Let us denote this distance o~\fd by e. Let us (for simplicity) consider the case when d = 2, and

when A is a convex polygon. Then, we can divide all points

p from the exterior of A that are e— close to A into several zones depending on what part of A is the closest to p: one

of the sides, or one of the edges. Geometrically, the set of all points for which the closest point a & A belongs

to the side e is bounded by the straight lines orthogonal

(perpendicular) to e. The total length of this set is is therefore equal to the length of this particular side; hence,

the total length of all the points that are the closest to all the sides is equal to the perimeter of the polygon. This

total length thus does not depend on £ at all. However,

the set of all the points at the distance e from A grows

with the increase in e; its length grows approximately as the growth of a circle, i.e., as const f:. When e increases,

the (constant) perimeter is a vanishing part of the total

length. Hence, for large e, the fraction of the points that

are the closest to one of the sides tends to 0, while the

fraction of the points p for which the closest is one of the

edges goes to 1. Similar arguments can be repeated for any dimension. For

the same noise level a, when d increases, the distance e =

a\fd also increases, and therefore, for large d, for "almost

all" observed points o, the reconstructed signal is one of

the extreme points of the a priori set A.

Much less probable is that the reconstructed signal belongs to the 1-dimensional face of the set A, even much

less probable that s belongs to a 2-D face, etc. The main methodological consequence of this result is that even when the actual state space is continuous, when

we determine the state from measurements result, we inevitably obtain (most often) one of the discretely many

states. On the large-scale level, we get one of the few clusters. When we add new measurements and thus, get to

the next level, each original cluster sub-divides into new

clusters, etc., so that we get a hierarchical structure.

Comment: Schroedinger's paradox and other

methodological applications of Tsirelson's result.

In quantum mechanics, this result explains why pure states

(extremal points) are much more frequent that mixed ones;

in history, it explains why there are finitely many types of

social organization; in logic, it explains why in spite of the

clearly fuzzy character of most human reasoning, binary

logic describes most of this reasoning pretty well, etc. In

particular, it explains the famous "cat" paradox proposed

by E. Schroedinger, one of the founding fathers of quantum

mechanics,

In classical physics, it is assumed that for each state of a

physical system, every property is either true or false. For

example, a particle is either located in a certain interval

147
of space coordinates [x — A, x + A], or it is not located

inside this interval. In quantum mechanics, in addition to the states in which a particle is located within this interval, and to the states in which the particle is definitely

outside it, there are states in which some measurements of

the coordinate will lead to results within the interval, and

some to the results outside this interval. In such states,

we cannot say that a statement "the particle is located in

the given interval" is true or that this statement is false; at best, we can determine the probability of the "yes" answer. (To describe such unusual "truth value", quantum

logic has been introduced.)

States with unusual "truth values" are not an exception,

but rather a general rule in quantum mechanics: e.g., for

every two states ip and ip' with certain values A ^ A' of a measured quantity, there exists a state called their su- perposition in which the value of this quantity is no longer

certain. (In the standard formalism of quantum mechanics,

where states are described by vectors in a Hilbert space,

superposition is simply linear combination.)

Such superposition state is easy to generate. Schroedinger

has shown that this superposition principle seemingly contradicts our intuition: indeed, suppose that we have a cat

in a box, and a light-controlled rifle is aimed at the cat

in such a way that a left-polarized photon would trigger

the rifle and kill the cat, while the right-polarized photon

would keep the cat alive. If we send a photon with a cir- cular polarization (that is, according to quantum mechanics, a superposition of left- and right-polarized states), we

would get (due to the linear character of the equations of

quantum mechanics), the superposition of the states resulting from using left- and right-polarized photons. In other

words, we will get a superposition of a. dead and alive cat

states. This is, however, something that no one has ever observed: for macroscopic objects (cats included), an object is either dead or alive. Tsirelson's result explains why

such non-extremal states are indeed difficult to observe.

Second explanation: Fractal (hierarchical) structure of the Universe [11]. At first glance, the Universe

as a whole seems to be uniform: in whatever direction we

look, there are, on a large scale, approximately the same

amount of galaxies. However, as early as the 19th century,

Olbers showed (in his famous paradox) that this impression is false: If indeed the matter was homogeneously distributed, then the total brightness of all the stars located

at distances between R and R+AR would be proportional

to the volume R

2 AR of the corresponding spherical segment. Since the brightness dims with distance as R~ 2

, the

resulting Earth-observed brightness would be the same ir- respective of R, and the total brightness caused by all the

stars would be infinite or at least very large. As a result,

argued Olbers, it would be as bright at night as it is at daytime. The only way to avoid this paradox and to retain the observable homogeneity with the observable night

darkness is to take into consideration that the Universe is hierarchical: stars form galaxies, galaxies form galaxy clusters, etc. The larger scale we go it, the less space is taken

by matter, and the more by vacuum. The resulting fractal

description of matter distribution is indeed consistent.

Olbers paradox was the first but not the only occurrence

of meaningless infinity in seemingly meaningful physical

equations. Such infinities consistently emerge in field theory, both classical and quantum. An interesting mathematical fact that is that if we consider field theories in

space-time of arbitrary dimension d, then infinities only

occur for (small) integer d, in particular, for the physically

meaningful d — 4, but they do not occur for d = 4 — e

for a small e > 0. Currently, this idea is used as a formal

trick, to compute the physical quantities by using fractal dimensions, but it is reasonable to conclude, from this result,

that the actual dimension of space-time is fractal, i.e., that

space-time indeed has a fractal structure [4]. Since spacetime is also homogeneous, this conclusion means, crudely

speaking, that not all points from the 4-D continuum describe events from the actual space-time, but that these

events actually form a hierarchical structure.

4. MULTI-RESOLUTION DATA PROCESSING: PROBLEMS AND CHALLENGES

Traditional statistical methods are based on nonhierarchical data. Traditional statistical methods treat the entire data processing as a single process, going from

input (initial data) to the output (classification or values

of different quantities). To be more precise, there exist

multi-step methods, but these are methods that simplify

the computations at the expense of the artificially added

hierarchical structure, and not by using the actual hierarchical structure.

Traditional statistical methods and multi-resolution data processing: a problem. Since traditional statistical methods are oriented towards one-step data processing, when we have a multi-resolution, multi-stage processing, we apply the traditional statistical methods to

each stage separately, as if at each stage, we start with

the raw data, and return the final results of data processing.

In reality, after, e.g., the first step of data processing, we do

not have raw data any more, we have pre-processed data;

due to this pre-processing, the error probability distribution for pre-processed data is different from a typical error probabilities for raw data, and therefore, strictly speaking,

traditional methods are no longer applicable.

This problem is very urgent for processing environmental

data, especially for processing earth-based environmental

148
data (that usually supplements the data coming from satellite imaging). This data, usually, does not come directly

from measurements: the raw measurement results are processed and generalized; then measurements corresponding

to a certain small area are processed together, etc.; quite a few levels of data processing pass before we even get the

data.

2-D example. How does this multi-stage processing affect the results? Let us give a simple illustrative example.

We have already mentioned (when describing Tsirelson's

result) that, from the geometric viewpoint, standard data

processing techniques correspond to finding the point s from the a priori set A that is the closest to the observation point 6 (the closest in the sense of either the standard

Euclidean distance or of its multi-dimensional analogue).

Let us start, for simplicity, with a 2-D case (d = 2), and

let us consider an a priori ellipse

A={(Xl ,x2)\£ + xl=R>}.

To get a point s £ A is the ultimate goal of data processing.

At each intermediate step, we achieve this goal only partly,

i.e., we get a intermediate point from some larger set; at each stage, this set gets smaller and smaller until finally,

we get a point from the desired set A. It is natural to assume that these intermediate sets are also ellipses that

are similar to the desired set A, with the only difference

that they correspond to larger values R; from one step of

data processing to the next, the value R gets smaller and

smaller until we reach the desired value.

In other words, we start with a point o that comes from

observations. On the first step of data processing, we find a

point s from the ellipse A^ (corresponding to the value

i?'

1 )) that is the closest to o. One the second step, we find

the point s ( 2

> from the ellipse A^ (corresponding to the

value #(2) < 7?(1)

) that is the closest to etc. After

N processing steps, we get a point s ( N' from the desired

ellipse A. This point is the closest to the previous point

s (-W-i) as one can easiiy see geometrically, this point

is not necessarily the closest to the original observation o from all the points from A. In other words, the result

of multi-stage processing algorithm is different from the

desired point s. How different is it? And how can we

compensate for this difference?

To simulate the effect of a large number TV of stages on

the result of data processing, let us consider the limit of

infinitely many stages. In this limit, instead of finitely

many different ellipses A^ l \ .

.

. , A^ that correspond to

decreasing values R^ > . . . > R(N' = R, we get a contin- uous family of ellipses that correspond to decreasing value

of the parameter R. Similarly, instead of finitely many intermediate results s^

1 ), . . .

, s ( N> of data processing, we get

a continuous family of points. Geometrically, this contin- uous family of points forms a curve — j{x\).

To describe this continuous process, let us describe how the

"next" point on the curve (that describes different stages

of data processing) is related to the "previous" one, i.e., to be more precise, let us describe a differential equation

for this curve. Each point (x\, #2) °n this curve belongs to a certain ellipse (with the value R — \Jx\l'A 2 + x\). To

get the "next" point on this curve, we consider a slightly

smaller ellipse, with the parameter R — AR, and take the

point on that smaller ellipse that is the closest to the given

one. The straight line that connects the original point with

the "next" one is, in geometric terms, a tangent to the

curve. It is well known from geometry that the straight

line segment from any point to its closest point on any

surface or curve (in particularly, on an ellipse) is orthogonal

to this surface or curve (i.e., to the tangent to this surface

or curve). Thus, at any point, the tangent to the desired curve is orthogonal to the tangent to the ellipse that this curve currently passes through.

The tangent to the ellipse x\jA

2 + x\ = const can be

obtained if we differentiate both sides of the ellipse's equation: (2x\/A2

) dx\ + 2x2 di2 = 0. Dividing both sides

by 2, we get (xi/A2

) dx\ + x-i dx2 = 0. The orthogonal line to this tangent is, therefore, described by the

equation dxi/(xi/A2

) = A

2 dxi/x\ = dx2/x2- This

differential equation can be easily integrated, leading to

c + a ln(xi) = ln(a;2), where a — A

2 and c is an ar- bitrary constant, i.e., to X2 — C ij (where we denoted

C — exp(c)).

We can use this equation to correct the effects of multistage data processing: namely, if we know the values

(xi , X2) that correspond to several different stages of data

processing, then we can:

• use the least squares method to find the parameters

a and c from the equation ln(x2) = c + a ln(xi);

• use the resulting formula X2 — exp(c) • x\ to reconstruct the original values x\ and X2\ and then,

• use least square method again to find the point s on the ellipse A that is the closest to the original

observations (£1,2:2).

Multi- dimensional case. In a 2-D case, we get reason- ably simple formulas. It turns out that in a more realistic

multi-D case, the resulting formulas are only slightly more

complicated. Indeed, if instead of ellipses, we consider el- lipsoids

A = {(x 1 ,...,xn )\^ + ...+ ^ = R

2 },

then a similar orthogonality condition means that a tangent to the curve (that represents the consequent intermediate results of multi-stage data processing) is orthogonal

149
to the surface of the ellipsoid. This condition leads to a system of equations

dx\ dx2 dxn xi/Al ~ x 2 /A2

2 ~ xn /Al

'

from which we conclude that ln(xj) = a* • ln(xi) + ct-, i.e., that Xi = C{ x\'

.

Surprising emergence of symmetries. An interesting

side effect of our analysis is that the resulting curve has an unexpected symmetry: namely, if we change a unit in

which we measure x\ to a unit that is A > 0 times smaller

(i.e., if we replace x\ by x,; = A Xj), then we get exactly

the same formulas for the relationship between Xj if we

appropriately change the units for all other variables x,. Moreover, the relationship Xj = d -x°* is the only possible

relationship with this property.

This particular symmetry is very important (for numerous

examples of using this and more complicated symmetries

in computer science and data processing, see, e.g., [14]).

The very fact that this important symmetry comes as a consequence of the hierarchical structure of data processing makes us believe that, maybe, symmetry in general,

with all its important applications in physics and in other

areas, can be explained based on the granular hierarchical

structure of the Universe.

Acknowledgments. This work was supported in part by

NSF under grant No. EEC-9322370 and by NASA under

cooperative agreement NCCW-0089.

5. REFERENCES

[1] Alefeld, G., Koshelev, M., and Mayer, G. "Fixed Future and Uncertain Past: Theorems Explain Why It Is Often More Difficult To Reconstruct the Past Than to Predict the Future" , in Proceedings of the NASA University

Research Centers Conference, Albuquerque, New Mexico,

February 16-19, 1997, pp. 23-27.

[2] Alefeld, G., Koshelev, M., and Mayer, G. "Why is it computationally harder to reconstruct the past than to

predict the future?", International Journal of Theoretical

Physics, Vol. 36, pp. 1709-1715, 1997.

[3] Carrillo, G., Cabrera, S.D., and Portillo, A. A. "Inspection of Surface-Mount-Device images using wavelet processing" , in Proceedings of SPIE Applied Imagery Pattern

Recognition, Washington D.C., October 1996.

[4] Finkelstein, A.M., and Kreinovich, V. "The singularities in quantum cosmology," Astrophysics and Space Sci- ence, pp. 73-76, 1987.

[5] Gallegos, J.M., Villalobos, J.R., Carrillo, G., and Cabrera, S.D., "Reduced-dimension and wavelet processing of

SMD images for real-time inspection", In Proceedings of

the IEEE Southwest Symposium on Images Analysis and

Interpretation, San Antonio, April 1996.

[6] Kosheleva, 0., and Brito, A.E. "Interval + Image =

Wavelet", submitted to Reliable Computing.

[7] Kreinovich, V. "Spacetime isomorphism problem is intractable (NP-hard)," International Journal of Theoretical

Physics, Vol. 30, pp. 1249-1257, 1991.

[8] Kreinovich, V., Lakeyev, A., Rohn, J., and Kahl, P. Computational complexity and feasibility of data processing and interval computations, Boston: Kluwer, 1997 (to

appear).

[9] Kreinovich, V., Sirisaengtaksin, O., Cabrera, S.D.

"Wavelet neural networks are optimal approximators for

functions of one variable," in Proceedings of the IEEE In- ternational Conference on Neural Networks, Orlando, FL,

July 1994, Vol. 1, pp. 299-303.

[10] Kreinovich, V., Vazquez, A., and Kosheleva, O. "Prediction problem in quantum mechanics is intractable (NPhard)," International Journal of Theoretical Physics, 1991,

Vol. 30, pp. 113-122, 1991.

[11] Mandelbrot, B.B. The fractal geometry of Nature, San

Francisco: Freeman, 1982.

[12] Meystel, A. "Evolution of knowledge in large complex

systems" , in Control Mechanisms for Complex Systems:

Issues of Measurement and Semiotic Analysis, Proceedings

of the Workshop, Las Cruces, NM, 1996, pp. 231-254.

[13] Meyer, Y. Wavelets algorithms and applications,

Philadelphia: SIAM, 1993.

[14] Nguyen, H.T., and Kreinovich, V. Applications of

continuous mathematics to computer science, Dordrecht:

Kluwer, 1997 (to appear).

[15] Tsirel'son, B.S. "A geometrical approach to maximum

likelihood estimation for infinite-dimensional Gaussian lo- cation. I", Theory Probab. Appi, Vol. 27, pp. 411-418,

1982.

150
Multi-resolutional Planning with Minimum Complexity

J. Albus* A. Lacaze** A. Meystel*o

* National Institute of Standards and Technology

o Drexel University

• University of Maryland

Abstract

This paper introduces a method for evaluating the

planning complexity. Finding the optimal branching

allows for evaluation of the optimum number of levels

in a hierarchy of planning.

I. Problem Definition

A classical planning problem can be characterized

by a number of tasks to be performed (t), a number

of resources that can perform those tasks (r) and the

value of a cost function to be minimized ($). This

description is general enough that tasks and resources can be of different levels of coarseness, and thus make

the solution more general.

The duty of the planner is to assign the tasks to

the resources and schedule the times at which these

tasks should be performed so that they minimize the

cost function [1, 2, 3]. Earlier, it was demonstrated that planning a minimum-cost trajectory in a graph organizing the

process of planning in a hierarchical fashion and the

optimum number of levels was obtained [4]. In this

paper, we find the optimum number of levels levels

for a multi-resolutional hierarchy of planning.

"Assignment" is a task-resource couple. Plan is defined as a time tagged concatenation of assignments.

"Decision" is all the assignments in a plan with the

same time tag. A plan is a list of decisions. "First

decision" has earliest time tag "second decision" has

the second.

Planners will create possible plans, investigate them

and choose the least expensive. The complexity of the

planner depends on the maximum amount of combinatorially possible plans that can be created. It the

worst case, optimal planners will study all plans. In this paper, the assumption of full allocation will

be taken. No task will be left unprocessed if there is a free resource. This is an assumption that reduces

the amount of plans calculated by the planner.

II. One Level Planning

Theorem II. 1 If the number of tasks t is smaller

than the number of resources r then, the worst case number of decisions that the planner investigates is

Proof. The number of combinations of resources in

tasks is CI — (

r

t ) = t ,^L t y. in order to find all the

possible assignments, we have to permutate each of

those combinations:

D(t,r) = Cl-Pt =

r

'

t\(r-t)\ (1)

r! " (r-t)\

Since t < r the planner only needs to make one

decision to complete the plan, it is not necessary to

assign each resource with more than one task.

In most cases, t > r, thus plans will have more then one decision.

Theorem II. 2 If the number of tasks t is larger than

the number of resources r then, there are D(t,r) =

/ t ^r y

possible first decisions among all possible plans.

Proof. The number of combinations of tasks in re- sources is C* = (') = r ,(tL r y

In order to find all the

possible assignments, we have to permutate each of

those combinations:

D{t,r) = Cl Pr = r

, r\(t-r)\ ' (2)

t\ ~ (t-r)\

Theorem II. 3 If the number of tasks t is equal to the

number of resources r, then the worst case number of

decisions that the planner investigates is

D(t,r) = r\ = t\ (3)

Proof. In this case, we have a simple permutation.

Note that both Equation 1 and 2 reduce to Equation 3

when t = r.

151
Theorem II. 4 The worst case number of plans that

the planner must investigate in a one level system

where t > r is

P(t,r) =

[t-(z-l)r]\

(r — m)\ ^n [t — i • r]\

(4)

where m — t mod r and n = int(^)

Proof. Since plans are strings of decisions, the total

number of plans the planner must investigate in the

worst case can be found by multiplying the number of

different first decisions times the number of different

second decisions, and so forth.

P(t,r) = l[Dt (5)

i=i

where D{ are the number of ith decisions. For the

number of first decisions, Equation 2 shows that

D\ — (t- r y. assignments are created. For the second

decisions, the number of resources is the same, but r tasks have already been processed by the first decision. Thus, if t — r >= r, D2 = rez^Tp i or if t — r < r by using Equation 1, D2 =

( r _ t ^od r )<

- The same

thing happens for the third decision D3 — h°

t — 2 r >= r, or D3 if t - 2 • r < r. (r — t mod r)\ We need to multiply Equation 2 £ times adjusting

for the previously processed tasks, and then multiply

the number of possible last decisions created by the

leftover (t mod r) tasks using Equation 1

P(t,r) =

r\

(r — m)\

last decisions

fr [t - (i - l)r]!

II [t-i-r]\

i=l

first n decisions

(6)

where m = t mod r and n = int(-). Please note

that if t < r, then n — 0, the part labeled as "first decisions" disappears, and m = t. Therefore, Equation 6 becomes Equation 1. If t — r then m = 0, the

part labeled "last decisions" disappears, and n — 1. Therefore, Equation 6 becomes Equation 3.

III. Using the Scheduler to Reduce the

Number of Investigated Plans

In Section II, the planner worked in two distinct

stages. First, the tasks are assigned to the resources

until all tasks are finished. This creates all the

possible string of assignments. Then, the scheduler

takes these strings and assigns time tags to the task- resource couples. This creates plans that can be evaluated against the cost function. In [5] a planning

method where the assignment of the tasks is woven

with the scheduler is presented. In [5], this planner is

called a tightly coupled JA-SC planner, where JA-SC

means "Job Assigner-SCheduler." The scheduler is invoked after each decision. So, this planning procedure knows (or estimates) which resource will finish

earlier in all the decisions. [5] assumes of "full allocation," where no unprocessed task (that is within the

assigned ordering constraints) and free resources will

be left unassigned.

Theorem III.l The worst case number of plans that a tightly coupled JA-SC planner must investigate in one level where t > r is

P(t,r) = t\ (7)

assuming that no two resources are available exactly

at the same time except in the first decisions.

Proof. For this case, Equation 5 still applies. For

the set of first decisions, the tightly coupled JA-SC

planner behaves the same. Equation 2 shows that

D\ = jtzhy. assignments are created. For the set of

second decisions, however, the scheduler that investigates each of the assignments in the first decisions, can estimate which resource finishes the assigned task

first. At that time, only one resource is available and

t — r tasks to process; therefore, D2 = t — r. Similarly,

Z?3 = t — r — 1. In turn,

P(t,r) = t! (t-r)! (t-r) (t -r - 1) • ... • 1

= t\

The ratio between the plans explored by the loosely

and tightly coupled JA-SC planners can be expressed

as follows:

P(t,r) L _

P(t,r) T

II; : [*—(» — l)r]!

(r-m)\(t-r)\ n

[«-(*-iH!

i=2 \t-i-rV.

(8)

Figure 1 shows this ratio plotted for different number

of tasks and resources. As expected, the ratio is one when t <= r but, it quickly increases with increasing

number of tasks and resources.

IV. Effects of Ordering Constraints

Very seldom is a planning problem set up where

there are no constraints in the task order execution.

In Sections II and III, constraints were not considered when calculating the amount of plans created

and their complexity. There are two main changes

caused by the insertion of constraints to the complexity of the planner:

1. The most obvious change is that the number of

tasks and resources available to execute at any

point of time is reduced. This reduces the total

152
tasks

Figure 1 : Ratio between the number of plans of the

loosely coupled to the tightly coupled JA-SC planners

amount of plans. Unfortunately, because there

various kinds of constraints it is not a simple job

to determine the effect that many ordering constraints can make into the total number of plans.

2. The other change causes Equation 7 to overstate

the number of decisions created. Suppose there

are a set of tasks waiting to be processed, but

cannot be executed because of an ordering constraint. Once the constraint is satisfied, the plan- ner will have to deal with all the new tasks that

are now available for processing and one or more

than one available resources. If we have more

than one resource available and more than one

task ready to execute, then the conditions of Theorem III.l are not satisfied. In those cases, the

worst case number of plans lays between Equation 4 and Equation 7. Note that the tightly

coupled JA-SC planner cannot be more complex

than the loosely coupled, since the loosely coupled is creating all the possible alternatives.

Theorem IV. 1 Every ordering constraint imposed

in a planning problem can only decrease the number

of plans that need to be investigated.

Proof. Equation 4 shows the total number of plans;

all possible alternatives are counted. Among those

possible alternatives, some follow the newly imposed

constraints and some do not. But, there are no newly

created plans, because there are no more possible

plans. By imposing the constraint, we should only

count the plans that follow the constraint, which is smaller (or equal) than the original number of plans.

Theorem IV. 2 if t > r then by introducing an or- dering constraint in the form: ti must be processed

after tj is finished, where t x and tj are two tasks, then

the number of plans is reduced by at least tz~ .

Proof. By expanding Equation 4 we find that

t\ (t-r)\ [t-2-r)\

P(t,r)

(t-r)\ (t-2-r)! (t - 3 r)\

(9)

but since we know that in the first decision, task ti cannot be processed since tj has not been processed,

then the amount of decisions made in the first decii

t-1

sions is ^, . The second decisions becomes more (i-r-l)! ' complex since there are some alternatives in the set of

first decisions that have processed t

d and some have

not. The total number of alternatives in the set of sec- ond decisions is smaller than

(t-r)<

( t _ 2 . r)! since this equation contains the number of all alternatives of the sec- ond decisions. Then we find the ratio using only the

first term,

P(t,r)i

(t-r)! C-D!

(i-r-l);!

t (10)

(t-r)

V. Complexity

If we assume the following, the complexity of the

planner can be represented as a polynomial:

• the complexity planner is directly proportional to

the amount of times that the simulator is invoked.

This simulator has a complexity of 0s necessary

to find the next state for each explored decision

• the complexity of the planner is directly proportional to the complexity of the combinatorics that

are necessary to create each assignment. In this case since the nodes in the hierarchy are composed of decisions and we assume a loosely coupled JA-SC case, the complexity of a decision

&D — tQa where 0,4 is the complexity of creating an assignment.

For example, if we have one resource and one task,

the complexity of the planner is0p = 0s + ©D For

this paper, we assume that Qs + ©d is a constant.

Theorem V.l // the complexity of the planning al- gorithm Qp(t,r) is directly proportional to the complexity of the each investigated decision Qp and its simulation Qs then assuming loosely coupled JA-SC

planner:

e P «,r) = (eD + es) j=l |_i=l

n

[t-(i-l)r]\

[t-i-r]\

+

r! A [t-(t-l)r]!

(r-m)! [t-i-r]\

where m = t mod r and n = int(-)

(11)

153
Proof, since the complexity of the planner depends

on the amount of assignments explored,

n QP (t,r) = (0 D + ©s) • ^Different j

th decisions

We use Equation 4 to calculate the number of decisions at each decision column. Since in the first n — 1 decision columns, there are more unprocessed

tasks than resources available the part labeled, "last

decisions," in Equation 6 cancels out. This "last decisions" part will only count for the n— decision column. That is,

&p(t,r) =(QD + QS ) (t-r)\

+

n

[t-(i-l)r]\

L [t-i-r]l

[t-(i- Dr]!

n

+

+

(12)

fr [<-(»-l)r]!

11 [t-i-r]\

[t-(i-l)r}\

(r — m)\ n [t — i r]\

which reduces to Equation 11

VI. Hierarchical Planning

The benefits of hierarchical control systems are obvious. Although there is no consistent theory of hierarchical system design or optimization, general rec- ommendations are often based upon heuristics or intuition. Hierarchical control systems are based on the

idea that tasks and resources can be clustered into

lower resolution tasks and resources. NIST-RCS is an example of how these control structures can be organized.

In order to go from a one level planner to a system with multiple levels, lets start by assuming the

following:

• The tasks cluster in a clusters. These clusters are lower resolution tasks.

• The resources cluster in b resource clusters. We

will call these cluster lower resolution resources.

• The number of tasks in each lower resolution task

is approximately equal . • The number of resources in each lower resolution resource is approximately equal.

Theorem VI. 1 In a two level control hierarchy, the

worst case planning complexity created by both levels

is

©2 iev(r,t) = e(a,b) +

6 © I ceil

a)'

CeU Q

(13)

Proof. The total planning complexity should be

equal to the complexity created by the low resolution

level plus the complexity created in the high resolution level. The complexity created in the high reso- lution level are ©(a, b) since we have a low resolution

tasks and b low resolution resources. When the plan- ner of this lower resolution level is finished and there is one low resolution plan that is chosen based upon the

cost function, this plan goes to the higher resolution

level. This level has b control nodes, each one with

its own planner. The number of low resolution tasks

sent to the higher resolution level is a, so, the number of high resolution tasks that have to be planned

in each low resolution resource is |, and they should

be processed by r high resolution resources. The ceil function is used to round up. This compensates for

the branching factor which may not exactly divide the

number of tasks or the number of resources. Theorem VI. 2 In a I level control hierarchy, the

worst case planning complexity created in all levels

is

1-2

©/ Ur,t) = YJ b

l -e(a,b) +

i-0

.1-1

(14)

b

l 1

• © ( ceil

(

j- j

, ceil

'

hi-\

Proof. The lowest level in the hierarchy will always

create ©(a, b) complexity regarding the amount of levels that we have. If / > 2 then the second level of the

hierarchy will have b 0(a, b). If / > 3 then the third

level will have b

2

• 0(a, b) complexity. In other words,

Yli-o b

l

' 0(a, 6) will account for all the complexity

created at each level of the I levels control hierarchy

except the highest level of resolution. This last level

will have b

l ~ l 0 (ceil (-i=t) > ce^ (p^r)) complexity,

since there are ceil (^r) highest resolution tasks in

each cluster, and ceil (tt=t) resources in each cluster.

Thus Equation 14.

VII. Optimizing the Control Hierarchy

Important questions include the following: Given

t and r, what is the best clustering criterion? What

is the optimal number of levels that should be used

to minimize complexity? The answers come from numerically inspecting the complexity equations.

154
Figure 2: log

^ es +eP J for a one level control system

as a function of the r and t

40 1

1 r

' 1 1 1 1 1

1 t~

10 l 1 1 1 1 1 1 1 1 1 0 5 10 15 20 25 30 35 40 45 50

r

Figure 3: log

(^ q®+qd j for a one level control system

for 20 tasks as a function of r

The following experiment was conducted. The complexity of a one level system was calculated (Fig- ure 2) as a function of the number of tasks and re- sources. The graph was calculated by finding the logarithm of Equation 11 by assigning / = 2, assuming ©5 + QD constant and equal to one unit of complexity. The folds that this figure presents (See Fig- ure 3) can be explained by the fact that the number of assignments can decrease when the number of resources increases. An obvious example of this is 0P (3,2) = 18 > 0p(3,3) = 6 (using Equation 11),

that can be seen in the big fold at r = t, the other

folds occur when r is a multiple of t. Equation 14 was used to find the optimal a, and b

for each possible combination of t and r within the

shown range. These optimal values where found by

using brute force search over the a and b spaces. Fig- ure 4 and Figure 5 show these optimum values afFigure 4: Results of searching for the best a as a

function of the r, t and b

50 0 {

r

Figure 5: Results of searching for the best 6 as a function of the r, t and a

ter the search procedure is finished. The results are non-monotonically increasing as r (in the case of a

in Figure 4) and t (in the case of b in Figure 5) are

increasing.

Then, using these optimal o and 6, the complexity

of the 2 level system was found for the same range

of t and r. The results are shown in Figure 6. Compare the difference in complexity with the one level

system shown in Figure 2 This same procedure can be repeated for more levels. Although it is interesting to find what is the optimal

clustering criterion for a given amount of tasks and

resources, it has more applications to find the optimal

number of levels for a certain number of tasks and

resources. This is done in the following way:

1. Given the number of tasks t and the number

of resources r, the optimal a and b are numerically found by searching using Equation 14 for

155
Figure 6: log

( qs^@d J

f°r a two level control system

as a function of the r and t and using optimal a and

6

level

Figure 8: log ( q^qd

1 as a function of the number

of levels (2-10) for some fixed combinations of r and

Figure 7: log ( qj+^ ) as a function of the number

of levels (1-10) for some fixed combinations of r and

2,3,4,... ,10 levels.

2. The minimum complexity versus level function is numerically found.

Figure 7 show 4 examples: {t = 50, r = 30},

{t = 50,r = 5}, {t = 10,r = 30}, {t = 10,r = 5}.

Figure 8 shows the same figure excluding the one level

data. If both t and r increase, the general rule is that

the number of levels necessary to minimize their complexity will also increase. Different levels create significantly different complexity and that having this curve determines the optimum amount of levels necessary

to minimize complexity. Some overhead is created by

adding levels of resolution, this overhead is partly ac- counted for in Equation 14, where extra terms may

be necessary.

VIII. Conclusions

• The process of planning was analyzed and mathematical expressions were obtained for both the

single level and multi-resolutional cases.

• The complexity of loosely and tightly JA-SC

planners was analyzed and compared.

• Some of the effects of ordering constraints in the

planners complexity was studied.

• The optimal number of levels which minimizes

the complexity of a hierarchical control system is found.

References

[1] J. Albus and A. Meystel. A reference model architecture for design and implementation of semiotic

control in large and complex systems. In Semiotic

Workshop of the 10th IEEE Intenational Symposium on Intelligent Control, pages 33-45, Monterrey, CA, 1995.

[2] J. Albus. An intelligent system architecture for

manufacturing (ISAM). Technical report, NIST,

1996.

[3] J. Albus and A. Meystel. Behavior generation.

Technical report, NIST, 1995.

[4] Y. Maximov and A. Meystel. Optimum design

of multiresolutional hierarchical control systems.

In Proceedings of IEEE Int'l Symposium on Intelligent Control, pages 514-520, Glasgow, U.K.,

1992.

[5] J. Albus, A Lacaze, and A. Meystel. Planning

in the hierarchy of NIST-RCS for manufacturing.

In Intelligents Systems: A Semiotics Perspective,

1995.

156
Multi-Resolution Data Processing is Optimal:

Case Study of Detecting Surface Mounted Devices

A.E. Brito, O.M. Kosheleva, and S.D. Cabrera

Department of Electrical and Computer Engineering

University of Texas at El Paso

El Paso, TX 79968, USA

email {alexb,olga,cabrera}@ece.utep.edu

ABSTRACT

In computer and electronic manufacturing, it is very important to be able to automatically check whether the sur- face mounted devices (SMD) are correctly placed on the

printed circuit boards. The inspection of these boards has

to be done on a shop floor, where statistical characteristics

of the noise vary so much that, in essence, we only have

interval estimates for this noise.

We show that under this interval uncertainty, the optimal

image processing technique consists of using Haar wavelets.

Wavelets indeed lead to much better results than previously used Fourier transform techniques.

On a more fundamental level, our result is a step to- wards solving an important problem related to wavelets

and multi-resolution data processing: these methods of- ten empirically work much better than other methods,

but there are very few theoretical explanations of this efficiency. Our results shows that, probably, such a theoretical explanation can be obtained if we take (interval)

uncertainty into consideration.

1. INTRODUCTION TO THE PROBLEM

1.1. Case Study: Inspection of Surface Mounted

Devices

Modern electronics manufacturing requires fast and effi- cient production. As a result, the assembly of printed cir- cuit boards (PCB) with surface mounted devices (SMD) is usually done by robots. This manufacturing and assembly

process is usually at the edge of the current manufacturing

abilities, with a reasonable amount of PCB produced with

defects. Therefore, it is extremely important to inspect

and test the devices in order to weed out the defective ones. Most SMD devices are so small that it is very difficult

and very time-consuming for a human inspector to check

whether the device is mounted at all, and whether it is

mounted correctly. This problem is further complicated by

the fact that many PCB have hundreds of SMD. Therefore,

we need an automatic inspection. For that, we take a photo

of the board, and we process the resulting image; see, e.g.,

[4,5,12] and references therein.

1.2. It is Necessary to Compress the Image

The image that we need to process is a photo. The camera

produces an array of electronic signals f(x) that describe

the brightnesses f(x) at different pixels x. The values f(x)

corresponding to different pixels x are fed into the computer.

In the manufacturing environment, we need to process lots

of images, and for each image, we need to process all these

values fast, ideally, on a reasonably cheap PC-type computer. If we were to apply complicated processing techniques to all the pixel values, this would require lots of

computer processing time: a good image consists of about

1 million pixels, and even the most crude images that we

have been processing still consist of 53 x 27 « 1 , 400 pixels. It is therefore desirable to compress this data to a few

numbers, and then base our decisions on the compressed

data only.

1.3. How Can We Compress the Image?

How is data compressed in general? For example, how do

physicists represent a dependency y = f(x) between the

two quantities?

Usually, this dependency is smooth (and even analytical),

and therefore, the corresponding function f(x) can be represented (at least for small x) as a sum of its Taylor series:

/(*) = /(0) + /'(0) • x + |

• f"(0) • x

2 + . .

.

Since measurements are usually imprecise, we do not need

all these terms to represent the measurement results; it is

sufficient to take only a few first terms in this expansion:

157
• To describe the most crude measurements, it may be

possible to keep only the first (constant) term and

take /(x) fa c\ for some constant c\.

• To describe better measurements, we may need linear

terms as well. In other words, we take

f(x) fa ci + c2

• x

and use the coefficients c\ and c2 to make decisions

about the analyzed dependence.

• To get an even better approximation, we may want

to retain quadratic terms as well, and take

f(x) fa ci + c2 x + c3

• x

2

,

etc.

In this case, we start with a basis consisting of the functions e\(x) — 1, e2{x) — x, c$(x) = x

2

, etc., a basis

in which every function (at least every function that is smooth enough) can be represented as an infinite series

f(x) = ci • ei(x) + c2

• e2 (x) + ... + ck e k (x) + . . . , (1)

and then we take several first coefficients c\, . .

.

, cjy as the

desired compressed representation of the function f(x).

In most physical cases, the monomials 1, x, x

2

, etc., form

a physically reasonable basis; in other cases, sines or other

functions may be a better first approximation that linear or quadratic ones. But in general, the idea of using the

first few coefficients of the expansion seems to be a reason- able data compression method. This approach is used in

imaging as well. In this paper, therefore, we will consider

data compression methods based on this idea.

1.4. It is Best to Use Orthonormal Bases

Some of the known bases (e.g., sines and cosines) are or- thonormal in the sense that

J

e;(x) • ej(x)dx = 0 when i j- (2)

J

e

2i(x)dx = 1 for all i. (3)

In principle, a physical basis need not be orthonormal; e.g., the monomials do not have this property. However, it is always possible to transform each basis {ej(x), e 2 (x), .

.

.}

into a new orthonormal basis {ei(x), e 2 (x), . . .} by using

the known orthonormalization procedure:

ei(x) = 0ii • ei(x);

t2( x ) = 92i ei(x) + 022 • e2 (x);

etc., for appropriate coefficients gij; e.g., gn = 1

l/yjfe2 (y)dy.

jj When we move to an orthonormal base, we do not lose i anything, and we do not change the actual compression:

indeed, for all N, the class of all functions of the type

ci • ei(x) + . . . + cjv • e/v(x) is exactly the same as the class

of all functions of the type ci -ei(x)+. . .+cjv-e;v(x). On the

other hand, we do gain in computation time when we turn

to orthonormal bases (and computational time is what we

try to minimize in the first place): Indeed, for orthonormal

bases, the computation of the coefficients becomes much

'

computationally simpler than for the general bases:

d =

J

f(y) ei(y)dy. (4)

j

In view of this important advantage of orthonormal bases

(and also in view of the absence of any disadvantages),

it makes perfect sense to use such bases. In the following text, we will therefore assume that the basis ej(x) is i orthonormal, i.e., that the conditions (2)-(3) are satisfied.

1.5. Taking Measurement Errors into Considera- ! tion

l Brightness values are measured with a non-negligible inaccuracy. In general, in image processing, we use statistical

j methods of processing data that are based on the assumption that we know the probabilities of different imaging

errors. It is often possible to collect these probabilities:

j we measure the frequencies of different errors and we see that as the number of experiments grow, these frequencies

tend to a certain limit which is the desired probability.

However, in our case, we are dealing with images taken on the shop floor. The situation on the shop floor changes

so frequently and so unpredictably that there are no stable

frequencies of errors. Therefore, we do not know the probabilities of different value of noise; the only information that 1 we have about the noise is the upper bound A on its value:

For every point x, the difference A/(x) = f(x) — f(x) between the actual (unknown) brightness /(x) and its measured value f(x) is bounded by A:

|A/(x)| < A.

In other words, after measuring brightness, we only know,

for each point x, the interval [f(x) — A, /(x)+A] of possible

values of brightness /(x) at this point x. This measurement inaccuracy leads to inaccuracy in the ; coefficients c;, i.e., to the difference Ac, = c, — c; between

the ideal values (4) of these coefficients (the values that

we would have gotten if we had the ideal image) and the

actually computed values

% = J

f(y)-ei(y)dy. (5)

j

158
If this inaccuracy is huge, then the resulting values of the

coefficients c,- are very unreliable and cannot be used to make any conclusions about the actual image. So, we must

make this difference as small as possible.

How can we express this idea numerically? If we reconstruct the image from the compressed data, we get the

following formula:

fTec (x) - rhi(x) + . . . + mN (x),

where we denoted

fhi(x) = Ci e,(x). (6)

If we used the precise image instead, we would have gotten

a similar (but more accurate) representation

frec {x) = mi(x) + . . . + mjv(x),

where we denoted

mi(x) = Ci ei(x). (7)

It makes sense, therefore, to estimate the relative quality

of choosing a function €i(x) as the largest possible value of

the difference

Am,(x) = rrii(x) - fhi(x). (8)

So, we arrive at the following definitions.

2. MATHEMATICAL FORMULATION

OF THE PROBLEM

Let X be a space with a measure \i (e.g., a line R or a plane R2 equipped with a standard (Lebesgue) measure fi). By an orthonormal basis, we mean a sequence of squarely

integrable functions ej : X — R (e; £ L

2 (X)) that satisfy

the properties (2)-(3).

Definition 1. By a compression scheme, we mean a pair

({ei(x),e 2 (x), . . .}, N), in which:

• {e\{x), e2(x), .

.

.} is an orthonormal basis, and

• N is an integer.

Definition 2. Let ({e,(x)}, TV) be a compression scheme,

and let A > 0 be a positive real number. This number A

will be called measurement inaccuracy. By the reconstruction inaccuracy qi of i-th term of this basis ei(x), we mean

the largest possible value qi of the difference \Am,i(x)\:

qi = max |Am,(x)|,

where maximum is taken over:

• all points x £ X,

• all functions f £ L

2

,

• all function Af £ L

2 for which |A/(x)| < A for all x£X,

and Ami(x) is determined by the formulas (4) — (8) with

f(x)=f(x)-Af(x).

Our goal is to find, for each N, the basis for which the

reconstruction accuracy is the smallest possible. We want

to minimize N different numbers qi, . .

. , q^. In general, if we minimize one objective function, it is difficult to expect

that any other objective function will be simultaneously

minimized. However, in our case, we are lucky: for the

cases of X — R and X — R

2 that correspond to imaging,

there is a basis for which all the reconstruction inaccuracies

qi take the smallest possible value.

Definition 4. By a ID Haar basis, we mean the basis that

consists of the following functions:

• the function <t>(x) that is equal to 1 for 0 < x < 1 and to 0 otherwise;

• the function w(x) = </>(2 x) — <j>(2 x — 1) (that is equal to 1 for 0 < x < 1/2, to -1 for 1/2 < x < 1, and to 0 for all other x);

• functions Wjk{x) = 2~^2 w(2:> x — k), where j and

k are arbitrary integers.

Comment. In general, if we have a function w(x) that

tends to 0 as \t\ —> oo, and for which the functions w{23 x —

k) are orthogonal to each other, so that after normalization,

we get an orthonormal basis cjk • w(2J x — k), then this

basis is called an (orthonormal) wavelet basts; see, e.g.,

[2,7,11,14].

Definition 5. By a 2D Haar basis, we mean the basis

consisting of the functions fij{x\,X2) = e t (xi) ej(x2),

where e, and ej are functions from the ID Haar basis.

THEOREM. For every i, the imaging inaccuracy of the

Haar wavelet basis is the smallest possible.

Comments.

• The proof of this theorem is given in the following

section.

• For SMD, wavelets, in particular, Haar wavelets, indeed lead to much better results than more traditional Fourier transform techniques [1,5,6,8,9].

159
• On a more fundamental level, our result is a step

towards solving the following important problem re- lated to wavelets and multi-resolution data processing:

— these methods often empirically work much bet- ter than other methods, but — there are very few theoretical explanations of

this efficiency.

Our result shows that, at least on some cases, such

a theoretical explanation can be obtained if we take

interval uncertainty into consideration.

• A related problem is: Which wavelet is the best?

This problem is raised, e.g., in [11].

— In [3,10], this problem is analyzed under the as- sumption that the measurement errors are ran- dom, Gaussian, and independent. In this case, the best approximation corresponds to minimizing the sum of the squares of these errors. Special wavelets are presented that minimize this sum. — In our paper, we consider a similar problem, but

under the assumption that the measurement er- rors belong to the corresponding intervals. The

optimization of the corresponding worst-case er- ror leads to Haar wavelets.

3. PROOF

1. Let us first show that for an arbitrary basis

{ei(x),e2 (x),...,}, we have

qi = A max|e,(x)| • J

|e,(y)| dy.

Indeed, for each function /(x), we have

Am,(x) = mj(x) — m,(x) — C{ • e,(x) — Cj • ej(x) =

c*(*) • J

f(y) ei(v) dv - ei(x) Jf(y) e «(y) dv =

e,(x) Je,(y) Af(y)dy.

Hence, |Am,(x)| = |/| • |e,(x)|, where we denoted / =

/ ei(y) Af(y)dy. Since the function |Am,(x)| is proportional to |e,(x)|, the maximum of |Amj(x)| is proportional

to the maximum of |ej(x)|, i.e.,

max|Amj(x)| = |/| -max|ej(x)|.

For a given basis e,(x), the maximum of the left-hand side

is, therefore, attained when the value |/| is the largest possible. In the definition of qi, the maximum is taken over all function Af G L

2 for which |A/(x)| < A for all For

each such A/(x), we have |e,(y) • A/(y)| < A • |e,(y)|, and

therefore,

\I\=\Jei (y).Af(y)dy\< J

|e,(y) • Af(y)\ dy <

J

A |e,(y)| dy = A - J

\ ei (y)\dy.

On the other hand, for arbitrary B, we can take Af(y) = A • sign(ej(y)) for \y\ < B and Af(y) = 0 otherwise. For

this choice of Af(y), we have

1= f

e,(y) • Af{y)dy = A f

\ei(y)\dy.

J J\y\<B

The larger B, the closer this value to A-f |e,(y)| dy. Therefore, the largest possible value of / is indeed A • J

|ej(y)| dy,

and therefore, the largest possible value qi of |Am,(x)| is indeed equal to

A •max|e,(x)| • / \ei(y)\dy.

The formula is proven.

2. Let us now show that for an arbitrary basis, we have

qi > 1.

Indeed, clearly, for all y,

max|e,(x)| > |e»(j/)|. X

Therefore,

qi = max|e,(x)| / |e,(y)| dy =

= J

max|e,(x)| • \ei(y)\ dy >

J

|e,(y)| • |e,(y)| dy.

Since {e,(x)} is an orthonormal basis, the right-hand side

is equal to 1 and therefore, q% >1.

3. To complete the proof, we must show that for Haar

basis, qi = 1.

Indeed, for each of the functions from this basis, there

exists a non-zero real number C such that for every x,

either e,(x) = 0, or |e,(x)| = C. Therefore,

qi = max |e 8

- X J

\ei(y)\ dy

160
CJ

\ei(y)\dy=

J

C |e,-(y)| dy.

We know that for every y, either e,(y) = 0, or |e t (y)| = C.

Therefore:

• When e,(y) = 0, we have C |e,(y)| = 0 = e

2 (y).

• When | ei (y)| = C, then C |e,(y)| = e

t2 (y).

In both cases, C |e,-(y)| = |e,(y)| 2 and therefore,

?, = /

C-|e,(y)|dy = | My)|2 dy.

Since {ej(y)} is an orthonormal basis, we have g, = 1. The

statement is proven, and so is the theorem.

Acknowledgments. The authors are thankful to Vladik

Kreinovich and Mikhail Zakharevich for valuable discussions.

4. REFERENCES

[1] Carrillo, G. Cabrera, S.D., and Portillo, A. A. "Inspection of Surface-Mount-Device images using wavelet processing" , in Proceedings of SPIE Applied Imagery Pattern

Recognition, Washington D.C., October 1996.

[2] Chui, C. An Introduction to Wavelets, Academic Press,

1992.

[8] Mallat, S., and Hwang, W.L. "Singularity detection and

processing with wavelets" , IEEE Transactions on Information Theory, Vol. 38, pp. 617-643, 1992.

[9] Mallat, S., and Hwang, W.L. "Characterization of signals from multiscale edges", IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 14, pp. 710-

732, 1992.

[10] Matviyenko, G. "Optimized local trigonometric

bases", Applied and Computational Harmonic Analysis,

Vol. 3, pp. 301-323, 1996.

[11] Meyer, Y. Wavelets algorithms and applications,

Philadelphia: SIAM, 1993.

[12] Pau, L.F. Computer vision for electronics manufacturing, N.Y.: Plenum, 1990.

[13] Strang, G., and Nguyen, T. Wavelets and Filter Banks,

Wellesley, MA: Wellesley-Cambridge Press, 1996.

[14] Vetterli, M., and Kovacevic, J. Wavelets and subband

coding, Englewood Cliffs, New Jersey: Prentice Hall, 1995.

[3] Coifman, R.R., Matviyenko, G., and Meyer, Y. "Modulated Malvar-Wilson bases", Applied and Computational

Harmonic Analysis, Vol. 4, pp. 58-61, 1997.

[4] Computer vision: theory and industrial applications,

Berlin-N.Y.: Springer-Verlag, 1992.

[5] Gallegos, J.M., Villalobos, J.R., Carrillo, G., and Cabrera, S.D. "Sequential algorithms for the inspection of Surface Mounted Devices", in Proceedings of the 13th SPIE

Conference on Intelligent Robots and Computer Vision,

Boston, MA, SPIE, 1994, Vol. 2354, pp. 215-226.

[6] Gallegos, J.M., Villalobos, J.R., Carrillo, G., and Cabrera, S.D. "Reduced-dimension and wavelet processing of

SMD images for real-time inspection", in Proceedings of

the IEEE Southwest Symposium on Images Analysis and

Interpretation, San Antonio, April 1996.

[7] Mallat, S. "A theory for multiresolution signal decomposition: the wavelet representation", IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 14, pp.

710-732, 1992.

161
AN ARTIFICIAL LIFE VIEW ON INTELLIGENT ENTERPRISES - FUZZY EVOLUTIONARY MULTI-AGENT SYSTEMS

Valery TARASSOV*

Bauman Moscow State Technical University,

2nd Baumanskaya St., 5; Moscow 107005, Russia

Tel. +(7095)-92 1.73.66

Fax: +(7095)-263.61.70

E-mail: tar@srv-m.mpei.ac.ru

* Presently a visiting professor of

University of Valenciennes and Hainaut-Cambresis,

LeMont Houy BP311,

59304 Valenciennes Cedex, France

Fax: +(333)-27. 14. 12.88

E-mail: tarasov@pulsar.univ-valenciennes.fr

ABSTRACT

The aim of this paper is to propose a new methodological framework

for large-scaled intelligent systems based on bioreengineering

concepts, and more generally, on artificial life principles. Two

viewpoints on artificial life content are presented: a narrow one where

artificial life models are considered as a special case of multi-agent

systems, and general approach concerning the specification of basic

principles and mechanisms of living. These approaches, underlie the suggested model of fuzzy evolutionary multi-agent system seen here

as a kernel of intelligent enterprise. After specifying main properties

of intelligent and virtual enterprises, principal architectures of basic

fuzzy multi-agent system and generic fuzzy evolutionary multi-agent

system are built and studied in the context of enterprise integration

and reengineering problems.

Keywords: Artificial Intelligence, Multi-Agent Systems,

Distributed Intelligence, Bioreengineering, Artificial Life, Evolutionary Semiotics, Intelligent Enterprise, Fuzzy Evolutionary

Multi-Agent System

1. INTRODUCTION

Classical AI models are penetrated by individual rationalism,

because they reduce natural intelligence mainly to rational

individualized problem solving with the use of some heuristics.

Such a conventional view seems to be very restrictive: it does

not make into account the emergence and evolution of

intelligence in communication, cooperation and coordination

processes. A brilliant criticism of classical AI paradigm may

be found in [1], where Winograd and Flores have suggested a new approach to model the intelligence phenomena based on

Searle's speech acts theory. This approach studying the

interactions between two agents - Customer and Performer -

has been successfully applied to represent the coordination

processes in organizations by means of workflow model.

Another important keystone which has considerably

contributed to the change of classical AI paradigm was the

book [2] by Minsky where a social AI paradigm has been

introduced in detail. Following this social standpoint, the

modeling (and specifically, semiotic modeling) of abstract

agents interacting in some organization represents the main

content of AI studies [3].

Such a social paradigm underlies two main tendencies in the

modern AI - integration and decentralization. Following

Minsky, for the sake of versatility, one can exploit and manage

the advantages of several types of representations at the same

time. Specifically, the problem is to find out how to build an

efficient bridge between top-down and bottom-up design [4]. One may speak about various levels of integration. First of all, since eighties, one has began to couple expert systems with

conventional informational technologies that implies the

arrival of hybrid expert systems or integrated intelligent

systems.

162
The development of integrated intelligent systems has

necessitate the elaboration of some empirical and theoretical

integration and communication techniques, in particular, the

blackboard architecture that is also of primary concern in

distributed AI systems. Such integrated systems are required

to support various knowledge models and various reasoning

types, to realize both knowledge and image processing.

Furthermore, one proceeds the way of integrating some

intelligence attributes (or, some specific working definitions of

intelligence) with the aim of obtaining non-linear, synergetic

effects [5] by compensating the shortcomings and enhancing

the advantages of component models in coupled models. Some

typical examples are: integrated neuro-logical and specifically

neuro-fuzzy models [6-8] underlying Zadeh's soft computing

[9] and often using logic-based neurons and distributed fuzzy

system modeling [10], neuro-optical models by Kuznetsov

[11], computational intelligence models [12], integrated

concurrent engineering models [13], Petri net models of fuzzy

neural networks [14], etc.

The most well-known instances of hybrid AI strategies are computational intelligence and soft computing. So in the

framework of soft computing three AI trends - logical,

neuronal and evolutionary - or, in other words, three

intelligence aspects - uncertainty/ fuzziness processing,

learning and adaptation - are amalgamated by representing

fuzzy production rules in a trainable neural network which is optimized with the use of genetic algorithms. These three

components also form a kernel of a more general area called

computational intelligence; besides, it involves chaotic

systems, inductive learning, probabilistic reasoning and some

other techniques.

Integrated concurrent engineering models tending to model

design process (and more generally, product's life cycle)

require building hybrid (fuzzy modal and fuzzy non- monotonic) logics. At last, neuro-optical models suggest a coupling of connectionism with wave (oscillation) theory.

Second, more fundamental tendency, is closely related to the

first one - AI distribution and/or decentralization. Here

distributed intelligent systems may have a unique centralized

control module (or agent), and the control in decentralized

systems is reduced to local interactions between agents [15].

Sometimes, this difference is taken as the main classification

criterion for dividing multi-agent systems (MAS) into: a)

distributed AI systems composed from a few intelligent (and

often heterogeneous) agents (where one of them may play the

subordinator role); b) artificial life (in the narrow sense of

term) or purely collective intelligence [16, 17] systems, where

group intelligent behavior emerges from local communications

between many not necessarily intelligent agents.

2. SYSTEMIC APPROACH VERSUS

LOGICAL APPROACH IN AI

The classical intelligent systems using symbolic (or, more

specifically, logical) approaches in AI based on cognitive

psychology satisfy the following main postulates [18, 19].

1. Centralization postulate

2. Internal representation postulate (AI epistemology);

3. Knowledge-centered postulate;

4. Disembodied AI postulate;

5. Closed world assumption (CWA)

6. Independence postulate (cognitive processes may be

considered independently from evolution);

7. Concertation postulate (between cognition and language in AI);

8. Homogeneity postulate (interacting models have the same,

homogeneous nature).

Nowadays, due to the integration and decentralization

tendencies mentioned above, these earlier unchanging

postulates must be revised. What postulates are to be revised

depends on the kind of integrated models and on the

integration basis. For example, the advocates of artificial neural networks related to neurophysiological studies

emphasize a crucial role of knowledge distribution, massive

parallelism and learning, as well as the emergence of symbolic

representations in the system of artificial neurons. The

development of evolutionary modeling in AI means making

over the independence postulate. Such AI (or close to AI)

trends as moboticism [20] and virtual reality [21] represent

completely opposite viewpoints to compare with logical

approach. So the moboticism introducing «beings» as reactive

agents without representations focuses on the importance of

coordinated local reactions for intelligent behavior and denies

the ideas of knowledge-centrism, disembodiment, rational

kinematics, centralization and independence. In addition,

virtual reality systems suppose direct experience acquisition

and introduce artificial sensory-motor coordinations. A rather

close but less radical position concerning the withdrawal from

the postulates above is proper to the adepts of such approaches

as «societies of minds» by Minsky [2], decentralized [15] and

distributed AI [22, 23], etc.

In our opinion, the essence of the paradigm change in modern

AI may be caught by recalling the title of the well-known

monograph «From Being to Becoming» by Prigogine [24]

(here it is interpreted as a call to modeling the genesis of

intelligence for AI needs) and the words by Bobrow [25] «to throw away the isolation assumptions It is necessary to introduce the interaction dimension enabling to move from

individual intelligent systems to intelligent organizations and

societies of intelligent agents.

163
So, a convergence of symbolic, neuronal and evolutionary

approaches takes place in modern AI. Here various integration

schemes lead to the generation of hybrid (or synergetic) AI.

Below we shall discuss artificial life issues in the context of

intelligent organizations.

3. ARTIFICIAL LIFE

Artificial life (AL) is an interdisciplinary field that focuses on

the functional analysis, modeling and simulation of living

systems. The sources of AL raise to von Neumann's theory of

self-reproducing automata [26] and complexity theory

introduced by Kolmogorov [27] and Chaitin [28]. Its first

practical results are related to simulated evolution concept [29]

and genetic algorithms [30]. The official AL birth date is 1987

when Langton organized at Los-Alamos (USA) an

interdisciplinary workshop on the synthesis and simulation of

living systems [31] (recent results in the field of AL are

collected in [32]).

Actually there are two different viewpoints of AL. In a narrow

sense, AL is seen as a branch of multi-agent systems, where

intelligent behavior emerges from local interactions between

agents, and it does not exist any centralized control agent [16,

17]. More precisely, this viewpoint on AL content may be

expressed by the following 5 statements:

• the MAS consists of a «population» of rather simple and

relatively independent agents;

• each agent himself specifies his own reactions to events of

his local environment and his interactions with other

agents;

• there is no special agent who subordinates other agents;

• there is no rules for specifying global agents behavior;

• all behavior, properties and structure on the superior

(collective) level emerges from local interactions between

agents.

In a more general context, AL is a pluridisciplinary branch that

integrates some trends of biology and cybernetics, artificial

intelligence and robotics, physics and mathematics, chemistry

and synergetics (Figure 1). In this sense, AL embraces and

extends AI studies. Like artificial intelligence tending to comprehend and to model various phenomena of human

psyche and specifically of natural intelligence (or at least to solve problems or to perform actions related to intelligent

behavior), AL deals with general principles and mechanisms

of life. Artificial life aims at abstracting crucial properties of

living systems (for example, autoreproduction,

autoconservation and autoregulation) and putting them into

practice via computer-based simulation and development of

various applied systems. This definition is based on

functionally-structural approach to life phenomena: the essence of life is mainly related to specific modes of

organizing units, functions and processes and cannot be

completely reduced to the properties of material substratum

(carbon chains and DNA structures). So according to Kolmogorov, basic AL metaphor can be formulated in the

following way: if an artificial organization is in some sense

equivalent to a living organism and it has analogical output

functions to compare with living system, then such an

organization may be refered as "living". In other words, AL

considers mainly "living processes" beyond the usual scope of

organic chemistry and concentrates on their computer analysis

and simulation (virtual life processes mediated by computer).

In this paper we shall use both narrow and general AL

concepts. On the one hand, in our model of fuzzy evolutionary

multi-agent system (FEMAS) underlying the concept of

intelligent organizations, the analysis of local interactions

between agents and coordination links specifying decentralized

system management will be of primary concern. On the other

hand, general life principles, such as autonomy, homeostathis

and autopoiesis principles, and specifically basic evolutionary

theory principles including evolution, adaptation for survival,

mutation and natural selection, will be used to drive the

evolution of FEMAS model.

4. INTELLIGENT ENTERPRISES

Generally the concept of intelligent enterprise includes both

the organizational structure aspects and the way of its development and functioning.

On the one hand (from a structural viewpoint), enterprise

intelligence is attributed to the progressing reversibility of its functionally-dynamic structures, or the increasing number of

symmetrical horizontal relations that implies the higher level

of coordination and collaboration.

On the other hand, following the intelligence definition given

by Piajet [33], enterprise intelligence as a systemic attribute

may be defined from a behavioral viewpoint as a flexible and

at the same time stable equilibrium of enterprise behavior. If

the forms of enterprise's influence on its environment become

more complex and variable, leading to progressive

compositions and associations, then its behavior may be

refered as more intelligent. Generally speaking, intelligence

164
Figure 1. Branches and models of artificial life

includes the capacities of learning, understanding, acquiring

and using competences acquisition to adapt to new situations.

Intelligent enterprise is characterized not only by a capacity of

using in an efficient manner the knowledge and competences

of its personnel. Moreover, it is conceived as a collective

learning system which can permanently apprehend and to transform itself for attaining its goals. So the enterprise

intelligence underlies the ability to continuously develop the

capacity to co-evolve and to build its own future and associates

the competitivity level with the capacity to learn and to adapt

faster than competitors.

Definition 1. Intelligent enterprise (IE) is a kind of posttaylorian enterprise that emerges as a result of both interenterprise and intra-enterprise communication processes,

enabling enterprise semiosis, and is driven by principles of

maximal adaptation to its environment, optimal

autoreengineering for autoconservation, and activity

autoregulation via permanent knowledge mining and

accumulation, needs anticipation and strategic planning, shared

motivation and collective learning.

So the genesis of the enterprise intelligence in communication

processes means that the enterprises and their divisions act as semiotic entities. To differ from conventional formal systems,

semiotic systems formally introduced by Pospelov [34] and

thoroughly studied by Meystel [35], are open and take into

account semantic and pragmatic informations aspects of

knowledge; moreover, they support multi-resolution,

nonmonotonic and common-sense reasoning. Thus, semiotic

systems admit a variable sign interpretation and open the

possibilities to change knowledge and its processing mode

(inference rules, axioms and even language).

So enterprise semiosis is the process of enterprise knowledge

generation, accumulation and transformation through

communications with specifying its syntax, semantics and

pragmatics. Here the syntax is associated with the enterprise

knowledge structure, semantics refers to the sense (a relation

"knowledge - source") and pragmatics corresponds to some

knowledge use (a relation "knowledge - consumer").

The intrinsic features of intelligent enterprises are the

capacities to deal with uncertain and fuzzy informations. The

main "product-based" or "service-based" sources of

imprecision and fuzziness in enterprise environment are: (a)

multiple interpretation in "client - supplier" communications;

in particular, product specification or service request

formulation in terms of natural language that leads to semantical ambiguity and multivalued interpretation; (b)

incomplete and fragmentary character of available data on new

products and services; (c) lack or complexity of analytical

equations describing future product parameters and, as a consequence, rather vague knowledge about their relationships

(d) principal limitations to the precision in specifying both

quantitative and (in particular) qualitative parameters.

Below we shall introduce fuzzy evolutionary multi-agent

systems as a formal tool of representing intelligent enterprises.

5. FUZZY EVOLUTIONARY

MULTI-AGENT SYSTEMS

Evolutionary modeling of multi-agents systems in the context

of intelligent and virtual enterprises represents an important

step from traditional mechanistic vision toward a new living

paradigm in enterprise engineering and reengineering. On the one hand, this living paradigm is inspired by modern artificial

life approaches and specifically by neodarwinian approach

reposed on the principles of survival, reproduction and

mutation. On the other hand, the introduction of evolutionary

mechanisms into MAS provides a natural framework for

studying various situations of human and artificial agents

interactions within the enterprise with taking into account

mental and social aspects. A comparative analysis of agents

goals, resources and competences enables to specify a concrete

intermediate type of interaction from pure competition to pure

cooperation, or from pure conflict to pure collaboration.

In this session the concept of fuzzy evolutionary multi-agent

system is introduced and formalized, and a generic FEMAS

architecture is proposed. We consider a special case of

intelligent organization, where agents roles are specified

through virtual enterprise metaphor [37, 38].

165
Definition 2. Virtual enterprise (VE) is a sort of metaenterprise merging in an electronic way the objectives, the

resources and the competences of different enterprises in order

to develop complex innovative projects and to obtain new

world-class products.

So the birth of VE as an innovative intelligent organization is connected with selecting and sharing common goals, unique

competences, compatible resources, including the most

advanced technologies, from different enterprises situated in

different places around some complex project that cannot be

achieved by isolated VE components. The composition of VE

also fulfills a compensatory function: it gives the opportunity

to diminish disadvantages and to enhance advantages of

heterogeneous components. In particular, it permits bridging

the gap between big enterprises (powerful but not very

reactive) and small enterprises (rather weak but ordinarily

having prompt reaction and better adaptation facilities to

changes).

So the development of VE environments enables to model

multi-sites and multi-trade enterprise aspects, including the

transactions between producer, customer, supplier and

subcontractor. It is aimed at attaining better enterprise

flexibility, reactivity or agility to compare with its components

and integrates various informations, applications and processes

concerning a given project.

Definition 3. A basic fuzzy multi-agent system (BFMAS) is a

pair

BFMAS = (X, R), (1)

where X = {1, ...n} is a set of heterogeneous intelligent

agents, R is a family of basic types of (generally) fuzzy

relations between agents.

According to virtual enterprise metaphor, BFMAS is seen as a FEMAS cell, and the set X consists of 5 elements or contains 5

roles: X = {1,..., 5}, where: 1 - Customer agent; 2 -

Coordinator agent, 3 - Performer agent, 4 - Subordinator agent,

5 - Observer (Meta-Coordinator) agent. Let us discuss in a more detailed way the content of roles of these intelligent

agents.

The Customer is defined as the agent which initiates and

determines the tasks to accomplish or the works to do for

satisfying its need. Customers evaluate performed work and

declare if it meets their satisfactions. So the customer may be

any physical or civil person outside or inside the enterprise.

The customer function based mainly on gnoseological

considerations (specifying the content of the work) may be

seen in some sense as enterprise's service function and

expressed in terms of conversation systems by the questions of

type "What to produce?" or "For what can the product be

used? . From informational viewpoint it determines the

semantics of information exchange during virtual enterprise

agents transactions.

The Coordinator (or the Manager) is defined as the agent that

creates, supports and coordinates a network of requests and

commitments necessary to perform some work. The

Coordinator distributes the works and selects available resources to ensure a good performance. Hence his (or its in case of electronic coordinator) principal function may be

refered as resource function. He inspects also work

performance and evaluates the quality. So the coordinator may

be seen as a mediator between the customer and the performer.

The Coordinator function based mainly on ontological

considerations may be considered as enterprise's operatory

function and corresponds to the questions of type "Who,

When and Where must do the work?" Moreover it is related

to structural aspect of information.

The Performer is defined as the agent (or agents team)

personally responsible for the work being done and for

declaring its completion. It needs to be emphasized that mainly

praxeological considerations related to methods and

techniques of accomplishing given work underlie performer's

activity. The Performer function is in fact enterprise's basic

technical function containing its know-how; it corresponds

to the question "How to do the work?" and specifies the

pragmatics of information exchange in agents' transactions

The Subordinator (or the Supervisor) is defined as the agent

carrying up the integrating meta-function of organizing and

supervising the virtual enterprise functions mentioned above

and consequently governing the enterprise processes viewed

here in the scope of the transactions "customer - coordinator -

performer". His principal functions are the enterprise

functioning supervision, inspection and evaluation (including

the agents efficiency evaluation). He (it) has the power to intervene at critical situations and to redistribute enterprise's resources in a timely manner. For instance, he (it) can replace

the coordinator and hence organize a new business process.

The Subordinator functions concern the specification of virtual

enterprise policies including customers choice, leading

management personnel selection, functional duties definition,

conflict resolution. To summarize, it means activating

enterprise functions and neutralizing enterprise dysfunctions.

So the Subordinator meta-function (to compare with the

functions performed by other agents) is based on axiological

consideration related to the field of motivation, principal

objectives and strategies development. It needs anticipating

future tendencies and investigating possible ways of

166
development. Specifically it includes the questions like "Why

one will begin to manufacture or to sell a new product (to

render a new service) and how much of it will be produced

(sold)?" From the semiotics viewpoint it gives the necessary

meta-information and ensures the semiosis of virtual

enterprise cell.

In a general case the family of fuzzy relations R contains three

types of relations and may be represented by a partition

R = R,uR2 uR3 (2)

where R,= {l-»2; 2->l; 2->3; 3-»2; l->3; 3->l} is a set of

fuzzy horizontal relations;

R2 = {4—>2; 4->l; 4—»3} is a set of fuzzy vertical top-down

relations;

R3 = {2—>4; 1—»4; 3-»4} is a set of fuzzy vertical bottom-up

relations.

To depend from the context, the set R, may contain

coordination, collaboration or cooperation relations, and the set R2 - subordination, competition or conflict relations. The set R3 mainly contains informing relations.

These fuzzy relations can be specified by gradual transitions on continuous «gray» scales. They depend on the following

principal factors: a) goal compatibility; b) presence of

commitments and mutual responsibility; c) level of

competences; d) level of individual resources.

So the agents above together with the appropriate relations

compose the basic multi-agent structure (or cell) for virtual

organization called SuPerCoC (derived from Subordinator - Performer - Coordinator - Customer). This cell is invariant

in respect to organization type and activities, as well as environment influences.

In this paper one reduces the enterprise cell representation to a

two-level BFMS represented by a tetrahedron whose basis is composed by the agents (1), (2), (3) together with their links

(the PerCoC-basis) and the summit corresponds to the

supervising agent (4) (Figure 2). This representation is inspired

by a structural-functional unit introduced in [39].

Here the exchange of roles is possible. Moreover each agent can play concurrently several roles (the cases of coinciding (1)

and (2) , (1) and (4) , (1) , (2) and (4)), which reduce the

SUBORDINATOR

PERFORMER

praxeological

aspect

Figure 2. Representation of basic fuzzy multi-agent system

tetrahedron SuPerCoC to the triangle PerCoC or the segment

PerC.

Definition 4. A generic fuzzy evolutionary multi-agent

system is given by a sextuple

FEMAS = (X, R, A, Ac , S, E), (3)

where:

X = {l,...,n} is an heterogeneous set of agents; R is a family

of basic fuzzy relations between agents; A is a set of agents

actions; Ac c A is a finite set of agents communication acts

called a communication protocol; S is a set of fuzzy states of

FEMAS; E is a set of fuzzy evolutionary strategies in multiagent system. The sets A, Ac

, S and E may include fuzzy

parameters.

A typical communication protocol for VE agents can be

written in the following form P = {request, offer, accept,

decline, transfer, cancel, etc.}. Here some linguistic modifiers

and quantifiers like very, rather, often, rarely, possibly,

necessarily etc., which may act on the verbs above, as well as inexact time constraints imply the need in fuzzy models given

by possibility distributions.

The state space includes such states as initial, normal, critical,

degraded, etc. Each evolutionary strategy implies some

transformation in FEMAS such as vertical or horizontal

growth, bifurcation, self-reproduction, etc.

A basic FEMAS architecture underlying the representation of

intelligent organizations is given in Figure 3. The processes

167
Figure 3. Basic FEMAS architecture

of intelligent organization emergence, development and

degradation may be modeled on the basis of FSU. So the

results of using different evolutionary strategies in enterprise

management may be specified by defining some

transformations in FSU, such as its vertical or horizontal

growth, self-reproduction or bifurcation, etc. For example, the

adoption of empowerment strategy may be seen as Subordinator's (4) power delegation to Coordinator (2) who

becomes the Subordinator on the inferior level (4^ and hence

initiates the next coordination process (l'<->2'<->3'), etc. (Figure 3). This top-down scheme may be attributed to the

enterprise growth via (2—^-type transformations. On the

other hand, the inverse bottom-up scheme is possible, where

the next organization level is generated after exhausting the resources of preceeding level. Here the Ex-Subordinator (4)

Figure 4. Representation of autonomous team

evolution: a case of Coordinator's degraded functions

is affected by new subordination and coordination links,

and becomes the Coordinator (2') on the new level. This.

(4—>2) model corresponds for instance to generating enterprise

associations and consortiums. Moreover both normal and

degraded modes of virtual enterprise management processes

may be modeled on the basis of FSU. Normal management

process is associated with coordination loop (l<->2<->3) and

only episodic activation of (4—>2) and (2—»4) relations

(Principle of Exceptional Subordinator's Intervention).

Besides, the direct "customer-performer" 1—>3 and 3—»1 are not activated too. Here a complete routing may usually have

the form (l->2-»4->2-»3-»2->4-»2->l).

Degraded mode may result, for example, from the conflicts

between Coordinator and Customers, or Coordinator and

Performer. In this case informing links 1—>4 or 3—>4 may be

used, and as a rule the Subordinator intervention, expressed by

(4—»1) and (4—>3) links is necessary. For instance, in case of

conflict between the Customer and the Coordinator, the

Subordinator can temporarily perform the Coordinator

functions and hence activate the loop (4314). Moreover he can

replace the Coordinator 2 by some other agent 2'. For

instance, the Subordinator may entrust the Coordinator

functions 2 to Ex-Performer 3 who finds a new Performer that corresponds to horizontal evolution of enterprise FSU via 3(2'

transformations). These situations are depicted in Figure 4.

6. CONCLUSION

168
A special language for intelligent enterprise evolutionary

modeling is being constructed on the basis of the introduced

formal representation. It will contribute to the implementation

of agent-oriented approach to enterprise reengineering related

to the development and use of new integrated software tools

combining the capacities of groupware and liveware.

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169
i
VII ORDINAL OPTIMIZATION
I

j
ORDINAL OPTIMIZATION FOR A CLASS OF

COMBINATORIALLY HARD PROBLEMS

Christos G. Cassandras

Dept. of Manufacturing Engineering

Boston University

Boston, MA 02215

cgc@enga.bu.edu

Liyi Dai

Dept. of Systems Science and Mathematics

Washington University

St. Louis, MO 63130

liyi@zach.wustl.edu

Christos G. Panayiotou

Dept. of Electrical and Computer Engineering

University of Massachusetts

Amherst, MA 01003

panayiot@ecs.umass.edu

ABSTRACT

We consider a class of discrete resource allocation problems which

are hard due to the combinatorial explosion of the feasible

allocation search space. In addition, if no closed-form expressions

are available for the cost function of interest in a stochastic

environment, one needs to estimate the cost function through direct

on-line observation or through simulation. We will present an

optimization scheme driven by ordinal comparisons of cost

estimates and show that it converges in probability to the global

optimum. An important feature of this scheme is that it exploits the

fast convergence properties of ordinal comparisons, as well as

eliminating the need for "step size" parameters whose selection is always difficult in optimization algorithms. An application to a

stochastic discrete resource allocation problem is included.

EXTENDED SUMMARY

Discrete optimization problems often arise in the context of

resource allocation. In the basic model we consider here,

there are K identical resources to be allocated over /V user

classes so as to optimize some system performance measure

(objective function). Let the resources be sequentially

indexed so that the "state" or "allocation" is represented by

the ^-dimensional vector s = [sj ,.. .fjA where s- e { 1,. .. JV} is

This work was supported in part by the National Science

Foundation under grants EEC-95-27422 and ECS-9624279, by

AFOSR under contract F49620-95- 1 -01 3 1 , and by the Air Force

Rome Laboratory under contract F30602-95-C-0242

the user class index assigned to resource j. Let S be the finite set of feasible resource allocations

5 = {[s

1 ,...^K] :s.e{l,...fl}}

where "feasible" means that the allocation may have to be

chosen to satisfy some basic requirements such as stability or

fairness. Let L.(s) be the class i cost associated with the

allocation vector s. The class of resource allocation problems

we consider is formulated as: N

where ft. is a weight associated with user class i. (RA) is a

special case of a nonlinear integer programming problem and

is in general NP-hard. However, in some cases, depending

upon the form of the objective function (e.g., separability,

convexity), efficient algorithms based on finite-stage

dynamic programming or generalized Lagrange relaxation

methods are known (see [1] for a comprehensive discussion on aspects of deterministic resource allocation algorithms).

Alternatively, if no a priori information is known about the

structure of the problem, then some form of a search

algorithm is employed (e.g., Simulated Annealing, Genetic

Algorithms).

In general, the system we consider operates in a

stochastic environment; for example, users may request resources at random time instants or hold a particular resource for a random period of time. In this case, L.(s) in

(RA) becomes a random variable and it is usually replaced

173
by E[L.(s)]. Moreover, we wish to concentrate on complex

systems for which no closed-form expressions for L.(s)] or

E[L.(s)]. are available. Thus, E[L.(s)]. must be estimated

through Monte Carlo simulation or by direct measurements

made on the actual system. Problem (RA) then becomes a

stochastic optimization problem over a discrete state space.

While the area of stochastic optimization over continuous decision spaces is rich and usually involves

gradient-based techniques as in several well-known

stochastic approximation algorithms [2]-[3], the literature in the area of discrete stochastic optimization is relatively

limited. Most known approaches are based on some form of

random search with the added difficulty of having to estimate

the cost function at every step. Such algorithms have been

recently proposed by Yan and Mukai [4] and Gong et al [5]. Another recent contribution to this area involves the ordinal

optimization approach presented in [6]. Among other

features, this approach is intended to exploit the fact that

ordinal estimates are particularly robust with respect to estimation noise compared to cardinal estimates; that is, estimating the correct order of two costs based on noisy

measurements is much easier than estimating the actual

values of these costs. The implication is that convergence of

such algorithms is substantially faster. These recent

contributions are intended to tackle stochastic optimization

problems of arbitrary complexity, which is one reason that

part of the ordinal optimization approach in [6] includes a

feature referred to as "goal softening". On the other hand,

exploiting the structure of some resource allocation problems

can yield simpler optimization schemes which need not

sacrifice full optimality. This is the approach we take in

tackling problems of the form (RA)

In this work, we first consider the deterministic version

of problem (RA) and provide a necessary and sufficient

condition for global optimality, based on which we develop

an optimization algorithm. We analyze the properties of this algorithm and show that it yields a globally optimal

allocation in a finite number of steps. We point out that,

unlike resource allocation algorithms presented in [1], an important feature of the proposed algorithm is that every

allocation in the optimization process remains feasible, so

that our scheme can be used on line to adjust allocations as operating conditions (e.g., system parameters) change over

time. Next, we address the stochastic version of the resource

allocation problem. By appropriately modifying the

deterministic algorithm, we obtain a stochastic optimization

scheme. We analyze its properties treating it as a Markov

process and prove that it converges in probability to a

globally optimal allocation under mild conditions.

Details are provided in a full paper [7]. Here, we limit

ourselves to pointing out two features of the resource

allocation scheme we analyze which are worth noting

because of their practical implications. All iterative

reallocation steps are driven by ordinal comparisons, which,

as mentioned earlier, are particularly robust with respect to noise in the estimation process. Consequently, (i) As in other

ordinal optimization schemes, convergence is fast because

short estimation intervals are adequate to guide allocations

towards the optimal, and (ii) There is no need for "step size" or "scaling" parameters which arise in algorithms driven by

cardinal estimates of derivatives or finite differences;

instead, based on the result of comparisons of various

quantities, allocations are updated by reassigning one

resource with respect to the current allocation. This avoids

the difficult practical problem of selecting appropriate values

for these parameters, which are often crucial to the

convergence properties of the algorithm.

REFERENCES

[1] Ibaraki, T., and Katoh, N., Resource Allocation

Problems: Algorithmic Approaches, MIT Press, 1988.

[2] Kiefer, J., and Wolfowitz, J., "Stochastic Estimation of

the Maximum of a Regression Function", Annals of

Mathematical Statistics, 23, pp. 462-466, 1952.

[3] Robbins, H., and Monro, S., "A Stochastic

Approximation Method", Annals of Mathematical Statistics,

22, pp. 400-407, 1951.

[4] Yan, D., and Mukai, H., "Stochastic Discrete

Optimization", SIAM Journal on Control and Optimization,

30, 1992.

[5] Gong, W.B., Ho, Y.C., and Zhai, W., "Stochastic

Comparison Algorithm for Discrete Optimization with

Estimation", Proc. of 31st IEEE Conf. on Decisiona nd

Control, Dec. 1992.

[6] Ho Y.C., Sreenivas, R.S., and Vakili, P., "Ordinal

Optimization in DEDS", J. of Discrete Event Dynamic

Systems: Theory and Applications, Vol. 2, pp. 61-88, 1992.

[7] C.G. Cassandras. L. Dai, and C.G. Panayiotou, "Ordinal

Optimization for Deterministic and Stochastic Discrete

Resource Allocation," to appear in Proc. of 35th Conference on Decision and Control, Dec. 1997.

174
Three Techniques for Ordinal Optimization:

Short Simulation Runs, Crude Analytical Models, and Imprecise Simulation Models

Jeffrey E. Wieselthier

Information Technology Division

Naval Research Laboratory

Washington, DC 20375

wieselthier @ itd.nrl.navy.mil

Craig M. Barnhart*

TRW Data Technologies Division

16201 Centretech Parkway

Aurora, CO 80011

Craig.Barnhart@trw.com

Anthony Ephremides

Electrical Engineering Dept. and

Institute of Systems Research

University of Maryland

College Park, MD 20742

tony @ eng.umd.edu

ABSTRACT

In the study of discrete-event dynamic systems (DEDS),

accurate analytical models are generally either unavailable or too complex to evaluate numerically. Thus, the determination of optimal

control policies often entails the simulation of many alternative

systems in parallel. To reduce the computational burden, we

investigate the use of ordinal optimization. This approach focuses on

determining control policies that perform relatively well (although

not necessarily optimally), without necessarily obtaining accurate performance measures.

In this paper we study three techniques for the ordinal

optimization of DEDS, namely the use of short simulation runs, crude

analytical models, and imprecise simulation models.

KEYWORDS: optimization, ordinal optimization, simulation,

standard clock

1. INTRODUCTION

The motivation underlying ordinal optimization [1] is that finding the optimal solution (or control policy) is often too

costly or time consuming, although a suboptimal solution (that

may be found quite easily) may provide sufficiently good

performance.

In this paper we study three techniques for the ordinal

optimization of DEDS. First, we demonstrate that remarkably

accurate performance rankings can be obtained on the basis of

short simulation runs. In particular, for our example of

admission control in communication networks, we

demonstrate that the high degree of correlation introduced by

the Standard Clock parallel simulation technique provides

considerably better performance (i.e., faster convergence to accurate rankings) than the use of Common Random

Numbers. Our second approach is the use of crude analytical

models that capture the crucial aspects of system behavior.

Again, remarkably accurate policy rankings are achieved (in

this case without using simulation at all), even though such

crude models provide poor estimates of actual performance; if accurate performance measures are needed, it is sufficient to simulate performance for only the best few policies

determined in this manner. Our third approach is the use of

imprecise simulation models that, like the crude analytical

models, incorporate the salient features of the communication

network model.

C. M. Barnhart's contributions to this paper were made while he was at the Naval Research Laboratory.

This work was supported by the Office of Naval Research.

2. THE STANDARD CLOCK TECHNIQUE

The SC simulation technique [2, 3, 4], which permits the

simultaneous evaluation of system performance under a large

number of control policies, is a primary component of our

ordinal optimization techniques. Although the basic SC

simulation technique is limited to exponential interevent

times, the technique has been extended to some more general

examples as well [5], [6], [7]. In SC simulation, each event is determined by two

random numbers, one to specify the timing of the next event,

and the other to specify its type. It is possible that an event

determined in this manner turns out to be infeasible (e.g., a departure from an empty system). The interevent time of such

a "fictitious" event is used to update the system time as if the

event were "real" and did in fact occur, but no state change

occurs (the fictitious event is discarded).

The improved efficiency of the SC method is achieved by

using the resulting sequence of (interevent time, event type)

pairs, known as the clock sequence, to simultaneously

generate sample paths for a number of structurally similar, but

parametrically different, systems. This reduction in the

number of events that has to be generated has a dramatic effect on the overall simulation time because the generation of

events is considerably more time consuming than the

consequent updating of system state [7]. Furthermore, the use of a common event sequence introduces a high level of

correlation among the parallel simulations, greatly

accelerating the determination of good control policies by means of ordinal-optimization techniques, as we demonstrate

in this paper.

3. THE ADMISSION-CONTROL PROBLEM

IN CIRCUIT-SWITCHED NETWORKS

We have studied the problem of admission-control in

circuit-switched, multihop, wireless networks. In our

examples, a circuit is established over a predetermined path

between the originator of a call and its destination node for the

duration of the call. Contention-free channel access is implemented by means of frequency-division multiple access (FDMA); thus a necessary and sufficient condition for a call to be established is that a transceiver is available at every node in

its circuit. The model is described in greater detail in [8] and

[9].

Figure 1 shows an example of a ten-node wireless

network that supports circuit-switched voice. The multihop

paths corresponding to each of J = 5 circuits are distinguished

by different shadings. The dashed lines connect nodes that are within communication range of each other, but that do not

support any of the five circuits.

175
Fig. 1 - An example circuit-switched voice network.

Calls for circuit j are generated according to a Poisson

process with rate X, and their durations are exponentially

distributed with parameter fi

;

. A vector description of circuit /

in terms of the nodes it traverses is given by Cj = {c^, cj2 , cjN), where

f 1, if circuit j traverses node i

Jl [0, otherwise

and /V is the number of nodes in the network. The state of the

system with J source-destination pairs, and hence J circuits, is described by the vector x = {x x , x2, Xj), where Xj is the

number of calls currently active on circuit j, each of which is referred to as a call of type j. A central controller makes the

decisions on whether or not to accept calls based on perfect

knowledge of the number of calls of each type that are

currently in progress (i.e., the system state x), and hence the

set of resources that are available for new calls. The

transceivers needed to establish a circuit are acquired

simultaneously when the call arrives, and are released

simultaneously when the call is completed. Calls are blocked

when one or more nodes along the path do not have a transceiver available, or when a decision is made not to accept

a call despite the availability of transceivers. Blocked calls are

lost from the system. These assumptions, coupled with the

class of coordinate-convex admission-control policies

discussed below, lead to a mathematically tractable

description of system performance.

The number of transceivers at node i is denoted by T,. No

more than T{ calls can simultaneously use the resources at node i, i.e., j

, x

j cH

<T;, i = !,-,#.

7=1 These equations, which are termed the "system constraints,"

limit the state space Q0 in which x is allowed to take values.

We refer to a system that is solely constrained by these system

constraints as an "uncontrolled" system.

Network performance can often be improved by

administering an admission-control policy that blocks some

calls even though resources are available [9]. We define the

admission-control policy, denoted by Q, in terms of a set of

circuit "thresholds" and a set of "linear-combination

constraints." Thresholds restrict the number of calls that will

be admitted to the individual circuits, and can be expressed as xj < Xj = threshold on circuit j, j = 1,. The linear-combination constraints are defined as

2j Xj <Yj = threshold on total number of call types

jes, that are members of set 5/

for suitable subsets 5/ of the set of all call types. In particular,

for the example of Fig. 1, three linear-combination constraints

are imposed by node 5 (jc, + x3 < Yu x, + x5 < Y3

, and x3 +x5 < Y4) and two are imposed by node 7 (xt + x4 < Y2 and x4 + x5 < Y5

). Thus, the control policy is given by Q. = {Xu Xj, Yx , ...}. Now the problem is the determination of the optimal

admission-control policy Q.*, i.e., the values of the X; and the

Y, that yield the optimal network performance.

The use of this form of control policy assures us that the

state space is "coordinate convex" [10]. A coordinate-convex

policy is specified in terms of the set of admissible states; completed calls are not blocked from leaving, on-going calls do not get rerouted, and new calls are admitted with

probability 1 if the state to be entered is in the admissible

region.

Under our assumption of Poisson arrival statistics, the use of coordinate-convex policies results in the so-called productform characterization of the system [11, 12]. To determine the

optimal policy, performance must be evaluated for many

candidate policies. In view of the computationally intensive

nature of the evaluation of product-form solutions, it is desirable to develop efficient simulation approaches for this problem.

4. SC SIMULATION OF CIRCUITSWITCHED NETWORKS

We have used SC techniques to evaluate the performance

of the circuit-switched network of Fig. 1 under a number of

different admission-control policies. The discrete parameters

of interest in this case are the circuit thresholds Xj and the

linear-combination constraints Y,. The events that must be

generated are arrivals and departures. An arrival to circuit j is denoted by ap and occurs at a rate of X,. The departure rate for

each active call on circuit j is thus, if there are x, active

calls on circuit j, the departure rate for calls of type j is Xj\lj.

This situation is translated to events in the simulation as follows. We define Xjmax to be the maximum value Xj can have

over the entire set of policies. Thus

xjmax = min (Ti)-

i*cji=l

Because there may be up to X- active calls on circuit j, we

must consider Xjmax different departure events djn (n = 1, Xjmax) f°r circuity, namely

djn => feasible departure from circuit j if x; > n, otherwise fictitious event. Following the usual technique used in uniformization [13], the

maximal rate of this system is J

7=1

Xjmax

The upper part of Fig. 2 shows the "ratio yardstick" for

the network of Fig. 1 , where the maximum threshold on each

circuit is three. To determine the event type, a random

number, uniformly distributed over [0,1], is generated. The

event type (e.g., a, or djn) is determined by the interval into

which the random number falls. 1 This ratio yardstick

corresponds to operation of the network at the maximal rate, and it can generate all events that are needed for the

simulation of systems with control policies in which the circuit

1 The computational effort involved in determining the event type by means of the alias method [14] is independent of the number of event

types, thus making this method suitable for complex systems.

176
thresholds do not exceed 3. In our example X,= = \x = 1, which

implies that all events are equally likely; therefore, all the

intervals have the same width. All arrival events in this

system are real, and the corresponding calls are accepted as long as their acceptance does not violate any of the system

constraints or control constraints. However, departure events

are fictitious if an insufficient number of calls of that type are currently active, as discussed above. For example, referring

again to the upper part of Fig. 2, an event of type dn will be

fictitious (and hence ignored, although time will be updated) if there are less than three calls of type 1 currently active.

Ratio Yardstick based on Maximal Rates;

I Threshold on all circuits = 3; A = 20; Xj= u,= 1 (=> all events equally likely) :

I 1 !

a. a2 a3 a4 a5 d l2 dp d 21 d22 d23 d31 d32 i33 d4 , d42 d43 d5i d52 353

-arrivalsa, a2 a3 a4 a5 d,, d2 , d22 d23 d 3] d d 4 , d42 d43 d5 ,

-departures

I Custom Yardstick for Controlled System with

: j Threshold X= (1,3,2,3,1); A' = 2(X.

7

- + Xj\ij) = 15; X^u,^ 1 (=> all events equally likely)

Fig. 2 - Ratio yardsticks for the circuit-switched network.

To reduce the number of fictitious events (and thus

further improve the efficiency of the simulations) we have

considered the use of "custom" ratio yardsticks, which are constructed to conform with the particular parameters of each

sample path. The lower part of Fig. 2 shows a custom ratio

yardstick for an example in which the circuit thresholds have

been lowered to {1,3,2,3,1}. A number of events have been

eliminated because they will always be fictitious, thus

resulting in a reduction in the event rate from A = 20 to A' =

15; e.g., with the threshold on circuit 1 reduced to 1, the

departure events dn and dn will always be fictitious. Clearly,

by eliminating them from the ratio yardstick we can increase

the percentage of real events. The remaining events are again

equally likely, although there are only 15 of them instead of

20.

Despite the potential advantages of custom ratio

yardsticks, we have found in our SC simulations that the

added burden of maintaining and accessing separate custom

yardsticks for every sample path outweighs the reduction in

the number of fictitious events provided by their use [15].

Furthermore, the use of custom ratio yardsticks reduces the

level of correlation among the sample paths, thus resulting in poorer ordinal rankings, as is shown in Section 5.2.4.

5. ORDINAL OPTIMIZATION USING

SHORT SIMULATION RUNS

We have performed SC simulations of the network shown

in Fig. 1, with the goal of determining the optimal policy, by

using the model discussed in Sections 3 and 4. Eight

transceivers are assumed present at each node in the network.

Recall from Section 3 that a policy for this network can be

written as Q. = {X, X5 , Yu y5 )- For XAl = 4.0, 2 we

2 Blocking probability does not depend on the individual values of ^,

and [Lj, but only on the ratios p; = A./u

y

.

have simultaneously evaluated the 120 different control

policies {X,, 6, 6, 6, X5 , 8, 8, K3 , 8, 8}, where X,, X5 = 0,...6;

y3 = 0,. . .,8; y3 < X, + X5 ; X, < y3

; and X5 < Y3

. 0.48

0.46 -

£>0.44

0.34 _ ^

P

V =4

0 20 40 60 80 100 120

Policies ranked on exact blocking probability

Fig. 3 - Probability of blocking across the range of policies.

5.1. Evaluation of Voice-Call Blocking Probability

In Fig. 3 we show the exact and simulated voice-call

blocking probability associated with the 120 control policies.

The exact results are determined numerically from the

product-form solution, and simulated results are based on runs of 104 and 106 voice-arrival events. The horizontal axis is simply the ordering from the best (minimum blocking

probability) policy to the worst, based on the exact model;

thus blocking probability is a monotonically nondecreasing

function of the horizontal axis. It is apparent from the

closeness of the curves in Fig. 3 that the results of the longer

simulation are extremely accurate; the simulation error is never more than 0.2%. It is also apparent that the shorter

simulation is not long enough to predict blocking probability

accurately.

120-

>.100-

o

DCe

!2u

e3

s

,o

Ja

"3Su

V3

80-

60

40-

20-

104 voice arrivals

106 voice arrivals

1

I

1 1 1 I 0 20 40 60 80 100 120

Policies ranked on exact blocking probability

Fig. 4

5.2

Blocking probability found in SC simulations compared to the exact value, p = 4. Ordinal Ranking of Policies in Terms of Voice-Call

Blocking Probability

In Fig. 4 we compare ordinal rankings of the voice-call

blocking probability obtained from two SC simulations to the

exact rankings. The two SC simulations differed only in their

durations, which were based on 104 and 106 voice-call arrivals.

The ordinal ranking of the simulation results shows

177
remarkable agreement with the exact ordinal ranking (ideally

the curve would be a straight line with unit slope). For long

simulations this is not surprising; however, it is remarkable

that the short simulation placed eight of the top ten policies in

the top ten positions. This agreement is achieved despite the

insensitivity of blocking probability to the policy used. It is apparent from Fig. 3 that there is little sensitivity to the policy

that is used when blocking probability is the only performance measure of interest. For example, as the policies are examined

from the best to the 80th out of 120, the blocking probability

increases by only a small amount, i.e., from 0.358 to 0.365.

5.3 The Impact of Common Event Sequences on Rankings

The SC method uses a common event sequence for all control policies; thus it permits the direct comparison of the

performance of these policies under the same input conditions.

The benefits of the use of common event sequences for

comparing policies, as compared to the use of independent

brute force (BF) simulations, has been noted in [14, 16, 17,

18]. It was shown in [19, 20] that the use of different randomnumber generator seeds can produce differences in

performance in our problem that are considerably greater than

those resulting from the use of different admission-control

policies, especially for short simulation runs. The failure of the independent BF simulations to provide

good rankings for short simulation runs clearly demonstrates

the benefits obtained by using a common event sequence. In our example, the use of independent event streams appears to require a simulation duration of about two orders of magnitude

greater than that required for SC simulation to obtain

comparable performance. Thus, in addition to the benefit of

simulation speedup (in terms of the time required to simulate a specified number of events), the SC technique's use of a common event sequence introduces correlation into

experiments so that accurate rankings are obtained early in the

simulation. Therefore, highly accurate ordinal rankings can be

obtained with much shorter simulations than would be

required with independent BF simulation runs.

5.4 The Use of Common Random Numbers, but Different

Event Sequences

In Section 4 we noted that the use of custom alias tables

(custom ratio yardsticks) may, in some cases, permit higher

efficiency in SC simulations because of the consequent

reduction in the number of fictitious events. However, when

custom alias tables are used, different events may be passed to different sample paths, even though the same random-number

sequence is used to drive all of the parallel experiments. We

now address the quality of the ordinal rankings that are obtained when common random numbers (CRN) are used in conjunction with custom alias tables to simulate the same

example considered above for SC simulation with a common

event stream and for independent BF simulations. In

particular, we address the conjecture that the use of a common

underlying random-number sequence can introduce beneficial

correlation among the sample paths, even though the event

sequences are different. It was recently demonstrated that the use of CRN maximizes the rate of convergence for ordinal

comparison in systems that satisfy "positive quadrant

dependence" 3 [21]; however, this condition is not satisfied in our problem.

Figure 5 shows the blocking probability and ordinal

rankings for simulations of length 106 events for the present case of CRN simulations; results for six sample paths are shown. A comparison with curves for the case of independent

experiments [19, 20] shows that little, if any, benefit is achieved by using the CRN method. The rankings appear to be comparable to those shown in Fig. 5 for the case of a simulation of duration 104 events.

i i

j

• i i

i i

i 0 20 40 60 80 100 120

Policies ranked on exact blocking probability

Fig. 5 - Ordinal rankings for CRN simulations with custom alias tables; six random-number generator seeds; simulation duration = 106

events.

5.5 A Performance Measure for Ordinal Rankings: The

Spearman Rank Correlation Coefficient

To facilitate the comparison of sets of rankings, it is helpful to use a quantitative measure of the quality of a set of

rankings. To provide the basis for such a metric, let H, be the

performance measure value (in this case blocking probability)

associated with policy i (1 < i < N), based on a simulation run; and let *P, be the exact performance measure value associated

with policy i (where the index i is arbitrary, i.e., not based on performance measure values). Thus the pair (E„ *P ,) represents the simulated and exact performance values

associated with policy i. Now define /?, = rank H, (where /?, =

1 means that policy i is the policy with the best value of

and S, = rank *F,-. One method of comparing these sets of

rankings is the use of Spearman's rank correlation coefficient

[22]

rr = 1

l—z ,

3 Two random variables X € R and Y e R are said to be positively

quadrant dependent if Prob[X>x, Y> y] > Prob[X>;c] Prob[r>y].

JV(AT-1)

which provides a scalar measure of the "association" between

two sets of rankings. If all of the simulated rankings are correct (i.e., /?, = S„ 1 < i < N), rs = 1. Figure 6 shows the Spearman rank curves for the three

approaches to simulation we have used, namely the commonevent, independent-event (BF), and CRN examples. Six

sample paths are shown for each case to demonstrate the

degree of variation among of the results. (The Spearman

rankings for the CRN examples show much greater variation

among the different random seeds than those for the commonevent and independent-BF examples.) The use of custom alias

tables in SC simulations is detrimental, apparently because the

differences introduced into the experiments reduces the

correlation among them (as compared to the case of commonevent SC simulation), thus resulting in poor ordinal rankings

of policies. To obtain comparable ordinal rankings, it may be

necessary to run simulations that are several orders of

magnitude greater in length than those required for common178
event SC simulations. In that case, however, all of the

efficiency gained through the reduction of fictitious events

would be eliminated.

0.3 - i iii—i i i i

1 1—i—i—i—i i i 10000 100000 1000000

Simulation duration (events)

Fig. 6 - Quality of ordinal rankings of blocking probability, based on

Spearman's rank coefficient, for SC, BF, and CRN simulations of

various lengths.

6 ORDINAL OPTIMIZATION USING

CRUDE ANALYTICAL MODELS AND

IMPRECISE SIMULATION MODELS

In this section, we demonstrate the use of crude analytical

models and imprecise simulation models for ordinal

optimization. The particular problem we address is the

determination of the voice-call admission-control policy that

minimizes the delay of data packets in integrated voice/data

networks, subject to a constraint on the blocking probability of

voice calls. Data traffic, which consists of fixed-length

packets that arrive according to exponential interarrival times,

is added to the basic model of Fig. 1 . The integrated network

model is described fully in [7, 20], where it is demonstrated

how fixed-length packets can be incorporated into the SC

methodology.

The development of accurate data-packet delay models is a difficult problem. Data-packet delay depends not only on

the statistics of the data-packet process itself, but also on the

time-varying properties of the circuit-switched voice-call

process. In particular, a data packet can be successfully

transmitted only if a transceiver is available at the designated

receiving node when the transmitting node transmits. The

availability of a transceiver for reception depends on the

current state of the voice-call process at that node because data

traffic is permitted to use only those transceivers that are not

currently supporting an active voice call. Nevertheless, we

make the oversimplification of modeling the data-packet

process at node i as an M/D/l queueing system, for which the

delay (under admission-control policy Q) is

where C, is the "residual capacity" of node i (the expected

number of transceivers available for data, i.e., not being used

for voice traffic), pf is the expected normalized load at node i, and ji is set equal to 1 without loss of generality (i.e.,

implicitly, we assume that delay is measured in slots, where a

slot is the time required by a transmitter to transmit one fixedlength data packet (all transceivers transmit at the same rate)). In the subsequent discussions, the delay metric we have used

is the average nodal delay taken over all nodes.

This delay model is deficient in several ways. In addition

to the fact that it ignores the need to pair transceivers at the

transmitting and receiving nodes, it also ignores other critical aspects of network operation. Most significant is the implicit

assumption that the number of data packets that are serviced

per unit time at node i is constant at C; (the fact that C; is not,

in general, integer-valued is a minor point here), whereas the

number of servers available in the real system varies, based on

the voice state. An accurate estimate of delay would have to take into account not only the expected voice state (which

determines residual capacity) as we do in our model, but also

the fraction of time spent in each voice state as well as the

statistics of the duration of each state visit. Thus, not

surprisingly, the delay estimate based on this model is not

accurate. However, we demonstrate shortly that this estimate

does provide a remarkably accurate indication of the relative

performance of a large number of different policies (and thus

of their rankings), as demonstrated by SC simulations.

In Fig. 7 we compare the ordinal rankings obtained from

four of our SC simulations of the integrated network to the

ordinal rankings that were obtained by using the simple

analytical M/D/l model for delay. We again consider the

network of Fig. 2 with eight transceivers at each node, and

examine the same 120 policies as in the voice-call blocking

probability example; however, we plot our results only for the

best 87 policies because the estimated delay based on the

analytical M/D/l model is infinite for the remaining policies

(the system is in saturation because the offered load is greater

than the residual capacity at one or more nodes). Two of the

simulations used the "receivers-assumed" model [7, 20],

which neglects the need to verify that a transceiver is actually

available at the intended receiving node. The other two used

the more-accurate "receivers-verified" model, under which a data packet is not transmitted unless a transceiver is, in fact,

available at the intended receiving node. In all cases, the

duration of the simulation was 106 voice arrivals.

0 10 20 30 40 50 60 70 80

Policies Ranked on Analytical Delay Estimate

Fig. 7 — A comparison of the ranking of the policies by SC

simulation and by the analytical delay estimate.

For all four runs shown, pj = p

v = 4 (j = 1,2, 5) and

the loading on each of ten data queues is p

d = 0.5. For each

model (i.e., receivers-assumed and receivers-verified) we used

two different expected voice-call durations (A,v= 4.0, |iv = 1.0)

and (Xv = 0.4, U7 = 0.1). The data service rate \ad was 10.0 in

all the simulations, thus, the expected voice-call duration is 10

179
times the data-packet length when u/ = 1.0, and 100 times the

data-packet length when [iv =0.l. Therefore, the total offered

voice and data loads are the same in these simulations, but the

parameter sets differ in the voice rates and \xv. This is of

interest because our analytical delay estimate, which is based on the product-form solution of the voice process, only

considers the offered voice load (i.e., pj). It does not account

for the actual values of AXand \\Y. By keeping the offered load

the same, and varying the voice rate (i.e., vary A,v and (iv

subject to Ay/(iv = 4), we can evaluate the impact of this

simplification in the analytical delay estimate.

The y axis represents the rank assigned to the policy (x

axis) as a result of SC simulations. Again, a straight line with

unit slope would indicate perfect agreement. The figure

shows that the agreement for all four simulations, although

imperfect, is impressively good; the four curves are virtually

indistinguishable, and therefore they are not labeled. The

deviation in ranking among the top 54 policies is never more

than three. Furthermore it is interesting that, despite the

significant differences between the simulation models (data

receivers assumed vs. data receivers verified) and the voice

rates (k v = 4 vs. = 0.4), which produce significantly

different values of delay (the difference can be several orders

of magnitude [7, 20]), the rankings are very similar among the

different simulation runs. This is true even though, for the case of the receivers-verified model, all but the top four

policies represent operation in the saturation region. Thus, we

see that both the crude analytical model (i.e., the M/D/l

model) and the imprecise simulation model (the receiversassumed model) produce highly accurate ordinal rankings, even though they provide poor estimates of actual

performance.

7. CONCLUSIONS

A variety of approaches are available for ordinal

optimization. Most of our work has been based on the use of

the Standard Clock approach, which provides an efficient

means to simulate structurally similar, but parametrically

different, systems in parallel. With this technique, the ability

to rapidly determine good ordinal rankings is a consequence of

the use of a common event sequence to drive all of the parallel

simulations. This common event sequence introduces a high

level of correlation among the parallel experiments. In this paper we compared SC techniques to the use of the method of

Common Random Numbers (CRN), which is implemented by

using custom ratio yardsticks (and hence custom alias tables).

We have observed that the use of the CRN approach provides

little improvement over the use of independent brute force

simulations, apparently because there is little correlation

among the experiments.

We also demonstrated that crude analytical models and

imprecise simulation models, which are incapable of

providing acceptable estimates of system performance,

nevertheless can be useful tools for ordinal optimization.

REFERENCES

[1] Y.-C. Ho, R. S. Sreenivas, and P. Vakili, "Ordinal Optimization

of DEDS," Journal of Discrete Event Dynamic Systems, 2 pp. 61-88,

1992.

[2] P. Vakili, "Using a Standard Clock Technique for Efficient

Simulation," Operations Research Letters, 10 pp. 445-452, 1991.

[3] Y.-C. Ho, S. Li, and P. Vakili, "On the Efficient Generation of

Discrete Event Sample Paths under Different Parameter Values,"

Mathematics and Computation in Simulation, 30 pp. 347-370, 1988.

[4] C. G. Cassandras, J. -I. Lee, and Y.-C. Ho, "Efficient Parametric

Analysis of Performance Measures for Communication Networks,"

IEEE J. SAC, 8 -No. 9 pp. 1709-1722, December 1990.

[5] Y.-C. Ho, C. G. Cassandras, and M. Makhlouf, "Parallel Simulation of Real Time Systems via the Standard Clock Approach,"

Mathematics and Computers in Simulation, 35 pp. 33-41, 1993.

[6] C.-H. Chen and Y.-C. Ho, "Extension of the Standard Clock

Method for Discrete Event Simulation," submitted to IEEE

Transactions on Control Systems Technology, 1993.

[7] J. E. Wieselthier, C. M. Barnhart, and A. Ephremides, "Standard

Clock Simulation and Ordinal Optimization Applied to Admission

Control in Integrated Communication Networks," Journal of Discrete

Event Dynamic Systems: Theory and Applications, 5 pp. 243-279,

April/July 1995.

[8] C. M. Barnhart, J. E. Wieselthier, and A. Ephremides, "An

Approach to Voice Admission Control in Multihop Wireless

Networks," Proceedings of IEEE INFOCOM'93, San Francisco, CA,

pp. 246-255, March 1993.

[9] C. M. Barnhart, J. E. Wieselthier, and A. Ephremides,

"Admission-Control Policies for Multihop Wireless Networks,"

Wireless Networks, 1-4 pp. 373-387, December 1995.

[10] J. M. Aein, "A Multi-User-Class, Blocked-Calls-Cleared,

Demand Access Model," IEEE Transactions on Communications,

COM-26-No. 3 pp. 378-385, March 1978.

[11] S. Jordan and P. Varaiya, "Control of Multiple Service, Multiple

Resource Communication Networks," IEEE Transactions on

Communications, 42-11 pp. 2979-2988, November 1994.

[12] S. Jordan and P. Varaiya, "Throughput in Multiple Service,

Multiple Resource Communication Networks," IEEE Transactions on Communications, 39-No. 8 pp. 1216-1222, August 1991.

[13] H. C. Tijms, Stochastic Modelling and Analysis: A

Computational Approach, Chichester: John Wiley & Sons, 1986.

[14 P. Bratley, B. L. Fox, and L. E. Schrage, A Guide to Simulation,

New York: Springer Verlag, 1987.

[15] J. E. Wieselthier, C. M. Barnhart, and A. Ephremides, "Efficient Simulation of DEDS by Means of Standard Clock Techniques:

Queueing and Integrated Radio Network Examples," NRL/MR/5521-

-93-7392, Naval Research Laboratory, September 1993.

[16] P. Glasserman and P. Vakili, "Comparing Markov Chains

Simulated in Parallel," Probability in the Engineering and

Informational Sciences, 8-3, 1994.

[17] P. Glasserman and D. D. Yao, "Some Guidelines and

Guarantees for Common Random Numbers," Management Science,

38-6 pp. 884-908, June 1992.

[18] P. Heidelberger and D. I. Iglehart, "Comparing Stochastic

Systems Using Regenerative Simulation with Common Random

Numbers," Adv. Appl. Prob., 11 pp. 804-819, 1979.

[19] J. E. Wieselthier, C. M. Barnhart, and A. Ephremides, "Ordinal

Optimization of Discrete-Event Dynamic Systems: A Comparison of

Standard Clock and Common-Random-Number Methods,"

Proceedings of the 1997 Conference on Information Sciences and

Systems (CISS), Johns Hopkins University, Baltimore, MD, March

1997.

[20] J. E. Wieselthier, C. M. Barnhart, and A. Ephremides, "Ordinal

Optimization of Admission Control in Wireless Multihop Integrated

Networks via Standard Clock Simulation," NRL Report

NRL/FR/5521-95-9781, Naval Research Laboratory, August 1995.

[21] L. Dai and C.-H. Chen, "The Effect of Correlation on Ordinal

Comparison of Discrete Event Dynamic Systems," Proceedings of

the 35th Conference on Decision and Control, Kobe, Japan, pp. 3316-3321, December 1996.

[22] S. Kotz and N. L. Johnson, ed., Encyclopedia of Statistical Sciences, New York: Wiley, pp. 584-587, 1982.

180
Selection Schemes in Ordinal Optimization and

Their Computational Advantages*

T. W. Edward LauT

Division of Engineering and Applied Sciences

Harvard University

Cambridge, MA 02138

ABSTRACT

In this talk, we explain the advantages of selection-based search

schemes from a theoretical perspective. The role of selection in

tackling many difficult engineering problems has been empirically

demonstrated with noticeable successes. This is also confirmed in the recent AI researches. We show that one can achieve impressive

gain in computational efficiency when certain strategic definition of

optimization goal is adopted. In tliis light, we propose a

generalized optimization paradigm called ordinal optimization,

which pertains to performance analysis of many computationally

hard problems in a pragmatic sense.

KEYWORDS; stochastic optimization, sampling and

selection, goal softening, learning algorithms

1. INTRODUCTION

The following optimization objective is often sought in various

design problems:

mine0 J(0) = E[L(0)] (1)

where © is the design space in which 0 is a design parameter,

and JO) is an expected value of performance measurements

L(0). While mathematically succinct, equation (1) is difficult to solve in many real-world design scenarios, e.g. intelligent

systems, owing to the following challenges:

A. Search —the design space © is huge and may have little structure to be exploited. Typical examples are problems

in combinatorial optimization, which involves discrete or even symbolic variables. On top of the exponential

growth in the size of search space, local properties such as gradient and convexity information may not be easily

constructed.

R. Estimation — the functional JO) has to be calculated via

monte-carlo simulation or through crude approximating

models. Lengthy and repeated computer experiments for

averaging out 1/0)' s are needed in order to obtain quality answers. Theoretical limit on how fast statistical estimates can converge also makes simulation by itself an arguably

insufficient means to solve statement (1) in view of limited

computing budget.

Despite the above challenges, problems such as (1) are still faced by designers who are eager to obtain quality answers in a

time-efficient and computationally affordable manner. Ordinal

optimization, proposed by Ho et al. [1] (see also Ho [15]), aims

at getting around the above mentioned challenges. In fact,

ordinal optimization is a complementary technique which

enhances the capabilities offered by existing search methods

and estimation algorithms We shall elaborate ordinal

optimization in Section 2.

Sampling and search methods have recently gained

attention in AI researches. Successes were reported in chess

tournament, planning and scheduling applications [2], in

control problems [3], and in the networking area [4]. Intelligent search schemes combined with the advent of faster

and parallel computing technology provide a new avenue of

problem solving possibilities. A pertinent idea is to iteratively

learn about good solution ''properties" by means of sampling

the search space. These "properties" can be, for example,

useful solution representation, promising regions of the search

space, or better heuristics, etc. Genetic algorithms and

reinforcement learning are techniques that embrace these ideas

of iterative sampling and learning.

Meanwhile, due to the imprecision or randomness

involved in estimating design performances (e.g., in montecarlo experiments), it becomes necessary to devise selection

methods so that learning can be effectively achieved through

i This work is partially supported by NSF grants EID-9212122, EEC9402384, Army contracts DAAL03-92-GO1 15, DAAH04-95-

0148 and Air Force contract F49620-95-1-0131.

1 Post-doctoral fellow. Division of Engineering and Applied Sciences, Harvard University. Email, twel@arcadia.harvard.edu.

181
evaluating the design samples. This motivates our main topic

in this paper — selection schemes in ordinal optimization,

which will be discussed in Section 3. Subsequently, we will

connect the selection schemes to some ideas of iterative learning in Section 4.

2. GENERALIZED SELECTION AND GOALS

Consider a collection of N design samples drawn from the

design space. There is a true order of these N designs with

respect to the true performances. If this order were known,

then we could easily pick out the best, the second best, etc., and the selection problem is essentially solved. However, the

observed order of these N designs is inevitably perturbed from

the true order due to noisy evaluation of design performances.

In particular, suppose the designer insists on getting one

design which is the true best. Then lengthy evaluation is needed so that the resulting order of the TV designs would rum

out the true best design showing up as the observed best. If

the noise factor is large, then it is possible that the true best is displaced to the last position of the observed order of the N

designs. Therefore, we bring forth two major ideas in ordinal

optimization:

• Ordinal comparison —it is much easier to decide whether

"A > 5?" than "A - B = ?" In other words, one can

estimate the observed performance order better than the

magnitude of performance values. In fact, this has been

formally established by Dai [5] and Xie [6], and extended

by Dai and Chen [14]. Their results show that the

probability of answering the former question correctly occurs exponentially fast along with the simulation

horizon.

• Goal softening — instead of picking a single design to match the very best in a population, which is an unlikely

event, one may soften the goal to settle on the top-«% of

the population by selecting a subset of designs. Lee et al.

[7] has studied this viewpoint using an order statistics formulation, and show that it also has exponential

advantage in terms of correct selection.

These two tenets are manifested by a quantity called

alignment probability- defined as

Pfos,k)=P(\Gr&\ zk,t) (2)

where G is the set of top-g true best designs (called good

enough designs), and S is the set of top-s observed best

designs, k is called the alignment level and / is the index for

simulation horizon. Notice that in conventional optimization one often asks for g = s - 1 . The alignment probability of such

a case is often too small to be of any interest. On the other

hand, Dai [5] has shown that 1-P/(1,1,1), decays exponentially

as the simulation proceeds, i.e., for some a > 0 (which

depends on the Ndesign performances), we have

< exp(-a/).

Xie [6] has generalized the result for other values of g, s and k.

Meanwhile, in Lee et al. [7], it is shown that \-Pt(g,s,\)

decreases exponentially as the sizes g and s are relaxed, i.e.,

1-PKg, s,l) z exp(-fcn(gyy,0)-

The implication ofthese results is that if one is willing to relax the goal and select a subset of design for further

analysis or learning, then it is possible to

i) execute shorter simulation to tolerate large confidence

intervals ofperformance estimates; and/or

ii) run crude or surrogate model that is computationally

cheaper and more amenable to analysis.

These advantages translate into impressive computational

saving and speed-up, and have been confirmed by various

empirical studies (see [4] and [8] to [12]).

3. EXPECTED ALIGNMENT LEVELS

In this section, we look closer into the effects of goal softening.

Given that the designer is willing to accept a good enough

subset G and to select a subset S from short simulation or crude evaluation, a useful quantity to assist decision is the

expected alignment level Et [k] given by

Et [k] = T,k kP( I GnS | =k;f) (3)

It is not difficult to see that the expected alignment level is an

increasing fiinction of g and s. In the absence of true

performances, one has to estimate Et[k] based on noisy

observed performances. However, we shall demonstrate that

this can be approximately obtained if the designer is able to estimate the type of underlying true performance profile and

noise magnitude. The true performance profile will be referred to as the ordered performance curve (OPC). It is a nondecreasing curve of true performances plotted against the

integral values of the true performance order. In general there

are infinitely many possible form of OPCs but several types of

OPC can be categorized, which are shown in Figure 1 below.

See Lau and Ho [13] for detailed discussion regarding ordered

performance curves.

182
Performance

I Ordered Designs

Figure 1. Different types of OPCs

For illustrative purpose, let us consider the case that

all true performances are equally spaced apart, which is equivalent to a linear OPC ofthe form

•/(%]) = <*<%) + co (4)

where is the ith true best design, and gives the true

rank of a design. Notice that />(%]) = » Clearly this

relationship would not be available, for otherwise there would

be no problem for selection in the first place. Consider that the

observed performance values are generated by the

additive noise model

J'(%]) = -W+<»(%i) (4)

where <!>(%]) is me noise disturbance which we assume to be

independent across designs. Typical picture of observed

performances is shown in Figure 2.

«) 300 -

True Performance Order

Figure 2. Design order is perturbed by noisy observations

Suppose the designer is able to give a rough guess that the

underlying true performances are approximately uniformly

separated (by means of short simulation, for example). Then,

the expected alignment levels can be shown as in Figure 3a, 3b

and 3c for signal-to-noise ratios 1:5, 1:2 and 1:1 respectively.

1

These diagrams are generated based on a total of 1,000 design

samples with linear OPC and independent uniform noise

density \-WJY\.

20.00 -|

15.00

E[k] looo

10 20 30 40 50 60 70 80 90 100

9 = K3|

Figure 3a. E[k] vs. g for s = 10 to 100 with linear OPC and

signal-to-noise ratio 1:5.

10 20 30 40 50 60 70 80 90 100

g = K5|

Figure 3b. E\k] vs. g for s = 10 to 100 with linear OPC and

signal-to-noise ratio 1:2.

0.00 1 1 1 1 1 1 1 1 11

10 20 30 40 50 60 70 80 90 100

g = |G|

Figure 3c. E[k] vs. g for 5 = 1 0 to 100 with linear OPC and

signal-to-noise ratio 1:1.

1 Signal-to-noise ratio is defined as the ratio between the

range of true performances to the range ofnoise values.

183
Let us interpret these diagrams. In the presence of

very large noise, such as 1:5, if one is willing to relax the goal

to g = 50 designs, then one can expect about 5.5 designs in a

selection of s = 50 designs. If more simulation is performed

and signal-to-noise ratio is reduced to 1.2, then on average

about 10 .5 of the top-50 true best designs are found in the top50 observed best designs. Notice that should the designer

insist on getting g = s = 1, then much longer simulation is needed in order to get the selected best to be indeed the tme

best. The computational advantage here is several folded.

4. DISCUSSIONS

We have seen in the previous section that softening the goal of

selection provides practical savings in the simulation budget.

The selection scheme is based on observed performances and

thus the name Horse Race selection rule is coined. Other

selection rules are also possible and generally produce

different alignment results. The study of various selection

rules is an on-going research topic. Besides the above

illustrative results, we also have extensive calculations based on a variety oftypes of OPC and noise ranges, also reported in

Lau and Ho [13].

From an algorithmic point of view, with a selected

subset that guarantees certain alignment of good enough

designs, a designer can run longer simulation on this subset to

learn about good "properties" of solutions, as mentioned in

Section 1 . The subsequent steps would be to develop adaptive

search schemes that utilize as much as possible the knowledge

learned from this selected subset. This sampling-selectionlearning approach laid out by ordinal optimization carries

important implications in the design ofintelligent systems.

Furthermore, ordinal optimization advocates a new

paradigm to perform stochastic optimization for

computationally difficult problems; namely, ordinal

comparison and goal softening. It serves as a complementary

methodology to existing approaches such as genetic

algorithms, reinforcement learning, other artificial intelligence

techniques, and nonetheless conventional procedures

discussed in many optimization literature. We believe that this

should warrant further research attention. In the theoretical

development of ordinal optimization, we have current results

that tackle noise estimation, design-dependent noises and

constrained optimization problems.

5. REFERENCES

[I] Ho, Y.-C, R. Sreenivas, and P. Vakili, "Ordinal

Optimization of Discrete Event Dynamic Systems,", J. DEDS,

vol. 2(2), pp. 61-88, 1992.

[2] Ginsberg, M. L., "Do Computers Need Common Sense?,"

Proc. of Knowledge Representation and Reasoning

Conference, 1996.

[3] Deng, M., and Y.-C. Ho, "Sampling-Selection Method For

Stochastic Optimization Problem," submitted to AUTOMATICA, i995.

[4] Wieseltheir, J. E., C. M. Bamhart, and A. Ephremides,

"Ordinal Optimization of Admission control in Wireless

Multihop Voice/Data Network via Standard Clock

Simulation,'V. DEDS, Vol.5, #2-3, 1995.

[5] Dai, L.-Y., "Convergence Properties of Ordinal

Comparison in the Simulation of Discrete Event Dynamic

Systems," JOTA, Vol. 91(2), pp. 363-388, 1996.

[6] Xie, X., "Dynamics and convergence rate of ordinal

comparison of stochastic discrete event systems." IEEE Trans. on Automatic Control, vol. 42(4), pp. 586-590, 1997.

[7] Lee, L.-H, T.-W. E. Lau, and Y.-C. Ho, "Explanation of

Goal Softening in Ordinal Optimization," IEEE Trans, on

Automatic Control, to appear, 1997.

[8] Patsis, N., C.-H. Chen, and M. Larson, "Parallel Simulation

of DEDS," IEEE Trans, on Control Teclmology, 1996.

[9] Ho, Y.-C, and M. Larson, "Ordinal Optimization and Rare

Event Probability Simulation," J. DEDS, vol. 5, #2-3, 1995.

[10] Xie, X.-L., "An Ordinal Optimization Approach to a Token Partition Problem for Stochastic Timed Event Graphs,"

Proc. of the 1994 Winter Simulation Conference, Orlando,

Florida, pp. 581-588, December 1994.

[II] Yang, M. S., L.-H. Lee, and Y.-C. Ho, "On Stochastic

Optimization and Its Applications to Manufacturing," to appear in Lectures in Applied Mathematics, pp. 317-331,

AMS. 1997.

[12] Tang, Z. B , and Y.-C. Ho, "Modification of Adaptive

Partitioned Random Search," Proc. of 1995 Conference on

Decision and Control, New Orleans. December 1995.

[13] Lau, T.-W. E., and Y.-C. Ho, "Universal Alignment

Probabilities and Subset Selection for Ordinal Optimization,"

JOTA , Vol. 39(3), pp. 455-490, June 1997.

[14] Dai, L.-Y., and C.-H. Chen, "Rates of convergence of

ordinal comparison for dependent discrete event dynamic

systems,'V07^, Vol. 94(1), July 1997.

[15] Ho, Y.-C, "On the Numencal Solution of Stochastic

Optimization Problems," IEEE Trans, on Automatic Control,

Vol. 42(5), 1997.

184
Intelligent Computing Budget Allocation for

Discrete Event Simulation and Optimization

Chun-Hung Chen

Department of Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104-6315

Karen Donohue

Department of Operations and Information Management, The Wharton School,

University of Pennsylvania, Philadelphia, PA 19104-6315

Liyi Dai

Department of Systems Science and Mathematics, Washington University, St. Louis, MO 63130

Enver Yucesan

Technology Management Area, INSEAD, 77305 Fontainebleau Cedex, France

ABSTRACT

Simulation plays a vital role in analyzing many discrete-event

systems. Usually, using simulation to solve such problems

can be both expensive and time consuming. We present an

effective approach to intelligently allocate computing budget

for discrete-event simulation. This approach can intelligently

determine the best simulation lengths for all simulation

experiments and significantly reduce the total computation cost

to obtain the same confidence level. Numerical testing results

are included. Also we compare our approach with traditional

two-stage procedures. Numerical results show that our approach is much faster than the traditional two-stage

procedures.

KEYWORDS: Discrete-event simulation, optimization,

ranking and selection.

1 . WHY INTELLIGENT COMPUTING

BUDGET ALLOCATION?

It is often necessary to apply extensive simulation to design or

efficiently manage large real-life systems such as communication networks, traffic systems, and automated

* This work was supported in part by the National Science

Foundation under grant No. DMI-9322830 and grant No. ECS962479.

manufacturing plants. Unfortunately, simulation can be both

expensive and time consuming. Suppose we want to compare

k different discrete-event systems (designs or alternatives), we

do N simulation replications for all k designs. (Without loss

of generality, we consider terminating simulation in this

paper. Our approach is also applicable to steady-state

simulation although we need to have N independent samples

rather than N independent simulation replications.) Therefore,

we need kN simulation replications. The simulation results

become more accurate when N increases. If the accuracy

requirement is high (N is not small), and if the total number of

designs in a design problem is not small (k is large), then kN

can be very large, which may easily make total simulation

cost extremely high and preclude the feasibility of the

simulation approach. How to effectively reduce computation

cost to obtain a good decision is crucial to apply simulation.

Instead of equally simulating all k designs, a more

efficient way is to have different simulation replication

numbers for different designs. The numbers of replications are determined using preliminary simulation information. A

central issue is how to effectively utilize the available

information and how to intelligently determine the best

simulation replication numbers for al designs. Our goal is to significantly reduce simulation cost while obtaining the desired

simulation quality. In fact, this question is equivalent to optimally decide which designs will receive computing budget

for continuing simulation or to find an optimal way to reach an optimal design.

Dudewiczand Dalai (1975) develop a two-stage procedure

for selecting the best design or a design which is very close to

185
the best system. In the first stage, all systems are simulated

with n0 replications. Based on the results obtained from the

first stage, we estimate how many more simulation

replications for each design should be conducted in the second

stage in order to reach the desired confidence level. Rinott

(1978) presents another way to estimate the number of required

simulation replications in the second stage. Many researchers

have extended this idea to more general ranking and selection

problems in conjunction with new developments. Among of

them are Chiu (1974), Gupta and Panchapakesan (1979),

Charnes (1991), Matejcik and Nelson (1993), Bechhofer,

Santner, and Goldsman (1995), Futschik and Pflug (1996), and

Hsu (1996).

With further development from Chen (1995), we will

present an effective approach to intelligent allocate computing

resource for discrete-event simulation. Also, we will compare

our approach with the traditional two-stage procedures by

conducting a numerical experiment. Numerical results show

that our approach is more than ten times faster than the twostage procedures. We formulate the problem of intelligent

computing resource allocation as a "optimal computing budget

allocation" problem in the next Section. In Section 3, we

present a simple sequential approach. We will show the

numerical results in Section 4. Section 5 compares our method with the two-stage procedure. Section 6 concludes this paper.

2 . OPTIMAL COMPUTING BUDGET

ALLOCATION

Suppose that our goal is to select a design associated with the

smallest mean performance measure among k designs with

unknown variances that are not necessarily equal. Further assume that the computing budget is limited and the number

of designs is not small.

Denote

k : the total number of designs,

Xjj-. the j th i.Ld. sample of the performance measure from

Design i,

Mj : the number of simulation replications for Design i,

1 H^. the sample mean for Design i; /i

( = — Xtj

, Ni j=\

jdj : the mean performance measure; fl ( = E(Xtj

)

.

For steady-state simulation, Batch Means method

(Schmeiser 1982) can be used if the simulation samples from

any design are not independent. Again, we consider

terminating simulation in this paper. Independence

assumption is not a problem for practical applications.

When Nj 's are large, Jli can be a good approximation for

Hi, since, according to the law of large numbers, —> ^u,} —> 1, as Af, —> oo. Given the fact that we can only do a finite number of simulation replications, Jii is simply an approximation to (J.^ Using the approximation results to

select the best design (without loss of generality, we consider

minimization problems in this paper; thus the "best" design means the design with the smallest /J,), we have to ask what

the probability of correct selection is. Correct

selection can be defined by that a design with the smallest

sample performance measure is actually the best design (the

smallest population performance). In the remaining part of

this paper, let "CS" denote the event "correct selection."

Chen (1996) provides an effective way to quantify

confidence level when the number of systems is large.

Furthermore, the sensitivity information of the confidence

level with respect to simulation replications can be easily

obtained when the approach in Chen (1996) is applied, which

will provide the basis to determine how to allocate computing

in this paper. From Chen (1996) we have

P{CS} = P{ a system with the smallest sample mean

performance is actually the best system}

> Y[P{fib <fii) =APCS (1)

i=l

where index b is the design having the smallest sample mean

performance, i.e.,

b = arg min { /J, },

i

and fit is the posterior distribution which consists of

information from both prior distribution and the samples {X,-,,

j = 1, 2, .., N, }. Under the assumption of normality

1 N' a

2 M,~N( — I X9 ,-M, fori =1,2,..,*.

ty;=l Ni

We refer to this lower bound of the correct selection

probability as the Approximate Probability of Correct

Selection (APCS). While P{CS} is very difficult to obtain,

APCS can be computed very easily. We will use APCS to approximate f{CS}. Numerical testing in Chen (1996) shows

that it can provide reasonably good approximation.

As motivated in Section 1, we intend to minimize the

total computation cost while obtaining a desired confidence

level. If simulations are performed on a sequential computer,

the computation cost can be approximated by Nl + N2 + + Nk. Ideally we want to

186
min { Nj + N2 + • + Nk }

s.t. APCS > P*. (2)

where P* is a user-defined confidence level requirement.

3. A SEQUENTIAL APPROACH

We now present a sequential approach to intelligently

determine the number of simulation replications. Instead of

finding the best Nx , N2 , .., Nk at the beginning of simulation,

we sequentially select some PROMISING designs and

simulate these selected PROMISING designs. The

PROMISING designs are those by simulating which we

anticipate the improvement of APCS is maximized.

Before doing the simulation, there is neither knowledge

about APCS nor an idea about how to allocate budget,

therefore all designs are simulated with n0 replications, and the

posterior distribution for design i is

1 n

° o N(— I Xij,^-)

n0 7=1 n0

We use this statistical information to decide on the further

allocation. In other words, after running n0 replications for each design, we have the basic idea about each design and can

decide which designs are worthy of being allocated more

computing budget. Let A, be the additional computing budget

allocated to system i in each step (A, is a non-negative

integer). In order to find the PROMISING designs and

effectively allocate computing budget for further simulation, it

is necessary to know how APCS would be affected if additional simulation budget A, is added to system i. Under

the Bayesian model, it is convenient to use the statistical information at nt) to estimate APCS at n0 + A, by using an approximated posterior distribution

1 "o N(— I Xtj , "0 7 = 1 n0 + A,-

for design i.

for design i.

Let A = X^i- Thus A is one-time incremental

computing budget in our sequential algorithm. In Section 5 we

have more details about how to choose nQ and A. We hope that

APCS becomes larger as simulation proceeds, we sequentially

add computing budget by A each time until that APCS

achieves a satisfactory level P*. In order to reduce to the total computation cost, this budget A should be optimally allocated so that the EAPCS is maximized. Thus, at step /, / = 1, 2,

we have

max

t EAPCS( N[ + A\ , N

l2 + A'2

,

• • , N

lk + Alk ), A, ,...,A k

k

s.t. £A\ = A and A'( > 0 for all i. (3)

In summary, we have the following algorithm:

A Sequential Algorithm for Optimal Computing

Budget Allocation (OCBA)

Step 0. Perform nQ simulation replications for all designs,

/ <r- 0,

Nl=Nl2 =- = N

lk =n0

.

Step 1. If APCS( Ni,N2 ,---,N

lk ) >P\ stop, otherwise,

go to Step 2.

Step 2. Solve (3),

Step 3. Perform additional A' simulation replications for

design /', i = 1, k..

Nj+] = Nj + A',, for i = 1, k..

I <- /+ 1.

We refer this approximation to EAPCS (estimated

approximate probability of correct selection). We assume that

A, is not large and nn is close to n0 + A,, otherwise EAPCS is not a good estimator for APCS.

Similarly, when simulation proceeds until (Nu N2 , .., N,_

i, Nh Ni+l , .., Nk ), we can also use the available information to estimate how APCS will change if design i is given additional

budget A„ i.e., EAPCS(/V„ N2 , .., tfM, N,+A„ Ni+l , .., Nk), by using an approximated posterior distribution

To solve (3), we assume the variables are continuous and

apply steepest-descent method (Luenberger 1984 and Nash and

Sofer 1996) to approximately solve (3). Then the results for the numbers of simulation replications are rounded off to

integers. The gradient of EAPCS with respect to Af, is estimated by the following formula:

187
EAPCS(N] ,N2 ,---,Ni + T,Ni+] Nk )-APCS(N] ,N2 ,---,Ni ,Ni+i Nk ) T

(4)

where T is a small number. To avoid spending much time in iteratively finding the solution of (3), we only do a very

limited numbers of iterations when applying steepest-descent

method. In fact, we can also use other optimization techniques

to solve (3), please refer to Chen et al. (1997) for more details. Chen et al. 1997 also gives guidelines for selection of n{) and

A.

4. NUMERICAL TESTING

This section present the numerical testing results using our OCBA algorithm. We test a simple G/G/l/°° queue (k=W).

There is one server with uniformly distributed service times

and interarrival times. In this single-node example, all designs

have the same arrival time uniform[0.1, 1.9], and service time

in system i is uniform[0.1, 1.8-0.05 i], i = 1, 2, 10. We

want to find a design with minimum average system time for customers served in the first 10 time units (terminating

simulation). Obviously, higher service rate results in shorter

system time in this simple example, therefore, design 1 is the true best design. In the numerical experiment, we compare

their computation costs and the actual convergence

probabilities P{CS} for using OCBA and without using

OCBA approaches.

We set A = 12 and n0 = 10 in this example. To avoid

spending too much time in solving (3), we only do two

iterations in the gradient method. 10,000 independent

experiments are performed so that the average computation

cost and P{CS} can be estimated. Different confidence level requirements are also tested. Table 1 contains the numerical

results using OCBA algorithm and Table 2 contains the results

without using OCBA.

p* Total # of

Replications

P{CS}

60% 196.4 72.2%

80% 344.3 86.6%

90% 523.6 96.3%

95% 735.4 98.1%

Table 1 . Average total number of simulation replications and

P{CS) for OCBA application (n0 =10).

p* Total # of

Replications

PICS)

60% 541.8 82.9%

80% 863.6 90.7%

90% 1474.6 96.9%

95% 2175.5 99.0%

Table 2. Average total number of simulation replications and

P{CS} without applying OCBA algorithm (nG = 10).

Comparing Tables 1 and 2, we observe that our OCBA

can achieve the desired P{CS} with much lower computation

cost. Figure 1 shows how the OCBA algorithm allocates

computing budget to different designs.

5 . COMPARISON WITH OTHER

METHODS

In this section we will compare our approach with twostage procedures given by Dudewicz and Dalai (1975) and

Rinott (1977) using the testing example in Section 4. Unlike

our Bayesian approach, these two-stage procedures are developed based on classic statistical model. Also the idea of

indifference-zone is required to apply such two-stage

procedures.

Two confidence level P* = 90% and 95% have been tested. When applying Rinott' s and Dudewicz' s procedures, we set the

indifference zone d* = 0.059 (p.m

- jtz(1) = 0.059). In both cases 10,000 independent experiments are run to evaluate the

computational efficiency and to estimate the actual convergence probabilities. The computation cost and P{CS}

are given in Table 3. From Table 3, significant speedup is observed for our method over both two-stage procedures, while

the actual convergence probabilities for all approaches are no

less than the desired levels. The speedup factors are higher

than 14 in all cases.

Methods Total # of

Replications

P{CS) Speedup

factor using

OCBA

OCBA 523.6 96.2%

Dudewicz' s Proc. 8059.9 98.3% 15.3

Rinott' s Proc. 9479.3 98.6% 18.1

Table 2. Comparison of our OCBA approach and traditional

two-stage procedures. P*= 90%.

188
Total M V'lClI #IT ofKJ X Replications

Sneedun

factor using

OCBA

OCBA 735.4 98.1%

Dudewicz's Proc. 11023.2 99.4% 14.6

Rinott's Proc. 12464.1 99.5% 16.5

Table 3. Comparison of our OCBA approach and traditional

two-stage procedures. P*= 95%.

6. Concluding Remarks

In this paper we present an optimal computing budget

allocation technique that can intelligently determine the best

simulation replication numbers for all designs. We also

compare our approach with traditional two-stage procedures by

conducting a numerical experiment. Numerical testing shows

that our approach is more than ten times faster than two-stage

procedures. For more details regarding this techniques readers

are recommended to see Chen etal. (1997).

References

1. Bechhofer R. E., Santner, T. J., and Goldsman, D. M.

1995. Design and Analysis of Experiments for Statistical

Selection, Screening, and Multiple Comparisons. John

Wiley & Sons, Inc.

2. Charnes, J. M. 1991 "Multivariate Simulation Output

Analysis," Proceeding of the 1991 Winter Simulation

Confidence, 187-193.

3. Chen, C. H. 1995. 'An Effective Approach to Smartly

Allocate Computing Budget for Discrete Event

Simulation," Proceedings of the 34th IEEE Conference on

Decision and Control, 2598-2605.

4. Chen, C. H. 1996. "A Lower Bound for the Correct

Subset-Selection Probability and Its Application to Discrete Event System Simulations," IEEE Transactions on Automatic Control., Vol. 41, No. 8, 1227-1231.

5. Chen, C. H., Chen, H. C, and Dai, L. 1996 "A Gradient

Approach for Smartly Allocating Computing Budget for

Discrete Event Simulation," Proceedings of the 1996

Winter Simulation Conference, 398-405.

6. Chen, C. H., Dai, L., Chen, H. C, and Yucesan, E.

1997. "Efficient Computation of Optimal Budget

Allocation For Discrete Event Simulation," submitted to Operations Research.

7. Chiu, W. K. 1974. "Selecting the Populations with

Largest Means From Normal populations with Unknown

Variances," Australian Journal of Statistics, 16, 144-147.

8. Dudewicz, E. J. and Dalai, S. R. 1975. "Allocation of

Observations in Ranking and Selection with Unequal

Variances," Sankhya, B37:28-78.

9. Futschik, A. and Pflug, G. C. 1996. "Asymptotically

Optimal Allocation of Simulation Experiments in

Discrete Stochastic Optimization," Working Papers,

International Institute for Applied Systems Analysis,

Laxenburg, Austria.

10. Gibbons, J. D., Olkin, I., and Sobel, M. 1977. Selecting

and Ordering Populations: A New Statistical

Methodology, John Wiley & Sons, Inc.

11. Goldsman, G., B. L. Nelson, and B. Schmeiser. 1991.

"Methods for Selecting the Best System," Proceedings of

the 1991 Winter Simulation Conference, 177-186.

12. Goldsman, G., and B. L. Nelson. 1994. "Ranking,

Selection, and Multiple Comparison in Computer

Simulation," Proceedings of the 1994 Winter Simulation

Conference, 192-199.

13. Gupta, S. S. and S. Panchapakesan. 1979. Multiple

Decision Procedures: Theory and Methodology of

Selecting and Ranking Populations, John Wiley.

14. Luenberger, D. G., 1984. Linear and Nonlinear

Programming, Addison-Wesley.

15. Matejcik, F. J., Nelson, B.L. 1993. "Simulations

Ranking, Selection and Multiple Comparisons for Simulation," Proceeding of the 1993 Winter Simulation

Confidence, 386-391.

16. Rinott, Y. 1978. "On two-stage Selection Procedures and

Related Probability Inequalities," Communications in

Statistics A7, 799-811.

17. Schmeiser, B. 1982, "Batch Size Effects in the Analysis

of Simulation Output," Operations Research, Vol. 30,

No. 3, , 556-567.

189
0 10 20 30 40 50 60 70 80 90100110120130140150

Average simulation replications

Figure 1. Computing budget allocation determined by OCBA. P*= 90% and n{) = 10. (design 1 is the best design).

190
Comparison of Performance Orders of Different

Designs for Discrete-Event Dynamic Systems*

Liyi Dai

Dept. of Systems Science and Math.

Washington University

St. Louis, MO 63130

Abstract

In this paper, properties of ordinal comparison for discreteevent dynamic systems are investigated by employing the

large deviation principle which allows one to have an ex- pression for the rate of convergence of ordinal comparison.

With this expression, conditions are obtained under which

the rate of convergence of ordinal comparison is exponential. Such expression also enables one to obtain bounds on the rate of convergence and design sample path generation schemes that maximizes the convergence rate of ordinal comparison.

1 Introduction

Many design problems in Discrete-Event Dynamic Systems

(DEDS) require choosing one design from a large, discrete

design space, such as the problem of resource allocation

[5]. Such problems are of combinatorial nature and known

to be NP hard (difficult to solve [17]). The design of DEDS

is further complicated by the fact that not only the design

spaces are large and discrete but also the performance measures on which designing is based do not have closed-form

solutions. Except for special cases, discrete-event simulation or sample path observation is usually used in performance estimation and evaluation of designs in DEDS.

Such performance estimation is time-consuming and costly.

Typically, a performance estimator converges slowly at

rate of 0(1 /y/i) in simulation or observation time t [9]. On the other hand, in reality, we often face a decision

making problem of choosing one relatively better design

from all possible alternatives. As long as we can single out

the "good" and "satisficing" designs, the exact values of

their performance measures are of secondary importance.

Such goal relaxation can bring great saving of effort. In the

context of recently proposed ordinal optimization methods,

ordinal comparison of different designs by their relative

ranks is very efficient, as observed in many experiments.

Ordinal comparison is able to discern quickly the good

designs using noisy information [1, 6, 7, 10, 13, 14, 18].

By ordinal comparison, we mean comparing the relative

"This work was supported in part by the National Science Foundation under grant No. ECS-9624279 and by the University of Pennsylvania Research Foundation.

Chun-Hung Chen

Dept. of Systems Engineering

University of Pennsylvania

Philadelphia, PA 19104-6315

goodness (rank) of different designs without knowing the

exact values of corresponding performance measures. Recent research has revealed a more interesting phenomenon:

Ordinal comparison is beneficial when used in conjunction

with conventional methods such as stochastic approximation and simulated annealing as reported in [3, 11, 22].

Consider the problem of finding the best or a good design among N possibilities. Let 0 = {#1,02, ••> #jv} denote

the set of all designs and J(9) € R denote the performance

measure of a particular design 9 € O. In general DEDS,

the exact form of J(9) is not available. We can only use

noisy estimate of J(9) in our decision making. Let us consider the dynamics of the following experiment. We si- multaneously simulate N parallel DEDS with designs 0j,

1 — 1,2, ...,N. This can be done, for example, using the

standard clock [21] or the augmented system analysis [4]. As the simulation continuous, we collect data and output an estimate of J(9), denoted by L(9,t), for every 9 6 0.

Convergence of L(9,t) to J(9) is generally slow at the rate

of at most 0(1 /y/t) according to the law of large numbers (assuming the validity of convergence). However, it has been observed that the observed order of performance measures L{9i,t), i — 1,2,..., TV, can quickly converge to an order very close to the true order of performance measures J(9i), i = 1, 2, TV, despite possible presence of

large noises [1, 6, 7, 10, 13, 14, 18].

This paper is concerned with several fundamental properties of ordinal comparison in DEDS. By applying the

large deviation principle one is able to obtain an expression

for the rate of convergence of ordinal comparison. With

this expression, conditions are obtained under which the

rate of convergence of ordinal comparison is exponentially

fast. Such expression also enables one to obtain bounds on

the rate of convergence and design sample path generation

schemes that maximizes the convergence rate of ordinal

comparison.

2 Problem Statement

The DEDS under investigation is described by a rightcontinuous stochastic process {X(9,£,t) £ X,t > 0} parameterized by 9 € 0 and defined on a common probability

space. Here, X C R is the state space, 9 is used simply

to indicate a design, and £ represents all the randomness

191
involved. For each design 9 G 0, let L(9,t) G R be an

estimate of a performance measure J'(d) G R based on a

particular sample trajectory of {X(9,£,t)} over [0,t]. In

DEDS, J(9) is often a steady state performance and L(9, t)

is a sample performance over [0, t]. Note that L(9,t) converges slowly with rate at most 0(l/\/t). Long and timeconsuming simulation has to be performed in order to have

a good estimate of the (steady state) performance measure J(9).

Now consider the problem of comparing performance

measures corresponding to a set 0 of iV, 1 < N < oo, designs. Design 9{ is said to be better than design 9j

if J(9i) > J(9j). Without loss of generality, we as- sume that the N designs are indexed in such a way that

oo > J(6i) > J{92 ) > J(03 ) > ... > J(9N) > -oo. Particularly, we are interested in finding a design that is one

of the M, 1 < M < N, true best designs in 0. For

convenience, let us define 0g = {9i,i = 1,2, ...,M} and

06 = {9i} i = M + 1, M + 2, ...,N} the sets of "good" and

"bad" designs, respectively. For the problem of finding one

of the M best designs based on the simulation over [0,i],

we choose the design with the largest sample performance,

i.e.,

9t — axs max. L(6,t). 1 eee

(2.1)

Experimental results have shown that (2.1) can qi : ~kly

find the true desired design [1, 6, 13, 18]. Intuitively, . implies that relative order of performance measures converges very fast.

In order to characterize the convergence of ordinal comparison, we define the following indicator process

I(t) = i 1 if max^eeg L(^,t)>maxg€@b L(9,t)

' 0 otherwise.

(2.2)

Then I(t) is equal to 1 if the observed best design is among the true good designs and equal to 0 otherwise.

Since maxaeeg L(a, t) is the maximum of the observed true

"good" designs and maxgeet L(0, t) is the maximum of the

observed true "bad" designs, I(t) is a function of t indicating when the observed best design determined by (2.1)

is one of the M true best designs.

Our main goal is to examine the behavior of

3 The Large Deviation Principle

The concept of large deviation has been proven useful in

the study of the convergence of ordinal comparison. The

following definition is adopted from [8]. Definition 3.1 Let {Xt } be a family of random variables defined on a state space X. We say that {Xt } satisfies the large deviation principle with a rate function 0 if, for every closed set A C X, limsup£ _> 0 elogProb[X£ C

A] < — inf A6j4 0(A), and for every open set B C X,

liminfe _>.oelogProb[Xe CB]> -infA6 B0(A), where the

mapping 0 : X -> [0, oo] is lower semicontinuous, i.e., liminf^^A <j)(\n ) > 0(A) for all A G X.

Now define the logarithmic moment generating function Ae (s) = log£[esA_e

] and suppose that the limit A(s) =

lim£ _> 0 eAe (s/e) exists pointwise. The following theorem

from [8] gives an expression for the rate function <fi. Theorem 3.2 Assume that {Xe } satisfies the large

deviation principle with a rate function <f). If (j) is convex

and, for all c G R+ , the set {A : (j>(\) < c} is a compact

subset of X, then <j> is the Fenchel-Legendre transform of

A(s), namely,

(p(X) = sup{As - A(s)}.

s

If, in addition,

inf 0(A) = inf 0(A)

X€A

(3.3)

for A C X where A

0 and A are the interior and closure

of A, respectively, then we know from Definition 3.1 and

Theorem 3.2 that

lim elogProb[Xe C A] = - inf_0(A). (3.4)

£->0 xeA

Choose A - (0, oo). Then,

inf 0(A) = inf sup{As- A(s)}= - inf A(s).

A€[0,oo) A<E[0,oo) s >0 s€[0,oo)

Therefore,

lime log Prob[X£ C (0,oo)]= inf A(s). (3.5) t—>0 s€[0,oo)

It gives an expression for the convergence rate of

Prob[X£ C (0, oo)] as e goes to zero.

Prob[7(i) = 1] and Prob[7(t) = 0]

as a function of time t. If limt _^oo L(9, t) = J(9),a.s., then

([6])

lim Prob[/(t) = 1] = 1, lim Prob[/(t) = 0] = 0. t—too ' t—too

The convergence rate of I(t) will be taken as the rate at which Prob[/(£) = 0] goes to zero (or the rate at which

Prob[7(i) = 1] goes to 1).

4 Rate of Convergence

The large deviation principle can be used to investigate

the convergence rate of ordinal comparison.

Lemma 4.1 ([16, 19]) Let ft (a) be a sequence of functions on A. Suppose lim€ _>.o fe{a>) = f(a) for every a £ A.

If {/£ (a)} are convex, differentiate at ao G A, and f(a) is differentiate at ao, then

lim

^(Qo) =

d/(Qo)

e->o da da

192
let

and

Theorem 4.2 For any pair of designs a G Qg

, 9 G ©(,,

Xt {(T,6) = L{6,t) - L(a,t)

A(s,a,e) = lim ilogE[ealX' (<7 - fl) ].

Assume that

(i) Xt {a, 9) satisfies the large deviation principle and the

rate expression (3.5) holds,

(ii) \ogE[estX,{a ' e)

] and A(s,a,6) are differentiate at

s = 0,

(iii) and for every design 9 G 0,

lim E[L($,t)] = J{0).

t-»oo

Then there exist positive constants a > 0, (5 > 0 such that

Prob[/(*) = 0] < (3e~ a\

in other words, the convergence of ordinal comparison is exponentially fast. Q

Proof. According to the definition of the indicator

process,

Prob[I(t) = 0] = Prob[max L(a,t) < max L(9,t)}

<r€© 9 9e®b

< min Prob[L(a,i) < max L{6,t)}

9eQb

min Prob[ (J {L(<M) < L(0,«)}]

o-ee

< mm Prob[L(a, t) < L(0, t)] . (4.6) eeeb

Since Xt (<T, ^) satisfies the large deviation principle, we

know from (3.5) that

lim - log Prob[L((7, *)<£(#,*)]

t—>oo t

1 = lim -logProb[Xt(a,0) C (0, oo)] t—>oo f = inf A(s,cr, ^).

se[o,oo)

(4.7)

Since log E[estXt ^ a ^} is convex in a neighborhood of s = 0

and is differentiate at s = 0, we know from Lemma 4.1

that

as t-^oo r at/ = lim E[Xt ((7,0)]. t—>-CX3 The assumption (iii) implies that

lim E[Xt (a,6)} = J{9) - J(a) < 0. t—>oo

s=0

Therefore, A(s,a,9) < 0 for small s, which implies that

there exists an a > 0 such that

inf A(s,er, 9) < -a.

se[o,oo)

Combining the previous inequality with (4.7) yields,

lim -logProb[L(<r,i)<L(0,i)l < -a.

The proof of the theorem follows from this inequality and

(4.6).

Theorem 4.2 assures the exponential convergence of or- dinal comparison under some conditions in terms of the

large deviation principle. Other conditions that also guarantee such exponential convergence are given in [6, 10]. In

particular cases, the requirement for the rate expression

(3.5) can be relaxed. Some important cases are discussed

in detail in [6].

5 Bounds on Convergence Rate

In this section, we find bounds for the rate of convergence

of ordinal comparison. Based on these bounds, we propose

simulation schemes that maximize the rate of convergence

of the indicator process. The results also shed useful insight for sample path reconstruction in performance analysis.

Let

Yt = maxL(9,t) — max L(a, t). eeeb

v

'

«r G es

v

' 1

If Yt satisfies the large deviation principle and if the rate

expression (3.5) holds, then the convergence rate r of

Prob[/(*) = 0] is

r — - inf lim iw E[est(maX96e b L(6l ' t)_max'Te0 9 L ( <T ' t "l

s€[0,oo)*-+oo t

(5.8)

Therefore, maximizing the rate is equivalent to maximizing

(5.8). It is sufficient to minimize

At (s)

d= £^e

s *( maxe€e i,£'(0,<)-max,r€ e 9 L(<r,t))i

for all s > 0, t > 0, and consequently

r = — inf lim -logAf (s).

sG[0,oo)t->-oo t (5.9)

A function g(X\,X2) : R

2 —> R is said to be superadditive if, for any Xx < X[, X2 < X'2 ,

g(X'1 ,X2)+g(X1 ,X2 )<g(X1 ,X2 ) + g(X'1 ,X£. (5.10)

If g(Xi,X2) is twice differentiable, it is superadditive if and only if d

2 g(Xu X2 )/dX1 dX2 >0. The following result

is due to [2, 20].

193
Lemma 5.1 Let Xi,X2 be random variables with

marginal distributions Fi(xi), i = 1,2, and joint distribution H(xi,x2 ). Assume that g{X\,X2 ) is rightcontinuous and superadditive and E[g(Xi,X2 )] is finite

for all H(xi,x2 ). Then

snpE[g(X1 ,X2 )}=E[g(F1- 1 (u),F2- 1 (u))] (5.11)

{"}

inf E[g(X1 ,X2 )] = E[g{F^\u) t F^{\ - u))] (5.12)

where the random variable u is uniform over [0, 1] and the

inverse F

-1

(u) is defined as F

_1

(u) = inf {a; e R | F(x) > it}.

Lemma 5.1 says that l?[<7(Xi, X2)] is maximized by

sampling Xi and X2 using the same random number u

according to

Xi = Fr1 {u), i = 1,2.

This scheme of generating samples of random variables is known as the scheme of common random numbers (CRN).

It is perhaps the most popular scheme for variance reduction in simulation.

Let fix t and denote by Ge(w) = Prob[L(9, t) < w] the

c.d.f of L(9, t) for each 0 e 0. Define

Gg (w)^mm{Ge (w)},Gg (w)^max{0^-J2[^e(w)}}

G6 H=ym{G,(^)},G^H=fmax{0,l-^[l-G9 (u;)]}

Then the following theorem gives lower and upper bounds

for the convergence rate r of ordinal comparison.

Theorem 5.2 Suppose that Yt satisfies the large deviation principle and that the rate expression (3.5) holds.

Then

— inf lim -logAt (s) < r < - inf lim -logAt (s)

se[0,oo)<->oo t se[0,oo)*->oo t (5.13)

where

At (s)=E[es' ((5 " (u) -^1(u))

], At (s) = E[est ^

1(u)- e9"

1(1 - u))

].

Proof. Let

W\ = max L(9,t), W2 = max L(cr, t). ee&b o-e©9

For any t > 0, s > 0, consider the function _e st(W,-W2

)^ (514)

It is continuous and superadditive in (Wi, W2 ). Therefore,

Lemma 5.1 applies and, for all i > 0, all s > 0, and all 9 e e6 ,

sup E[-est ^-w^} = Ei-e

3^^-^^}, (5.15)

inf E[-est W-w^] = E[-est(F">) - F

TMl {1 - u))

) (5.16)

{/fu.}

where {Hw } is the set of all correlations among {Wi,W2 ) and Fw! and Fw2 are the distribution functions of Wi and

W2, respectively.

However, from the definitions of W\ and W2 and ac- cording to basic probability properties, we know that

Prob[Wi <w] = Prob[maxL(0,i) < w]

< min Prob[L(9,t) < w] = min Gb (w) = Gb (w).

On the other hand,

Prob^ >w] = Prob[max L(9,t) > w]

< PTMb[L{6,t) >w}= ]T [1 - Gg(w)}

oe@b eeeb which implies

Prob[Wi <w] >max{0,l-^][l-Ge H]} = GjH.

eeeb

Therefore,

Ob (w)<FWl (w)<Gb (w). (5.17)

Similarly,

Gg (w) < FW2 (w) < Gg (w). (5.18)

With those bounds, it is easy to verify that

_est{F-\(u)-F-\{u)) < _est(G; l (u)-Gg

x (u))^

_e st(F-\{u)-F-\(l-u)) > _e

st(G- 1

( U)-GJ 1 (l-U))

for any st > 0. Combining this with (5.15) and (5.16), we

know that

E^est(G-\u)-G-\u))^ < E[e

stYt

] < E{ e st{G-\u)-G-\l-u))^

(5.19) or equivalently,

At (s) > At (s) > At (s).

The combination of the preceding inequality with (5.9)

yields (5.13). The proof is thus complete.

Theorem 5.2 makes it possible to design simulation ex- periments so that the rate of convergence of ordinal comparison is maximized.

Corollary 5.3 Assume M — 1. Suppose that Yt satisfies the large deviation principle and that the rate ex- pression (3.5) holds. Then the rate of convergence of the

indicator process is maximized by sampling L(8,t) using

the scheme of CRN.

Proof. For M = 1, Qg — {9\} contains only one design 9\. In this case, Gg (w) — Gg (w) = Gq1 (w). Then

Theorem 5.2 shows that the rate of convergence of ordinal

194
comparison is given by (5.9) in which At (s) is bound from

below by

At (5) > Kt(s) = E[e

at ^

u) -G>>\

that is mf At (s) = E[e b "i

J

where {Hl} is the set of all correlations among {L(6,t)}.

Since the lower bound can be achieved by sampling all L(9,t) using the scheme of CRN. Therefore, (5.8), or the

convergence rate of ordinal comparison, is maximized by

the scheme of CRN.

As far as ordinal comparison is concerned, it is important to be able to design simulation experiments so the

upper bound in (5.13) is achieved. Let us consider this

problem for different values of M.

(i) M = 1. In this case, Corollary 5.3 shows that the

upper bound in (5.13) can be achieved by the scheme

of CRN.

(ii) M = 2. We know from the proof of Theorem 5.2

that the upper bound is achieved when W\ and W2 are sampled using the scheme of CRN when the distribution of W\ = maxe e 0i, L(9, t) is

FWl {w)=Gb (w), (5.20)

and the distribution of W2 = maxffe es L(a,t) is

FW2 (w)=Gg (w). (5.21)

The distribution (5.20) is achieved by setting

L(6,t) = GJ1 ^), 9 e 06 .

The distribution (5.21) is achieved by setting

L{6u t) = Gj*{v), L(62 ,t) = G^{\ - u).

It is easy to verify that such sample scheme yields the

upper bound in (5.13). However, it should be pointed

out that such scheme is not practical because the set Qg and ©6 are unknown a priori. Nevertheless, this

fact shows that the scheme of CRN does not give the

maximum rate for ordinal comparison.

(iii) M > 3. In this case, it can be shown using counterexamples that Gg (w) is not a distribution but can be asymptotically achieved by a sequence of random

variables [20]. As a result, it is impossible to find

sampling schemes that achieve the bounds in (5.13)

for M > 3. This means that the scheme of CRN does

not give the maximum rate for ordinal comparison

for M > 3.

To sum up, it is difficult, if not impossible, in practical

simulation to achieve the maximum rate for M > 2. For

M = 1, or for the problem of selecting the best from possible N designs, Corollary 5.3 shows that the maximum

rate of convergence in (5.13) can be achieved by sampling

using the scheme of CRN. This assures the positive role

of CRN when L(9,t) can be sampled from a single ran- dom number u. Of course, for practical problems L(0,t)

has more complicated form. In simulations or sample path

constructions of DEDS, L(9,t) is usually a function a set of random numbers, i.e.,

L(9,t) = L(u(l,0),u(2,d),...,u(n,0))

where n is an integer determined by the system structure

and t. It is possible to write L(9,t) as a non-decreasing

function of u(i,6) for a large class of DEDS (we shall not

describe the exact class of systems because of the limited

space. See [7] for further details). The following discussion is restricted to a case that is easily realizable in simulation and that has explicit solution. We assume that

{(u(n,#i),u(n,#2)> u(n,$N))} is a sequence of independent random vectors. We would like to find the correlation

among u(n, u(n, 62), ...,u(u,9n), for every fixed n, that

maximizes the rate of ordinal comparison. This scheme can be easily realized and most useful.

Assume again M = 1. For any 6 € ©6, let xt {o) = L(d,t)-L{eu t).

Then it has been proved that the scheme of CRN maximizes the rate of convergence of ordinal comparison as summarized by the following theorem. The details can be

found in [7]. Theorem 5.4 Assume that L(9,t) is right-continuous,

non-decreasing in u(n,9) for every t and every n > 1. If, for every 9 G ©t, Xt (9) satisfies the large deviation principle and if the rate expression (3.5) holds, then the rate

of convergence for the indicator process is maximized by

choosing

u(n,e) = v(n), (5.22)

where {v (n)} is a sequence of i.i.d. random numbers uniform on [0,1], in other words, the rate is maximized by

using the scheme of CRN.

Additional results regarding the effect of correlation on

the convergence of ordinal comparison can be found in [7, 10, 15].

The following example, modified from an example of

[12], illustrates the difference in the rates of convergence

for independent simulations and simulations using CRN.

Example 5.4 Consider an M/G/l FCFS queue with

arrival rate A. The service times have the Weibull distribution G(x) = 1 — e~ (7I ) a ,x > 0 for constants j,a > 0. Let the design parameter be 9 = (A, 7, a). The performance measure is the mean queue length in steady state. We consider 5 designs with the following parameters:

195
a

u a

Vl "3 (74 0

&5

A 1.0 0.5 0.5 1.0 0.7

Q 1.3 2.0 1.0 1.0 2.5

7 2.0 0.75 1.0 1.6 1.0

AO) 0.78 1.12 1.0 1.64 1.21

The performance is taken as the negative of the mean

queue length. The true best design is 6\. The simulation

performances for independent simulations and for simulation using CRN are shown respectively in Figures 1 and 2. Note that the displayed time is the real queue time, not

the simulation time. The simulation was completed within

seconds.

0 500 1000 1500 2000 0 500 1000 1500 2000

(a) Sample performances (b) Indicator process

Figure 1. Independent simulations

0 500 1000 1500 2000 00 500 10O0 ISOO 2000

(a) Sample performances (b) Indicator process

Figure 2. Simulations using CRN

Figures 1 and 2 show that correlation could significantly speed up the convergence of ordinal comparison.

References

[1] CM. Barnhart, J.E. Wieselthier, and A. Ephremides,

"Ordinal Optimization by Means of Standard Clock

Simulation and Crude Analytical Models," in Proc.

33rd Conf. Decision Control, 1994, pp. 2645-2647.

[2] S. Cambanis, G. Simons, and W. Stout, "Inequalities for Ek(X, Y) When the Marginals are Fixed,"

Zeitschrift fur Wahrscheinlichkeitstheorie und ver- wandte Gebiete, Vol. 36, pp. 285-294, 1976.

[3] C.G. Cassandras and G. Bao, "A Stochastic Comparison Algorithm for Continuous Optimization with Estimations," in Proc. 33rd Conf. Decision and Control,

1994, pp. 676-677.

[4] C.G. Cassandras and S. Strickland, "Observable Augmented Systems for Sensitivity Analysis of Markov

and Semi-Markov Processes," IEEE Trans. Automatic

Control, Vol. 34, pp. 1026-1037, 1989.

[5] C.G. Cassandras, L. Dai, and C.G. Panayiotou, "Ordinal Optimization for Deterministic and Stochastic

Discrete Resource Allocation," manuscript, 1997.

[6] L. Dai, "Convergence Properties of Ordinal Comparison in the Simulation of Discrete Event Dynamic Systems," J. Opti. Theory Appli., Vol. 91, pp. 363-388,

1996.

[7] L. Dai and C.-H. Chen, "Rates of Convergence of Ordinal Comparison for Dependent Discrete Event Dynamic Systems," J. Opti. Theory Appli., Vol. 94, 1997.

[8] A. Dembo and 0. Zeitount, Large Deviations Techniques, Boston: Jones and Bartlett, 1993.

[9] V. Fabian, "Stochastic Approximation," Optimizing

Methods in Statistics, Edited by J. S. Rustagi, New

York: Academic Press, 1971.

10] P. Glasserman and P. Vakili, "Comparing Markov

Chains Simulated in Parallel," Prob. Engr. Info. Sci.,

Vol. 8, pp. 309-326, 1994.

11] W.B. Gong, Y.C. Ho, and W. Zhai, "Stochastic Comparison Algorithm for Discrete Optimization with Estimations," manuscript, 1996.

12] P. Heidelberger and D.L. Iglehart, "Comparing

Stochastic Systems Using Regenerative Simulation

with Common Random Numbers," Adv. Appl. Prob.

Vol.11, pp. 804-819, 1979.

13] Y.C. Ho, "Heuristics, Rule of Thumb, and the 80/20

Proposition," IEEE Trans. Automatic Control, Vol.

39, pp. 1025-1027, 1994.

14] Y.C. Ho and M. Deng, "The Problem of Large Search

Space in Stochastic Optimization," in Proc. 33rd

Conf. Decision and Control, 1994, pp. 1470-1475.

15] Y.C. Ho, M. Deng, and J. Hu, "Effect of Correlated

Estimation Error in Ordinal Optimization," in Proc.

1992 Winter Simulation Conf., 1992, pp. 466-475.

16] J.Q. Hu, "Strong Consistency of Infinitesimal Perturbation Analysis Estimates," Ph.D. Thesis, Division of

Applied Sciences, Harvard University, 1990.

17] T. Ibaraki and N. Katoh, Resource Allocation Problems: Algorithmic Approaches, Cambridge: The MIT

Press, 1988.

18] N. Patsis, C.-H. Chen, and M. Larson, "Parallel Simulations of DEDS," IEEE Trans, on Control Technology, 1997, to appear.

19] R.T. Rockafellar, Convex Analysis, Princeton:

Princeton University, 1972.

20] A.H.T. Tchen, "Inequalities for Distributions with

Given Marginals," Annals of Prob., Vol. 8, pp. 814-

827, 1980.

21] P. Vakili, L. Mollamustaflaglu, and Y.C. Ho, "Massively Parallel Simulation of a Class of Discrete Event

Systems," in Proc. IEEE Frontiers MPC '92 Symposium, Washington, D.C., 1992.

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Probabilistic Estimation," J. Opti. Theory Appli.,

Vol. 79, pp. 345-371, 1993.

196
ARCHITECTURES
I
A Case-Based Integrated Learning Architecture And Its Applications*

Gennady Agre

Institute of Information Technologies - Bulgarian Academy of Sciences

Acad. G. Bonchev St. Block 29A, 1113 Sofia, Bulgaria

E-mail: agre@iinf.acad.bg

ABSTRACT

The paper presents an approach to building an Integrated

Learning Architecture in which Case-Based Reasoning is used

both as a corrective of solutions inferred by other problemsolving paradigms and as a method for accumulating and refining knowledge of a knowledge based system. The proposed

architecture is intended to solve the classification task. The applications of the approach for case-based maintenance of rule- based systems and for case-based refinement of neural networks

are briefly described.

KEYWORDS: Machine Learning, Integrated Learning Architecture, Case-Based Reasoning, Knowledge Refinement, Neural Networks.

solving paradigms and as a method for accumulating and

refining system knowledge. The proposed ILA is intended

to solve the classification task which is assumed to be described by one of its existing generic model (e.g. [5, 14]).

2 INTEGRATED PROBLEMSOLVING AND LEARNING

2.1. The System Architecture

The case-based ILA structure (see Fig. 1). consists of

three main parts: an original KBS, a Case Base Formation

Module (CBF) and a case-based reasoning module (CBReasoner).

1 INTRODUCTION

An important requirement to the modern knowledge based

systems (KBS) is the ability to operate in the real (open)

environment [1]. In order to do this they should be pro- vided by the mechanisms allowing them to correct automatically partially incomplete and incorrect expert knowledge used. This means that the modern KBS should be

able to learn.

From the other side the modern technology of KBS development is radically changed. The emphasis now is on

analyzing, identifying and adapting the already developed

KBS components (databases, acquired domain knowledge,

KBS shell and models) rather then on the development of

KBS "on scratch"

A promising approach to solve both problems is the

development of Integrated Learning Architectures (ILA)

which are able to use several different problem-solving

paradigms or/and machine learning methods [15, 1, 2]. The present paper describes an approach to building

such ILA in which case-based reasoning (CBR) [10] is used

both as a corrective of solutions inferred by other problem-

*This research was partially supported by National Science Foundation, Grant 1-606/96

2.1.1. The Case Base Formation Module

The CBF module uses domain knowledge, training examples and the KBS problem-solving model for creating a memory of cases. A case is represented as a single information structure containing the case name, a list of case features (attribute - value pairs) and the case solution.

The module should decide i) what training examples are worth to be transformed and stored into the memory as useful past cases, ii) how the memory should be indexed

to retrieved only relevant to the current situation cases and iii) how to construct failure predictors for recognizing

potentially "dangerous" situations in which the KBS solutions should be corrected. The module should also be able

choose an appropriate similarity metrics which measures

the degree of likeness between the problem at hand and

the retrieved past cases. The CBF module runs off-line and initializes the CB-Reasoner.

2.1.2. The Case-Based Reasoner

As an input to the reasoner the output case and its solution formed after solving the problem by KBS are used.

The CB-reasoner architecture is an instance of the general

architecture of a case-based planer adapted for solving the

classification task [9, 2].

199
( Domain ^ ( ~~\ Knowledge/ "

Input Case 1 ~

Trai Exampl nplesy

KBS ^ Model J " KBS

CBF

Module

r

Output

Case

KBS

Solutions

Modifier

Best Case ~T7

Indexes

Failure Explanation

.( Case \

I Memory /

L

Case-Based Reasoner

(g|g>—

C

SB)

Repaired Case

Rep airer

End User

Figure 1. The Case-Based Integrated Learning Architecture

The KBS solutions are initially processed by the Analyzer which should decide whether the solutions must be

corrected and if so which set of indexes should be used to determine relevant past cases. The indexes and the current problem description along with the predefined similarity

metrics are used by the Retriever to find the most similar

("best") case which solution could be applied to the cur- rent problem. The decision about what solution should be

preferred - provided by KBS or by the CB-reasoner - is the

responsibility of the Modifier. The final solution is given

to the end user and the Storer forms and "remembers"

the current case into the memory.

After receiving a "feedback" from the user who approves

or rejects the final solution, the Repairer starts its operation. In case of approval, the Repairer sends the con- firmation to the Storer which then decides whether it is worthwhile to continue remembering this correctly solved

case or it may be forgotten. Otherwise, the Repairer tries to "explain" the failed case. In such situations the Repairer creates failure predictors which then used by the

Analyzer to avoid repetition of similar failures in the future.

2.2. Failure Prediction

The process of searching a case-based solution starts only

when the current situation is recognized as "dangerous",

i.e. if there is a sufficiently convincing evidence that the

KBS solution is wrong. This prediction process is based on comparing the KBS solution to the set of failure predictors

formed by the CBF module and extended by the Repairer.

The roles of such predictors are played by the KBS solutions of the training examples included in the case base

(if such examples are available) and/or by the system so- lutions recognized as wrong by the user. In other words,

the fact that KBS has inferred once an erroneous solution

is considered as a sufficiently convincing evidence for sus- pecting the system every time when it infers the same so- lution of another problem. Conversely, if a KBS solution

of a new problem is different from the known failure pre- dictors, there are no reasons to "suspect" the system and

its solution is accepted without any doubt.

2.3. Case Retrieval and Conflict Reconciling

The success of integrated approaches combining several problem-solving paradigms crucially depends on the

scheme for reconciling the conflicts between them. Most of

the proposed methods (see e.g. [8] for integration of CBR

with rule-based reasoning) use a threshold scheme in which

the threshold values are selected ad hoc. We avoid this deficiency by forming a proper set of cases to be retrieved. In

this set we include not only the cases denying the proposed

KBS solution but also the cases confirming it. In such a way the retrieval set reflects the ILA problem solving ex- perience and restricts the search space only to the relevant

(from the ILA point of view) cases.

3 CASE-BASED MAINTENANCE OF RULE-BASED SYSTEM

The described above architecture was applied to the task

of improving a rule-base system (RBS) problem-solving behavior in the course of its operation [3] - an important part

of the adaptive maintenance task [6]. In this application

200
the KBS training examples are assumed to be unknown 1

. 3.3. Indexing Scheme

3.1. Knowledge Components

Domain Knowledge is non-probabilistic rules represented

as flat structures associating conjunctions of the problem

features with problem solutions. A feature is a nominal attribute-value pair. KBS Model treats the system

problem-solving behavior as a hypothesis driven process.

It is assumed that KBS is able to perform both backward and forward chaining since forward chaining is nor- mally used for generation of a list of differential hypotheses (possible solutions) and backward chaining - for testing

them. A hypothesis is considered to be confirmed if there

is a satisfied rule having the solution as its conclusion and

to be rejected if all rules leading to it have failed. The

system stops its operation either if a confirmed hypothesis has been found or all generated hypotheses have been

tested and rejected.

3.2. Case Base Formation

To avoid the problem with the absence of training examples

the CBF module treats the rules as generalized "typical" cases describing the domain concepts. Each rule is interpreted as a case represented by a list of features extracted

from the rule conditions. The rule conclusion defines the

case classification. The typicality of a case is defined as

its family resemblance and measured by the ratio of its intra-concept similarity to its inter-concept similarity. The

intra-concept similarity of a case is its average similarity to other members of the same concept and the inter-concept

similarity - its average similarity to members of all others

concepts. The similarity s(X,Y) between two cases with

known classifications is defined as the inverse of the distance between them [18]: s(X,Y) = 1 — S(X,Y), where

6(X, Y) is computed as the normalized Euclidean distance

between the corresponding cases:

S(X,Y) =

\

xj (yj) is the value of j-th attribute of case X (Y), k —

\AX U Ay

\, A

z (z = x,y) - the set of attributes of the

corresponding case. Weight Wj denotes the importance of

j-th attribute of the case and is calculated as the ratio of

the number of all case containing this attribute to the whole

number of all cases (rules) in the rule base, xj — y3: = 1

if Xj ^ j/j and xj — yj = 0 otherwise. For missing values

(xj — yj)

2 = £-*(! — rr), where Lj is the number of

possible values of j-th attribute.

'See [2] for more detailed description of the task.

A case is indexed by all possible roles it may play in the

process of rule-based problem solving. Each solved case is indexed as true negative (TN) by each hypothesis rejected

during problem solving and as true positive (TP) by the

solution found along with the name of the rule inferred

this solution.

TP- and TN-indexes are used for indexing cases which

have been successfully solved by the RBR system, i.e. when

the user has confirmed their solutions. A case is indexed

as false positive (FP) by the rule if it satisfies the rule but

the real case solution differs from the inferred one. A case

is indexed as false negative with respect to (w.r.t.) a given

concept which is the real solution of the case if it has been

tested and rejected by the concept rules. A failed case is indexed as untested w.r.t. a given concept

- its real solution - if the solution has not been tested by

the concept rules.

3-4- Case Matching

The distance between a stored case X and a new problem

Y is defined as: A{X, Y) = Wx * 6{X,Y) , where S{X, Y)

is the distance measure described in the previous section

and Wx is the weight of X. The weight of a stored case is simply reciprocal of its typicality. The matching procedure

is organized as a nearest neighbor algorithm in which a new

case is classified according to the class of the best matched

case - the case with the minimum value of distance A.

In the case of ties the most typical case (i.e. with the

minimum value of weight W) is preferred.

When measuring the similarity between an example with

unknown classification and a case belonging to a known cat- egory, it is naturally to consider only such features of this

example which are relevant to the case class. For each cate- gory the corresponding set of relevant attributes is defined

as the union of all attributes which the rules corresponding

to this category refer to. In such a way we avoid the influ- ence of any redundant (for a particular category) features.

3.5. Storing New Cases

All cases erroneously solved by the system are stored.

Such cases are indexed as false positive or true negative

w.r.t. the faulty solution and false negative, true positive

or untested (depending on the results of the failure analysis made by the CB-reasoner) w.r.t. the real solution of

the problem. The solved case is also indexed as true negative w.r.t. all hypotheses tested and rejected by the system

during problem solving session.

A case successfully solved by the system is stored only if

its solution has been found as a result of reconciling a conflict between the paradigms and an identical case has not

been stored. Such cases confirm the correctness of applying

201
the concrete rule or using the concrete case to obtain the

problem solution. For each newly stored case the value of

weight W reflecting the case typicality is calculated.

3.6. Selection of Casts to be Retrieved

The set of cases to be retrieved is determined by comparing the main characteristics of the current situation (the

rule which has inferred the problem solution and the set of

rejected hypotheses) with indexes connecting stored cases

rules. The retrieval set is formed not only by the exceptional cases rejecting the particular rule but also by the

cases confirming it. Since the set of such true positive cases may be empty the case representing the rule itself is also

retrieved. In situations when no KBS solution has been found all generalized cases associated with the rejected hypotheses

are retrieved along with all solved cases uncovered by the

corresponding rules. In both situations the final solution is determined by the best matched case.

3.7. Empirical Evaluation

The approach was implemented in the experimental ILA

system CoRCase (Correcting Rules by Cases) and tested on two medical domains - prognosis of breast cancer re- currence (BC) and location of primary tumor (PT) - well

known in ML community benchmark data bases2 (see Table 1).

Domain Examples Classes Attrs Vals/Attr

BC 286 2 9 5.8 PT 339 22 17 2.2

Table 1. Main characteristics the databases used in empirical

evaluation.

For the evaluation of the results the random sub-sampling

strategy was used [17]. Each database was randomly split

into two non-overlapping subsets, one for training (70%

of examples) and one for testing (30% of examples). The

experiments were repeated ten times for different splits and

the results were averaged.

The training sets were used to induce corresponding sets of rules. Since we wanted to prove applicability of the

approach to the expert rules with unknown principles of

building, two algorithms of different types were used to simulate the rules. The first one was an ID3-like algorithm inducing discriminating rules and the second - an AQ-type one producing covering rules. The CBF module

transformed each rule set into generalized cases which ware

then tested on the corresponding set of testing examples.

To evaluate the contribution of CBR and RBR to the

final classification accuracy of the system four different

problem-solving algorithms were tested. The first one

2 The data was prepared by M. Zwitter and M. Soklic from the University Medical Center, Institute of Oncology, Ljubljana, Slovenia.

was pure RBR. In the second algorithm the solution was

searched by matching a problem at hand against the generalized cases produced after the rule transformation. In this

algorithm (named TC-search) no testing cases had been

stored. The third algorithm was an incremental extension

of the second one. In this algorithm each solved case had

been stored and then used for searching solution of the next

problem. The algorithm may be seen as a naive CBR with

exhaustive search in the case space. And the last algorithm was an implementation of the method for integrating RBR

and CBR described in this section. The average accuracy

and standard deviations obtained are presented in Table

2

3

.The results of the experiments show that the best accu- racy is achieved by the proposed scheme for combination of

rules and cases. It is particularly interesting that on the PT

database both the TC-search and the naive CBR methods

used separately have worse performance than RBR. It once

again proves the effectiveness of the used indexing scheme

used which allows to retrieve for matching comparatively

relevant cases.

Domain RBR (AQ) TC-search CBR CoRCase

BC

PT

62 0 ± 0.6 34 7± 4.2

70.2 ± 2.3 33 5 ± 1.8

70.6 ± 1.4 33.1 ± 2.0

71.3 ± 3.0

37. 0± 1.6

Table 2. Classification accuracy (%) of the tested problem-solving methods.

4 CASE-BASED REFINEMENT

OF NEURAL NETWORKS

The second application of the proposed approach for building ILA was to the problem of case-based refinement of

neural networks (NN) 4. Our main goal was to study the

potential of CBR for further improvement of a trained NN.

That is why in that application only a part of the CBreasoner architecture was used (Analyzer, Retriever and

Modifier).

4-1. Knowledge Components

Training examples used for training NN is a main source of

knowledge. The same training set along with information

how the examples were solved by NN after completion of

its training phase were used as an implicit problem- solving

model of the network.

4-2. Indexing Scheme

A case is represented by a list of (normalized) attributevalue pairs and its real solution (classification). Each case

3 See [3] for more detailed description and evaluation of the exper- imental results.

4 Initial results are described in [4]

202
is indexed both by its real and NN solutions. If an ex- ample has been correctly classified, it is considered as a

"typical" case confirming the NN solution, otherwise - as an "exceptional" one.

4-3. Case Base Formation

In our previous research [4] the process of case base for- mation was implemented as a two steps procedure trying

to identify that part of "noisy" (from NN point of view)

training examples which might be used by a CBR method.

However, the analysis of the initial experiments with the

system has shown the low effectiveness of this procedure

so now all training examples unsolved by NN are stored as useful cases. The case matching process is implemented as a Nearest Neighbor algorithm which uses the weighted Euclidean

distance5:

glass (GL), diabetes (DB), breast cancer (BC) 6 and iris (IR)[13] (see Table 3).

A(X,Y) =

f 77U - iiihi,

where n is the number of attributes describing a case,

Xi and j/,- stand for the values of z-th attribute for cases X

and Y , and max, and mm,- - for the maximal and minimal

values of z'-th attribute.

The attribute weights w, are calculated by the CBF pro- cedure using ReliefF algorithm [11].

4-4- Failure Prediction and Case Retrieval

The process of prediction is based on comparing the NN

solution to the set of failure predictors formed after construction of the case base. The roles of such predictors

are played by the erroneous NN solutions of the training

examples included into the case base. In all "suspected" situations the final system solution is found by means of CBR method that matches the current

situation against the past cases which are not only exceptional but also typical w.r.t. the NN solution.

The formation of the case retrieval set is organized as a two steps procedure. During the first step the exceptional

case which is the most similar to the current problem is found. Then k nearest to this case neighbors confirming NN

classification are retrieved. The final solution is searched

among these k + 1 cases.

4-5. Empirical Evaluation

The approach was implemented in an experimental ILA

system CorNCase2 (Correction Network by Cases - ver- sion 2). The system was tested on four well-known ML

benchmark databases described by numerical attributes -

Domain Examples Atts Classes Missing (%)

BC 699 10 2 2.2 DB 145 5 3 0.0 GL 214 9 6 0.0 IR 150 4 3 0 0

Table 3. Main characteristics of the databases used in the empirical

evaluation'.

Each database was randomly split into two non- overlapping subsets, one for training (70% of examples)

and one for testing (30% of examples). The experiments

were repeated ten times for different splits and the results were averaged.

The TB-RBF system [12] was selected as an instance of

NN. TB-RBF uses domain knowledge in the form of decision trees (or rules) to define the topology of a radial basis

function network. Each class is mapped to an output unit,

each attribute - to an input unit and hidden units corre- spond to the branches of the tree. To evaluate the CorNCase2 behavior we also tested weighted (ReliefF-INN) and

unweighted variants of the Nearest Neighbor (INN) algorithm working on the TB-RBF training set. The average

accuracy and standard deviations obtained are presented

in Table 4.

Domain TBRBF INN ReliefF-INN CorNCase2

BC 95.5 ± 1.2 95.6 ± 1.1 95.8 ± 1.2 96. 3± 1.2 DB 91. 9± 4.1 93.9 ± 4.4 94.4 ± 3.3 92. 3± 4.0 GL 70.2 ± 4.6 69.5 ± 6.5 70.6 ± 6.2 75.0 ± 6.8 IR 97.1 ± 2.3 95 .3 ± 1.9 96.4 ± 2.1 97. 3± 1.7

Table 4. Classification accuracy (%) on the test data bases used in the experiments.

It can be seen that CorNCase2 outperforms TB-RBF in

all databases. Moreover, in 3 of them (BC, GL and LD) the

proposed integrated method outperforms both problemsolving paradigms used in the integration. These results prove the effectiveness of the proposed scheme for indexing

and retrieving cases.

It should be mentioned that the value of parameter A; (the

number of typical nearest neighbors for each exceptional

case) used in the experiments was set to 30 (for DB, GL

and IR the same classification accuracy was achieved when

k = 15). That means that it is not necessary to store the whole training set - we need only those cases which are members of such lists of neighbors. As a result CoRNCase2

uses in testing phase about 80% of training examples for DB, 72% - for GL, 60% - for IR and only 36% - for BC.

This shows that the selection of the proper value for k (e.g.

by applying some cross-validation techniques) may lead to

significant data compression.

5 Only numerical attributes are used.

6 Missing values were replaced with the most frequently occurring

values for the respected attributes.

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5 CONCLUSION

In this paper we propose an approach to building an inte- grated learning architecture in which case-base reasoning

is used both as a corrective of solutions inferred by other

problem-solving paradigms and as a method for accumulating and refining domain knowledge. The architecture is intended to solve the classification task. The applications

of the approach for case-based maintenance of rule-based

systems and for case-based refinement of neural networks

are briefly described. The different aspects of the archi- tecture have been tested on several well-known machine

learning databases. The experimental results prove that

the approach is an encouraging step towards creating the

integrated learning architectures.

ACKNOWLEDGMENTS

The author thanks Dr. Irena Koprinska for providing the

results of the experiments with TB-RBF system.

References

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to problem solving and sustained learning. Ph.D. Dissertation, University of Trondheim, 1991.

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Problem-Solving Experience, Proceedings of the 6th

International Conference AIMSA '94, World Scientific

Publ., pp. 257-266, 1994.

[3] G. Agre. KBS Maintenance as Learning Two-Tiered

Domain Representation, In: Lecture Notes in Artificial Intelligence 1010, Springer, pp. 109-120, 1995.

[4] G. Agre and I. Koprinska. Case-Based Refinement of

Knowledge-Based Neural Networks. In: Proceedings of

the International Conference "Intelligent Systems: A

Semiotic Perspective", October 20-23, Gaithersburg,

MD, USA, 1996, Vol. 2, pp. 221-226.

[5] W. Clancey. Heuristic classification. Artificial Intelli- gence, 27(3), pp. 289-350, 1985.

[6] F. Coenen and T. Bench-Capon. Maintenance of

Knowledge-Bases Systems: Theory, Techniques and

Tools, Academic Press, 1993.

[7] S. Cost, S. Salzberg. A Weighted Nearest Neighbor

Algorithm for Learning with Symbolic Features. Machine Learning 10, pp. 56-78, 1993.

[8] Golding A.R., Rosenbloom, P.S.: Improving RuleBased Systems Through Case-Based Reasoning. Proceedings of the National Conference on Artificial Intelligence, Anaheim, MIT Press, pp. 22-27, 1991.

[9] K. Hammond. Case-Based Planning: Viewing Planning as a Memory Task, Academic Press, 1989.

[10] J. Kolodner. Case-Based Reasoning. Morgan Kaufmann Publ., 1993.

[11] I. Kononenko, M. Robnik-Sikonia. ReliefF for Estimation and Discretization of Attributes in Classification,

Regression and ILP Problems. In: A.M Ramsay (Ed.)

Artificial Intelligence: Methodology, Systems, Applications, IOS Press, 1996, pp. 31-40.

[12] M. Kubat and I. Ivanova (Koprinska). Initialization of

RBF Networks with Decision Trees. In: Proceedings

of the 5th Belgian- Duch Conference on ML (BENELEARN'95), pp. 61-70, 1995.

[13] P. Murphy. UCI Repository of Machine Learning

Databases, @ics. uci.edu, Irvine, CA: University of California, Department of Information and Computer Sci- ences, 1995.

[14] Patil, R.S. Artificial Intelligence Techniques for Diagnostic Reasoning in Medicine. In: H.E. Shobe (Ed.).

Exploring Artificial Intelligence: Survey Talks from

the National Conferences on Artificial Intelligence,

Morgan Kaufmann, San Mateo, CA, pp. 347-379,

1988.

[15] E. Plaza, A. Aamodt, A. Ram, W. van de Velde,

M. van Someren. Integrated Learning Architectures.

Pavel B. Brazdil (Ed.) Proceedings of Machine Learning: ECML-93, Springer-Verlag, pp. 429-441, 1993.

[16] J. Quinlan. C4-5. Programs for Machine Learning,

Morgan Kaufmann Publ., 1992.

[17] S. Weiss and C. Kulikowski. Computer Systems That

Learn, Morgan Kaufmann, 1990.

[18] J. Zhang. Selecting Typical Instances in Instance- Based Learning. In: Proceedings of the Ninth International Workshop on Machine Learning (ML'92), Morgan Kaufmann, San Mateo, California, pp. 470-479,

1992.

204
Computational Embodiment: Software Architecture

Christopher Landauer

National Systems Group, The Aerospace Corporation

The Hallmark Building, Suite 187, 13873 Park Center Rd., Herndon, Virginia 20171

Phone: (703) 318-1666, FAX: (703) 318-5409, E-mail: cal@aero.org

Kirstie L. Bellman

Information Technology Office, Defense Advanced Research Projects Agency

3701 N. Fairfax Dr., Arlington, Virginia 22203-1714

Phone: (703) 696-2219, FAX: (703) 696-0564, E-mail: kbellman@arpa.mil

Abstract

Computational Embodiment is the computer implementation of principles that we believe will lead to more au- tonomous and self-generating behaviors that will allow

software systems to exist in and interact with complex

environments. We restrict our attention here to symbolic

environments (MUDs), as an initial step towards understanding and constructing "interaction spaces" in which

humans and computer programs can interact on an equal

footing.

Our approach to constructing autonomous software sys- tems is based on theoretical work on the structures that

underly language and movement in biological systems and

on the structure of constructed complex systems mediated

or integrated by software.

This paper describes how our "Wrapping" approach to

software integration, which is a computationally reflective dynamic integration infrastructure, can implement

autonomous systems. The wrapping approach supports

autonomy by providing at least primitive versions of the

functions that are necessary, and by providing an infrastructure that makes changing those functions easy.

1 Introduction

In this paper and its companion [4], we describe an approach to constructing autonomous agents that is based on theoretical work on the organization of structures that

underly language and movement and on the structure of

constructed complex systems mediated or integrated by

software.

We are constructing autonomous software agents in symbolic environments called Multi-User Domains (MUDs)

[18] [19] [11], using a style of "computational embodiment" , which is part of our research program on interaction spaces [15].

In our view, a system is "autonomous" if it can be said to have "purposeful behavior", e.g., act independently based on internally generated intentions [5]. There are really

only two classes of (difficult) requirements for effective

autonomy: robustness and timeliness. Robustness means

graceful degradation in increasingly hostile environments,

as well as an ability to exploit unexpected advantages in

the environment, which to us implies a requirement for

adaptability. Timeliness means that situations are recognized "well enough" and "soon enough" , and that "good

enough" actions are taken "soon enough". There is not

necessarily any optimization here.

In this paper, we describe our notion of wrappings as dynamic infrastructure (Section 2). Then we turn to a description of the architecture we use (Section 3), and show

how wrappings are used to implement the architecture, so we can study some fundamental theory of computational

embodiment from the companion paper [4]. Finally, we

discuss our prospects for the future (Section 4).

2 Wrapping Background

Our research in complex systems has shown the importance of infrastructure, that is, explicit components and

activities of the system whose function is to help organize the rest [16]. No matter what kinds of computational models are used, the system will need infrastructure which supports complex interactions. Our "wrapping" approach to intelligent integration infrastructure for

constructed complex systems provides a natural means for

incorporating adaptation and other processes as computational resources. It is based on automatic processing of ex205
plicit qualitative information about all of the system components and their interconnection architecture. Its advantages are (1) a simplifying uniformity of description using

the meta-knowledge organized into Wrapping Knowledge

Bases, and (2) a corresponding simplifying uniformity of

processing that meta-knowledge using algorithms called

Problem Managers, which are active integration processes

that use the meta-knowledge to organize the system's computational resources in response to problems posed to it by users (who can be either computing systems or humans). In particular, since the entire process is recursive

[13] [14], wrappings provide a general way to allow specialized methods to participate.

We believe that effective use of any sufficiently complex

system requires the system itself to provide many different

kinds of assistance to its users, whether they are humans or other computer systems. The system must provide what

we have called the Intelligent User Support (IUS) functions:

• Selection (which resources can be applied to a particular problem),

• Assembly (how to let them work together),

• Integration (when and why they should work to- gether),

• Adaptation (how to adjust them to work on certain

kinds of problems), and

• Explanation (why certain resources were or will be

used or not used).

2.1 Wrapping Overview

The wrapping theory has four basic features:

1. ALL parts of a system architecture are resources, including programs, data, user interfaces, and everything else;

2. ALL activities in the system are problem study, (i.e.,

apply a resource to a posed problem), including user interactions, information requests and announcements

within the system, and service or processing requests,

etc.;

3. Wrapping Knowledge Bases (WKBs) contain wrappings, which are explicit machine-processable descriptions of all of the resources and how they can be applied to problems to support the five IUS functions

above;

4. Problem Managers (PMs), including the Study Managers (SMs) and the Coordination Manager (CM),

are algorithms that process those wrappings to collect and select resources to apply to problems. They

are also resources, so they are also wrapped.

The wrapping information and processes form expert interfaces to all of the different ways to use resources in a heterogeneous system that are known to the system.

2.2 Wrapping Information

The main information entities are Wrapping Knowledge

Bases (WKBs). The WKBs contain explicit, machinereadable descriptions of each computational or information processing element (called a resource) in the system:

not just how to use it, but also whether and when and why

and in what kinds of combinations it should or can be used.

The entries in the WKB are called "wrappings". Wrappings have a variable syntax, according to our "variables

all the way down" principle, but there are some common

features in the semantics [12], which we describe briefly

next.

Each wrapping is a list of "problem interpretation" entries, each of which describes one way in which this re- source can be used to deal with a problem. There may be

several problem interpretation entries for the same problem if the resource has many different ways of dealing with

it. Each of these problem interpretation entries has lists of conditions that must hold for the resource to be considered or applied. These sets of conditions are important at

different times; one at resource consideration or planning

time, and the other at resource application time. These

conditions range from data type and interaction protocol

statements (for "how" to apply the resource) to qualitative

knowledge about the context under which it is appropriate to apply the resource. These act as pre-conditions for

the application of the resource. The post-condition is the

"product" list of context component assignments, which

describe what information or services this resource makes

available when it is applied.

2.3 Wrapping Processes

The wrapping processes are active coordination processes

that use the wrappings for the Intelligent User Support

functions [12] [13]. They also provide overview via perspective and navigation tools, context maintenance functions, monitors, and other explicit infrastructure activities. Since they are also wrapped, the entire system is Computationally Reflective [17] [10] [13]. It is this ability

206
of the system to analyze its own behavior that provides

some of the power and flexibility of resource use.

2.3.1 Coordination Manager

The alternation between problem definition and problem

study, and the determination of an appropriate context of

study, are organized by the Coordination Manager (CM),

which is one of the resources that coordinates the wrapping processes. The basic problem study sequence is managed by a kind of resource called the Study Manager (SM),

which organizes problem study into a sequence of basic

steps that we believe represent a fundamental part of problem solving.

The CM runs a sequence of steps that manages the overall

system behavior:

Find context : get a containing context from the user

loop:

Pose problem : determine the current problem

Study problem : use an SM to address it Present result : to user

Each step is a problem posed to the system by the CM,

which then uses the default SM to manage the system's

response to the problem.

The main purpose of the CM is cycling through the other

three problems, which are posed by the CM in the context

found by the first step. This way of providing context

and tasking for the SM is familiar from many interactive

programming environments: the "Find context" part is usually left implicit, and the rest is exactly analogous to

LISP's "read-eval-print" loop, though with rather different

processing at each step, mediated by one of the SMs. In

this sense, the CM steps represent the basic heartbeat of

the system.

2.3.2 Study Manager

The Study Manager is the central algorithm of our problem study strategy. It is the default resource for the problem "Study problem". Its purpose is to organize the re- sources that process the wrappings, and to cause and monitor the behaviors the wrappings describe. There may be

other resources that are intended for this same problem,

but the SM is the one that is chosen if no other resource

applies. This overlap of function illustrates a general principle of resource coordination we have used throughout:

instead of trying to find one general method for all cases (which we do not believe is possible anyway), we combine

general methods for certain processes with powerful specialized methods that apply in certain contexts.

The SM process begins with a problem poser, a problem

defined by its name and associated data, and the context

in which the problem was originally posed.

We have divided the "Study problem" process into three

main steps: "Interpret problem", which means to find a

resource to apply to the problem; "Apply resource", which

means to apply the resource to the problem in the current

context; and "Assess results" , which means to evaluate the

result of applying the resource, and possibly posing new

problems. We further subdivide problem interpretation

into five steps:

Interpret problem :

Match resources : get list of candidates

Resolve resources : reduce list, make bindings

Select resource : choose one resource to apply

Adapt resource : finish the bindings

Advise poser : describe bindings chosen

Apply resource : go do it

Assess results : evaluate

2.3.3 SM Recursion

Up to this point in the description, the SM is just a

(very) simple type of planning algorithm. Several additional design features make it a framework for something

more. First, all of the wrapping processes are themselves

wrapped. Second, the processing is completely recursive.

All of the steps listed above for the SM are also posed

problems. Third, there are other SMs that have slightly

more interesting algorithms (such as looping through all the candidate resources to find one that succeeds, as described in the next section). These three things mean

that every new planning idea that applies to a particular

problem domain (which information would be part of the

context) can be written as a resource that is selectable

according to context; it also means that every new mechanism we find for adaptation or every specialization we

have for application can be implemented as a separate

resource and selected at an appropriate time. It is this re- cursion that leads to the power of wrapping, allowing basic

problem study algorithms to be dynamically selected and

applied according to the problem at hand and the context

of its consideration.

This recursion has profound implications in other applications of wrapping [14], but for its application to software

development, the fact that the SM can be selected is a key.

207
Since the SM steps above that interact with the Wrapping

Knowledge Bases (WKB) are themselves posed problems,

we can use completely different syntax and largely different semantics for different parts of the WKB in different

contexts, and select the appropriate processing algorithms

according to context. In particular, whether one writes

about one WKB or several is a matter of taste and viewpoint. Finally, the SM is only one of a family of processes

called Problem Managers (PMs), each of which is wrapped

and selectable according to context, and each of which can

pose problems and organize their study in different ways.

3 Implementation Issues

In this section, we first describe the MUD environment

with which the agent must interact, and then the architecture of the experimental system we intend to use for our autonomous agent, based on wrapping. Multi-User Domains (MUDs) are an interesting new kind of groupware

that incorporates people into the program. MUDs have

become enormously popular as games and as educational

support tools over the last few years because they get the

human interactions right in some fundamental sense, and

because they engage our sense of "place" [18] [19] [11] [15].

MUD clients and servers are easy to obtain and run (most

servers and clients are free), but they usually only provide text worlds; there is little interaction with existing

tools that are outside the MUD; though some have construction languages that allow complex programming, it

is the usual kind of programming; and it is not very easy

to access large volumes of information.

3.1 MUD Architecture

We start with a description of MUD architecture [15],

because that characterizes the environment in which the

agent needs to act. We also characterize the MUD en- vironment via the important styles of interaction, so that

the agent can distribute incoming interaction items appropriately.

The MUD environment is defined by its architecture:

• Connectivity Management,

• Virtual World, and

• Computational Infrastructure.

The Connectivity Management Layer is responsible for the

multi-user capabilities of a MUD. This layer is responsible for the information transmission in both directions between users (i.e., humans or computer programs that use

the MUD), and characters (i.e., objects within the MUD

that have externally provided behavior). It is common

across many styles of MUD, and will not be discussed further in this paper.

Our autonomous agent interacts mainly with the Virtual

World, using a small separate layer for interaction with the

Connection Management part of the MUD. The Virtual

World consists of locations (called "rooms") and interconnections (called "exits"), each of which has a description.

We say that an exit is "linked" to a room if the room

is its destination (all links are one-way). The only kinds

of behavior that are allowed are issuing commands to the

server and following links.

For our discussions of MUD architecture, we use one of

the simplest MUD servers, called TinyMUD [2] [18] [19],

since it has all the essential technical features we want. It

is not too complex to extract and describe those features

easily, and because it illustrates one of the most important aspects of MUDs: it is the writers and artists that

define the culture (not the technical substrate), and it is the culture that makes a MUD viable or not.

The important aspects of the Virtual World are:

• places and connections between them,

• movements,

• objects and their locations,

• actions, and

• relationships among aspects

Everything in the system is a model, which we use to represent objects, relationships, and actions. Everything

has attributes, one of which is location. Connections are maps from one place to another. Movements are actions

that attempt to use connections or connectionless maps

(e.g., teleport). Actions can change any attributes. This

is one classification hierarchy of everything, which is derived from the ones common to many MUD servers and

other Virtual environments. It will be mapped into a hierarchy appropriate for understanding our experimental

environment.

3.2 Architecture of Experimental System

The basic architecture of a wrapping system has three

layers [12] [13]: the bottom two layers are the Message

Distribution Layer, which can be implemented with explicit messages or in other ways, and the Wrapping Core

Layer, which contains the default Coordination Manager

and Study Manager, and the default resources for CM and

208
SM steps. Above that are the wrapping resources (other

SMs and PMs), utilities (optimizers and such), and applications. These can be thought of as a single Resource

Layer.

It follows that our architecture problem becomes a matter of identifying appropriate resources and their wrappings. We need to describe the problems, resources, and

wrappings for the autonomous agent. The architecture

is adaptive, so that we can insert new computational re- sources into connections when they become available. It

is also different for different experiments, and there is a

meta-architecture that helps build new architectures.

3.3 Agent Architecture

Our computational version of the language and movement

theory [3] is that there are layers of symbol systems that

separately normalize external signals into interesting information spaces, so that the useful processing can take

place in those spaces (this separation is the analogue of

the behavior of different senses).

The agent runs a set of steps that manages its overall

behavior:

Login : to remote server

concurrent loop:

Look around : determine current local environment

Talk : to characters, local or remote

Move around : to other places

Do commands : choose some available commands

All of these processes are concurrent, making suggestions

about what to do next, but the agent usually doesn't move

around or do commands and talk locally at the same time,

(these processes interfere with each other because of focus

of attention).

Some of the major low-level communication resources in

the agent have the following tasks (these are problems):

• login to remote server,

• convert incoming character strings into interaction

items,

• convert outgoing items to characters, and

• distribute interaction items according to context and

content.

The agent interacts with the Virtual World with other

tasks:

• parse room descriptions and other information,

• identify connections, commands, and conversational

streams,

• generate movement and other actions, and

• generate conversational interaction items.

We have constructed a number of local interaction grammars, using CYKPL (my variant of V. Pratt's combination of the widely used Cocke-Younger-Kasami and Early

parsers [7] [12]), but we can use any of the common table or chart parsers [9], or any other mechanism we choose [1], and with that mechanism we can use whatever new user language we choose (of course, some language choices are better suited to certain kinds of parsing, and vice versa).

4 Prospects

Autonomous systems must be complex systems, with an

ever-increasing repertoire of possible behaviors and processes for selecting them, fallback choices to account for

incorrect situation estimation, and quick partial solutions

to reduce decision time. All activity is situated, strongly

dependent on context, and there need to be different decision processes in different situations. This flexibility re- quires an architecture in which many parts of the system

are infrastructure, organizing other parts of the system to identify and address problems, and monitoring their behavior [8]. The wrapping approach provides several simplifying uniformities for the infrastructure: Wrapping Knowledge

Bases uniformly represent the computational resources (uniformity of description), wrapping processes uniformly

treat system activity as problem study (uniformity of processes), and treating the wrapping processes as resources

also provides a computationally reflective system, which

can reason about its own behavior. The ability to reflect on one's own behavior (and modify it) is one of the main

keys to effective autonomy.

Our study of autonomy is part of a larger research program

on Interaction spaces [15], which are computer-mediated

virtual places in which computer programs and humans

meet. Since wrappings allow many special case processes

to be combined with general case methods, and MUDs

allow multiple programs to be connected together with

multiple humans as users, all in the same environment, we

have taken the wrapping architecture and applied it to the

MUD servers to define these interaction spaces.

209
Interaction spaces are a new way for computer programs

to be integrated, by combining the interactions among the

different kinds of users of the space, be they human or computer programs. The idea is that explicit attention to using co-experience as an integration mechanism can lead

to very different styles of interaction among computational

agents and humans, and therefore possibly much more in- teresting program structures and behaviors. This paper

is about the integration infrastructures and architectures

that support adaptive and reflective behaviors. We believe

that using them, we can build agents that are much more

useful partners in an increasingly complex information en- vironment.

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[17] Pattie Maes, D. Nardi (eds.), Meta-Level Architectures and Reflection, Proceedings of the Workshop

on Meta-Level Architectures and Reflection, 27-30

October 1986, Alghero, Italy, North-Holland (1988)

[18] Mike O'Brien, "Playing in the MUD", Ask Mr. Protocol Column, SUN Expert, Volume 3, No. 5, pp.

19-20, 23, 25-27 (May 1992)

[19] R. Riner and J. Clodius, "Simulating Future Histories", Anthropology and Education Quarterly (Fall

1994)

210
Emergence of Complex Organized Natural Systems. A Hierarchically

Structured Conceptualization and Notation of Organization.

Jerry LR Chandler

Krasnow Institute for Advanced Studies,

George Mason University, 837 Canal Drive, McLean, VA 22102

and

Washington Evolutionary Systems Society.

JLRChand @ erols.com

ABSTRACT

Our natural world is dynamically composed in real time.

Despite frequent perturbations and structural irregularities,

substantial zones of stability are observable. The historical emergence of such structurally stable zones from simpler

components is supported by lines of evidence from many

disciplines (2,3,12,10,16). In order to construct a common

semiotic lineage among the diverse symbol systems used by

various disciplines, a theory of organization was constructed.

The foundations of the theory are developed from observations on the nonlinear dynamics of organisms within ecoments - ecoments being defined as the immediate surroundings of

systems. Each system, (sub-system, sub-sub-system ... ) is assigned four primitives attributes (closure, conformation,

concatenation and cyclicity). In principle, each of these four terms is enumerable for a local system. Degrees of organization

(symbolized as 0°) are composed from lesser organized systems

to higher organized systems in terms of the enumeration of the four primitives. The emergent organizations are enumerated:

1°, 2°, 3°, ... . The patterns of organization at any particular

level, O

0

, are composed from patterns at other levels. Thus, no

particular science or philosophy is assigned a privileged role in the unfolding of the dynamics.

Mathematically, the systems are composed under the scientific representations of categories as developed in Ehresmann and

Vanbremeersch, [10] and Chandler, [4,5,7]. Categorical

transitions can be viewed as homologous to Thorn's four

archetypal singularities [17, 18]. This notation parallels

natural history and allows the facile accounting of the molecular biological mechanisms within a living system.

Implications of this theory of natural organization for the design of artificial hierarchical systems are apparent.

Key WOrdS! Category theory, complexity, hierarchy,

emergence, theoretical biology, biochemistry, semiotics,

modeling, information theory, nonlinear dynamics,

structuralism, organizational theory, conceptual bindings,

cell, genetics, health and disease

1. SEMIOTICS OF REPRESENTATIONS

How are dynamics of the organic components organized to form organisms? The semiotic character of the problem is exemplified by noting that the terms organic, organism,

and organization are all derived from the same root! The

common semantic origin of these terms suggests the

existence of a common perceptual pattern underlies the

phenomena of complex pattern generators. If such a

perceptual pattern exists, then it should be possible to construct a network of symbols and languages such that the representation of physical, chemical, biochemical,

cellular, individual and population processes are meaningfully interrelated. For example, for material

objects, a criteria of meaning could be a common

understanding of the scale of an object, it parts, its forms

of birth and death, and its capacities to unite with or separate from other objects (analogous to Thorn's

archetypal singularities (17)). Meaningful transdisciplinary

communication depends on a mutual understanding among

the participants, for example, between the business

manager and the mathematician. To understand the

meaning of a semantic term for a material object implies some knowledge of the relationships among the parts, the

whole and the embedding system surrounding the object

itself (6). This is a major task for a biological notation

because of the unique sequences of macromolecules which

generate the unique dynamics of each individual organism.

Since the role of individual DNA base changes (mutations)

in the genesis of specific disease states is frequently

observed, a useful notation must represent both the

structural form of a complex system as well as its dynamic

unfolding. Causal pathways are intrinsic to complex

behaviors. A semiotics of complexity should include a

crisp representation of causality in order to construct to a

useful notation. Analogously, the meaning of the

mathematical models should provide a basis for

predictions. If the scientific models of complex systems are not relatable to practice, the primary goal will not be

achieved.

2. Structures for Scientific Semiotics

If science is to become a unified body of knowledge, a congruency must be extensible from simple to complex

systems. Can the search for congruence among what we

observe, what we symbolize and what we describe be

viewed as an alternative expression of a desire for scientific predictions? Predictability for a complex system requires a congruence among observations, languages and symbols,

as geometrically illustrated in Figure 1 . Can this figure

also be viewed as a genitive symbol which is independent

of the scale, history, or behavior of any particular system

211
and for organizing transdisciplinary communication? Are

these questions complementary to one another?

Observations

Symbols Languages

Figure 1. Inchoate symbol for a common scientific

semiotics.

Traditionally, scientists have sought to isolate individual

objects or classes of objects for study. Disassembly of

natural systems into component parts and analysis of the

individual units was a successful strategy for the study of

simple natural systems. Such work tends to accent the

independence of the components. Indeed, physical theories

often further accent the notion of independence or autonomy, both in the conceptualization and the

mathematical representation. The examples of quantum

mechanics and thermodynamics illustrate the critical importance of the concept of independence to scientific

thought. However, emergence of a new degree of

organization depends on interdependence - a special

cooperation among the components such that a vertical

genesis process occurs in order to construct a hierarchy.

For example, the organic bases within a DNA sequence of a genetic system are not independent, but are tightly linked

to each other to form a double helix. This assessment of

interdependence among objects was crucial to a logical

construction of complexity (the C* hypothesis) in the

WESScomm I, II, and III papers, (4,5,7) where the

observed logical interdependence among the classes

explicitly motivated the symbolic representation. The

description of complexity was built by organized systems

of constraints. Thus, conceptual mferdependence formed

the basis for the organization of the C* hypothesis.

A motivation for logical interdependence comes from the

necessary and sufficient conditions for life (5). More

explicitly stated, causality in biological systems requires an interdependence among three degrees of organization -

the genetic system, the organism and the ecosystem as

illustrated by the following relations:

A genome is a necessary but not a sufficient condition

for the existence of an organism.

An ecosystem is a necessary but not a sufficient

condition for the existence of an organism.

The sufficiency of a specific ecosystem to sustain life of a specific organism depends on the genome.

The sufficiency of a specific genome to sustain life depends on the specific ecosystem.

Abstractly stated, internal and external causes fit together

dynamically to create necessary and sufficient conditions

for the emergence and sustenance of life's' patterns.

A primary objective this notation is express the structure of complexity in symbolic terms such that mathematical

relationships among the patterns can be explored. Which

mathematical structures are sufficiently rich to support a

representation of interdependence, of hierarchical degrees of

organization and of nonlinear dynamics? Ehresmann [11]

noted an abstract freedom in creating mathematical

structures and that the "theory of categories seems to be the

most unifying trend in present day mathematics;... ." Ehresmann and Vanbremeersch (10), Thorn (17), Rosen

(15), and Baas (1) have suggested the use of category

theory in science. The structural simplicity of category

theory (objects, morphisms, and compositions) lends itself to logical applications. It has found wide application in the design of computer algorithms (object oriented

programming) (19). Ehresmann and Vanbremeersch, in a

long series of papers starting in 1987, have pioneered the use of category theory to describe mental processes by

constructing categorical "Memory Evolutive Systems." A

hierarchical perspective on complexity (the C* hypothesis)

and the Memory Evolutive Systems are closely related

theories (8). We have published a model of a cell based on

category theory and pointed out the critical role of time

scales in decision making processes (17). Enhanced graph

theory, which is somewhat related to category theory, is widely used in the computations of chemical structures. It appears that augmented category and graph theories, along

with singularity theory will play a substantial role in the

construction of emergent dynamics of complex systems.

A robust, constructive, scientific notation is needed to support the mathematical explorations of organizations of

interdependent objects.

3. Proposal for a robust notation for

organized systems

Historically, a symbol is used to denote, among other

possibilities, a category or object or concept or belief or a

class of categories, objects, concepts or beliefs.

Let 0° be any degree of organization of an object.

Here, a symbol of the form 0° is used to denote a general

class of organization. The natural question now arises: How can I create a procedure for assigning scientific

meaning to the natural sequence of symbols? Since

science has a number of organizational principles, a

selection is necessary to construct an ordering relationship.

The objective of the procedure is to construct a notation

such that a one to one correspondence between the

languages of scientific observations and the symbolic

212
representation of the degree of organization creates a conceptual basis for the enumeration of complexity.

Therefore, I choose to select the meaning of the symbols

0°1, 0°2, 0°3, ... such that a construction of one to one

correspondences between natural numbers and material

objects is feasible. I have selected the following specific

semantic ordering for material objects of a cell:

0

01 subatomic particles

0

02 atoms

O

0^ molecules

biomacromolecules

O

o5 cells 0°*> ecoment

(W environment

This ordering relationship was selected for living systems;

it may also be sufficient for general chemical and physical

usage, since it uses the atomic table as a guide. The

meaning of these symbols is given.

0

01

, subatomic particles, consist of three material

objects: protons (+), electrons (-) and neutrons.

0

02

, atoms, consists of somewhat over one hundred

unique objects, composed from the three subatomic

particles. The composition of atoms from particles can be enumerated systematically in terms of the

natural numbers, preserving the one to one

correspondence between particles and particles bound

into atoms.

O

0 ^, molecules, consists of a very large number of

different material objects composed from atoms or

ions. The binding operations which form neutral

molecules from atoms preserve one to one

correspondences between atoms and atoms bound into

molecules. These binding operations concomitantly

form the patterns of chemical structures. The patterns

formed in molecules are created from the organization

of the quantum numbers.

0°4, biomacromolecules, consists of many material

objects (not an infinite number), composed from

specific classes of molecules. The binding operations

preserve one to one correspondences between

subgraphs the molecules and the bound subgraphs

within the macromolecules.

0°5, cells, consists of living objects which can be

represented as have a boundary sustained by a genetic

system. The genetic system is composed of

components of a consisting of O

o1

, subatomic

particles, O

o2 atoms, 0°3 molecules, and 0°4

biomacromolecules. The ordering relationships

among the components of a cell are not completely

specified by internal relationships. Nonetheless,

orderings relate all the essential components of a cell.

O

0

^, ecoment, consists of the surrounds of the cell. In natural systems, the surround may include O

ol >

subatomic particles, O

o2 atoms, O0 ^ molecules, 0°^

biomacromolecules, 0°5 other cells and potentially

more highly organized systems. The ordering

relationships among the components of an ecoment

are not readily specified for natural systems. However,

the minimal essential components of an ecoment are known for many cells and higher organisms - they are named "essential nutrients."

(W, environment, is the embedding system for the

surrounds of organisms.

As suggested by the ordering relationships, the term

ecoment is introduced to describe the immediate

surrounding of the living organism. It is this immediate

surroundings which provides the nutrients (the necessary

and sufficient conditions) for sustaining life. The term

ecoment implies a specific subset of the environment

which is experienced by the organism.

A sequence of degrees of organization can be designed for

other systems. These designs may require either a smaller

number or a larger number of degrees of organization. For

example, less complex systems composed from mechanical

and / or electrical components would not require as many

degrees of organization as a living organism.

As noted above, the conceptual basis of this proposal for a

scientific semiotics is the recognition that three degrees of

organization are essential to predicting the complete

behavior of any system and these three 0° must form an

ordering relationship (6,7). Philosophically, these three

degrees of organization can be expressed in common

language as the parts, the whole and the surroundings of

the whole. Co-extensive with this language and these

symbols are the scaling factors - the parts are smaller than

whole, the whole is smaller than it's ecoment.

4. Language of description of a degree of

organization

The next step in designing a scientific semiotics for

accounting for complexity is to list a common set of

concepts which can be applied to a specific system. Four

terms can be used to describe the behavior of any degree of

organization (7). These four terms are interdependent with

each other and must be defined sequentially.

Closure: a domain of discourse, a category, a system, an object, a unity.

213
Conformation : the components of the closure of a system, the internal patterns of the system, the

relationship among the parts of the system, a three

dimensional depiction of the internal description of a

system, a specific geometric and algebraic description

of components of the system.

Concatenation : binding parts together, linking

changes in the conformation, changes in the internal

patterns of a system, the specific linkages between

parts of the whole, dynamic processes of the system

linking patterns to patterns.

Cyclicity : a pattern of concatenations which sustains

the system, the potential cyclic walks or pathways

over the conformations of the system, the habitual

behaviors of the closure.

These four concepts serve as the basis for a linguistic

description of simple and complex material systems. In

principle, each concept can be applied to the enumeration

of each degree of organization. When the material state of

a system is known, then these concepts provide a basis for

specifying specific objects and may allow an accounting of

the complexity. An example illustrating the application of

these symbols and concepts to fermentation of wine was

reported (Chandler, in press). The description of the

fermentation of sugars from natural juices illustrates the

interrelationship between scientific languages and scientific symbols at degrees O

o1

, 0°6. Indeed, the organization

of entire internal process of fermentation can be

symbolized in terms of causal pathways among the labeled

asymmetric psuedographs and dynamic processes

symbolizing the role of collaborative configurations in generating singularities and accelerating the flow of energy.

Since fermentation has been cultivated by human cultures

since ancient times, these examples can also be extended to higher degrees of organization to describe the role of

fermentation in the history of science and law. For

example, cultural controls (laws) governing the purity and

wholesomeness of beer were among the earliest food safety

rules.

5. Complex Causal Pathways

Examination of the differential equations representing

fermentation illustrate that the cause - effect relationships

in complex systems can be deterministic, highly organized,

and extremely selective. Of all the possible singularities

which could occur among the O

o1

, 0°2

, 0°3, 0°4, 0°5 and

O

0 ^ components of fermentation, the selection of one

specific causal walk from glucose to alcohol, among the

virtually infinite number of potential chemical

singularities, symbolizes a degree of determinism

unprecedented in the physical or chemical sciences. How

are we to describe or symbolize this unique set of cause

effect relationships? I suggest that complex causal

pathways be organized in terms of the relative degrees of

organization being symbolized in the ordering relationships

of the languages of observations. This suggests four terms

for directional causality:

Bottom-up < > Top-down

Outside-inward < > Inside-outward

One description of cause effect relationships (in

thermodynamics, for example) is based on energy flow.

This will be call this 'bottom - up' causality. Processes at

all degrees of organization involve action and energy flow

and hence bottom - up causality. Merely describing energy

flow fails to predict the unprecedented determinism

observed in living systems. For any particular

hierarchical structure, the sum of the mass will uniformly

increase with the degree of organization (since the mass of

the whole must be greater than the mass of a one component of the whole.) When one or more higher

degrees of organization collaborates with lower degrees of

organization, it can be formally defined as top - down

causality. Thirdly, examination of the yeast cell fermentation example (that is, the material process of a brewery) indicates the necessary role of the ecoment in organized processes. The ecoment is driving the

conformation from outside the closure by supplying a component necessary to the cycles. This is named outside

- inward causality. Finally, a cell sustains it boundary, its internal structures and its capacity to divide by responding

as a whole to its ecoment. It is termed inside - outward

causality and is quasi-conserved over generations. It emerges from the organization of the first three forms.

These four directions of causality within a categorical

perspective, are used to describe the directions of energy

flows within 0° of a cell.

6. Discussion

Semiotics is the study of meaning. (The Greek root, sema, can be translated as 'mark, sign.') How is a scientific

description of natural structure related to our common

semiotics and transdisciplinary communication?

I seek to place organized systems [0°] within the higher

framework by comparing the constrained scientific usage

with the more common general usage. In "Signs, an

introduction to semiotics," the American semiotician, T. Sebeok [16], asserts that six species of signs are distinct. He asserts that the two parts of the sign are the signifier

and the signified. With regard to hierarchy, he asserts: "It should be clearly understood, finally, that it is not signs

that are actually being classified, but more precisely,

aspects of signs: in other words, a given sign may - and more often and not does - - exhibit more than one aspect, so that one must recognize differences in gradation. But it

is equally important to grasp that the hierarchic principle is inherent in the architecture of any species of sign. " The

contrast between a scientist's and a semiotician's (Sebeok)

view reflects the two cultures. Next, Sebeok's' six species

are contrasted with the scientific semiotics developed here.

214
6.1.1. SIGNAL

Semiotic perspective: "The signal is a sign which

mechanically (naturally) or conventionally (artificially)

triggers some reaction on the part the receiver."

0° systems perspective: The signal is an outside - inward cause which pre-supposes the existence of a poised or anticipatory system. In the absence of

knowledge about the ratio of scales of the objects, the

nature of the relationship between the signal and the

poised system is ill-defined. Signals may or may not

trigger an observable reaction, depending on the

intensity of the signal, the degree of organization and numerous other variables.

6.1.2. SYMPTOM

Semiotic perspective:: "A symptom is a compulsive,

automatic, non-arbitrary sign such that the signifier

coupled with the signified in a manner of a natural

link."

0° systems perspective: A symptom can be viewed

as a special (abnormal) internal conformation. It can

inform the skilled observer on one specific category or on a collection of linkages of a hierarchy of categories.

6.1.3. ICONIC

Semiotic perspective: "A sign is said to be iconic

when there is a topological similarity between a

signifier and its denotata." (Sebeok sites Pierce's

1867 paper on 'On a New List of Categories' in which

Pierce asserted three kinds of representations ~ (a)

likenesses (icons) whose relation to their objects is a mere community in some quality' (b.) indices 'whose

relation to their objects consist in a correspondence in fact and (c) symbols those the ground of whose

relation to their objects is an imputed quality.

Subsequently, the category of icon was partitioned

into three subclasses, images, diagrams and metaphors

by Pierce.)

O

0 systems perspective: Insofar as one has a likeness

(icon, mental image) in mind for each degree of

organization, one seeks a topological representation

which is consistent among all degrees of

organization, not just an immediate one. 0°

complexity is grounded on observations of many

alternative iconic representations for a single closure

as illustrated by correspondences between the degrees

of organization.

6.1.4. INDEX:

Semiotic perspective: "A sign is said to be indexic

insofar as its signifier is contiguous with its signified, or is a sample of it. The term contiguous is not to be

interpreted literally in this definition as necessarily

meaning 'adjoining or adjacent'; thus "Polaris may be

considered an index of the celestial pole..."

0° systems perspective: Organization hierarchy

require two radically distinctive types of indices -

vertical and horizontal. Vertical indices represent the

composition of new degrees of organizations with

emergent properties. Each degree of vertical

organization is described with a novel logical language

of dynamic description. Horizontal indices may simply

denote an ordering relationship on an arbitrary list within one language of description. Horizontal

indices can create ordering relationships along a causal

pathway.

6.1.5. SYMBOLS

Semiotic perspective: "A sign without either similarity or contiguity, but only with a conventional link

between its signifier and its denotata and with an in- tentional class for its designatum, is called a symbol."

0° systems perspective: Scientific usage of a symbol

requires observations. If one views science as a

unified body of knowledge, then a specification of

meaning is within organized natural structures.

6.1.6. NAME

Semiotic perspective : "A sign which has an

extensional class for its designatum is called a name. An extensional definition of a class is one given 'by

listing the names of the members or by pointing to every member successively." (see Reichenbach, 1948).

0° systems perspective: A name within a given

degree of organization constrains the material

composition of the object to specific patterns of

relationships. For a specific living system, a

biological name intrinsically distinguishes a unique

historical (genetic) path.

6.2 Role of Supra-ordination in scientific

semiotic and organizational theory

Distinctions between scientific notation and general

semiotics go beyond the meanings of definitions. Sebeok

writes of applying the "Law of Inverse Variation," "The

terms, sign, symbol, emblem, and insignia are here

arranged in the order of their subordination, each term to the left being a genus of its subclass to the right and each

term to the right being a species of its genus to the left. Thus, the denotation of these terms decreases; for example,

the extension of 'symbol' includes the extension of

emblem but not conversely."

The example used to illustrate the Law of Inverse Variation

consists of a series of four terms: sign, symbol, emblem

and insignia. Set theoretic language is used to indicate that the denotation of each term decreases in a subordination of

semantic content — or, in mathematical terms, a nested

sequence of subsets of denotata exists among the four

215
terms. If viewed as a discrete sequence of natural numbers,

the Law of Inverse Variation implies the extension of a term may become vanishingly small.

Supra-ordination, rather than sub-ordination, is intrinsic to the semiotics of cellular organization presented here.

Supra-ordination follows a historical, evolutionary

perspective of the emergence of complexity — a path of

creativity from the simple to the more complex [9, 12, 14,

3, 4]. Supra-ordination is composed by combining lower

symbols to form higher symbols, O

o1

, O

0^, O0

^,..., in a sequence of natural numbers. While the law of

subordination of general semiotics deduces a decreasing

domain, this scientific semiotics generates an

exponentially increasing domain within the material

structure of natural degrees of organization. The number of

potential combinatorial binding relationships is mathematically unending. No stopping rules for the

series O

0 *, O0 ^, O0

^,... is known. Assuming the

historical trends continue, this implies that more highly

cooperative systems will emerge in the future. This is not novel idea, but it provides a new line of support for the

thesis [9].

This 0° hypothesis provides a basis for scientific semiotics

which is both richer and poorer than linguistically-based

semiotics. 0° is richer in the sense that scientific

semiotics is based on enumeration of material complexity,

hence it demands both algebraic and geometrical patterns

within the symbology and semantics of objectivity. It is also richer in the sense that 0° provides a basis for the

transdisciplinary communities to communicate within a common symbolic framework. By the same token, this scientific semiotics is poorer than general semiotics when

attempting to aggregate human desires, values, feelings,

longings, ambitions or objectives. Spiritual traditions,

literature, the performing arts, and the sciences continue to create more higher organized learned structures, ever more

remote from the autonomy of O

o1 particles. Natural

history is a history of generating options and generating

selections of ever greater complexity.

Discussions with B. Chandler, A. Ehresmann, K. Harbaugh, J. Long, R. Khuri, A. Vogt, and B. Weems have added to the pleasure of this composition.

7. References

[1] Baas, N. A. (1994). Emergence, Hierarchies and

Hyperstructures. Artificial Life III. Ed. C.G. Langton,

Addison-Wesley pp. 515-537.

[2] Chaisson, E. (1996). "Cosmological Complexity on

the Grandest Scales" Actes du Svm ECHO. Amiens,20-26.

[3] Chaisson, E. (1989). The Life Era W.W.Norton, NY.

[4] Chandler, Jerry LR (1991). "Complexity: A

Phenomenologic and Semantic Analysis of Dynamical

Classes of Natural Systems," WESScomm 1 34 - 40.

[5] Chandler, Jerry LR (1992). "Complexity II. Logical

Constraints on the Structure of Scientific Languages,"

WESScomm 2 34-37.

[6] Chandler, Jerry LR. (1995). "Third Order Cybernetics,"

Proc. of 14th Int'l Congress on Cybernetics, Namur,

Belgium, p. 489-493.

[7] Chandler, Jerry LR (1995). Complexity III. Emergence.

Notation and Symbolization. WESScomm 5, 1-12.

[8] Chandler, Jerry LR, Ehresmann, A. C, and

Vanbremeersch, J-P. (1994). Contrasting Two

Representations of Emergence of Cellular Dynamics" 6

Intl Symp. Systems and Cybernetics, Baden-Baden, DE.

[9] de Chardin, Pierre. T. (1959). The Phenomenon of

Man. Harper and Row, NY.

[10] Ehresmann, A. C. and Vanbremeersch, J.-P. (1987).

"Hierarchical Evolutive Systems," Bull. Math. Biol. 49

13-50.

[11] Ehresmann, C. (1966). Trends toward unity in

mathematics. Cahier de Topologies et Geometrie

Differentielle 8, 759 - 765.

[12] Jantsch, Erich (1980). The Self-Organizing

Universe. Scientific and Human Implications of the

Emerging Paradigm of Evolution. Pergamon Press,

Oxford.

[13] Miller, J. (1978). Living Systems . McGraw-Hill,

NY.

[14] Morowitz, H.J. (1992). Beginnings of Cellular Life.

Metabolism Recapitulates Biogenesis. Yale Press.

[15] Rosen, Robert (1991). Life Itself. A Comprehensive

Inquiry into the Nature. Origin and Fabrication of Life. Columbia Univ. Press, NY.

[16] Sebeok, Thomas A., (1994). Signs: An Introduction

to Semiotics. Toronto Press.

[17] Thorn, Rene (1990). Semiophysics. Addison-Wesley.

[18] Vanbremeersch, J.-P, Chandler, Jerry LR and

Ehresmann, A.C. (1996). "Are Interactions among

different Time Scales a Characteristic of Complexity?"

Actes Du Symposium ECHO Amiens, Fr., 162-167.

[19] Walters, R. F. C, (1991). Categories and Computer

Science . Cambridge Press.

216
A HOLONIC APPROACH TO INTELLIGENT CONTROL OF

A FLEXIBLE TRANSFER SYSTEM FOR

MANUFACTURING

Mihaela Ulieru

School of Engineering Science

Simon Fraser University

Burnaby, BC V5A 1S6 CANADA

http:// www.sfu.ca/eng-sci/irms

Tel. +1-604-4150636 Fax. +1-604-2914951

Abstract. This paper presents the design

and implementation of a holonic

approach to intelligent control of a

flexible transfer system which is

regarded as a multi-agent system. After a brief introduction in the concepts of

holonic manufacturing the design of a multi-agent architecture for the flexible

transfer system is presented. Then a behavioral control strategy supporting

the triplet Planning-ExecutionMonitoring is presented together with its

implementation for the control of the

work-pieces transfer on the optimal path.

Keywords. Multi-agent architecture,

holonic control, flexible transfer system.

1. INTRODUCTION - HOLARCHIES OF

HOLONS

In the past few years the application of

the socio-economic principles developed

by Artur Koestler in his book "The Ghost

in the Machine" has revolutionized the

organizational/management principles

of the manufacturing industry worldwide^]. Briefly, holonic manufacturing

systems can be regarded as a unified way

to approach the hierarchical control of

any manufacturing unit, from the

production process to the whole

enterprise level. Broadly speaking holons

have most of the generic properties of

agents, being mainly distinguished

through their dual " whole-in-the-part"

nesting properties of super ordination to

the part(s) which is (are) contained b y

them and subordination to the bigger

whole to which they belong. Families of

"wholes within wholes" (named

holarchies) replicate the same properties

starting from an overall highest level

which includes several "sub-wholes" with

similar properties, these in turn

including other "sub-sub-wholes", etc.

until a last level contains atomic parts

which don't contain any other "subwholes" and which usually have different

properties than the (sub-)wholes Fig. 1. As an example one can consider a federation of states (e.g. USA or Canada)

within a country. The country as a holarchy of states, has its own political

structure. Each state in turn replicates a n own political structure. Within each state

there are districts with there own

political organizations. These are the

atomic elements which don't contain any

other holons.

2. THE FLEXIBLE TRANSFER SYSTEM

In this paper a holonic approach to the

implementation of the control strategy

for a flexible transfer system is

presented. The system, Fig. 2, consists of a

set of pallets (organized in a grid which

can have different shapes) which

transfer a certain number of work pieces

simultaneously. Each pallet is regarded as an agent, which is a sub-holon in the

holarchy represented by the whole

system of pallets constituting the transfer

system.

217
rules for external behaviors

Subordination to whole

Co-operation

with peers

Super-ordination to parts

(sub-holons) X,

co-operation

co-operation

co-operation

Co-ordination

with environment

\

Holon boundary

internal structure & rules

Fig. 1: Holarchy as a system of nested holons [from 9]

Each pallet (regarded as an agent/subholon) has the ability to act autonomously

via a computational system which

includes ability to process sensor

information and data carriage, which

allows as well communication with the

other pallets (agents/sub-holons) via a communication module, Fig. 3. The spatial

configuration of the holarchy can be

changed while preserving the overall

control strategy which allows each holon

to move the work-piece in any direction

via an OMNI-wheels mechanism. The

overall goal is to minimize the time of

transfer of all work pieces from their

initial place to a desired destination while

minimizing the conflictual situations

(like e.g. when two work pieces should

cross at the same time a pallet on their

minimal path, (etc.)

3. THE PROPOSED ARCHITECTURE FOR

THE FLEXIBLE TRANSFER

SYSTEM REGARDED AS A MULTIAGENT SYSTEM

The representation of a pallet presented

in Fig. 3 can be regarded as an

intelligent agent, as the term is

generically understood in the AI

community being an entity capable of

understanding its environment and able

to independently deliberate and reason

how to use own resources to reach a desired goal. The agent has the ability to

move in a certain manner and can

manipulate objects in its environment.

The main concern from an architectural

perspective is to find the most adequate

way for agent interaction and

cooperation such that agents can achieve

their goals optimally (in our case the

fastest transfer of the work pieces from

their initial positions to the desired

destinations.)

218
As presented in Fig. 4, the proposed

architecture for the flexible transfer

system consists of groups (sets) of

specialist agents. Each group is able to

perform a certain kind of specialized task.

The interactions among specialist agents

Fig. 2: The Flexible Transfer System

belonging to the same group are

coordinated by a supervisor of the group.

The supervisor's goal is to provide its

agents with necessary information which

would allow them to achieve their own

goals. A group of agents can be regarded

as a blackboard system where specialists

represent knowledge sources regarding

execution of a certain kind of task and the

supervisor plays the role of both

blackboard and control mechanism of the

system. Since the architecture contains

many supervisors, the proposed multiagent-system model can be viewed as a multi-blackboard architecture.

219
Fig. 3: Generic structure of a pallet (agent/sub-holon)

in the flexible transfer system holarchy )

The two main classes of agents:

supervisor and specialist will be

instantiated for the flexible transfer

system as follows. Any "leader" pallet (i.e.

any pallet that carries a workpiece) is a supervisor for the whole time it carries

the workpiece or transports it towards its

next carrier-pallet (leader). All the

potential next carriers (potential next

"leaders") are specialist agents belonging

to the same group, for which the group

supervisor is the pallet that carries the

work-piece at that moment in time. There

are as many groups of specialist agents as many work pieces are transported at once. Each group has as supervisor the

carrier of the work piece. Each group is

on-line dynamically organized in order to

form a path to transport the work piece to

its final destination. Group supervisors

220
Gobal

Supervisor

Group

Su per visor

(^Specialist J

(^Specialist)^—»^Specialist"^

Group

Su per visor

L J

(Specialist ^ (^Specialist ^

Peers

Fig. 4: Multi-agent architectural model of the FTS

cooperate in order to solve conflicts i n case two paths cross each-other o r overlap on a certain portion. In extreme

situations decisions are made through

negotiation as of which piece should pass

first through the same cell (pallet).

Each specialist agent on a path will

become a supervisor when the work piece

reaches it. So, the configuration of the

architecture is dynamically changed. The

next carrier becomes from specialist

agent a supervisor and in turn the last

supervisor becomes a specialist agent

after the work piece has been transported

on the next carrier. Each group defines a

class of agents consisting of individual

objects which are specialist agents.

Interactions between groups are

managed by the group supervisors at

each step. The goal of each group is to

transport the piece carried by the

supervisor as soon as possible to the

desired destination. Supervisors are able

to do optimal path planning, conflict

resolution, cooperation, negotiation and

other intelligent tasks.

Given that the upper limit in the number

of supervisors equals the maximal

number of pieces that can be transported

at once, this number has to be determined

together with the analysis of the

feasibility of the proposed control

solution. As well an upper limit of the

number of workpieces to be transported

at once by the flexible transfer system

without need of a global supervisor has to

be determined. Once this threshold is

exceeded the control architecture has to

be enhanced with a higher level of

overall control implemented via a global

supervisor. The role of the global

supervisor would be to

manage/coordinate the interactions

between group supervisors, solve

conflicts between them and help their

negotiation strategies in making adequate

decisions by setting priorities according

to a-priori established rules.

221
Within a group, specialist agents have

two types of communication: horizontal

(characteristic to the autonomous

architectural paradigm) and vertical

(characteristic to the blackboard

architectures .

)

Horizontal communication aims to

support interactions between specialists

belonging to the same group.

Vertical communication indicates how

specialists interact with their group

supervisor.

Specialist agents are endowed with

capabilities for perception (sensors)

reasoning and planning (i.e., they are

cognitive). They must have the capability

to adapt themselves to unexpected

situations. This is achieved through

adequate adaptive and dynamic control

strategies.

4. HOLONIC CONTROL WITH

PLANNING-EXECUTION-MONITORING

The proposed control strategy is based o n

the triplet of Planning, Executing and

Monitoring (in short PEM.) In designing

intelligent multi-agent control and

especially in building a logical model, all

activities (manipulation, motion and

sensing) are implemented with

corresponding planning, executing and

monitoring elements. Each activity is

expressed as an instance of the PEM

triplet.

The connections between the generic

activities Planning, Execution and

Monitoring are made by means of control,

data flow and related models. There are

different choices to carry out the

activation and deactivation of planning,

executing and monitoring. Ability to cope

with re-planning in dealing with

unexpected situations is essential. It is the

responsibility of executing and

monitoring to decide whether the current

plan is considered valid or not. If not, replanning will be activated. The actual

decomposition takes place in the

execution phase, while the planned

operations are activated. The execution

mechanism takes care of activation and

deactivation of planned operations as described in the plan. Activation of a decomposable operation means activation

of the meta-control at the immediate

lower level.

The atomic operations pass control

commands and sensing requests to

actuators and sensors through devicedrivers. They process and pass

information for the use of planners and

executors to the local models, either to

their own level or upper levels of the

control hierarchy. Atomic operations also

update the global models and therefore

are used to maintain model consistency.

The way the system reacts to erroneous o r unexpected situations (not covered with

the possible conditional structures in the

plans) depends not only of the capability

of the planners to find recovering plans

but also on the timing logic of the metacontrol. Reactive behavior can be

achieved only if replanning and the

subsequent execution are done as quickly

as possible.

The proposed control strategy is inspired

by the synchronous planning principle

of Albus [2]. In his model, Albus assumes

instant planning done synchronously i n

a frequency typical to the level of

hierarchy. It means that the ordinary

planning is signaled to start by a clock

mechanism, while replanning is signaled

a-synchronously from erroneous

situations. The distinctive aspect of our

strategy is to decompose the execution

mechanism into lower level planning and

execution mechanisms (nested.) Planners

are considered to do all the planning

related activities, that is also the

computation based sensory information

during the execution. After a partial plan

has been created, the execution starts.

The planning is activated again when

acquired sensory information has to b e transformed into plan parameters. There

are several ways in which the executor

and the planner can be synchronized (i.e.

connected to the data in the local model

222
either with a direct control signal from

the executor to the planning function of

the planner - in case the goal exists -or

by passing the control signal via the

meta-control - if a goal does not exist.)

8. IMPLEMENTATION OF THE CONTROL

STRATEGY

Considering an object-oriented mail-box

based communication approach, an agent

is regarded as a concurrent object

blocked in waiting the next message to

execute. Each agent is characterized by its

mailbox which is managed by a thread.

This allows an asynchronous

communication between agents which

are physically distributed through a set

of stations.

We define five classes of objects: object,

class, meta-super, specialist and

supervisor , The basic executing model

contains following classes: object, class

and meta-super. The class object has two

kind of actions: ask - that enable object to

get a value from an attribute and give -

that enable object to affect a value to a n

attribute. In the class class the action

new allows to create a new class. In the

class meta-super, the action create-super

instantiates supervisor objects. The class

meta-super allows to generate as many

control levels as demanded by the

complexity of the system. The action

broadcast allows a supervisor to

communicate with its group's agents.

A group supervisor has a limited view of

the environment. All group supervisors

whose physical environment should be

crossed by a piece must cooperate i n

order to lead this piece to the desired

point. Each supervisor has a goal to move

the piece to the desired point, and

according to the environment it manages

it provides a plan for moving. The global

supervisor determines what supervisors

must cooperate and specify them the

trajectory the piece should pursue. By

knowing the initial position of the piece

as well as the final position the piece

should reach, the global supervisor has a

function sub-cooperate which takes

coordinates of these points, its belief base

(bell-base), and returns a list (List-ofsup) of group supervisors which must

cooperate to satisfy this goal.

Furthermore, its belief base contains

coordinates of a set of points situated o n

the intersection between two physical

possible paths. These points represent

"points" of cooperation between group

supervisors coordinating the specialists

groups on each of the intersecting path.

Consider for example S being a global

supervisor and SI, S2 group supervisors.

To plan the move of a piece from position

A to position B the global supervisor

should perform a sequence which can be

encoded as follows (given our above

considerations):

sup-cooperate (bell-base, A, B, Li st-of-sup);

any(Si,Sj) in List-of-sup X List-of-sup

inform (Si, M(x,y));

inform (Sj, M(x,y));

broadcast (List-of-sup, plan-path);

In the above sequence, M is an

intersection point between two possible

paths controlled by Si and Sj, and (x,y)

are its coordinates. As a result of message

execution plan-path, each group

supervisor plans a sequence of actions

for enabling a robot to move in its

physical environment.

For the supervisor SI the sequence of

operations would be:

move-straight (30 pallets);

turn-left (90 degrees);

move-straight (30 pallets);

For the supervisor S2:

move-straight (25 pallets);

turn-right (90 degrees);

move-straight (20 pallets);

turn-left (90 degrees);

move-straight (20 pallets);

turn-right (90 degrees);

move-straight (15 pallets);

223
Once the piece has reached the desired

position, it needs to be integrated within

the new group. The supervisor S2 must

initialize the new transfer by specifying

the belief rule base to load. The goal is to

enable the transfer of the piece in the

new environment. In this way the

supervisor represents a cooperation

framework which enables him to adopt a plan of actions by selecting (meta-

)capabilities at the group's agents.

9. CONCLUSIONS

In summary, the proposed architecture is

adjustable to applications with different

levels of complexity. The control of the

complexity is managed via the number of

hierarchical levels chosen for the

particular instantiation. In its simplest

instantiation the architecture consists of

a single group having one supervisor,

which represents a blackboard

configuration. There is practically n o upper limit for the complexity of the

system to be represented, which can be

encapsulated by increasing the number

of hierarchical levels in the architecture.

This increases the flexibility and

efficiency of the control strategy

responsible for the adequate

functionality of the proposed multi-agent

architecture. The hierarchical control

levels may be exploited as meta-levels for

learning in a multi-agent environment.

An agent has its own capability of

learning, but if it encounters a non

deterministic state it must interact with

its supervisor to decide what actions it

should choose to pass in a deterministic

state.

ACKNOWLEDGMENTS

The author would like to express

her gratitude to Toyo Engineering

Corporation from Chiba, Japan and

Intelligent Robotics Corporation,

North Vancouver, Canada for

sponsoring this work.

[1] AlbusJ., Barbera, V., Nagel, H., "Theory

and Practice of Hierarchical

Control", Proc. of the 23rd IEEE Computer

Society International Conference,

Washington, Sept. 1981, pp. 18-27.

[2] Albus, J., McLean, B., Barbera, V.,

Fitzgerald, A., "An architecture for

real-time sensory interactive control

of robots in a manufacturing

facility", Proc. of the 4th IFAC/IFIP

Symposium on Information Control

Problems in Manufacturing

Technology, Gaithersburg, 26-28 Oct. 1982,

pp. 81-90.

[3] Herman, I. and Albus, J. "Overview of

Multiple Autonomous Underwater

Vehicles Project", Proc. of the 1988

IEEE Int. Conf. on Robotics and

Automation,

Philadelphia, 24-29 April 1988, Vol.2,

pp. 618-620.

[4] Albus, J., McGain, W., Lumia H.,

NASA/NBS Standard reference Model

for Telerobot Control System

Architecture, NIST Technical Note 1235,

1989 Edition, 76p.

[5] Brooks, K. "A robust layered control

system for a mobile robot", IEEE

Journal of Robotics and Automation, 2,

1/1986, pp. 14-23.

[6] Brooks,K. FlynnJ. "Robot Beings",

Proc. of the Int. Workshop on Intelligent

Robots and Systems, 1989, Tsukuba,

Japan, pp. 2-10.

[7] Norelis, G. and Chantilla, T. "A general

structure for mobile robot action

control", Proc. of the IEEE

International Workshop on intelligent

Robots and Systems, IROS'89, Tsukuba,

Japan, pp. 550-556.

[8] Brooks, A. "Intelligence without

reason", MIT AI Lab. Memo 1293,

April 1991.

[9] Intelligent Manufacturing Systems

Consortium - Project on Holonic

Manufacturing Systems, Vols. 1-3,

Edited 1996 (proprietary info.)

REFERENCES

224
Learning Coordination Patterns from Emergent Behavior

in a Multi-Agent-Based Manufacturing System

Maturana, F. Graduate Student

Ph: 403-220-5782

Fax: 403-282-8406

maturana@enme.ucalgary.ca

Balasubramanian, S. Graduate Student

Ph: 403-220-5782

Fax: 403-282-8406

balasubr@enme.ucalgary.ca

Division of Manufacturing Engineering, The University of Calgary

2500 University Drive, Calgary, Alberta, Canada

[""Corresponding author]

Norrie, D.H. *

Nortel Chair in Intelligent Manufacturing

Ph: 403-220-5787

Fax: 403-282-8406

norrie@enme.ucalgary.ca

ABSTRACT

Multi-agent systems provide responsive and

reconfigurable information-processing structures that can

facilitate flexible, efficient use of manufacturing resources in a

rapidly changing environment. For maximum scalability and

fault tolerance, agents relevant for a particular task may be

dynamically gathered into communities where they are coordinated and arbitrated by mediator agents. In a dynamic

manufacturing environment, the collective behavior of such a system is an emergent property; hence, robust learning

mechanisms are required for effective mediation. A learning

mechanism that enhances the capabilities of a multi-agent

concurrent design and manufacturing system is presented, and

associated implementation issues are discussed.

Keywords: Multi-Agent System; Manufacturing; Emergent

Behavior; Learning; Coordination; Mediator.

1.0 INTRODUCTION

Heterogeneous multi-agent systems, comprising a network of dissimilar autonomous interacting software entities

called intelligent agents (Wooldridge and Jennings, 1995), are becoming increasingly popular for implementing distributed,

cooperative manufacturing planning and control systems.

Such systems provide responsive and reconfigurable

information-processing structures that facilitate flexible,

efficient use of manufacturing resources in a rapidly changing

environment.

Intelligent agents are knowledgeable in their local

domains and share the responsibility of achieving multiobjective system goals through concurrent negotiation. The

relevant agents for a particular task may be gathered into a

special community that is dynamically formed, coordinated

and arbitrated by mediator agents (Wiederhold, 1992) for

maximum scalability and fault tolerance. In this architecture,

the responsibilities of a traditional centralized supervisory

manager are distributed among the mediator agents (Duffie,

1990).

These mediators are also coordinators, possessing

organizational knowledge and meta-level rules necessary to

facilitate cooperation among intra- and interagent

communities. In a dynamic manufacturing environment, their

knowledge cannot be static, since the system's behavior

depends on problem solving. Thus, the system's collective

behavior is an emergent property, requiring robust learning

mechanisms for effective mediation.

One possible approach is learning from history. For

example, in manufacturing planning and scheduling many

repetitive activities can be learned for reuse. For this, the

intelligent system needs encoding models and specialized

reasoning agents to decide upon the use or rejection of learned

transactions. The learning ability facilitates improvement in the performance of both individual agents and the multi-agent

system overall.

In addition to learning, a sophisticated mechanism for

propagating the state of agent interactions into the future is

required. This attribute provides an intelligent forecasting

medium through which multi-agent system responses can be

adjusted and refined.

2.0 RELATED WORK

In recent years, researchers have explored various

approaches for learning and emergent behavior in multi-agent

systems. The notion of "behavior" has become recognized as a fundamental building block in the artificial intelligence,

control, and learning research community (Mataric, 1995).

Behavior is seen as a regulator in interaction dynamics

between agents and the environment. This phenomenon has

also been observed by Steels (1990); Maes (1990); Brooks

(1991).

The Touring Machine agent design architecture

(Ferguson, 1992) has been used to control multi-agent

activities in dynamic environments. The Heterogeneous

Reasoning and Mediator System (HERMES) (Subramanian,

1996) is an architecture designed to integrate heterogeneous

sources of data and reasoning paradigms through the creation

of specialized mediators.

Distributed Refinement Among Multiple Agents

(DRAMA) was developed as a machine-learning technique

(Byrne and Edwards, 1995) to improve agent knowledge. This

technique provides agents with the ability to learn their

organizational roles in a distributed cooperative search. In addition, the agents are also capable of learning meta-level

225
interactions in the search space. Dynamic reinforcement

learning algorithms (Q-learning) (Sandholm and Crites, 1995)

have been used in multi-agent systems to help individual

agents learn about the environment and from other agents.

Learning organizational roles in heterogeneous multi-agent

systems has been addressed in the L-TEAM (Prasad et al., 1995) framework.

Exploiting past experience from intelligent agent

interactions has been studied in the context of multi-agent

Case-Based Reasoning (CBR) (Ketter and Hendler, 1994).

The negotiated retrieval technique (Prasad et al., 1996)

retrieves and assembles "case pieces" from multiple sources in a corporate memory to create an overall problem case. Federated peer learning (Prasad and Plaza, 1996) uses two

models of cooperation: Distributed Case-Based Reasoning

(DisCBR) and Collective Case-Based Reasoning (ColCBR).

In DisCBR, an agent can delegate its authority to another

agent to solve a problem. In ColCBR, an agent maintains its

authority while exploiting the experience of a peer agent.

3.0 EMERGENT BEHAVIOR AND LEARNING

The multi-agent-based manufacturing system being used

for the present work comprises several design subsystems and

resource communities (virtual factories) of shop-floor

resources. Each design subsystem provides feature-based

capabilities through a part agent and various feature agents

(Balasubramanian et al., 1996). The part agent is the

repository for both product data and relationships among

feature agents. Each part has a set of features, which in turn have technological requirements that help structure

relationships with shop-floor resources. For each feature agent

in the part, resource communities respond with feasible

manufacturing plans and costs. Products are represented as

part agents, which are containers for various types of features.

The manufacturing system needs to be dynamically

configured to support changes in batch sizes, product mix, or design plans, which precipitate production setup changes.

Extensive search processes are required to identify the multiagent interactions for each problem case. These interactions

are an emergent property that evolves concurrently within

each level in the organization for different types of

requirements, constraints, and agents (Maturana and Norrie,

1996). For each new problem case, the whole space of

interactions is investigated using a restricted search approach

similar to a distributed, local breadth-first search. This search

mechanism achieves a global optimum but is computationally

expensive and involves non-trivial overheads, particularly for

large multi-agent populations. The learning mechanism

presented here enables more efficient use the system's

behavior, thereby reducing overheads.

Since the manufacturing system is highly dynamic, with numerous elements and constraints, it is very difficult

(generally impossible) to establish an optimum generic

procedure for manufacturing tasks using static knowledge

about manufacturing resources. However, properly identifying

dynamic interactions among agents and the emergent behavior

of the agent group as a whole facilitates a new-optimal

solution for these tasks. Organization of resource communities occurs at two

levels: macro and micro. Macro-level organization is static,

based on knowledge about closely related agents that are

distinct from others and can be physically separated. As

shown in Figure 1, such communities can be made of part,

inventory, machine, tool, and transportation agents.

^^Part Agents

Figure 1: Macro-Level Communities

Figure 3: Inter-Community Interactions

Within a macro-level community, heterogeneous agents

form micro-level communities whose composition is not static and therefore unknown. Such micro-level communities are determined by predominant behavioral characteristics

(grouped in classes), see Figure 2. These communities

typically contain primary or secondary process machine

agents, design features, or tools. There are three types of interaction among various agents

within a system. The first type lies entirely inside the

boundaries of a micro-level community. As shown in Figure

2, interactions of the second type involve two or more microlevel communities within a macro-level community. In the

third type, interactions span two or more macro-level

communities, as shown in Figure 3. The learning model

presented here considers all these organizational possibilities.

226
4.0 LEARNING MODEL

The system's learning focuses on the transactions

between the design system and the resource communities that

result in promissory plans. These promissory plans include

relationships among manufacturing resources ordered

according to precedence constraints and processing times

needed. For a given set of features, there are appropriate

combinations of resources (resource networks) for the

manufacturing operations. The composition of the resource network varies with time, since availability and service costs of resources are dynamic parameters affecting the decisionmaking processes. Thus, the learning model requires two main

classification functions, one feature-based and the other

resource-based.

Feature-based classification creates subcategories of

features that are progressively recognized by mediator agents.

These subcategories are associated with specific groups of

resources and emergent behaviors that define the relationship

between the features and the resources. Similarly, the

resource-based function classifies resources into subgroups

associated with specific families of features and emergent

behaviors.

A behavioral pattern includes knowledge about microlevel communities, their constituent agents, dynamic

associations among those agents for a specific time, work

load, product type, and product mix. These patterns recognize

how agents organize themselves into virtual clusters that

define the knowledge hierarchies through which

manufacturing tasks can be processed.

Initially, the multi-agent manufacturing system operates

in a "blind space" and every resource in it is involved in decision-making activities. The system, lacking knowledge

regarding behavioral patterns followed by agents during the

decision process, is forced to carry out a global search for

unknown patterns. At the beginning, generalized broadcasting

is used to inform resource agents about the manufacturing

tasks and their requirements. Subsequently, dynamic

hierarchies of coordination clusters are formed and selective

broadcasting can be used.

The behavioral knowledge gained through this learning

process can be used in two ways to improve system

performance. When a new task arises, a community mediator

has to identify related macro- and micro-level communities of

agents for initial broadcasting and for subsequent formation of

coordination clusters. Behavioral knowledge facilitates this

selection of agents for coordination clusters. The second benefit relates to how queries are propagated

among coordination clusters. Dynamic mediators can retrieve

the performance history of agents to rank the agents in the

cluster. Agents with higher rank are selected to propagate

sublevel clusters. In this manner, dynamic mediators replace a naive search with a distributed depth-first search, by inhibiting

the formation of coordination clusters by agents ranked below

threshold limits. Only if higher ranked clusters fail will lower

ranked clusters be formed.

This enhanced search process is shown in Figure 4. Ranking ranges from 1 to 10 and there are only two subranges

(higher and lower), with a threshold value of 5. All the

clusters ranked above the threshold value are allowed to propagate at every level. The lower ranked ones are allowed

to continue at each level only if the higher ranked clusters fail. This amounts to distributed backtracking without explicit

control.

Since the propagation of coordination clusters defines the

interaction among agents from various micro-level

communities and the distributed search process, it also defines

the potential domain of emergent behaviors. The ranking

defines only the propagation mechanism and has no influence on the outcome. Any combination of resource agents might

win the bidding process, despite their ranking.

Figure 4: Distributed Depth-First Search

The ranking keeps changing with every outcome,

necessitating continuous learning. Mediator agents possess the

requisite meta-rules to accomplish this. Since an inherent

characteristic of the multi-agent system is that multiple tasks

may be solved at any given time, multiple distributed search

processes can be carried out in parallel. The distributed depthfirst search mechanism helps this process by reducing the

computational requirements and communication bandwidth.

Distributed parallel learning is then possible during the

construction of partial promissory plans. Each coordination

cluster contributes with a set of partial relationships (among

the manufacturing resources) to solve a particular aspect of the

manufacturing requests. Partial relationships are associated

with both basic and dynamic costs, allowing cluster

coordinators to define priorities and control for the

propagation of clusters. By aggregating the partial

relationships, a set of final promissory plans is established and

subsequently refined to satisfy other dynamic constraints on

the shop floor. The final refinement provides the best possible

production sequence for the product, including relationships

that link machine agents and tool agents into an emergent

organization for it. Subsequently, promissory plans are used to define the best possible schedules for the resources in each

relationship, yielding the best overall promissory plan

(Maturanaet al., 1997).

In recent experiments, it has been shown that the time for

distributed planning in the system reduces by a factor of

227
between 100 and 500 as learned relationships become used.

5.0 LEARNING FROM HISTORY

The emergent relationships obtained during the search, to encode the solution plans for partial aspects of the

manufacturability request, are related to the individual

features of the product's design. Depending upon the feature's

category, geometric characteristics, and finishing

requirements, it is now virtually linked to resources. For a

single feature there may be several relationships, both

technological and dynamic. The virtual links vary dynamically

according to the status of the resources on the shop floor. Encoding these emergent relationships for manufacturing

is based on distributed machine-tool information. A machine

resource may require one or several tools to either partially or thoroughly meet the requirements for a single feature. This

information is dynamically captured in coordination clusters

and sent to the community mediator for encoding and storing

in information structures. Each community may implement

several of these learning systems to encode different

behaviors. After confronting the learning system with a previously recognized product, a set of relationships is obtained and accumulated. At this stage, the mediator agent

uses the macro-level static classification of resources to create

a hierarchical structure (i.e., primary, secondary, tertiary, etc.)

that satisfies precedence constraints.

As the system learns dynamically from interactions,

various emergent relationships define alternatives for the

manufacturing sequence, each partitioned into an ownerdependent link to establish a reduced group of resource

agents. An owner is an entity linked to a set of dependent

entities. Conversely, a dependent is an entity owned by a higher level entity. The primary-level owner-dependent link

initiates a primary-level coordination cluster, which is then

provided with the other owner-dependent links for forming

other sublevel clusters of either machine or tool agents. Each

sublevel cluster is also provided with the link information

associated with its searching domain. At this point, the

mediator agent can structure a feasible search region for a request and broadcast to selected agents to generate

promissory plans and costs.

6.0 LEARNING FROM THE FUTURE THROUGH

FORECASTING

Forecasting the system's behavior consists of capturing

the state of the multi-agent system (plans) and simulating it for a period of time into the future. The forecasting process

simulates the behavior of the virtual model, which emulates

the shop-floor activities. Since the agents' commitments are generated at a promissory level and based on distributed

estimations of the system's real state, this process is a highlevel simulation activity that propagates this behavior into its future environment. Machine mediators monitor the system's

status by conducting global performance evaluations. Various

forecasting triggering parameters are used based on system

load, extension of the scheduling horizon, and adjustment

periodicity. These parameters are quantified and combined

according to the following criteria:

1. System load: This parameter is set to promote a balanced work load among the resources. The number of new

jobs allocated is measured to calculate a load ratio (R,.) which

is then checked against a load threshold. R, greater than this load threshold satisfies the first condition for triggering the

simulation forecasting process. This condition is complemented by the adjustment periodicity parameter as shown in Equation 1

:

Number of new jobs allocated

>

1 Total number ofjobs allocated IfR > Threshold, 0)

Then

If (Periodicity)

Then Run Forecasting

Else Continue

By considering the natural adjustment of schedules after forecast scheduled times, resources may open availability slots

at previously occupied positions.

2. Extension of the scheduling horizon (R.): This

parameter changes the configuration of schedules to vary job

priorities. Since schedule adjustments either extend or contract

the scheduling horizon, lateness and earliness penalizations

affect the scheduling, differently. In order to extend the

scheduling horizon, new job allocations are more heavily

penalized if the jobs approximate the due-date boundaries. To

contract the scheduling horizon, resources that contract their

scheduling charts may allocate more jobs at a low penalization

rate. This parameter is shown in Equation 2. (Completion Time) _ 'max

s ~ (Due v Date)

'max

If R > Threshold (2)

s s Then

If (Periodicity)

Then Run Forecasting

Else Continue

3. Periodicity (Rp): This parameter regulates the time

delay between forecasting events. It may trigger the

forecasting event either alone or in combination with one of

the two parameters above. When Rp acts alone, the number of

new allocations must be greater than zero. A time periodicity

threshold is also provided to quantify the periodicity, as shown in Equation 3. IfR > Threshold

p p Then

If (number of new allocations) > 0 (3)

Then Run Forecasting

Else Continue

If(R

p and R| )or(R

p and R

$ )

Then Run Forecasting

228
The system's performance is measured through a composite function that measures average flow time,

maximum completion time, and number of late jobs, as shown

in Equation 4.

/> = wr *F + wc *C_+wj *Z,

y

where: w; -averageflow time weight (4) wc - maximum completion time weight

Wy-late jobs weight

F.-averageflow time

C^.-maximum completion time

L,.-number of late jobs

J\ -number ofjobs completed

Each performance value is weighted according to management policies. The composite function is not restricted

to these performance values. The performance ratio (R^ics) is

calculated as follows:

R - —

metrics p

(5)

P' -forecasting simulation performance

P.-system performance before adjustment

Lower and upper thresholds (—a, + o) are used to

define acceptance and rejection performance-ratio regions.

The system's state of commitments remains unaltered if ratios

fall within the thresholds.

The forecasting simulation period is established by the

system manager according to high-level policies. However,

the determination of the simulation-control parameter may be

customized to automatically adapt to the system's

requirements. Two main approaches can be used to establish

the forecasting period:

1 . The forecasting simulation may be run for a period of

time sufficiently large to permit the completion of every

committed job. But for large simulation periods, this criterion

incurs accumulative deviations, since several jobs may arrive

in the system that affect intermediate allocation slots. Because

these slots are not preempted during simulation, this approach

only produces rough estimations.

2. The second approach attempts to avoid the

accumulation of deviate behaviors, thereby extending the

forecasting simulation for short periods of time only. This

approach is more accurate, since the duration of the simulation

is much less than the arrival frequency of jobs. Here, the

multi-agent system can easily be adjusted while including the

intermediate requirements.

Either approach produces an estimated performance

value, which is used to decide upon the refinement of the

system's commitments. Figure 5-A, illustrates the variation in system performance. Here, the system performance for two

consecutive simulation periods is represented by f, and f2 and

the variation in performance for the forecast model is represented by f , and f 2

. It is assumed that the simulationtriggering parameters are satisfied at period 1 . At the end of

the simulation both performances ~ i.e., f, and f , - are

compared through a performance ratio function. In this model,

the system behavior is very close to the simulated behavior;

therefore, promissory planning is being developed within an

acceptable range. Thus, the system continues to plan using the

current state of commitments.

Fig. 5-B shows a second forecasting simulation occurring

at period 2. Since the performance ratio between f2 and f2 is

sufficiently large to exceed the performance threshold the

system decides to adopt the forecast scheduled times,

replacing current schedule times by these. The state of

commitments is modified at each planning level affected by

these changes. For the next period (period 3) of the

forecasting simulation, the performances were sufficiently

close, so the current state of commitments was retained.

Rrfcrrrance ftrfcrrrBrce

SirriMcn Triggering Sirrulaticn Triggering

Figure 5: System Performance Variation

6.1 Experimental Results for Learningfrom Forecasting

A product mix comprising 100 of each of three part types,

namely, Bearing cover, EMI housing, and Guide, were

"manufactured" in two shop-floor areas using an AGV

transportation system to handle raw materials and semifinished products. Shop floor #1 had 3 vertical machining

centers, 2 internal grinders, 1 surface grinder and 43 tools. Shop floor #2 had 3 vertical machining centers and 35 tools. A

profit margin of 35% of normal production cost was

specified.

Once the production orders were placed in the design

system interface, the static mediator made repeated broadcast

requests to each shop floor involved. Since each offered a

different cost, the static mediator applied a final integration of

plans to determine the best one to manufacture the products.

The final schedule data showed that 1 90 parts were produced

in Shop floor #1 and 1 10 parts in Shop floor #2. Shop floor #2

only manufactured EMI housing and Guide products. The

Bearing cover product was only produced at Shop floor #1.

Table 1 shows combined performance metrics of Average

Flow Time (AFT), Maximum Completion Time (MCT), and

Transportation Cost (TC) for both shop floors. Only 8 jobs in

all were tardy.

Table 1: Experiment Results

: AFT

(min.)

MCT

(min.)

TC ($)

(Max.) (Min.)

414.06 7164.81 50.21 25.39

229
The forecasting simulation proved to be a robust system

for adjusting and enhancing performance. The forecasting was

triggered 8 times through the entire planning process, as shown in Figure 6.

r —0— Promis sory —0— Forecast

1 2 3 4 5 6 7 8

Simulation Triggering

Figure 6: Triggering Thresholds

7.0 CONCLUSION

A learning mechanism for identifying multi-agent-based

manufacturing system organizational knowledge and selective

interaction propagation from emergent system behavior has

been developed. This mechanism enhances coordination

capabilities by minimizing communication and processing

overhead, and facilitates distributed, parallel depth-first

search. Though this learning model has been implemented in a

distributed mediator architecture that is part of a concurrent

design and manufacturing system, it is generic and can be

applied to other areas as well.

A learning from forecast-futures technique has also been

developed to dynamically adjust distributed schedules and

planning in a multi-agent manufacturing system.

Experimental results show the value of this approach for

adjusting and enhancing performance.

REFERENCES

Balasubramanian, S., Maturana, F., and Norrie, D. (1996).

Multi-agent planning and coordination for distributed

concurrent engineering. In International Journal of

Cooperative Information Systems Vol. 5, 153-179.

Brooks, R.A. (1991). Intelligence without reason. In Proceedings of the Twelfth International Joint Conference on

Artificial Intelligence (IJCAI-91), Sydney, Australia, pp. 569-

595.

Byrne, C, and Edwards, P. (1995). Adaptation and

learning in multi-agent systems. IJCAI'95 Workshop

Montreal, Canada, August 21, 22-39.

Duffie, N.A. (1990). Synthesis of heterarchical

manufacturing systems. Computers in Industry 14, 167-174.

Ferguson, I.A. (1992). TouringMachines: An Architecture

for Dynamic, Rational, Mobile Agents. Technical Report No.

273, University of Cambridge Computer Laboratory.

Ketter, B.P., Hendler, J. A., Anderson, W.A., and Evert,

M.P. (1994). Massively parallel support for case-based

planning. IEEE Expert, 8-13.

Maes, P. (1990). Situated agents can have goals. NorthHolland, Robotics and Autonomous Systems 6 (1990), 49-70.

Mataric, M.J. (1995). Evaluation of learning performance

of situated embodied agents. In Proceedings of the Third

European Conference on Artificial Life, Granada, Spain, June

4-6.

Maturana, F.P., and Norrie, D.H. (1996). A generic multiagent mediator for distributed manufacturing systems, In Journal of Intelligent Manufacturing, Vol. 7, 257-270.

Maturana, F., Balasubramanian, S., and Norrie, D. (1997).

Intelligent multi-agent coordination system for advanced

manufacturing. Submitted to Intelligent Systems and

Advanced Manufacturing Conference, 14-17 October 1997,

Pittsburg, Pennsylvania, USA.

Prasad, M.N., and Plaza, E. (1996). Corporate memories

as distributed case Libraries. Accepted for presentation at the

Corporate Memory & Enterprise Modeling Track in the 10th

Knowledge Acquisition Workshop, Banff, Canada.

Prasad, M.N., Lesser, V.R., and Lander, S.E. (1995).

Learning organizational roles in a heterogeneous multi-agent

system. IJCAI-95 Workshop on Adaptation and Learning in Multiagent Systems, August (1995), Montreal, Canada.

Prasad, M.N., Lesser, V.R., and Lander, S.E. (1996).

Reasoning and retrieval in distributed case bases. In the

Journal of Visual Communication and Image Representation,

Special Issue on Digital Libraries, Vol. 7, No. 1, 74-87.

Sandholm, T., and Crites, R. (1995). On multi-agent Qlearning in semi-competitive domain. 14th International Joint

Conference on Artificial Intelligence (IJCAI-95), Workshop

on Adaptation and Learning in Multiagent Systems, Montral,

Canada, 71-77.

Steels, L. (1990). Cooperation between distributed agents

through self organization. In Demazeau, Y., and Miiller, J. P.,

editors, Decentralized AI - Proceedings of the First European

Workshop on Modelling Autonomous Agents in Multi-Agent

Worlds (MAAMAW-89), 175-196.

Subramanian, V.S., Adali, S., Brink, A., Emery, R., Lu,

J., Rajput, A., Rogers, T.J., Ross, R., and Ward, C. (1996).

HERMES: Heterogeneous reasoning and mediator system.

Technical Report, Computer Science Department, Univerisyt

of Maryland, (http://www.cs.umd.edu/projects).

Wiederhold, G. (1992). Mediators in the architecture of

future information systems. IEEE Transaction on Computer,

38-48.

Wooldridge, M., and Jennings, N. R. (1995). Intelligent

agents: Theory and practice. The Knowledge Engineering

Review 10(2), 115-152.

230
I

IX EVOLUTION
I

!

I

I

i

j

I

I

li;

I

i

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lit
Speculation on the Evolution of Symbols

David B. Fogel

Natural Selection, Inc.

3333 N. Torrey Pines Ct., Suite 200

LaJolla,CA 92037

ABSTRACT

Evolutionary algorithms provide a framework for studying the evolution of symbols in dynamic environments. This paper offers a brief review of related efforts in evolutionary computation involving the in- vention of a language of descriptors, followed by preliminary experiments in evolving symbols describing an environment to be sent be- tween a sender and a receiver. The results indicate that as more precision in the description of the environment is offered, the greater the possible accuracy; however, the greater the number of symbols, the more challenging the task of decoding the symbols. Thus there is a

trade off between precision and accuracy.

KEYWORDS: symbols, communication, evolutionary computation

1. INTRODUCTION

vival. Under the assumption that such behavioral characteristics

are heritable, the logical outcome is a series of individuals that

are successively better predictors of regularities in their environment.

The search for underlying regularities in nature is also primary to the scientific method. Indeed, there is a fundamental

connection between the process of evolution and the scientific

process of discovery [3] (Figure 1). In nature, individual organisms serve as hypotheses concerning the logical properties of

their environment. Their behavior is an inductive inference concerning some as yet unknown aspects of that environment. Validity is demonstrated by their survival. Over successive generations, organisms becomes better predictors of their surroundings.

Model

hypothesis

Deductive

manipulation

Living organisms are predictors. All evolved biota continually

predict features of their surroundings. The essential criterion of

prediction is to minimize the cost of being surprised [1]. Those

that fail to predict with sufficient accuracy or in a timely manner

often face lethal consequences. The keystone of prediction in evolutionary systems may be taken even more broadly as a requisite component of all intelligent systems: Intelligence may be

defined as the capability of a system to adapt its behavior to meet its goals in a range of environments [2]. By consequence,

intelligent behavior requires a composite ability to predict one's environment coupled with a translation of each prediction into a

suitable response in light of a given goal [3]. Without prediction, adaptation becomes impossible.

In nature, adaptation is accomplished through evolution, a twostep process of random variation and selection [4]. Individuals

compete for resources in a finite arena. Natural selection sto- chastically eliminates those individuals that do not acquire sufficient resources. The primary purposeful goal imbued into all

living system is therefore survival. The recognition of repeated

patterns in natural circumstance with appropriate reactions (i.e., allocation of available resources) leads to greater rates of surInductive

generalization

Deductive

specialization

Measured «.

Estimated ^Independent

real world real world ~*

verification

Figure 1. The scientific method. Unknown aspects of the

environment are estimated. Data are collected in the form

of previous observations or known results and combined

with newly acquired measurements. After the removal of

known erroneous data, a class of models of the environment that is consistent with the data is generalized. This

process is necessarily inductive. The class of models is then

generally reduced by parameterization, a deductive process.

The specific hypothesized model (or models) is then tested

for its ability to predict future aspects of the environment.

Models that prove worthy are extended, or combined to form

new hypotheses that carry on a "heredity of reasonableness"

[2]. This procedure is iterated until a sufficient level of credibility is achieved (from [2]).

233
These surroundings include other organisms, and thus communication between individuals can affect the likelihood of survival. Communication requires a language, a sequence of symbols transmitted between a sender and a receiver. The symbols

can be transmitted through any of the senses. Common symbols

in biota include threat postures, mating dances, grunts and

whistles (or other sounds), disagreeable taste, and so forth. It is of interest to speculate on the evolution of such descriptive symbols and sequences of symbols.

This paper offers some speculations on the evolution of symbols as observed in recent efforts in evolutionary computation.

The paper does not purport to provide a suitable literature re- view of efforts to explain the evolution of symbols in humans,

other primates, or indeed any other natural system. Readers interested in these areas are referred to [5,6] and others.

2. EVOLUTIONARY COMPUTATION,

SYMBOLS, AND COMMUNICATION

2.1 Background

Evolutionary computation concerns efforts to simulate evolution on a computer (or other device). Efforts in simulated evolution date back to the early 1950s and 1960s, with three main

lines of investigation proceeding currently: evolution strategies,

evolutionary programming, and genetic algorithms. For a re- view of these methods, see [2], [7]. Within evolutionary computation, there have been efforts made

to study the evolution of symbols and communication. Werner

and Dyer [8] used artificial neural networks to represent the behavior of artificial organisms in the context of finding mates.

"Females" were given the ability to see males and emit sounds.

"Males" were blind, but could hear signals from females. Over

successive generations, starting from randomly configured net- works, the simulation generated nets that exhibited an increasing effectiveness in mate finding, as well as the evolution of

dialects that promote the development of "subspecies." Levin

[9] used a genetic algorithm approach to study the evolution of

understanding between artificial agents having various "internal states" and "observable features." Fitness was increased for greater understanding of the internal states by other observed

agents. Figure 2 offers a flow chart of Levin's procedure.

Whereas [8] and [9] were designed specifically to examine

the evolution of symbols 1

, other evidence of the evolution of

symbols can be found by reexamining experiments in the iter- ated prisoner's dilemma [10].

2.2 The Iterated Prisoner's Dilemma and the

Evolution of Symbols

The prisoner's dilemma is an easily defined nonzero-sum, noncooperative game. The term nonzero-sum indicates that whatever benefits accrue to one player do not necessarily imply similar

Start )

Initialize a population of agents with random matrices on genomes

For each agent A,

interact with / others: B, - B,

Over G interactions,

V = a random vector of internal states V = V encoded by individual A

V" = V decoded by individual Bn

Fitness of A = average distance for each (V.V")

Pick the top S% of the population

as determined by fitness

Replace the remainder of the population with mutated forms of the top S%

Plot statistics such as convergence and fitness of top individual

Figure 2. Flowchart of procedure in [9] to evolve communication based on how well other agents understand the of- fered signals regarding internal states (from [9]).

penalties imposed on the other player. The term noncooperative

indicates that no preplay communication is permitted between

the players. Typically, two players are involved, each having

two alternative actions: cooperate or defect. Cooperation implies increasing the total gain of both players; defecting implies

increasing one's own reward at the expense of the other player.

The optimal policy for a player depends on the policy of the

opponent.

The general form of the game is offered in Figure 3. The game

is conducted over a series of trials. If information regarding prior

plays can affect the decision making in future plays, learning can take place and even though defection is the dominant move

in any single trial, cooperative behavior can evolve.

Following the seminal efforts of Axelrod [11], Fogel [10]

evolved finite state machines to play the iterated prisoner's di- lemma. The initial interest was to determine if population size

had any association with the speed at which a population evolved

mutually cooperative behavior. The results were essentially nega234
Player B

C D

c (Yi , Yi

(y>, y-x) \

Player A

D (Y3. Y2) (Y4. Y4 )

Figure 3. The general form of the payoff function in the prisoner's

dilemma, where Yj is the payoff to each player for mutual cooperation, Y2 is the payoff for cooperating when the other player

defects, y3

is the payoff for defecting when the other player cooperates, and Y4 is the payoff for mutual defection. An entry

(a,P) indicates the payoffs to the players A and B, respectively.

The constraints 2yj > y2 + Y3 and Y3 > Yi > Y4 > Y2

^

typical.

tive: population size did not appear strongly correlated with the

number of generations required to evolve cooperation. Population sizes of 50, 100, 250, 500, and 1000 parents were considered. In each case, across several trials (up to 30), cooperation

always evolved. Figure 4 depicts one evolved finite state machine from these experiments for a population size of 50.

It was of interest to compare the behavior that occurs when

finite state machines from independent trials play each other to

that observed when they play copies of themselves. Fogel [10]

(also see [2]) reported that when each finite state machine chosen from a trial at any population size played against itself, it always eventually cycled into mutual cooperation. But when it played against a machine selected from a different independently

evolved population, it was equally likely to cycle into alternating cooperation and defection (Figure 5).

It is speculative but reasonable to presume that each population of finite state machines evolved initial sequences of symbols that form patterns that can be recognized by other machines.

This allows for the identification of machines that will tend to respond to cooperation with cooperation. The specifics of such

sequences will vary by trial and may be as simple as merely

cooperating on the first move. But the specifics are generally

unimportant. When two machines from separate trials played

against each other, the resulting behavior could vary because no

pattern of initial symbols was recognized by either player. Thus

it would be improper to describe the machines as being "cooperative" or "noncooperative" as such descriptions require qualification with regard to the circumstances in which they were

evolved and the expected behavior of the other players. Each of

c.c/c

D.C/C

D,D/D

I—

- Start Stats C - Cooperate D • Delect

Figure 4. The best evolved finite state machine after 25 generations for a population size of 50 parents from [10]. If this machine were played against itself, it would eventually cycle into

state 1, and always cooperate (C).

the machines tested for the results presented in Figure 5 was

cooperative in its naturally evolved population.

3. EXPERIMENTS

Of potential interest is the manner in which symbols are invented

on-the-fly in light of competition from other extant individuals.

Two simple experiments have been conducted to initiate an in- vestigation into this process. An environment is sensed and en- coded by an individual into a binary string of some length. This

string is then sent to another individual that must decode the

string and recreate the sensed environment or predict the next

state of the environment. The quality of communication and

encoding/decoding is judged in terms of the correspondence

between the desired response of the receiver and the actual re- sponse. The binary encoding, however, is made evolvable in that the number of bits used to describe the environment is a parameter of the sender, and is subject to random variation.

More specifically, in the first trial, a population of 250 senderreceiver pairs was initialized. Each sender and corresponding

receiver took the form of partitioned neural networks, with the

sender using threshold functions for hidden units (Figure 6). The

sensed input was a sine wave sampled 100 times over a single

period. The task was to encode the sensed value of the sine wave,

have the receiver decode the value and recreate the sensed value

235
(a) 673321644164

FSM„ CCDCDCDCDCDC

FSM„ CCDDCDCDCDCD

171284115151

C D - ALTERNATING D C

(b)

FSM.

FSM..

6 7 3 3 1 1 C C D C C C

C C D C C C

6 7 3 3 11

— MUTUAL COOPERATION

1715171512841 151

FSM100 CCDCCCDCDDCDCDCD CD

-* ALTERNATING

FSM^ CCCCCCCDDCDCDCDC DC 33324242 11313131

1 7 1 2 3 2 2 FSM100 C C D D D C C

FSM100 C C D D D C C

1 7 1 2 3 2 2

MUTUAL COOPERATION

FSM,

FSM„

3 3 3 3 C C C C

C C C C

3 2 4 3

- MUTUAL COOPERATION

FSMt

FSM,.

3 3 C C

C C

3 3

-* MUTUAL COOPERATION

FSM„

FSM,

3 2 4 3 C C C C

C C C C

7 7 7 7

-* MUTUAL COOPERATION

Legend

C = Cooperate D = Defect The numbers above and below the move Indicate

the current state for the respective FSM.

FSM„

FSM„

3 2 4 3 C C C C

C C C C

3 2 4 3

— MUTUAL COOPERATION

FSM.

FSM,

7 7 c c

c c

7 7

— MUTUAL COOPERATION

Figure 5. The results of playing the iterated prisoner's dilemma (a) with independently evolved machines in which each machine

plays against a machine that was created in a separate trial with a different number of parents in the population and (b) when each

independently evolved best machine plays against itself. The subscripts indicate the population size. Mutual cooperation is always

observed when finite state machines (FSMs) play against themselves, but not when they play separately evolved machines.

% over the 100 samples. All senders were initialized to have a single

hidden node. This could be varied by mutation with a 0.25 probability of adding a node (up to a maximum of 10 nodes) and a 0.25 probability of deleting a node (again to a minimum of 1 node). All initial connections were initialized uniformly over

[-0.5,0.5] and were mutated using Gaussian perturbations with

mean zero and a variance equal to the mean squared error of the

sender-receiver pair divided by the number of degrees of free- dom in the pair. Each sender-receiver pair generated a single

offspring, which was evaluated, and then selection was imposed

to probabilistically retain the best 250 pairs in accordance with

competition rules in [2]. This process was iterated for 400 generations. Typical results are shown in Figure 7a. A second trial used two successive inputs from the sine wave (jc[M], x[t]) and

required the receiver to predict the next sample (x[M-l]). Typical

results are shown in Figure 7b.

A general pattern covers typical results in both experimental

designs. There is a gradual increase in the number of evolved

encoding nodes coupled with a gradual decrease in the mean

squared error. A greater number of encoding nodes provides

greater precision, however there is no immediate leap to the

maximum number of possible nodes ( 1 0 in this case, which could

have been invented as early as the 10th generation). The diffi- culty in establishing the correct encoding-decoding mix appears

to increase with the number of encoding nodes. Thus there is a

trade off between precision and accuracy, and the appropriate

symbolization evolves over successive generations.

4. CONCLUSIONS

Symbols evolve because they are useful. Evolutionary computation offers a tool to study the evolution of useful symbols in a

variety of contexts. Previous efforts have identified patterns in

the evolution of symbols both in sending messages from sender

to receiver, and in abstracting meaning from an environment in

light of a given goal. The preliminary results offered here show

236
ENCODING NODES

Figure 6. The sender network in the evolutionary experiments. The input is a sine wave with 100 samples per period. The connections from the input node to the encoding

nodes are weighted and can vary with Gaussian mutation

(zero mean). The encoding nodes multiply the connection

strength by the input value, subtract a bias term (implicit)

and pass the result through a hard limiting threshold function. If the value is greater than or equal to zero, a 1 is transmitted, otherwise a 0 is transmitted. The receiver, by definition, has a number of input nodes equal to the encoding

nodes of the sender and, in the first experiment, must essential perform the inverse operation to recreate the input value

of the sender. In the second experiment, the sender has two

sensors and encodes two successive values of a sine wave. The receiver must in turn predict the next value of the sine wave. The number of encoding nodes is simultaneously subject to mutation and selection along with the connection

strengths and bias terms.

6.55

u .65

v>5

"SS 3 -07

oz

.01

6.55E-4

-O- Best MSE —•— Mean # of Nodes

' (a)

1 1

1—Mill] 1 —

i—i—r i tit ]

1 1—i—r i

1

r—r~ 10 1 00

Generations

1000

8.76 i

(/> .88 i O- Best MSE

-•— Mean # of Nodes

1 00

Generations

1 000

Figure 7. The progression of the mean number of encoding

nodes (and thus the choice for symbolization) taken over all surviving sender-receiver pairs at each generation and the

best mean squared error that was obtained, (a) Typical results for encoding and decoding a value from a sine wave,

(b) Typical results for encoding and decoding the last two

samples of a sine wave in order to predict the next value.

Note that although the probability of adding nodes was equal

to 0.25 there was no immediate jump to the maximum number of 10 nodes. Simply adding nodes did not automatically

lead to improved performance because it requires simulta- neous evolution of the appropriate connection weights. Nevertheless, increased precision allowed for increased accuracy.

237
a first step toward describing the trade off between the degree of

precision offered by a particular set of symbols and the accuracy that can be obtained when a receiver must decode these

symbols into a meaningful response. If the results serve to promote further thought and experimentation in this direction then

they will have fulfilled the author's purpose.

5. ACKNOWLEDGMENTS

The author appreciates the comments and criticisms of V.W. Porto

and L.J. Fogel, and A. Meystel's encouragement to participate

in this conference.

6. FOOTNOTE

Related efforts in evolving symbolic strings representing sensed

environmental conditions can be found in [12, 13].

7. REFERENCES

[1] Atmar, J.W., "Speculation on the evolution of intelligence

and its possible realization in machine form," Doctoral dissertation, New Mexico State Univ., Las Cruces, NM.

[2] Fogel, D.B ., Evolutionary Computation: Toward a New Philosophy of Machine Intelligence, Piscataway, NJ: IEEE Press,

1995.

[3] Fogel, L.J., Owens, A.J., Walsh, M.J., Artificial Intelligence

Through Simulated Evolution, New York: John Wiley, 1966.

[4] Mayr, E., Toward a New Philosophy of Biology: Observations of an Evolutionist, Cambridge, MA: Belknap Press, 1988.

[5] Warhurst, J., "Nationalism and Republicanism in Australia —The evolution of institutions, citizenship and symbols," Australian J. of Pol. Sci., vol. 28, pp. 100-120, 1993.

[6] Hewes, G.W., "Primate communication and the gestural ori- gin of language," Curr. Anthrop., vol. 33, pp. 65-84, 1992.

[7] Back, T, Hammel, U., and Schwefel, H.-P, "Evolutionary

computation: comments on the history and current state," IEEE

Trans. Evolutionary Computation, vol. 1, no. 1, pp. 3-17, 1997.

[8] Werner, G.M. and Dyer, M.G., "Evolution of communication in artificial organisms," Artificial Life II, C.G. Langton, C.

Taylor, J.D. Farmer, and S. Rasmussen (Eds.), Reading, MA:

Addison-Wesley, pp. 659-687, 1991.

[9] Levin, M., "The evolution of understanding: a genetic algorithm model of the evolution of communication," BioSystems,

vol. 36, pp. 167-178, 1995.

[10] Fogel, D.B., "Evolving behaviors in the iterated prisoner's

dilemma," Evol. Comp., vol. 1, no. 1, pp. 77-97, 1993.

[11] Axelrod, R., "The evolution of strategies in the iterated

prisoner's dilemma," Genetic Algorithms and Simulated Annealing, L. Davis (Ed.), London: Pitman, pp. 32-41, 1987.

[12] Holland, J.H. and Reitman, J.S., "Cognitive Systems Based

on Adaptive Algorithms," Pattern-Directed Inference Systems,

D.A. Waterman and F. Hayes-Roth (eds.), Academic Press, NY,

pp. 313-329, 1978.

[13] Fogel, D.B., "An evolutionary approach to representation

design," Proc. SecondAnn. Conf. on Evolutionary Programming,

D.B. Fogel and W. Atmar (eds.), Evolutionary Programming

Society, La Jolla, CA,pp. 163-168, 1993.

238
The Evolution of Intelligence from the Semiotic Perspective

John R. Alexander, Jr.

Computer and Information Sciences Department

Towson State University

Towson, MD 21204

E7ClALE@TOE.TOWSON.EDU

ABSTRACT

In this paper, we speculate that from both a semiotic

perspective and from a perspective of intelligence as given

in Albus' Outline of a Theory of Intelligence [2], we may

cast some light upon the early stages of the evolution of

intelligence by a simple, biologically plausible, model of

neural control circuitry. This model implies that the

ability of neurons to act as controllers is an inherent

property of neurons and that this inherent control is a form of fuzzy control. In employing this model to solve a well-known benchmark control problem (the inverted

pendulum on a cart balancing problem), the learning

needed to set the few weights (and parameters) was

accomplished using a genetic algorithm.

KEYWORDS: artificial neural net, average

firing rate, evolution.

INTRODUCTION

"The brain uses stereotyped electrical signals to process all the information it receives and analyzes. The

signals are symbols that do not resemble in any way the

external world they represent, and it is therefore an

essential task to decode their significance." These words

begin Nicholls, Martin and Wallace's From Neuron to Brain. [12] With this quotation this author began a paper

which appeared in the 1996 NIST Conference Proceedings

- Intelligent Systems : A Semiotic Perspective [8]. This

paper is a continuation of last year's work and discusses

how very early neural signals (symbols) might be viewed

from a semiotic perspective. SECTION 2 defines and

discusses the signs, interpretants, and objects in a context

of early neural signaling. SECTION 3 contains a discussion of why these early signals must have contained

control information and how inherent properties of the

integrating mechanism of neurons effects control. In SECTION 4, we describe the progress made using circuits

consisting of two input neurons and one output neurons

(Three Neuron Controllers or TNCs). We combined two

TNCs each of whose output serves as input to yet a third

TNC (creating a Seven Neuron Controller - Figure 3) and

solved the Inverted Pendulum problem. Further, our Seven Neuron Controller net was trained using a genetic

algorithm. SECTION 5 contains a discussion of why

TNC control is analogous to fuzzy control. This

information is included for completeness and summarizes

the discussion given in last year's paper [8]. In SECTION

6, we reiterate earlier discussions [3] [4] (speculations) of

how elements of intelligence, as Albus describes them,

could have evolved. Further, we look at the sign,

interpretant, object triad, and show that it, too, admits a description couched in terms of the evolution of a simple

neural model. Section 7 summarizes this paper.

SECTION 2

An article in the March-April issue of the

American Scientist [9] (the Sigma Xi magazine) entitled

The Origin of Animal Body Plans discusses the

"Cambrian Explosion." Our speculation affords a

plausible commentary on this phenomenon, that is, the

rapid increase in the number and variety of animals on the

earth which occurred about 530 million years ago. This

commentary on the Cambrian Explosion will be given in

SECTION 7. To discuss the evolution of intelligence

from a semiotic perspective, we must consider the neural

activity of the earliest of animals possessing neural control

mechanisms. Thus, from the semiotic perspective, since

the stereotyped signals are virtually identical in all nerve

cells of the human body and also very similar in different

animals [12], we assume that the information in the signs

to be studied is contained in the frequency of firing of the

neural signals (action pulses), that the interpretant is simply the neuron that integrates the neural signals from

the impinging neurons, and that the object which caused

the sign to be generated is either an external event

reported to the organism by means of some sensory neural

circuitry or a signal that was generated by some internal

mechanism such as the output of a pacemaker neuron.

SECTION 3

Let us focus our attention on a very elementary

form of life, a coelenterate, the jellyfish. These creatures have no associative memories [13], yet they can swim and

attack prey. Thus, creatures exist with only control neural

circuitry and no associative memory neural circuitry.

Further, we see no biological advantage to a creature

239
possessing associative memory neural circuitry but no

control circuitry. Thus it seems plausible to conclude that

control neural circuitry evolved before associative memory

neural circuitry. Certainly one neuron signaling a second

is the simplest neural net of all possible nets (of more than one neuron) to envision. The sending neuron in a two- neuron circuit can control the receiving neuron by either

enhancing its firing rate (excitatory) or inhibiting it

(inhibitory). Cortical neurons, because of the random

firings of the massive number of neurons to which they

are connected, possess a non-zero average firing rate [1].

It seems unlikely, however, that sensory or motor neurons

of very early organisms did have a non-zero firing rate. It would appear that the ability of one neuron to inhibit the

firing of another must have evolved to inhibit self-firing

(pacemaker) neurons, or after the evolution of circuits

with two or more neurons. Inhibiting self-firing or pacemaker neurons gives rise to the ability to generate

rhythmic or cyclic firing patterns [10]. Rhythmic patterns are used to control the heartbeating and swimming of the

leech. The flow of oxygen carrying blood eliminates the

need for oxygen to diffuse through an animal's body.

Creatures that rely on diffusion of oxygen are of necessity

flat [9]. Adding a third neuron to a two neuron circuit

could be done by adding the third so as to place three in

line, or adding the third in parallel to the existent sending neuron so that the receiving neuron has two inputs.

Figure 1 A Three Neuron Controller (TNC)

This latter circuit is pictured in Figure 1. This circuit

allows control of two different input signals. This is the

property of neurons which we assert is both natural and

useful. We have successfully used such circuits as

controllers, and have named them Three-Neuron

Controllers (TNC)s. TNCs have been used to control the

height of water in a tank at constant set point under

conditions of random inflow [5] and to back a truck to a loading dock [6]. In the height of water in a tank and the

truck backing problem, two neurons represent the inputs

of these problems, while the third or output neuron

represents or codes the control signal. In Figure 1, we have assumed that the input neurons (ml and m2 name both the input neuron and the

value of its output) possess some average firing rate called

Aver The input signal that the two input neurons receive

(Observj) is on [MinJ5 MaxJ and is mapped onto [-1,1] by

the following formulas.

m

[Observj - Ave^

[Max. - Avej]

IfJ Observ > Ave

j j

(1)

m.=

j

[Observ -Ave]

Otherwise (2)

[Avej-Mirij]

We further assume that the weight connecting

the input neurons to the output neuron, wl 1 and wl2, are constrained to be on [-1,1] also. Thus, the input signals

which a(t), the output neuron, receives are on [-1,1].

Thus far, we have studied two sets of non-linear

differential equations which describe the flow of activation

in Figure 1 [7] [8]. Both sets of equations constrain the

output neuron a(t) to be on (0,1). The first set studied was

the author's dissertation equations and were called the RX

equations. Most recently we have worked with

McClelland and Rumelhart's iac (interactive activation

and competition and which we call the ENIAC Equations

for extended iac) [11] translated from difference to

differential equation form. Their solutions are given in

Equation 3 when the weighted sum of its inputs m, and m2

is greater than zero, and Equation 5 when this sum is below zero.

a(t) - a l-(l-IL_£l) «exp(-^,*(l-o)*f)

Where K, = — ^ > 0

' (1 " a)

a{t) _

- a-aQ ) l+( )*sxp(-K2 *a* t)

(3)

(4)

(w.,m, + w.^m, + d)

Wliere £, = —U—! JLJ. - < 0

240
Observe, in Equation 3 when t = 0, a(t) = a,,, and when t is

infinite, a(t) = 1. In Equation 4 at t = 0, a(t) is also =

and when t is infinite, a(t) = 0. The output neuron a(t) has

a resting value, a. We generate the actual control output

by subtracting from a(t) the resting value and then scaling

the result onto the range of possible control values. For

example in the truck backing problem, the steering wheel

is limited to plus or minus 15 degrees and the resting

value of a(t), a, was assumed to be 0.5. Thus:

Control Signal = (a(t) - 0.5) * 30 (5)

Note that when a(t) = 0, the control signal is -15 degrees,

and when a(t) = 1, the control signal is +15 degrees and

all values inbetween are attainable.

SECTION 4

Other problems solved by extending to three

TNCs are: to back a cab with a trailer (truck and trailer) to

a loading dock [7], and more recently (discussed below) to

control (keep balanced) an inverted pendulum positioned on a cart and subject to random forces which tend to unbalance it. Both the truck and trailer and the inverted

pendulum problems have more than two inputs. For more

information on the truck and trailer case, the reader is

referred to reference [7] In the Inverted Pendulum (IP)

problem, pictured in Figure 2, there are four inputs x, and

x, the position and velocity of the cart and 9 and G, the

angle of the pendulum with the vertical and the angular

velocity of the angle. The task is to keep the pendulum

upright, and the cart centered over x = 0 while the cart and pendulum are subject to random disturbing forces.

Control is via a motor on the cart. The control task is to

calculate the appropriate torque to the motor.

The architecture of the neural net used to solve the IP problem is displayed in Figure 3. This is the first problem

where we needed to train the weights. It seems apparent

that in the IP problem, the control of the pendulum

must be of higher precedence than control of the cart's x

position. The pendulum must not fall and hence, it must

be controlled first. Only when it is stable, does it become

possible to "walk" the cart back to the position x = 0.

We designed a genetic algorithm determine the

appropriate weights for the system. The only weight

changed was the one from the x associated TNC to the

final control node. The values of this weight generated by

the genetic algorithm was .13. This reflects the fact that it

is necessary to first control the pendulum.

Figure 2 The IP Problem

Figure 3 The Seven Neuron Controller

SECTION 5

We have compared all of our neural control answers to those generated by a fuzzy controller, with the

exception of the IP problem. The results produced by all controllers were very similar. It is easy to see the

mathematical reason for this. The first two of the

problems with which we worked have had monotone

control surfaces. By this we mean that if one of the inputs

is held fixed at any point on its domain of [-1,1], and the

other input value allowed to increase from its minimum

value of -1, up to its maximum value of +1, the control

surface will either increase (monotone increasing) or decrease (monotone decreasing) over the complete range

of input values. This is true of both inputs. But it is not

true for all possible problems. Our model accepts the

241
normalized inputs, uses them as constant parameters in

the function to be integrated, and integrates over time up

to a fixed upper limit of time (which happens to be

different for each model, RX or ENIAC). Different

functions are used as integrands depending on whether the

input parameters are negative or positive. However, in

each case the integral is also a monotone increasing or decreasing function of the inputs. That is, the greater the

positive input (up to its maximum of 1) the larger will be

the value of the integral (and hence control signal). The

larger in absolute value (closer to -1) the negative input,

the smaller will be the value of the integral. The smallest

value possible for the integral is zero. By Equation 5 above, when a(t) (the value of the integral) is zero, then

the control signal will be as large in the negative direction

as is possible.

Note that none of the solutions calculated are in

any way optimal. They are just solutions to a problem in a dense set of solutions. There are an infinite number of

ways the fuzzy membership functions can be selected;

also, one may chose from an infinite number of shapes for

each membership function. Further, a wide variety of

defuzzification procedures may be employed. What we

have observed is that each reasonable method of solution

that we have studied thus far has produced solutions "near" each other in the solution space; that is, they

successfully control the process. Figure 4 shows why the

fuzzy solutions are closely approximated by the neural

techniques. For each fuzzy rule, there is a corresponding

integral which, because of the monotonicity of the control

surface, gives a similar result for a control value, as does

the fuzzy rule that it emulates. The inputs to the integrals are crisp, as are the integrals upper limit. How can we

claim that the process represents a fuzzy form of control?

This claim is made in recognition of the infinite number

of functions that could be used as integrand and give

similar answers. Also, slight variation in the upper limit

of the integral would effect the solutions very little. Thus, our fuzziness is in function space.

SECTION 6

Figure 5 displays what Albus [2] called an Element of Intelligence. In recent articles [3] [4], the

author suggested that Albus' model [2] admits an

evolutionary explanation as follows. The sensors and

actuators evolved first. These correspond to simple

sensory neurons directly connected to motor neurons. Note that these circuits at first involve no memory. As the

evolutionary process continued, refined sensory processing

and behavior generation abilities, which involved

memory, would mean greater success from a biological

standpoint to the organism possessing them. The

functions performed by the World Models and Value

Judgement elements could further enhance survival of the

possessing organism. The referenced articles [3] [4]

further suggested that the initial components, the sensors and actuators, could be emulated by a TNC, with the input neurons playing the role of the sensors, and the output neuron the role of the actuator. We suggest that this model appears logical from

the semiotic perspective also. As stated in SECTION 2, the sign of the semiotic triad is represented by the

frequency of firing of input neurons. Initially the

interpretant is simply a neuron that integrates the inputs

of its impinging neurons. In order not to distort its message, the object of the triad, existing perhaps in the

external world or perhaps internally as a self-generating

neuron, should map, in a linear fashion, the degree to which the object is to be considered by the interpretant.

From a practical standpoint, pressure sensitive neurons are

linear over a wide range of inputs [10]. That is, the

frequency of firing of the sensory neurons in the skin

which measure pressure applied, may be represented as a constant times the pressure applied. Non-linearities are introduced by the integration accomplished by the

interpretant. From a biological standpoint, this sequence

appears plausible. The sign is a direct measure (i.e.

directly proportional) to the magnitude of the object. The

interpretant may apply a gain (introduced by the nonlinearity) to the sign representing the object as best suits

the survival of the using organism. The reader should

keep in mind that the system being discussed contains no memory.

1 IF X -

2 IF X -

3 IT it -

4 IF X -

5 IF X -

« IF X -

7 IF X -

• IF X -

I IP I

10 IF X - 11 IF X -

12 IF X -

13 IF x -

14 IF X -

15 IF X •

16 IF X -

17 IF X -

18 IF X -

19 IF X - 20 IF X - 21 IF X « 22 IF X - 23 IF x

24 IF X

25 IF X • 26 IF X ' 27 IF X

26 IF X

29 IF X

30 IF X

31 IF X

32 IF X

33 IF X

34 IF x

35 IF X

LZ AND « -

LC AMD * -

CZ AMD « -

RC AND • -

III and * - IX AMD * - LC AND * -

CT5 AMD * -

JtC ADD « - RI AND * -

LZ AND « - LC AND » - CK AND -

• RC AND * -

> RI AND « -

• LZ AND * - LC AND •

• CE AND * -

• RC AND * «

- RZ AND * - - LB AND

- LC AND

- CE AND * • - RC AND « • - RI AND * • - LZ AND * - LC AND

- CE AND ' - RC AND « ' - RI AND # - LB AND

• LC AND » - CZ AND * - RC AND *

- RI AND #

i- <e

Figure 4 Neural and Fuzzy Rules

242
SECTION 7

Viewed as the evolutionary beginnings of one of

Albus' elements of intelligence, or from a semiotic

standpoint, or simply from the standpoint of how

intelligence might have evolved, this model seems

relevant. Neurons do integrate their inputs, and we have

shown that for a large class of problems, and for two

different functions, that this integration can yield useful

results. Since neural circuitry evolved in the Cambrian

Period it does not therefore, seem unreasonable to the

author, to assume that this property of neurons increased

the survivability of those organisms possessing neurons to

the extent that this property of neurons might have

contributed to the Cambrian Explosion.

This paper is highly speculative. Speculation

must be constrained in two ways as stated by Smith and

Szathmary [14]. "First each event must be explained in a way that is consistent with the general theory of

evolutionary change, the theory of natural selection.

Second, an adequate account of the origin of any system

must explain the peculiarities of the system as it exists

today..."

The examples ofjellyfish has led us to believe that control

neural circuitry existed before associative memory neural

circuitry. In the interest of enhancing our understanding

and use of ANNs as associative memories, it would appear

that a serious effort should be undertaken to understand

how memory abilities evolved from control abilities.

Figure 5 Albus' Elements of Intelligence

REFERENCES

[I] Abies, M. (1982) Local Cortical Circuits SpringerVerlag New York NY.

[2] Albus, James (1991) Outline of a Theory of

Intelligence IEEE Transactions on Systems. Man and

Cybernetics May/June 1991.

[3] Alexander, J. (1992) An Artificial Neural Net

Employing Probability Data as Weights and Parameters

1992 IEEE Systems. Man and Cvbernitics Conference

Proceedings.

[4] Alexander, J. (1994) Continued Speculation of the

Evolution of Learning, 1996 IEEE Systems. Man and

Cvbernitics Conference Proceedings.

[5] Alexander, J. (1994) Calculating the Centroid of a Fuzzy Logic Controller Using an Artificial Neural Net,

Intelligent Engineering Systems Through Artificial Neural

Networks 4, ASME Press, New York, NY.

[6] Alexander, J. and Bradley, J. (1995) The Three

Neuron Controller - History, Theoretical Foundations, and

Possible Employment in Addapitve Control, Intelligent

Engineering Systems Through Artificial Neural Networks

5, ASME Press, New York, NY.

[7] Alexander, J. and Cox, J. (1996) Backing Up a Truck

and Trailer Using Sets of Three-Neuron Controllers,

Intelligent Engineering Systems Through Artificial Neural

Networks 6, ASME Press, New York, NY.

[8] Alexander, J. (1996) Biological Suggestions for

Alternative Design of Artificial Neural Networks (ANNS).

Proceedings of the National Institute of Standards and

Technology 1996 International Multidisciplinary

Conference Intelligent Systems. A Semiotic Perspective

Volume II. Gaithersburg MD.

[9] Erwin, D., Valentine, J. and Jablonski, D. (1997) The

Origin of Animal Body Parts. American Scientist MarchApril (vol. 85) Sigma Xi Press Research Triangle Park,

NC.

[10] Muller, K., Nicholls, J. Stent, G. (1981) Neural

Circuits Generating Rhythmic Movements in

Neurobiology of the Leech Cold Spring Harbour, NY.

[II] McClelland, J. and Rumelhart, D. (1988)

Explorations in Parallel Distributed Processing A

Handbook of Models. Programs and Exercises MIT Press,

Cambridge, Mass.

[12] Nicholls, Martin and Wallace (1992) From Neuron to Brain Sinauer Associates, Inc. Sunderland, MA. USA.

[13] Olds, James 1994 Private Conversations.

[14] Smith, J. and Szathmary, E. (1995) The Maior

Transitions in Evolution W.H. Freeman Spektrum, New

York NY.

243
On Hardware Evolvability and Levels of Granularity

Adrian Stoica

Center for Integrated Space Microelectronics

Jet Propulsion Laboratory, California Institute of Technology

Pasadena, CA, 91109

ABSTRACT

Evolvable hardware addresses hardware that self-organizes/

reconfigures under the guidance of evolutionary mechanisms.

Some experiments in evolving at transistor level are briefly

presented and the perspective of transistors as functional

approximators is suggested. In a broader context one analyses

approaches to evolvable hardware specifying the level of

granularity at which evolution will operate, in accordance with the

level of design abstractions in the modeling hierarchy: primitive,

functional and behavioral levels in simulated circuits, and

transistor, subcircuit and high level function in hardware.

Comments are made linking the role of Automatically Defined

Functions in hardware evolution, the process of achieving

higher/coarser levels of granularity in the semiotic perspective, and

the evolution of modularity of organismic designs. Finally, it is suggested testing the effect of changing levels of granularity during

hardware evolution.

KEYWORDS: evolvable hardware, granularity, evolvability

1. EVOLVABLE HARDWARE

Evolution appears to be nature's solution to design.

Being able to replicate such a capability in an artificial system would offer tremendous insights into ourselves and

a powerful tool for building adaptive, intelligent systems.

From the perspective of space exploration, empowering

spacecraft with adaptive, intelligent capabilities is invaluable for autonomy. Adaptive features are needed to cope with the uncertainty of spacecraft remote operating

conditions, performing totally unexpected functions, and for

fault-tolerance. The on-board computer needs to be able to solve problems for which solutions were not specified on

ground, and command the spacecraft to adapt to new

situations. For adaptive, versatile spacecraft, electronic

hardware must posses the capability to reconfigure, or moreover, to self-reconfigure, as needed.

Evolvable hardware (EHW) is adaptive hardware that

reconfigures under the control of an evolutionary algorithm

[1]. Extrinsic EHW refers to evolution in a software

simulation using models of the hardware behavior,

downloading the configuration of the best evolved

architecture to programmable hardware. In intrinsic

hardware (to which most of the following discussion

applies) configuration bits are iteratively downloaded to

hardware, evaluating a degree of adaptation/fitness by

observing the behavior of the real hardware.

Hardware evolution is performed through a succession of

changes of elementary cell functions and cell inter- connectivity pattern, thus obtaining increasingly more fit configurations until a target functionality is reached. As it is the case in nature, evolution results in individuals that are increasingly more adapted to their environments, and can change themselves to match changes in environments and

modifications of their own goals. Unlike in nature,

evolution in silicon has the advantage that could be

extremely rapid, with millions of generations of "living"

circuits evaluated in only a few seconds.

Hardware evolution can be seen as an on-chip search for

the circuit/configuration whose behavior is closest to the

required one (e.g. gives best performance/adaptation to the

environment). The suitability for a parallel hardware

implementation of evolvable hardware, with multiple

"islands" of concurrently evolving circuits on the same chip, or in a multi-chip or stacked configuration is very attractive.

Evolvable hardware: a fully parralel process

Genetic creation of a nesv opularion ofchroraoioine-i

Reproduction of individuals with high FIT

r

a

is

o

Circuits 1 to n

Fig. 1 . Parallel implementation for evolvable hardware

The granularity of hardware building blocks for those

attempting intrinsic evolvable hardware is currently

influenced by the availability of certain programmable

devices. The paper presents results of simulated evolution at

transistor level and discusses on the role of the level of

granularity and evolvability.

244
2. EXPERIMENTS IN EVOLVING CMOS

CIRCUITS AT TRANSISTOR LEVEL

Successful evolution has been reported in simulations

(analog [2], [3] and digital [4] ) and in real hardware [5]

[6]. In the intrinsic EHW perspective, the focus has been on using commercially available FPGAs (Field

Programmable Gate Arrays) but custom designs of chips

using higher-level functional blocks are also reported [6].

A collection of papers dedicated to the subject is [18]. In here the distinct focus of attention is on issues related

to designing the reconfigurable part of an evolvable

CMOS chip. The choice is motivated by the fact that

CMOS technology is the basis of today's microelectronics

industry, and NMOS/PMOS transistors are the elementary

components of both analog and digital designs.

One can look at MOS transistors from the perspective of

function approximators. Function approximation has

recently been approached with computational intelligence

techniques, demonstrating general approximation

capabilities for structures of neural networks [7] [8] and

fuzzy systems [9] [10]. As hardware implementations

ultimately rely on silicon, a general functional

approximator (FA) implemented in hardware will

ultimately be relying on (e.g.) MOS transistors.

A set of experiments was performed to investigate

evolution-related issues at transistor and simple sub-circuit

level. The objective was to evolve a circuit that provided

a bell-shaped response when the input increased linearly.

This response can be obtained for example with the circuit

in Fig. 2, with one input kept at constant voltage and the

other increasing linearly. The evolution was performed on

simulated circuits (using SPICE). Constraints were

imposed on the mechanism generating the circuits such

that all the circuits produced were SPICE simulatable (this

differs than Koza's experiments where non-simulatable

circuits are eliminated by evolution (e..g in [11]). A

limitation existed also on the number of circuits evaluated,

which was much smaller than those reported by Koza

(~104 compared to~107)

.

Gaussian function circuit

Vinl Vin2

Fig. 2 A circuit producing a bell-shaped response

In the first set of experiments the circuit topology was considered known, and evolution concerned two types

of parameters: transistor channel Width and Length.

These parameter domains are discrete (they are a multiple

of the feature size), and for this case a total of 8 possible

widths and 8 lengths was considered. This led to a (3+3)* 8=48 bit coding for the circuit. Applying a Genetic

Algorithm on a population of 50 individuals, converged

easily to good solutions (an illustration of the population

after about 200 generations is given in Fig. 3. This is explained by the fact that, although the region searched is small (~2 10 in the search space of 2

48 possible

combinations), many combinations are good; in this case

the topology is the fundamental factor in circuit behavior.

A^AAAAA AyvAAAAA A^vAAaAa

A A a A A A A aAAaAaA

Fig. 3 Response of a population of 49 circuits after 200

generations

The problem becomes complicated when one tries to evolve the topology. Several alternatives were tried,

briefly described in the following:

- A 2D transistor array was considered, which resembled

an existing FPGA model (Xilinx 6216). The code for each

cell specified the type of the cell which could be a

transistor with a certain orientation, or a type of wire

routing (these are illustrated in Fig. 4). A 2D chromosome

was associated to the array. Only evolution by GA was

attempted. The problem appears in specifying 2D

crossover, determining which 2D zones should be

swapped. Crossover must consider the fact that the new

circuits must match their connections at cell borders.

Fig. 4 A transistor array patterned after an FPGA

- A leveled architecture (with a matrix arrangement as in Fig. 2) where components on a given level were from a

list of allowed components (see Fig. 5). Components

were low-level subcircuits (current mirror, differential

245
pair, pair of transistors). The coding was such that the

possible connections were limited to those that made

sense (e.g. the Source terminal of transistor in level 4

could not connect to VDD).

.ST .

Level 1 mmm&m

ST Separated Transistors CM Current Mirror DP Differential pair

Level 3

Level 4 CM

Fig. 5 Components allowed at different levels

The experiments can be interpreted as follows:

• When the topology of the electronic circuit is given,

the transistor parameters (in this case PMOS/NMOS

channel Width and Length) can be easily obtained

through evolution.

• If one attempts evolution in a space restricted at the

size of the human-designed solution (in our case when

the circuits were limited at 8 transistors) it was not

possible to evolve a circuit from specifications. The

methods attempted included genetic algorithms, and a search based on orthogonal arrays. With the

representation used, the search space appears very

much as a flat region, with a singular spike for the

solution circuit. Its neighbors, with genetic code

differing even one bit from the solution had extremely

low fitness; i.e. changing even one connection

between 2 transistors had a dramatic effect in circuit

behavior. This is possibly a consequence of the search

around the optimal size (minimal number of

transistors) solution. If the circuit would have

contained redundant circuitry changes in those regions

would have produce less significant effects.

It was however possible to evolve the topology using

genetic programming and an embrionic, growth-based

approach, in which the number of components (size of

the circuit) was not restricted (results obtained by Koza's

group, not published yet). The first set of simulations led

to a circuit with 36 transistors.

Evolving on a structure with fixed, minimal number

of transistors for the function (for which a solution

circuit is already known) suffers from the fact that any

mutation involving a connection/topology change leads

to a dramatically different response. One possible way in

which this can be alleviated is to allow gradual

connections (e.g. connections modeled by resistors in [0

100G]) during the evolution. Thus may be architecture

which allows gradual transitions between topologies are

possible. It could look like a densely-connected "sea of

transistors" in which components are connected by a "fuzzy" wire (i.e. with values in [0,1] rather than {0,1}),

appearing much like a neural network, but with transistor

instead of neurons. The graded connection would have a

catalyst role during evolution; it smoothens the search

space around the solutions (in this respect neural

architectures using gradual connections/weights appear

suitable for evolution).

3. HARDWARE LEVELS

GRANULARITY AND EVOLUTION

OF

A fundamental question is how does the choice of a level of design abstraction influence hardware "evolvability"?

(The search/optimization algorithm may be not that important: the "no free lunch" theorems establish that for

any algorithm, any elevated performance over one class of

problems is offset by performance over another class [12].)

When evolution takes place directly in the component space

the choice of the primitive building blocks affects the

evolvability (e.g. evolving a NN appears easier than

evolving a circuit with transistors).

The choices for the level at which evolution process

could operate are as follows.

For evolving simulated circuits. The levels of design

abstraction in the modeling hierarchy are [13]:

• Primitive Devices (Transistor level - MOS,BJT,etc)

represented by analytical equations or tables

• Functional Macromodels (e.g. Op. Amp. Level)

derived by circuit simplification, circuit build-up,

symbolic methods

• Behavioral High level language descriptions -

linear and nonlinear mathematical equations, tables,

etc. Evolution can be made at a certain level and then the

design converted for hardware implementation with

appropriate compilers and synthesis tools. For evolving directly in hardware. A similar

selection of level of primitives is available in a reconfigurable structure (specifying what should be the

"building blocks"):

• Transistor level . Some simulations were discussed

in the previous section.

• Subcircuit level. This is the Op. Amp./digital

gates level. Succesful hardware evolution taking

place on an FPGA chip was reported by Thompson

[5]. Versatile FPAA (Field Programmable Analog

Arrays) are still missing, but are expected to appear on the market within 2-3 years.

246
• High level/ functional level One way of coping with

difficulties in evolving circuits is to provide high

level building blocks, filters, modulators in the

analog domain, or adders, MUXs in the digital ones. This approach is followed by Higuchi [6 ].

The idea of modularity, and changing granularity during

evolution may be key to hardware to evolvability (in

intelligent systems, knowing presumes changing resolution

or granularity [14]). In the biological world modularity is most likely the result of evolutionary modifications [15]. In

the evolvable hardware context, Koza has indicated the

usefulness of Automatically Defined Function (ADF) for

evolving analog electronic circuits (an ADF is "a function

(subroutine, module, etc.) that is dynamically evolved

during a run of genetic programming and that may be called

by a program that is concurrently being evolved") [16]. In

effect the idea that no approach to automated programming

(and consequently hardware evolution) is likely to be

successful on non-trivial problems unless it provides "some

hierarchical mechanism to exploit, by reuse and

parametrization, the regularities, symmetries, homogeneities,

similarities, patterns, and modularities inherent in problem

environments" is central to Koza's book [17].

When choosing representation levels, it may be

interesting to consider having simultaneous representations

at different levels of granularity. During evolution one may

switch between levels of granularity depending which one

offers advantages at that time.

4. CONCLUSION

The paper presented simulation results and discussed

issues of evolution at transistor level. While parametric

evolution appears easy, topological evolution is hard.

Different levels of granularity are available for evolvable

hardware. It was suggested that changing/switching levels of

granularity during evolution may help.

5. REFERENCES

[1] De Garis, H. "Evolvable Hardware: Genetic Programming of a Darwin Machine". In Proc. Of the Int. Conf. On Artificial Neural

Networks and Genetic Algorithms, Innsbruck, Austria, Springer

Verlag, 1993

[2] Grimbley, J. B. Automatic Analogue Network Synthesis using

Genetic Algorithms, 1 st IEE/IEEE Conf: Genetic Algorithms in Engineering Systems, UK, 1995

[3] Koza, J., Bennett III, F. H, Lohn J., Dunlap, F., Keane M. A., and Andre, D. "Automated Synthesis of Computational Circuits

Using Genetic Programming". In Proc. of Second Annual Genetic

Programming Conference, Stanford July 13-16, 1997 (to appear)

[4] Hemmi, H, Hikage, T. and Shimohara, K. AdAM: A Hardware

Evolutionary System , In Proc. oflCEC, (193-196), 1997

[5] Thompson, A., Silicon Evolution. In Proc. of First Annual

Genetic Programming Conference, Stanford, 1996

[6] Higuchi, T., Murakawa, M., Iwata, M, Kajitani, I., Liu, W. and

Salami, M. , "Evolvable Hardware at Function Level." In Proc. of

ICEC, (187-192), 1997

[7] Cybenko, G. Approximation by Superpositions of a Sigmoidal

Function. Mathematics of Control, Signals, and Systems, 2 (303-

314), 1989

[8 ] Hornik, K., Stinchombe, M, and White, H. Multilayer

Feedforward Networks are Universal Approximators. Neural

Networks,! (359-366), 1995

[ 9] Kosko, B. Fuzzy Systems as Universal Approximators. In Proc. of the I st IEEE Conference on Fuzzy Systems, (1 153-1 162),

1992

[10] Wang, L. X. Fuzzy Systems are Universal Approximators. In Proc. of the I st IEEE Conference on Fuzzy Systems, (1 163-1 170),

1992

[11] Koza, J., Bennett III, F.H., Andre, D. and Keane, M.,

Automated WYWIWYG Design of Both the Topology and

Component values of Electrical Circuits Using Genetic

Programming, In Proc. of First Annual Genetic Programming

Conference, Stanford, (123-131), 1996

[12] Wolpert, D. H. and Macready, W. G., "No Free Lunch

Theorems for Optimization", IEEE Transactions on Evolutionary

Computation, Vol. l.No. 1, (67-82), 1997

[13] Mantooth, H. A. and Fiegenbaum, M., Modeling with an Analog Hardware Description Language. Kluwer Acedemic

Publishers, 1995

[14] Meystel, A. "What is 'semiotics 'after all? (Learning how to know: semiotics and multiscale cybernetics)". Semiotcs97

Internet at http://isd.cme.nist.gov/ proj/semiotics/isas97.html

[15] Wagner, G. P. and Altenberg, L., "Perspective: Complex

Adaptation and the Evolution of Evolvability". In Evolution, 50(3),

(967-976), 1996

[16] Koza, J., Andre, D., Bennett III, F. H., and Keane, M. A., Use of Automatically Defined Functions and Architecture-Altering

Operations in Automated Circuit Synthesis with Genetic

Programming. In Proc. of First Annual Genetic Programming

Conference, Stanford, (132-141), 1996

[17] Koza, J. R. Genetic Programming II: Automatic Discovery of

Reusable Programs. Cambridge, MA: MIT Press, 1994

[18] Sanchez, E. and Tomassini, M. (Eds), Towards Evolvable

Hardware - The Evolutionary Engineering Approach. Springer,

1996.

247
Evolution of Learning

The Merging of Semiotic and Evolutionary-System Theories

Wolfgang Hofkirchner

Social Cybernetics Group

Institute of Design and Technology Assessment

Vienna University of Technology

Mollwaldplatz 5

A-1040Wien

phone/fax **43 1 504 11 86 33

hofi@igw.tuwien.ac.at

Abstract

This paper deals with rather basic implications of theorizing

systems which are able to learn. Starting from the fact that a

unified theory of information is still missing it tries to sketch

roughly a conceptualization that merges the concept of

semiosis and the concept of evolutionary systems. This shall provide a framework for future research into every kind of

information processing systems, including socio-technical

systems.

KEYWORDS: Unified Theory of Information, semiosis,

evolutionary systems

I. The Quest for a Unified Theory of

Information

The Second Conference on the Foundations of Information

Science (FIS 96) taught us that we are still lacking a Unified

Theory of Information (UTI) which comprises the variety of

manifestations of information processing in natural, in social,

and in artificial systems. It showed at the same time that the UTI we are looking for may be well based upon a theory of

evolutionary systems, that is open systems which are capable

of self-organization [1]. This theory, however, is to be

elaborated, too.

With the transition from System Theory I to System Theory

II, as with the change from Cybernetics I to Cybernetics II and the increased scope of the Theory of Evolution, we can

see a theory of open, non-linear, complex, dynamic, self- organizing (in short: evolutionary) systems approaching. This

theory no longer deals merely with mechanisms, strategies

and controls for achieving/maintaining homeostasis and the development of species; it also concerns the birth, growth and

decline (i.e. development) of all systems, from the formation

of the earliest known particle, through the arrival of terrestrial

life forms, to the shaping of specific human socio-technical

systems (see e.g. [2], [3], [4])

.

As this theory of self-organization will conceive both system

and evolutionary aspects, that is both structural and process

aspects, I want to argue here that it offers the possibility of

serving as the appropriate background theory for unifying

information concepts and thus for understanding and designing

intelligent and reasonable information processing systems [5].

In order to interlink informational and evolutionary-systems

concepts they have to undergo some refashioning which will be described below (for preliminary work we have already

done see [6], [7], [8]). Firstly, three levels of a system shall be distinguished. Secondly, the well-known semiotic aspects

will have to be rearranged. Each of these will then be related

to a certain system level. The next step is to point out that

this fundamental structure of any information process shows

various kinds of manifestations according to the evolutionary

level the system belongs to. Three basic stages shall be

identified. Finally, a stage model describes the symmetry

breaking sign process.

2. The Merger of the Concepts of Systems

and Semiosis

2.1. Identifying Three System Levels

In identifying a system, three different levels of the system's

dynamics can be distinguished:

1. The level on which the elements of the system in question

are interconnected. This is the level of the internal structure of

the system (micro-level).

248
Output

2. The level on which the system itself is in one state or in another (meso-level).

3. The level on which the system exhibits its external behavior vis-a-vis its environment. The way the system

interacts with its co-systems in the net is examined here

(macro-level).

Each level is the base on which the next level is built; each

level has progressively less space for possibilities than the one below. From one level to the next there is a leap of

qualitative difference. This leap can (but need not) be bridged

by a self-organization cycle. Thus these levels give the

prerequisites for understanding the emergence of new system

structures, system states, or system behavior, or even the emergence of new systems.

2.2. Refashioning Semiotic Dimensions

According to semiotics, information can be conceived as something having syntactical, semantical and pragmatic

aspects. It seems sensible to interrelate these dimensions not

in the way semiotics did sometimes, but rather as a nested hierarchy such that:

1. the innermost dimension is the syntactical one;

2. the intermediate dimension is the semantical one;

3. the outermost dimension is the pragmatical one.

This means that they are not merely placed side by side,

without having anything to do with each other; each initial aspect is essential for the following one, and each following

aspect is a sufficient condition for the preceding one.

ehoviour

PRAGMATICS

SEMANTICS

SYNTACTICS

Figure 1. System Levels and Semiotic Dimensions in Information-Processing Systems.

The three semiotic aspects thus relate to one another in the same way that the system levels relate to each other.

Together they mark the varying qualities of information. That

is to say, in any particular system, information occurs when

as a result of a self-organization process there is a qualitative

change on any one of the three levels. The underlying

information process may result in structural changes to the

interior of a system (on the micro-level), it may result in changes to the actual state of the system (on the meso-level), or it may result in altered external behavior (on the macrolevel). We must note that changes in the interior structure need not lead to changes in the system's state, and that changed states need not necessarily entail changes in the behavior. But a difference in the output of a system must be

based upon a different state, and a different state must take as

a basis elements and relations that differ from previous

structures.

In this way they form an architecture which allows for emergent properties [9].

2.3. Assigning the Semiotic Dimensions to the

System Levels

Having done this, the system and semiotic aspects can easily

be linked to one another. Each of the three semiotic aspects can be related to an appropriate system level, as follows (see

Fig. 1):

1 . syntactics refers to the micro-level;

2. semantics refers to the meso-level;

3. pragmatics refers to the macro-level of a system.

3. Three Stages in the Evolution of

Information-processing Systems

3.1. Reflecting as the Most Primitive Form of

Semiosis

If open systems are exposed to fields in which the gradient of

the free energy density distribution exceeds a certain amount,

they exhibit the capability of organzing themselves in that they build up order, that is make use of energy for performing

work, depreciate it and remove the resulting entropy (so-called

dissipative systems). Pattern formation is thus the most

rudimentary form not only of self-organization, but also of

sign processes (see Fig. 2). The system selects a particular

option from the various structuring possibilities it has. The

selection ends up in a new structure. The information process

249
is the process of restructuring and its result is a structure which differs from the structure the system had previously.

There is a relation between the different structures which can be looked upon as the most primitive appearance of the

syntactical dimension of information. The way the system

restructures itself is the self-determined way it reflects outer conditions in its environment (cf. [10], [11]).

Figure 2. Pattern Formation in Primitive Self-organizing

Systems.

3.2. Building Representations as a Higher Form of

Semiosis

Reflection is the precondition for learning to behave in such a way that this makes the environment produce conditions

beneficial to the maintenance and improvement of the system.

Simple dissipative systems are, however, not in a position to perpetuate the flow of energy.

Biotic systems are a special category of dissipative systems

which are able to perform in this way. They exhibit division

into a sensorium and an effectorium, which involves two

cycles of self-organization, one on the top of the other. Structural change splits into structural and state/behavior

change. The self-organized structure, that emerges within the system, obtains a new function: it becomes a symbol which

has a meaning, namely that the change in the outer world of

the living system it represents is behaviorally relevant to the survival of the System (see [12]; see Fig. 3).

FUNCTIC NAUZINp OF [STRUCTURES

::::::: i/f^lV: :::::::: gggnmg

31

RESTRUCTURING

^symtol

Figure 3. The Differentiation of Meanings and Symbols in Self-organizing Systems.

The syntactical dimension of the difference between the old and the new structures is supplemented by the fact that this difference makes a difference regarding the goal of maintaining

the system. So a semantical-pragmatical dimension is added.

Thus representation is another step in the evolution of

semiosis. Due to the presence of this new informational

relation biotic systems show better adaptability to their environment. They are in a position to take advantage of the environment to such an extent that they can reproduce

themselves. This behavior is referred to as intelligent

behavior (see e.g. [13]).

3.3. Decision-making as Most Advanced Form of

Semiosis

Certainly social systems which involve human cognition and

communication are the most highly developed appearance of

information processing which is known to us at present.

They exhibit even greater adaptability than mere biotic systems: they alter their environment to suit themselves.

That is to say, their sphere of influence is characterized by a feedback loop, through which the systems can create the conditions necessary not only for their reproduction, but also

for creating themselves according to the goals they freely

choose. The behavioral decisions are no longer

indistinguishable from the representations, but now are conveyed with the knowledge via another phase transition as knowledge is mediated with data (see Fig. 4). The process of

information includes the activies of perceiving, interpreting,

and evaluating, and shows separated dimensions of semantics

and pragmatics. Knowledge makes a difference as to wisdom,

that is reasoned instruction of acting which then deserves to be called reasonable behavior of a system. —"Wisdom

[ knowledge i

Figure 4. The Differentiation of Wisdom, Knowledge and Data

in Advanced Self-organizing Systems.

250
4. A Symmetry-breaking Evolution of

Semiosis

Summing up, a stage model can be postulated in which a process of symmetry breaking unfolds from a stage which is characterized by simple reflective, self-organizing systems via

a stage of systems which produce representations toward a

stage on which decision-making systems produce perceptions,

interpretations and evaluations (see Fig. 5).

real world

mechanical semiotic

semantical pragmatical

Figure 5. The Unfolding of Semiotic Aspects in the Course of

the Evolution of Self-organizing Systems.

Thus a stage model of information merges the system aspects

and the evolutionary aspects of semiosis.

In each phase of evolution a new moment appears which

becomes characteristic of a layer for more highly developed

systems and gives the entire layering of this system its

nature.

This model may serve methodologically as a framework for theorizing information processes in all kinds of real-world systems and foPthe elaboration of a UTI. It may assist as well the design of artificial systems which aid human

cognition and communication processes.

[3] Goerner, S. J., Chaos and the Evolving Ecological

Universe. Amsterdam: Gordon and Breach, 1994.

[4] Mainzer, K., Thinking in Complexity. The Complex

dynamics of Matter, Mind, and Mankind. Berlin: Springer,

1994.

[5] Haefner, K. (ed.), Evolution of Information Processing

Systems. Berlin: Springer, 1992.

[6] Fleissner, P., Hofkirchner, W.: "Emergent Information.

Towards a Unified Information Theory", BioSystems, vol.

38, pp. 243-248, 1996.

[7] Fenzl, N., Fleissner, P., Hofkirchner, W., Jahn, R.,

Stockinger, G., "On the Genesis of Information Structures. A

View that is neither Reductionist nor Holistic" in Kornwachs,

K., Jacoby, K. (Ed.), Information, New Questions to a Multidisciplinary Concept. Berlin: Akademie Verlag, pp. 271-283, 1996.

[8] Fenzl, N., Hofkirchner, W.: "Information Processing in Evolutionary Systems. An Outline Conceptual Framework

for a Unified Information Theory" in Schweitzer, F. (Ed.),

Self-Organization of Complex Structures - From Individual

to Collective Dynamics. London: Gordon and Breach, 1997.

[9] Blitz, D., Emergent evolution - qualitative novelty and the

levels of reality. Dordrecht: Kluwer, 1992.

[10] Haken, H., Information and Self-Organization. Berlin: Springer, 1988.

[11] Atmanspacher, H., Kurths, J., Scheingraber, H.,

Wackerbauer, R., Witt, A., "Complexity and Meaning in Nonlinear Dynamical Systems", Open Systems & Inf. Dynamics, vol. 2/1, pp. 269-289, 1992.

[12] Ayres, R. U., Information, Entropy, and Progress. New

York: AIP, 1994.

5. References

[1] Hofkirchner, W. (Ed.), The Quest for a Unified Theory of

Information, Proceedings of the Second International

Conference on the Foundations of Information Science, World

Futures, vols. 49(3-4)-50(l-4), 1997.

[2] Ebeling, W., Feistel, R., Chaos und Kosmos. Heidelberg:

Spektrum, 1994.

[13] Stonier, T., Beyond Information. The Natural History of

Intelligence. London: Springer, 1992.

251
The Effects of Biological Aging on Genetic Algorithms

Tim Schmelmer and Frank M. Brown

Artificial Intelligence Laboratory

University of Kansas

Lawrence, Kansas, 66045

tim@eecs.ukans.edu brown@eecs.ukans.edu

Abstract

This paper investigates the applicability of the

biological concept of aging onto the performance of a Genetic Algorithm. It is explained how the natural

phenomenon of decline in vitality due to old age is translated into the domain of Genetic Algorithms,

and a GA implementation is tested on four partly NPhard problems. The basic rationale is that aging

factors, depending on the problem they are applied

to, can greatly influence the quality of the results

produced by the GA, and thus speed up or slow down

the search process. The results organized by test problem are presented, and compared quantitatively.

Rules of thumb are laid out as to how influential the

aging component of the fitness function should be

chosen in order to achieve the best search results for

the four problems treated in this research.

1. Introduction

In 1803, T.R. Malthus [7] stated his observation that a population in which the individuals reproduce will

grow geometrically and thereby deplete its natural resources, unless it is regulated by the mortality of its individuals. Also, species of immortal individuals

would stop evolving, because the process would stall, once all ecological niches fit for life had been

exploited. By putting a cap on the number of

individuals under competition and introducing new,

variant individuals, death only enables the dynamic

process of evolution. In other words, aging and

eventual death is a natural implementation to give someone else a chance.

Throughout most of the natural species that

reproduce sexually, it is a common fact that old

individuals lose vigor and are generally less likely

than young ones to survive in "struggle for

existence"[4]. Also, natural individuals die of age by

which they completely retreat from reproduction.

Researchers in evolutionary biology state several

different explanations for this phenomenon. Group

selectionists hold the point of view that dying is an

act of altruism for the rest of the species. They place

the selection process on the level of a race, or even

the entire species, which strives for perfection [14].

Old creatures would use up valuable resources for

younger and fitter individuals, and therefore slow

down the species' pace on its way to evolutionary

perfection. Such a breed would not be fit for

competition with other species, so it would die in the

long run. Gene selectionists on the other hand think

that there are lethal genes in every individual.

Selection simply favors lethal genes, which are either

only expressed at old age, or at least are suppressed

until after reproduction. According to these theories,

aging actually provides species with an advantage in the process of selection [3]. Some biologists (e.g.

[10]) have gathered evidence that aging and death

might be consequences of deleterious genes.

Irrespective of the viewpoint, aging is a major factor

in the system of natural evolution. Considering its influence, it has gone remarkably unnoticed or has

been passed by in the research of artificial evolution,

though this concept can easily be translated into

genetic algorithms. Holland's original and most

commonly used concept of Genetic Algorithms [15] can be viewed as strictly generational. The life span

of all individuals is simply one generation. After that they die and are replaced by offspring produced from

the previous generation. This very drastic change

introduces the necessary variation into the

population, but it does not pay tribute to biological

facts. It is important to understand that death does not

come all of a sudden. It is rather the result of the

dynamic process of first maturing, and then aging.

This detail has an important impact onto the

evolution of a species, because of the observation

that old individuals are less likely to survive and take

part in another mating phase. Evolutionary strategies

[2] and steady-state Genetic Algorithms [9] have a

different approach. Individuals are evaluated at the

end of a generation, and an artificial fitness function

determines an individual's likelihood to make the

transition into the next generation. The

implementation of the Reference Genetic Algorithm

also follows this stochastic approach. Still, these

approaches make death come to an individual all too sudden. They do not consider that death is just the

outcome of the inherently gradual process of aging.

Age does not play a role at all in an individual's

probability to be selected into the next generation, nor does it influence the reproduction process.

Nature does not work this way. This is why

researcher in the field of artificial life, who are

252
interested in simulating the emergence of life with

the help of computers came up with different ideas to simulate the natural processes of aging and dying. In Thomas Ray's Tierra system [12] where self- replicating programs consisting of assembly language

instructions for a virtual machine run competing for

computer memory and CPU time. Although in Tierra senescence does occur, the ideas of aging and death

are based on the individual's success in coping with

the system's requirements during its lifetime. As a consequence, individuals complying perfectly with

Tierra' s rules will live forever, unless more than 80

percent of the environment is filled up with infallible

programs. This can also lead to stalling in the

evolutionary process. This phenomenon of stalling is the reason why Peter Todd [13] in his system to study the evolution of behavior in a simulated

environment introduced a new kind of artificial death. An individual perishes if it runs out of energy,

so the only notion of aging in his original world is running out of energy. Still, Todd's examination of

this system exhibited the evolution of immortal

creatures, whose main feature was that they chose not

to take part in the very costly process of producing

offspring. The conclusion in [13] recommends that

new forms of death are needed to prevent immortals

from bringing the evolutionary process to a stop.

Research in the field of Genetic Algorithms has

vastly ignored the notion of age inherent in biological

systems. In traditional Genetic Algorithms where in each new generation the entire population is replaced

by their offspring individuals can die too quickly to spread good genes. In purely stochastic approaches on the other hand, immortal individuals can slow

down the evolutionary search process, or make it get

stuck in local plateaus of the search space. The

reason for this is that old individuals use up the resources for young ones. If they do not take part in the mating process a sufficient number of times then

they do not introduce any variation into the

population; they just sit in the population being an

obstacle to evolution. The population does not profit

from good genes they might have. Realizing this deficiency and inspired by the attempts made in Artificial Life to overcome this very unnatural way

of generational transition, the authors examined the

influence of a specific type of aging on process and

results of genetic search.

The remainder of this paper addresses this topic.

Section 2 below describes a basic Genetic Algorithm

(i.e. GA) that is used in this work to compare its results to those found by the GA that implements the

aging concept. This algorithm is described in section

3. The following four sections describe and compare

the application of both algorithms to a variety of

problems. First among these is the 0/1 knapsack

problem (KSP) [8] in section 4. It is followed in section 5 by the problem to optimize the amount of

resources needed to survey an area of special interest

(ASP). In section 6 we apply these algorithms to the

iterated version of the Prisoners' Dilemma Problem

(PDP) [1]. Section 7 is dedicated to the examination

of a timetable scheduling problem (SCP). Finally, in section 8 we draw some conclusions about the

general applicability of the aging concept in the field

of evolutionary search.

2. The Reference GA

The basic, traditional GA as presented here

implements a genetic algorithm as described in [Michalewiczl996]. In the following this GA will be

referred to as the Reference GA. It incorporates three

basic concepts of the evolutionary search procedure.

Selection process: Individuals that represent

solutions to the problem are evaluated according

to a fitness function that decides about the

quality of a solution. A solution's fitness is proportional to its chances to survive.

/" Genetic Operator — Crossover: A certain

percentage of the individuals in the population

are randomly chosen to mate and produce

offspring. The children's genetic code is a recombination of the parents' genome. This

introduces variation the necessary to make the

evolutionary search process work.

2

nd Genetic Operator — Mutation: The second

genetic operator randomly picks units of genetic

information from the gene pool and modifies

them. By this procedure the altered gene can

adopt a state that is not yet present in the

population, which again increases the level of

variety among the solutions.

These three concepts are incorporated into the

repetitive process which is described in the

following. Initially, half the population of bit strings

is created randomly. To increase variation, the other

half starts out to be the complement of the bit representation of the first half. Now the first activation of the selection process determines those

individual solutions that survive to form the second

generation. The main idea behind the distinction of

those individuals surviving the generational transition

is the probability distribution based on the

individuals' fitness values. In other words, the

probability for an individual to be selected to participate in the next generation is proportional to its fitness as defined by the problem to solve. A

metaphor Michalewicz uses for this process is that of

spinning a roulette wheel, where each individual has a reserved slot. The width of that slot is directly

proportional to its fitness, and the circumference of

253
the entire roulette wheel equals the sum of all slots for the individuals in the population.

Figure 1: The selection roulette. Each slot

delimited by dashed lines represents the fitness

value for one individual solution. The different

widths of the slots stand for the fact that there are

fitter and less fit individuals in the population.

Maintaining a fixed number of solutions in the

population is achieved by spinning the roulette wheel

with one slot for each individual exactly as many

times as there are individuals in the population. Since

the slot size for an individual is sized according to the

individual's fitness, the roulette ball is more likely to

fall into the slot of a fitter individual. Note that it is possible (and even very likely in the case of a population which is composed of a few very fit solutions and many unfit solutions) that some of the

individuals get chosen several times to take part in the next generation. The crossover operator simulates

sexual reproduction. It is applied to the population,

which results from the selection process. Initially,

each individual gets assigned a random number

between 0 and 1. All individuals whose number is smaller than a user-defined parameter for the GA,

which determines the probability for a single

individual to undergo crossover, will take part in the

mating process. Here, solutions gather in pairs to perform the recombination of their genome. The

method applied here is single-point crossover, which means that both parents switch their genetic code

after a randomly chosen position in their bit string.

Example: Two parents p, and pj are mated. Their

genome strings are

P ={av

a2>...' a

Pos' aPos^...> a) >

Pj=(t>1 >K>...' b

Pos, bpos +i ...> bN )

After crossover at position pos the resulting

individuals are

ft =(ai' a2-...' a^rbpoe ,1 ,...,b

t),

P i = (b

1 ,b2 ,...,b

pot ,apos ^ ,aN )

The children resulting from crossover will replace

their parents in the population. The population

effected by crossover is then rendered by mutation.

Here another parameter determines the likelihood for one bit of genetic information in the gene pool to be

flipped. This is done by randomly assigning a number to each bit in every individual, and then

inverting its value if the random number for this bit is smaller than the mutation rate parameter.

One such sequence of selection, crossover, and

mutation is called a generation. A limit is placed on

the number of generations that the GA can try to evolve a good solution to the problem it is applied to. If criteria are know about the fitness of an optimal

solution, then the evolutionary process is usually

stopped as soon as such an individual is found.

3. Implementation of Biological Aging

In order to test the effect of aging, the Reference GA

described in the previous section has to be adapted

mainly in two ways. First of all, the representation of

an individual needs to be extended to include

information about its age (i.e., the number of times it has survived the selection process). Secondly, the

term fitness has to be re-defined to encompass the

idea to penalize old individuals that have not

procreated. To serve the first purpose, each

individual solution is represented as a pair. Its first element is the list of bits encoding the solution's

genome. The second element contains the number of

times this particular individual has been chosen to take part in the next generation.

Example: The dotted pair

( (0 1 1 1 1 0 0 1). 15 ) represents a creature with the genome string (0111

10 0 1) which has survived 15 generations.

Individuals created during the population

initialization before the first generation, as well as the

child solutions, which result from crossover, will

start out having a zero in their age component. If one

or more of an individual's genes was subject to mutation, then the individual's age component will

also be reset to zero. This rejuvenation is done

because a change of one gene only can often trigger an important allele, which is not yet part of the

population's genetic pool. An old individual might

become too valuable to justify penalizing it for its old

age.

254
Apart from the adaptation of the representation the

selection process has to be changed to take the age of

a solution into account. Aging is supposed to have a negative influence on the creature's fitness. Still, age

does not play a role in the problem-specific, user- defined fitness function. The negative influence of

age should happen in a way that is transparent for

this external fitness. On the other hand, the impact of

aging onto the process should also be quantifiable for

the user. To ensure all these constraints, the influence

of aging onto the fitness of an individual in the

selection process is exerted in a special, internal

fitness function. Assigning higher or lower values to the parameter AGE_FACTOR can regulate the actual

importance of the aging,

(define (InternalFF ind)

(let ((fitness

(ExternalFF ind) )

(if ( = 0 fitness)

0

(max 0

(+ fitness

(* (ExternalFF

BEST_EVER)

AGE_FACTOR

(/ 1

(1+ (cdr ind) )

)...) The internal fitness of a solution is a function of its external fitness which is increased by a portion of the

external fitness value for the best solution found by

the GA up to the time of the call. The degree of this increase is inversely proportional to an individual's

age. However, an external fitness value of zero automatically effects the same internal fitness. The

selection procedure, which decides about the

survivors of a generation, is only based on the

internal fitness. The Reference GA with the changes

laid out in this section will be called Aging GA in the

rest of this article.

4. The 0/1 Knapsack Problem

The first problem for which the differences between

the Reference GA and the Aging GA are examined is the well-studied 0/1 -KSP. It belongs to the class of

NP-hard problems [Garey & Johnson 1979], so it is reasonable to try and approach it with heuristics like a Genetic Algorithm. Imagine a traveler trying to fill his backpack. The task complicated by the fact that

there are more objects to pack into the knapsack than

it can carry. He has to decide which objects to take

with him on the trip, and which objects to leave at home. In other words, he has to find the best packing

for his rucksack, so that it does not break but that he

still can transport the items that are most valuable to him. In the example instantiation of the KSP that

both Genetic Algorithms try to solve there are n=20

Objects, and the capacity of the knapsack is C=54.

The lists W and V store the weights and values of the

objects that can be packed. One possible optimal

packing with a value of 214 and a weight total of 54

would be to chose objects 2, 3, 4, 7, 8, 10, 12, 13, 14,

17, 18, and 20. Table 1 lists the objects and their

weights.

(define W '(1122446 6 10 10

1 1 2 2 4 4 6 6 10 10) ) (define V ' (3 6 5 8 3 7 18 30 2 40 365837 18 30 2 40))

The individual solutions (i.e. the knapsack packings)

are represented by lists in which each element

represents one component of the vector X . A 1 in the

component of vector x therefore indicates that

object number i is part of the particular packing,

whereas a 0 means that it is not in the knapsack.

Example: The representation of a solution, that

suggests packing objects 4, 6,

8-11,16, and 19, would be the following list: (0 001010111100001001 0)

By looking up each activated objects weight and

value, one can determine that the solution's weight

sum is 47, and its values add up to 99.

The genetic algorithm creates an initial population of

forty random solutions like the one in the example

above. Here, as well as through the entire

evolutionary process the GA can generate solutions

whose weight sum of the packed objects exceeds the

capacity of the knapsack. In the following these

solutions are referred to as invalid (or infeasible)

because they violate the constraint imposed onto a

solution to be considered feasible. The decision was made to lift the weight constraint from the solutions,

and thereby transform the constrained KSP into an

unconstrained problem. Still In order to favor valid

packings invalid solutions are penalized in proportion

to their degree of invalidity. This was achieved by

decreasing the individual's fitness according to its excess weight. The penalty calculated by the function

Pen(x)= Cl £x[)] W[T|-C

V (=1 / I* The value of this function increases with the

individuals excessive weight. The entire fitness

function can be stated as

Fitness (x ) = f £ V [i] £W[i )}- £(V [i ] - x[i ] V[i ])- Pen (x )

V .= 1 . = 1 / i = J

Both GAs were extensively tested for this problem.

840 runs of 200 generations each were conducted to determine the average and mean values for both

GAs' weight and value sum. The results are shown in Table 2.

255
Table 2: Results for the KSP

| Reference GA Aging GA 9.06

WAverage ..._:.„.f.TM_"ei. 52.075 52.274

WMean 52.119 52.226

Std. Dev. 0.337 0.278

Optimality 96.4% 96.8%

V Average 188.979 190.261

V Mean 189.036 190.311

Std. Dev. 2.240 1.456

Optimality 87.9% 88.5%

The level of optimality in this table compares the

average values of both GAs to the perfect solution,

which uses the full capacity of the backpack to take

item at a value total of 215 unit. Interpreting the

results one can say that both the average weight as well as the average value sum of the packings

produced by the Aging GA are closer to the optimal

value. Even if the improvement is within the range of

the standard deviation around the average of the

Reference GA values, the results clearly show that

aging can have a positive effect on the results of the

KSP. The impact of aging is very sensible to changes

of the AGE_FACTOR parameter for the internal

fitness function. Although the value 9.06 was the best

that the authors found during their test phase, an

exhaustive search for the best parameter value was

not attempted.

5. The Area Surveillance Problem

The setting for second problem is a 2-dimensional

plane, in which parts are of special interest. These

parts are later referred to as the surveillance area. A

surveillance area consists of a set of different

geometric objects. The types of these objects are

circles, half planes, annuli (i.e. the intersection of one

circle with the complement of another concentric

circle), convex polygons, pies, and area segments. In addition to the surveillance area, there are cover

objects. Their shapes can be chosen from the same

range of types as those of the surveillance area. Cover objects are meant to cover a maximal part of

the surveillance area. All objects (surveillance area as well as cover objects) have a permanent location.

Once assigned a position in the plane during the

problem description phase, they do not change it in the course of the problem solution. Another feature

of the cover objects is that operating them bears

certain costs. These costs are mainly influenced by

the amount of surveillance area they cover, and by

their position in the plane. Cover objects can be in one of two states: either they are engaged (switched

on), or they are disengaged (switched off). Each

cover object harbors a distinct part of the surveillance area once it is engaged. Cover objects can intersect.

All objects (surveillance area as well as cover

objects) are represented as a set of points in the plane

contained by the object. The number of points in an

object is proportional to the resolution used to describe the plane.

The goal is to maximize the percentage of

surveillance area covered by cover objects, and at the same time to minimize the costs resulting from

switching on a cover object. Depending on the

specific situation, a trade-off has to be found between

those two goals. The exact preferences of this tradeoff are defined by the user. The ASP problem can

easily be reduced to the vertex cover problem[6].

This shows that it is also NP-hard.

In the ASP considered here, a set of 15 cover objects

try to cover an area of 2 polygons and 2 annuli. Table

3 shows the objects and their activation costs, while

Figure 2 and 3 sketch the surveillance area's and the cover objects' location in the plane.

Figure 2 : The area to be surveyed

i

r* ft I f :

: : : k

1 r —

la >-

Table 3 : Cover objects and their cost

factors for the ASP

Object 1 2 3 4 5 6 7

Costs .50 .45 .40 .15 .35 .32 .10

8 9 10 11 12 13 14 15

.20 .25 .22 .22 .28 .18 .18 .15

256
Figure 3: The cover objects

A solution to the problem of surveying an area is represented as a list of 15 bits. A 0 in position m of

the solution means that the cover object m is disengaged, whereas a 1 would mean that it is switched on.

Example: The solution list (0 1001 10000000

01 0) would mean that the surveillance area is only

covered by the cover objects number 2, 5, 6, and 15. Such a solution list also functions as one individual

in the Genetic Algorithm.

For the ASP both the Reference GA and the Aging

GA made 400 runs of 15 generations. The population

size was set to 60 solutions. Table 4 presents the

results.

Table 4: Results for the ASP

1 Reference GA AgingGA-l.(i2

Average 126.791 127.972

Mean 126.547 128.037

Std. Dev. 1.0226 1.873

Optimality 93.6% 94.4%

Very much like before, the average and mean

fitnesses of the Aging GA reach a value which is closer to the fitness value of the best possible

solution. However, both GAs had enough time to evolve close-to-optimal solutions. A particularity that can be observed here is that the aging factor has a negative algebraic sign. This can be interpreted as support for older individuals in the selection process.

The optimal solution that both GA average fitnesses were compared to had a fitness value of 135.5.

7. The Scheduling Problem

The Scheduling Problem (i.e. SCP) is also a member

of the category of NP-hard problems. The particular

problem addressed herein may be described as follows. For a small school with four teachers and

four rooms a timetable for 20 courses has to be

created by a GA, so that each of the courses is scheduled in one of 8 possible time slots. The

timetable produced has to comply with certain

constraints. A constraint violation leads to a

penalization for the schedule's fitness. The smallest

penalty is placed on assignments which violate

constraints between courses. This happens if two

courses are scheduled in the same time slot although

they should not be held in parallel (e.g., because

students ought to be enrolled in both classes in the same semester). A medium penalty is imposed on

professor constraint violations. Such a penalty is given to timetables which schedule a professor to teach two courses at the same time. The hardest

penalty affects timetables that schedule two different courses at the same time and in the same room. An

individual schedule consists of 20 genes with 7 bit each. The first 2 bits of each gene represents one of

the 4 rooms in which the courses can take place. The

next 3 bits determine the time slot (out of 8 possible

slots) during which the course is scheduled. The third

element assigns one of the 4 professors to the course. One gene is also referred to as a schedule item.

The fitness function chosen for this problem

processes three matrixes in order to keep track of

constraint violations. The first matrix statically stores

all conflicts between courses. The second and third

matrix are dynamically updated during the process of

a schedule evaluation. One of the two serves to survey the courses that take place in a particular

room at a certain timeslot. The other one stores for

each possible pair of teacher and timeslot if a professor is already assigned to teach a course at a

certain time. The fitness function now examines each

single schedule item in the following manner. If a room has already been assigned to another course

during the same period of time, then the fitness

function assigns a fitness value to this item that is only 3.3% of what a conflict-free schedule item

would have scored. Otherwise the function tests the

schedule item for course conflicts and professor

conflicts. In case of a course conflict, the schedule

item scores 10% of a conflict-free item, while a professor conflict results in 5% of the optimal score per item. Table 5 shows a conflict-free schedule that

is in keeping with the course conflict matrix that was

chosen for the test runs. The columns represent the

four rooms Rl through R4, while the rows show the

eight timeslots SI through S8. Each entry Cn/Pm in

cell (Rj,Sk) stands for the scheduling of course Cn in room Rj at slot Sk, and assignment of professor P

so teach the course.

257
Table 5 : A perfect schedule without

constraint violations

' Rl R2 R3 R4

SI Cl/Pl C6/P2 C11/P3 C16/P4

S2 C2/P1 C7/P2 C12/P3 C17/P4

S3 C3/P1 C8/P2 C13/P3 C18/P4

S4 C4/P1 C9/P2 C14/P3 C19/P4

S5 C5/P1 C10/P2 C20/P4

S6 C15/P3

S7

S8

The SCP was tested in 840 runs of 300 generations

each. The number of schedules in the population was

30. Table 6 exhibits greater differences than notable

for the previous two problems

Table 6: Results for the SCP

1 Reference GA Aging GA -0.56

Average 152.524 172.687

Mean 152.579 172.558

Std. Dev. 0.971 1.1604

Optimality 76.3% 86.3%

The average result of the Aging GA is 10% closer

than the Reference GA to creating a schedule that

complies with all constraints. Here as before it is important to mention that this drastic improvement was only perceived for the exact value of -0.56 for

the influence of aging. Other positive and negative

values for aging exhibited worse results which

mostly even scored below the Reference GA's

average fitness.

8. The Prisoners' Dilemma Problem

The last problem that is used to show the importance

of aging in the field of Genetic Algorithms is quite

exceptional. The goal here is not so much to solve a computationally expensive problem than rather to learn more about the emergence of cooperative

behavior among selfish individuals. The PDP comes

from the field of game theory. Initially, the PDP was

formulated as a two-person game in which two

players, who have committed a crime together, were

held in separate cells without any means of

communication. Both players A and B are offered the same deal: if one defects and betrays the other one, whereas if the other player does not testify, then the

defectant will not be imprisoned while the

cooperative player will serve a 5 year sentence. If both players defect then their testimony will be

discredited and they will both be put away for 4

years. However, in the case that both players do not

testify against each other, they will only serve a 2-

year sentence. A game consists of two moves, one by

each player. The players independently decide which

move to make, namely either to defect (D) or to cooperate with the other player (C). The following

table describes the pay-off function for each player.

The number in the pay-off columns indicates by how

many years a player shortens his time in prison.

Table 7: Pay-off in years saved for Player

A and Player B in the PDP

Player A Player B Pay-off A Pay-off B

Defects Defects 1 1 Defects Cooperates 5 0

Cooperates Defects 0 5. Cooperates Cooperates 3 3

In this article we examine the case where the game is iterated several times. If in a repeated game both

players always defect, they will get a by far lower

total pay-off than in the case of mutual cooperation.

Each player will have a memory of the last 3 moves. Based on the experience of these 3 moves a decision

is made if the player's next move will be D or C. To

represent a strategy that decides on what to do in the

next move based on the history of the previous 3

games, we follow Axelrod's approach] Details about

the strategy representation can be found in [1].

To determine the fitness of Shis strategy, each player

plays against every other player 10 times. For the

population size of 20 chosen here this means 200

fights per individual and generation. The fitness

value that is assigned to a strategy is the average total score that it can achieve in each of the 20 one-on-one

encounters with another strategy. During 840 runs of

100 generations each, and with a population size of

20 individuals the following results were recorded.

Table 8: Results for the PDP

| Reference GA Aging GA 13.5

Average 30.363 31.933

Mean 30.433 32.015

Std. Dev. 0.570 0.809

Optimality 60.7% 63.9%

The values for the standard deviations around the

average fitnesses for both GAs justify the statement

that the improvement achieved by the Aging GA is

significant. The optimality measure applied here

compares the average result of each GA to a

theoretically prefect strategy that can always score

the perfect pay-off of 5 years. Taking this into

consideration, an increase of 3.2% in optimality of

average fitness appears even more significant.

258
9. Conclusion

This research introduced the concept of biological

aging to the domain of traditional Genetic

Algorithms. The effects of aging upon solving four

well-examined optimization problems have been

proven significant. Further research in this field has

to be done to develop reliable theories about the

relation between the problem domain and the degree

of aging that should be applied. A rule of thumb for

this appears to be that moderate values, which do not

override the effect of the actual, external fitness

function, are most appropriate. However, no signs of

linearity between the impact of aging and the results

of the optimization process were detectable. This

suggests the application of a Meta-GA onto the

problem of finding the best aging influence factor for a task.

References

[1] Axelrod, R. 1987. Genetic Algorithm for the

Prisoner Dilemma Problem. In Davis (ed.),

Genetic Algorithms and Simulated Annealing,

Morgan Kaufmann Publishers, pp. 32-41.

[2] Baeck, T., Hoffmeister, F., Schwefel, H.-P. 1991.

A survey of evolutionary strategies. In Belew,

Booker (eds.) Proceedings of the Fourth

International Conference on Genetic Algorithms.

Morgan Kauffman, pp. 2-9.

[3] Bell, G. 1984. Evolutionary and nonevolutionary

theories of senescence. American Naturalist, 124,

pp. 600-603

[4] Darwin, C. 1859. The Origin of Species. London.

John Murray. (Penguin Classics, London, 1985;

New American Library, Mentor Paperback)

[5]Dawkins, C. 1976. The Selfish Gene. Oxford

University Press, Oxford

[6]Garey, M.R., Johnson, D.S. 1979. Computers and

Intractability: a Guide to the Theory of NPCompleteness, Freeman, San Francisco, CA.

[15]Holland, J.H. 1975. Adaptation in natural and

artificial systems. Ann Arbor, MI: The University

of Michigan Press.

[7]Malthus, T. R. 1803. An essay on the principle of

population, or, A view of its past and present

effects on human happiness: with an inquiry into our prospects respecting the future removal or

mitigation of the evils it occasions. New edition

1992: Cambridge University Press, Cambridge.

[8]Martello, S., Toth, P. 1990. Knapsack Problems,

John Wiley, Chichester, UK.

[9]Michalewicz, Z. 1992/1994. Genetic algorithms +

Data Structures = Evolution Programs, SpringerVerlag, 175 5th Avenue, New York, NY, 10010,

(212) 460-1500.

[10]Medawar, P. 1952. An Unresolved Problem in Biology. H. K. Lewis, London.

[12]Ray, T. S. 1992. An Approach to the Synthesis of

Life. In (Langton, Taylor, Farmer & Rasmussen

1992), pp. 371-408

[16] Syswerda, G. 1989. Uniform Crossover in genetic algorithms, in J.D. Schaffer(ed.),

Proceedings of the Third International Conference on Genetic Algorithms, Morgan-Kaufmann, pp. 2-9

[13]Todd, P. M. 1993. Artificial death. Proceedings

of the Second European Conference on Artificial

Life (ECAL93), Vol. 2, pp. 1048-1059. Brussels,

Belgium: Universite Libre de Bruxelles

[14] Wynne-Edwards, V. C. 1986. Evolution through

group selection. Blackwell Scientific

Publications, Oxford.

259

X AUTONOMY

Adaptive Autonomy: The Key to Dynamic, Responsive Formation of

Sensible Agent Organizations*

K. Suzanne Barber

The Laboratory for Intelligent Processes and Systems

Electrical and Computer Engineering Department

The University of Texas

Austin, TX 787812

1. Abstract

The practical deployment of distributed agent-based

systems mandates that each agent behave sensibly. This

paper focuses on the development of flexible, responsive,

adaptive systems based on Sensible Agents. Sensible

Agents perceive, process, and respond based on an

understanding of both local and system goals. Each agent

is capable of (1) deliberative or reactive planning and

execution of one or more domain-specific service /task, (2)

maintaining and interpreting knowledge about states, events, and goals related to itself, other agents, and the environment, and (3) adapting its behavior according to its understanding of its own local goals and overall system

goals. This paper addresses the above issues in the context of applied semiotics, a field that analyzes and develops the formal tools of knowledge acquisition, representation,

organization, generation, enhancement, communication,

and utilization. A Sensible Agent architecture has been

developed where each agent is composed of five modules: a Self-Agent Modeler, an External Agent Modeler, an Action

Planner, an Autonomy Reasoner, and a Conflict Resolution

Advisor.

Keywords: autonomous agents, dynamic organizations,

adaptive systems, planning

2. Research Motivation

There are two critical aspects to the old maxim, "It was

the best decision that could be made under the

circumstances." "Best decision" and "circumstances"

reflect both the quality of the decision and the confining

constraints. If decisions were unconstrained, the best

decision would depend solely on relationships between

the decision variables and a suitable measure of decision

quality. Consideration of the circumstances reflects a more realistic view for decision-makers. The state of

the world or environment in which the problem presents

itself acts as a set of constraints restricting the

application or acquisition of knowledge.

Research investigations have explored the decisionmaking process and attempted to automated portions of

it. A large body of work has framed this problem as follows: Given a goal, how should the system search

through a set of solutions (a solution space) to arrive at the optimal goal state given a relatively static picture of

the world? In other words, what is the best decision or plan if the goal and constraints guiding the search for

that goal remain constant? Underlying the premise of a

constrained solution space, a limited set of

communications and controls is allowed for derivation

of feasible plan sets.

The true complexity of many problem domains (e.g.

military command and control) is reflected by the

following facts which make the above assumptions

impractical for dynamic applications:

• Goals are not static. • Multiple types of goals exist. • Goals and plans to achieve those goals can conflict

with one another.

• Circumstances change often and unpredictably.

Therefore, consideration of the decision-making as a

process by which some entity (human or automated)

searches through a set of possible solutions, known apriori, guided only by static constraints to arrive at its goals is just scratching the surface of the real problem.

To address the true complexity of dynamic and

unpredictable situations, it is important to understand

that making the "best decision under the circumstances"

involves not only intellect but the ability to be

innovative (make changes), flexible (adjust to change)

and responsive (react or execute readily).

This research is supported in part by the Texas Higher Education Coordinating Board #003658452 and the Applied Research Laboratories and Office of Naval Research Grant N00014-96-1-0298.

263
Decisions rarely occur in isolation. A decision-maker

must not only assess its own behaviors (its states and

the events it is capable of processing) but also the

behaviors of others possessing the ability to impact its circumstances. Additionally, the decision-maker must

recognize the impact or necessity of interacting with

others to develop and execute plans. These interactions

and behaviors impact decisions, often acting as "the

circumstances" driving a need to make a decision.

Therefore, intellect or knowledge as well as innovation,

flexibility, and responsiveness is often derived from a decision-maker's ability to dynamically 1) assess current and potential roles others play in interactions and 2)

establish beneficial roles in these interactions. As

situations change, the interactions supporting the

decision-making process must also change. Simply

put, the decision-maker must not only be smart but

capable of applying those "smarts," deciding who to work with, if anyone, in an appropriate fashion at the

right time. To address these issues, dynamic

configuration of organizations is a must.

Organizations of decision makers must be capable of

configuring themselves given dynamic constraints. For

a member of the organization, these constraints include

the state of the decision-maker, events triggering

responses, states and events observed from the

organization members and the environment, the decision

maker's own goals and the goals of the system in which

they are a member. The research presented here is driven by these motivations for dynamic organizations

and the requirements for underlying theory and

technology required to render this capability.

3. Research Overview

The practical deployment of distributed agent-based

systems in dynamic, complex environments mandates

that each agent behave sensibly, incorporating an understanding of both global system goals and its own

local goals. Sensible Agents, capable of Dynamic

Adaptive Autonomy, address many of the challenges

encountered by multiagent systems. A Sensible Agent

(1) maintains a representation of both behavioral

knowledge and declarative knowledge of itself and other

system agents, (2) develops and processes an understanding of both local goals and system goals, and

(3) performs either deliberative or reactive actions with

respects to its own internal events or external events from other system agents or the environment.

A critical consideration for this behavior is the agent's

level of autonomy. The term level of autonomy refers

to the types of roles an agent plays in its planning

interactions with other agents. Specifically, this

research seeks to prove the following hypothesis: The

operational level ofagent autonomy is key to an agent's

ability to respond to dynamic situational context, (i.e. the states, events, and goals that exist in a multiagent

system), conflicting goals, and constraints on behavior.

Levels of autonomy are defined along a spectrum. (1)

Command driven — the agent does not plan and must

obey orders given by another agent, (2) Consensus -

the agent works as a team member to devise plans, (3)

Locally Autonomous — the agent plans alone,

unconstrained by other agents and, (4) Master — the

agent devises plans for itself and its followers who are command-driven. These conceptual autonomy levels are

tied to the responsibility of an agent to plan for solving

its goals.

Sensible Agents maximize the innovation, flexibility

and responsiveness of multiagent planning systems

operating under dynamic and constrained military

situations. Consequently, the Sensible Agent

technology will increase the ability of agents to coordinate the following:

• planning activities driven by an understanding of both

local and system goals as well as the behaviors of

other system agents and the environment.

• the roles individual planning agents play in

interactions with other agents by allowing dynamic

assignment of autonomy (i.e. dynamic assignment of

responsibility, commitment, authority and

independence) with respect to each goal held by a

respective agent.

4. Related Work

Several researchers have addressed the development of

adaptive, intelligent, agent-based systems. These efforts range from representing coordination and collaboration

[1], to production rule-based systems for organizational

self-design [2], to partial global planning [3], to the

development of multiagent planning architectures [4],

and many others. The majority of previous work has

focused on providing architectures with a constrained set of control schemes for agent interaction. In other words, one organization of decision-makers is developed for a problem domain. Although some new architectures

provide the mechanisms through which different

organizations can be realized, these architectures do not

support the reasoning processes necessary to implement

self-reconfiguration by the agents themselves.

Therefore, a significant portion of this work makes an

a-priori assignment of autonomy to each agent in the

264
system. This Sensible Agent architecture and

underlying technology pushes this envelope in an effort

to provide dynamic configuration of organizations

allowing adaptive control of agent interaction to maximize their intellect and minimize the limitations

imposed by ever-changing constraints (e.g.

circumstances).

This research advances previous work in the field,

realizing that one specific level of autonomy may not

be appropriate or even achievable at all times and under

all conditions. Investigations of related research have

not identified a comprehensive method for agents to employ to select autonomy levels given dynamic

situations. Adaptive autonomy, the ability to transition

autonomy levels during system operation, provide

agents the ability to dynamically choose the most

appropriate scheme of behavior and interaction. This

research seeks to provide agents with the capability to reason about autonomy. This research effort does not

focus on improving the problem-solving methods

available at particular autonomy levels. Many ongoing

research efforts focus on optimizing the planning

process. Sensible Agents make use of existing problemsolving methods that best fit their particular tasks. To

accomplish this, agents must know how to plan at each

of the possible levels of autonomy. Previous and on- going research provides inroads to these capabilities.

The command driven / master agent relationship

employs traditional centralized planning or distributed

centers of planning control [5][6]. Planning under the

influence of a master agent has also been examined

specifically [7]. On the other hand, agents developing

plans for consensus must negotiate to reach an agreement by which all goals are satisfied. The

contract-net protocol and its extensions offer agents this

capability [8]. Additional negotiation mechanisms

[9][10] provide additional support for agent interactions

at the consensus level of autonomy.

Locally autonomous agents, which plan independendy

but act as part of a larger system, exhibit the most

diverse behavior. They may be fully cooperative and act under a functionally accurate, cooperative distributed

system (FA/C) [11][12][13]. Alternatively, they may

choose to act more selfishly. Durfee and Lesser's [3] method of communicating partial global plans allows

agents to interact within a system in many different

ways. However, they leave the method of choosing an

interaction style open. Locally autonomous agents are unique in that they may cooperate to solve a system

goal without communicating. This function can be

supported by Tenney and Sandell's work on

coordination [14][15]. If the autonomy level of agents

in a system is allowed to change, the effective

organizational structure of the system also changes.

For this reason, it is important to understand the effect of different organizational structures. Previous work

provides this insight in the form of formal studies of

large-scale dynamic systems [14] and investigations of

dynamic creation and destruction of agents [16]. The

mechanics of changing organizational structure is also an important area of study . Several researchers have

investigated how agents can form problem-solving

groups [17][1]. In addition, centralized, distributed, and

group approaches have been compared [18][19]. These

studies provide important insight for autonomy

reasoning. Gasser and Ishida [2] also provide an

understanding of both adaptive self-configuration

(through Organization Self-Design) and tradeoffs

corresponding to different organizational structures.

5. Research Approach

The Sensible Agent architecture (Figure 1) permits

dynamic adaptation of agent autonomy. One agent is highlighted and referred to as the self-agent in the

discussions below.

A Sensible Agent's behaviors are described by its internal states, events and goals. A Sensible Agent's

Figure 1: Overall Architecture of Agents

with Dynamic Adaptive Autonomy

265
understanding of the external world is built from

interpretations of the states, events, and goals of other

agents and the environment. Each agent is (1)

responsible for one or more domain-specific

service/tasks, (2) responsible for the maintenance of its

internal states, events, and goal structure, (3) capable of

interpreting external states, events, and goals, (4)

capable of detecting and resolving conflicts, and (5)

capable of assigning and adapting an autonomy level for each goal in the agent's goal structure. Each agent

consists of five major modules.

• The Self-Agent Modeler contains the behavioral

model of the agent. This module interpret internals or

external events acting on the agent and change its

state accordingly [20][21][22][23]. Other modules

(within the self-agent) can access this model for

necessary state information.

• The External Agent Modeler contains knowledge

about other agents and the environment. This module

maintains beliefs about states and events external to the agent and predict the actions of other agents

[20][21][22][23][24]. Other modules within the self- agent can monitor this model for changes external to the self agent that affect their reasoning processes.

• The Action Planner solves domain problems, store agent goals, and execute problem solutions. This

module interacts with the environment and other

agents in its system. It also carries out solutions for

conflict resolution. Communication between agents

is handled by this module. The Action Planner draws

information and guidance from all other modules.

• The Conflict Resolution Advisor module identifies,

classifies, and generates possible solutions for

conflicts occurring between the self-agent and other

agents [25][26]. This module monitors the action

planner, self-agent modeler, and external agent

modeler to identify conflicts. It then offers

suggestions to the action planner or Autonomy

Reasoner in order to resolve the conflict.

• The Autonomy Reasoner determines the appropriate

autonomy level for each goal, assigns an autonomy

level to each goal, and reports autonomy-level

constraints to other modules in the self-agent. It also

handles all autonomy level transition and requests for

transition made by other agents. The autonomy

reasoner contains utility-based assessment of

autonomy levels. The autonomy reasoner draws

information from all other modules.

All modules within a Sensible Agent are domain

independent except for the action planner. Specifically,

these modules contain domain independent

representations and reasoning mechanisms.

Instantiations (i.e. knowledge instantiated in a particular

representation) are, of course, domain dependent. For

example, domain independent behavioral representations

in the self agent models specify how states, events, and

transitions are represented. The actual instantiations of

states, events, and goals and their respective

relationships are, of course, domain dependent.

Analogously, reasoning mechanisms for detecting and

resolving conflicts are domain independent while the

actual execution utilizes knowledge instantiations (e.g.

goal priorities) which are very much domain dependent.

Organization Formation: Autonomy

Representation and Reasoning The autonomy

spectrum (i.e. command-driven, consensus, local and

master) conveys the intent and scope of each autonomy

level. However, these intentions must be formalized

and modeled computationally in order to implement

Dynamic Adaptive Autonomy (DAA) in agent-based

systems. Autonomy levels are represented by four

autonomy constructs: Responsibility (R): a measure of how much the agent must plan to see a goal

solved; Commitment (c): a measure of the extent to which a goal must be solved; Authority (A): a measure of the agent's ability to access system

resources; Independence(i): a measure of how freely

the agent can plan.

The autonomy level, AL, is a 4-tuple (R, c, A, i). These four autonomy constructs provide the foundation

for a complete computational model of an agent's

autonomy level. The autonomy constructs can be used

in numerous ways to reason about agent autonomy,

guide agent behavior, and facilitate system interactions

and formation of problem-solving groups. It is these

four constructs that the Autonomy Reasoner

manipulates to perform autonomy level assignments

and transitions.

A representation specifying how the different autonomy

constructs affect utility (i.e. costs and benefits) follows.

Utilities for a proposed autonomy level allow

determination of the feasibility for the agent to assume

the proposed autonomy level with respect to the goal.

An agent assigns two utility values (Uagent, Usystem ) to each goal, where Uagent represents the goal's value to the

agent itself, and Usystera represents the goal's value to the

agent's overall system.

Let A denote the set of agents in the system. Let g'j, denote the j

th goal of the agent A'. The autonomy level

of goal g'j is represented by the 4-tuple (R, c, A, i). Let

fc be a function that returns a tuple (/c, agent , /c, system)j

using the commitment index, c, for a specific goal, g'j, where /c agem and /c, systera denote the impact of the

266
commitment index on the agent and the system,

respectively. Similarly, we define /R and f, that denote

the impact of the responsibility distribution and the

independence index, respectively. Let /A denote the cost of accessing resources used by the agent to fulfill goal

g'j.

1 It is important to note that the value of /c , system (and the other functions) is not necessarily consistent

among agents, differences may appear due to the

perceptions each agent has about the system.

Let F'c denote (FCiagent, Fc>syslem) for a given agent A.

Fcagem

^

Fcsystem is computationally derived from all

the individual values of /Ciageni and /c>system from the

current goals of the agent. Similar values are derived

for F'R , F'A , and F'j. In this research, utility represents

the degree of benefit that an agent's goals provide an

agent. The utility of all an agent's goals to the agent

will therefore be given by:

* Uagenloc /z

; (Fca8enl,F^agenl ,FA^ ageiH ,FUgent) (Ecj 1)

TJagent is assumed to be positively correlated with the

four parameters of function h,. Similarly, Usystem is given by:

• Usystem°<:/j2 (Fcsys[era ,FRsystem ,FAsvstem ,Fisystem) (Eq 2)

Again, Usyslem may not be consistent among all agents.

Let U\ given by (Uagent,Usystem), denote a utility vector

for the agent. This utility vector is used in determining

the benefit that can be attained from a goal. Let A

1 be an

agent that has accepted a candidate-goal, gn

. Let the

candidate-goal's possible autonomy level assignments

be represented by the set of levels {L0,L1 ,...,Lm}. In selecting a level, A' is assigning an autonomy level to

gn and must therefore predict the utility vector associated

with each autonomy level.

6. Summary

Whether acting as completely automated decision

makers or acting as assistants for decision support,

Sensible Agents will allow planning systems to perform with the kind of innovation, flexibility, and

responsiveness demanded of dynamic situations (e.g.

dynamic requirements planning resources such as data,

communications and time). Significant progress has

been made in the area of intelligent planning systems

and should not be discarded. The Sensible Agent

architecture provides a mechanism to leverage legacy

1 For simplicity reasons, the subscripts i and j to denote the current

goal, g'j, of agent A', have been omitted from the description of

functions fc, /R, /A, and /j. When a distinction between two goals is necessary, we will use the corresponding subscripts.

planners while providing these planners the ability to dynamically adapt their level of autonomy.

Both the focus of previous research and the progression

of systems engineering and architecture work offer a

critical foundation. While a good foundation exists, current work is limited by a rather static view of the

architectures to support decision making. The

messages, or at least, the content of message may be

dynamic in current architectures. Yet, static interactions

(i.e. pre-defined control mechanisms) for planning

execution force the systems engineer of the decision

making system not the situation in which the decision

making systems operates to dictate the available

interactions for planning and execution. We have

developed simulations for the naval radar frequency

management problem which support our claims

regarding the limitations of static organizations. These

limitations include the following:

• Overuse of scarce communication resources in some

circumstances

• Slow response due to fixed communication and

negotiation protocol that does not vary with

circumstances (e.g. adaptation of interactions based on

geographical distribution of emitter, available

spectrum resources, and other factors).

• Inability to reason effectively about third party

interference sources and intentions (sources that are not members of the system).

A Sensible Agent's ability to 1) reason about the utility

of autonomy levels with respect to both local and

systems goals and 2) assign autonomy levels given

utility-based assessments provides significant advances

in the development of dynamic, responsive systems.

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Investigating Distributed Problem Solving

Networks. AI Magazine 4(3): 15-33. 1983.

13 Lesser, V. R. A Retrospective View of FA/C

Distributed Problem Solving. IEEE Transactions on

Systems, Man, and Cybernetics 2 1(6): 1347- 1362.

1991.

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Distributed Decision Making. IEEE Transactions on

Systems, Man, and Cybernetics 1 1(8):527-538,

1981a.

15 Tenney, R. R., and Sandell, N. R. Structures for

Distributed Decision Making. IEEE Transactions on

Systems, Man, and Cybernetics 1 1(8): 5 17-527,

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16 Ishida, T.; Gasser, L.; and Yokoo, M. Organization

Self-Design of Distributed Production Systems,

IEEE Transactions on Knowledge and Data

Engineering 4(2): 1 23- 1 34. 1 992.

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Activity, pp. 189-198. In Werner, E., and

Demazeau, Y. eds. Decentralized A.I. Vol 3. Proceedings ofthe Third European Workshop on

Modeling Autonomous Agents in a Multi-Agent

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Alternatives Based on Logistical Scenarios,"

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Intelligent Systems Conference, October 23-25,

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Supporting the Engineering Lifecycle: A Focus on

Behavioral Modeling and System Component

Integration," submitted to HICSS-30 Conference,

April 1996.

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"Behavioral Modeling of Sensible Agents," Semiotic

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"Extended State Charts for the Modeling and

Specification of Manufacturing Control Software

Systems," accepted to International Journal of

Computer Integrated Manufacturing, to appear

January 1997.

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"Extended Statecharts: A Specification Formalism

for High Level Design", accepted to the Fourth

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Robotics and Vision, December 3-6, 1996,

Singapore.

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MD.

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Albuquerque, NM.

268
Finding and Using Multiple Models For Autonomous Learning

I.N.P. Davidson

CSIRO - Mathematical and Information Sciences

723 Swanston St, Carlton, Victoria, Australia 3053

Abstract

Achieving autonomous learning systems which can govern

themselves is one of the goals of A.I. Most learning systems explore

a fixed model space to explain a set of data. We believe that the "best" but most distinct models in the available space can provide

insight into questions of autonomy such as when to change the model

space and how to generate new data points (via experiments). We

explore this idea by focusing on clustering problems where the initial data is known to be insufficient to find the true model. We propose a method to generate new data points via experiments. Our approach

results in convergence to the true model using half as many

additional data points than if they were randomly selected.

KEYWORDS: Autonomous learning, machine discovery,

clustering, unsupervised learning

1. Introduction and Motivation

If inductive learning aims at answering the question, "What

does the data tell us ?", autonomous learning adds the

question, "What can we now do to better understand the

domain ?". So what can we do to better understand the domain to which

we are applying our learning system ? Inductive learning like most artificial intelligence problems is inherently a search

through a predefined model space. Most inductive learning

tools whether they be unsupervised [1] or supervised [2],

primarily focus on finding the single best model with respect

to some criterion for a fixed set of data. This is quite adequate

if the tool is to be used by a human who can interpret the

results and make appropriate changes. To make such tools autonomously learn more about a domain we must address

problems of how to change the model space and how to generate new data. It is our belief that finding and using

multiple models can provide insight into these more complex

questions associated with autonomous learning.

In this paper we focus on using multiple models to answer the

question, "Given the current data and the best model(s) found,

what should be the next set of experiments to conduct be to find the true model for the domain ?". Which model is better

for a given set of data has been addressed by the minimal

encoding length approach independently proposed by Wallace

(1968) [1] and Rissanen (1978) [3]. Their approach has the

benefit that complex models are chosen over simpler ones

only if the data available justifies it. But to our knowledge the

approach provides no indication of how to generate new data

points. Whilst we focus on this question in this discourse, we

believe our approach could be used to determine how to

change the model space and other questions associated with

autonomous learning. We intend to explore these at a latter time.

This paper documents our approach for finding and using

multiple models for clustering problems otherwise known as unsupervised learning. The paper is divided into a further six sections. The first is a basic introduction to clustering which

provides the terminology used throughout this paper. In the next section we define in limited detail the clustering system

we have developed (a more complete description exists [4]). The criterion used to evaluate each model (the minimum

message length) and our search mechanism (simulated

annealing) are described. The subsequent sections outline how

we search the model space to find multiple models and then

how these can be used to answer our next experiment

question. The final two sections discuss and conclude our

current work and touches on future research.

2. An Introduction To Clustering

Clustering, also called unsupervised or intrinsic classification,

has a long history in numerical taxonomy [5] and machine

learning [6]. Clustering attempts to find groups within data so

as to better understand the domain the data is from. It has been

applied to generation of taxonomies for flora and fauna,

concept formation and data mining. The objects/entities to be

clustered are each described by a set of d attributes. Clustering

involves determining the number of classes (groups), a

description for each class which can be used to determine

membership and assigning each object to one or more of these

classes. As the number of classes is unknown and no preclassified training set exists, clustering is unsupervised. The

collection of classes and their descriptions form a taxonomy/model of the objects.

A clustering system contains three major parts. The knowledge

representation scheme (KRS) which defines the searchable

model space. The criterion which provides a "goodness" measure for each model and the search mechanism which

explores the model space attempting to find the model which

leads to the optimal criterion value.

The KRS determines the type of classes and their possible

interrelationships. A dichotomy for clustering options which

impact on the KRS has been defined elsewhere [7]. The

criterion evaluates the "goodness" of each of the models. It is usually a real value function that takes as parameters the

objects and/or class descriptions and is the objective function

of the search.

269
The search mechanism explores the model space attempting to find the best model by finding the optimal (either minimum or maximum) value of the objective function. For all but the

most restrictive model spaces the number of possible models

to evaluate is combinatorially large. Exhaustively evaluating

each model is not even considered as a search mechanism. The

search mechanism must consistently find the global optima or

at least a good local optima in a number of different

application domains with a minimum of computation.

3. Our Clustering System

The clustering system developed merges together two

problem-invariant (robust) technologies: the minimum

message length criterion (MML) and simulated annealing

(SA). This has so far shown to result in a clustering system

which can be applied to a number of different problems with

minimum changes. The objective function of our search is to minimize the message length for non-hierarchical and

probabilistic classes which objects are exclusively assigned to. However, most large and interesting search problems possess

many local optima [14]. We feel that SA is a good search

mechanism to explore these complex model spaces, since it can escape local minima [14]. In the following sub-sections

we describe the two technologies.

3. 1 The Minimum Message Length Criterion

Chaitin [8], Kolmogorov [9] and Solmonoff [10] in varying

forms independently proposed algorithmic information theory

(AIT). AIT intuitively allows us to quantify the notion of

complexity and compressibility of objects. Learning by

induction is inherently about compressing observations (the

objects) into a theory (the model). Boyle's law (P = k.N/V) on

ideal gases relates the number of molecules (AO in a measurable closed volume (V) to pressure (/>). A table could

store every possible combination of N and V and the resultant pressure. However, Boyle's law compresses this table into a much shorter description, the above equation.

Wallace and Boulton [1], extend this compressibility notion

into their minimum message length (MML) approach to induction. They define a criterion which can be used to select the most probable model from a given set of mutually

exclusive and exhaustive models, H*, for the objects, D. The

MML approach specifies that the minimal encoding of the

model and the objects given the model is the best. In terms of

Bayes theorem, we wish to maximise the posterior

distribution, P(Hj \ D,c) where c is the background context:

logP(HilD,c) = -\ogP(Hi \c) +

- log P(D\ H, , c) + const

(2)

P(H,\D,c) =

/>(//,[ c).P(D|//,.,c)

P{D)

(1)

Our interest is in comparing relative probabilities so we can

ignore const. Information theory [Shannon] tells us that -log

(P(occurrence)) is the minimum length in bits to encode the occurrence. Hence by minimising equation (2) we inherently

maximise the posterior distribution and find the most probable

model. The expression to minimise has two parts, the first being the encoding of the model and the second the encoding

of the objects given the model. The object collection is random if the size of encoding the model and the objects given

the model is approximately equal to the size of directly

encoding the objects. That is there is no way to compress the

objects into a shorter description/theory. The two part message

is precisely described for intrinsic non-hierarchical

classification [1] and [11].

The MML criterion only defines a goodness measure for a model with an inherent bias towards simple models. It does

not indicate how to search the model space. To do that we use simulated annealing.

3.2 Searching The Model Space Using Simulated

Annealing

The Metropolis criterion was first used as a Monte Carlo

method for the evaluation of state equations in statistical mechanics by Metropolis et al. [12]. Kirkpatrick et al. [13]

demonstrated how using the Metropolis criterion as a test in

iterative optimisation can solve large combinatorial

optimisation problems. They called their approach the

simulated annealing technique as it mimics the annealing of a piece of metal to minimise the energy state of the molecules

within the metal. SA is an iterative local optimisation

technique. At any time there is only one current solution

which is slightly changed at each iteration. As SA is a Markov

process the current solution, Sn, at time n, is a result of the

perturbation of solution Sn.j. The algorithm continually

perturbs the current solution to generate new candidate

solutions. SA unconditionally accepts candidates of better quality than the previous solution and conditionally accepts

those of a worse quality with a probability p, where:

(I Difference in Quality] \ _ System Temperature ) (3)

Taking the logarithm of this expression yields

Worse quality solutions can be accepted which allows the search to escape from local minima which are common in most complex search problems [13]. We set the initial temperature To, so there is a 90% probability of accepting an

increase in cost. This probability decreases as the temperature

decreases. The cooling constant, R reduces the temperature

such that, T/c = Tk-l-R.

270
Tn =-

loge (0.9)

Cq is the goodness evaluation of the initial solution.

(4)

The implementation of our algorithm can be found in [4]. Simulated annealing statistically guarantees that the global

optimum will be found, if the thermodynamic equilibrium is reached at every temperature and the cooling schedule is slow

enough [14]. However, this is an infinitely long process. We

do not maintain these two requirements due to the need to find a solution in finite time. Instead, after a fixed number of

iterations at a temperature, the temperature is reduced and the

cooling constant provides discrete changes in the temperature.

However non-ideal SA approaches, such as the one we use,

still find good, local optima solutions [14].

4. Finding Multiple Models

Our thesis is that distinct but good models can be used to generate new experiments whose results can be used to better understand the domain. This requires finding the n models

which provide the best values for the objective function but are sufficiently different from each other. Just finding the n

best models would most likely result in finding a good model

and slight variations of it. To achieve our aim we must handle two key issues. Firstly, we

must be able to quantify the difference between two models.

Secondly we must adjust our search mechanism. Let us

discuss the first.

4~l~Quantifying The Difference Between Models

A model can be characterised by its predictions or its syntactic

description. A model (the taxonomy) makes predictions on how to group together objects. Each model assigns each object

to a cluster. For two clusters from different models, we can measure the similarity between them by counting the number

of common objects. For two models we can measure their similarity by counting the number of common objects for every possible combination of cluster pairs (one from each

model). This is inherently a measure of the common "cluster

neighbourhood" (clusterhood) each entity has in two different

models. This measure can be achieved by building a r x c contingency table, P, where r is the number of clusters in model A (MJ and c is the number of clusters in model B

(MB). The cell Py in the table holds the number of objects

common to cluster / in MA and cluster j in MB

. The total count

of the table will be the number of objects/entities we are

clustering. Where MA

is the same as MB only the leading

diagonal of the resultant table will contain non-zero elements.

A model can also be characterised by its description. In

clustering, a model consists of classes and their descriptions.

In our approach each class description contains a probability

distribution for each attribute. The message we construct

(whose length we are trying to minimise) only encodes an

attribute distribution of a class if it is sufficiently different

from the population's (collection of all objects) distribution

for that attribute. We can characterise the descriptive

difference between two models in a contingency table, D,

which has the same structure as the contingency table P. For

each attribute we can determine which of the clusters for each

model has a distribution for that attribute that is the greatest

from the populations. The cell Djj holds the count of attributes for cluster /' in MA and cluster j in MB whose probability

distribution is of greatest distance from the population's

distribution. The total count for the table is the number of

attributes. The contigency table inherently holds the

distinguishing features (attributes) of each class. The contingency tables P and D contain the differences

between the two models A and B in their most rudimentary

forms (predictions and descriptions). We can use this information to measure if a relationship exists between the two

models. Note we do not attempt to determine what the

relationship is, only if it exists. This can be achieved by using

a number of different contingency table association measures

[15]. We choose the Goodman and Kruskal lambda measure

of predictive ability because it is both a readily interpretable

probability measure and is not symmetrical. The measure X^

measures the ability to predict the cluster in model B given we

know the cluster in model A. It should be noted that X/& * XBA

is generally true. That is, A may be predictable from B but not B from A and vice versa. Specifically X^ calculates the

relative decrease in the probability of an error in guessing the

class given by model A if the class for model B is known.

Formally we can write:

Pt-P,

1

Px - 1 - max(ttj)

r r

(5)

-z 1-

max(«,

N

By calculating the lambda value for the tables, P (X^P)) and

D (X^D)) we can measure the predictability of a model from

another in terms of predictions and descriptions respectively.

4.2 Adjusting The Search

The ideal annealing algorithm converges to the global

optimum. However the trajectory through the model space in getting there may not be sufficiently diverse to find other good

but different local optima. We must therefore adjust our search

method to be consistent with our aim. We can achieve this by

introducing a bias which guides the search away from already

found good local optima. This is facilitated by storing n models which are the best (with respect to the objective

function) but sufficiently different from each other. These

models are the best and most diverse models known.

271
Models are only considered to be stored if their message

length is less than any of the currently stored models. To be

stored, the summation of the models predictability from every

other stored model must be less than this same measure for one of the currently stored models. The model whose

predictability is the greatest is replaced. Predictability is calculated using the measures for either the P or D

contingency tables. Candidate models have a penalty added to

their "goodness" value in proportion to their similarity to the

stored models.

5. The Uses of Multiple Models

In the previous section we defined two measures of difference

between models. These measures can be encoded in a contingency table and the predictability of one model from

another calculated. How we should use these measures to influence our search depends on what we are trying to achieve. In this paper we focus on what the next best set of

experiments to conduct are. The question of how to guide the next experiments to conduct

has been addressed in Lenat's work on AM [16] and Kulkarni

and Simon's work on Kekada [6]. Lenat described the notion

of "interestingness" and felt the system should focus its attention on interesting phenomena. Similarly, Kekada focuses

its next experiments on surprising phenomena, believing that

if a result of an experiment was unexpected then the

knowledge of that area of the domain is obviously lacking and

should be explored. Both approaches use heuristics to describe

the notions of interestingness and surprise. As we hope to have

available the best but most different models we focus the next

set of experiments where these models' predictions differ. By

doing this we can resolve which of these models is the better for the domain. By continually running the clustering system,

finding distinct but good models, and then generating data

points where these models' predictions differ we generate data

points where our knowledge of the domain is contradictory.

To determine which of measure of predictability (model

description or predictability) is better we conducted

experiments on the following problem. Consider a population

of objects/entities each having m binary attributes. In the

population there exists m classes. Class /, i = 1 .. m can be

precisely described as having the value 0 (false) for all

attribute except the ith which is 1 (true). Table 1 provides the

precise description for a few classes for the m=10 situation.

Attribute 1 2 3 4 5 6 7 8 9 10

Class 1 1 0 0 0 0 0 0 0 0 0

Class 10 0 0 0 0 0 0 0 0 0 1 Table 1. Precise description for classes in m=10 situation.

To determine the proportion of each class in the population we

make use that the summation of the first r integers is given by:

from this the relative proportion, P^ / = /... m of class i in the

population is given by:

By using the MML equations described in [1] we can

determine the approximate number of objects (data points)

required to find the true model if the objects are randomly

sampled from the population. For our trial set of objects this number was 184. Below this amount of data the best model is to place all objects into one class, indicating that the data from

an information theoretic view is random. For this data set the

encoding of the model and data for the true model and one

class model were 566.21 and 570.24 nits respectively. The

difference between the lengths is the comparitive difference in likelihood. Thus the true model is approximately times more likely than the one class model for the given data set. We conducted trials to determine how successful our strategy

of focusing experiments on where the models predictions

differ is. In each trial the clusterer was given the first 60, 80

and 120 objects of our data set. As we have shown, this is insufficient to chose the true model over the one class model.

For 120 objects the true model and one class model had

encoding length of 415.56 and 368.32 nits respectively for this reduced data set. The true model is approximately e

A1 times

less likely than the one class model for the data. The class distributions follow in table 2:

Class 1 2 3 4 5 6 7 8 9 10 Number

Frequency 5 1 7 13 7 13 15 17 21 21 Table 2. Class distributions for initial 120 objects

Our aim is to generate new data points so that eventually the

true model is found. The number of new experiments required

to converge to the true model is one obvious measure of

performance.

5. J How To Generate New Experimental Data

The process of running the clustering system with a given set of data produces a number of theories (taxonomies/models) of

the data. We wish to generate new experimental data which

can be used in further applications of the clustering system to

better understand the domain and find the true model. We

focus on generating new data where the predictions of the theories are different. An example based approach is used

where an example of an object the models' predictions

disagree upon is used as input into an experiment. The

experiment takes the object as an input and returns similar

objects. For additional complexity there is a stochastic aspect

272
to the experiments which results in the chance that the

experiment will return the wrong result. In our studies this

error is 25%.

The examples can be selected by re-arranging a P contingency

table so that the leading diagonal has the largest counts. The

remaining elements represent objects which are predicted

indifferently for these two models. Completing this task for all possible pairs of models can determine those objects for which

the model's predictions differ the greatest.

Experiments could also be generated by prescription. This

would involve a description of an exemplar object for which,

if it were to exist, the current stored models would make

contradictory predictions for. This exemplar could be

constructed from where cluster descriptions differ the most

between all clusters from one model with all clusters from

another. We have not explored this option as yet.

We established two control trials. One generated new objects

by sampling them from the population (sampPop) whilst

another generated new objects from each class in equal

proportion (equProp).

Table 3 illustrates the comparison between each model search

and experiment generation technique. Both search techniques

stored the five best models which had the shortest message

lengths but were different from each other. The techniques

differed in the notion of difference. Search technique A used

the predictive difference between models; B the description

difference between models. Two experiment generation

techniques were tried: technique C generates new objects in batches of 10 whilst technique D generated objects in batches

0^20^ After each batch was generated, the clusterer was re-run and the process repeated until the true model was discovered.

The control trial generated objects in batches of 5. All four of

our variations outperformed the two control approaches by

requiring approximately half as many data points to converge

to the true model.

Search Technique A B A B samp

Pop

equ

Prop

Experiment Generation

Technique C C D D

New objects required to find true model. 60 initial objects. 70 70 80 80 170 140

Additional objects required

to converge to true model.

80 initial objects. 50 60 80 60 140 120

Additional objects required

to converge to true model.

120 initial objects. 40 40 60 60 100 80

Table 3. Results of trials

6. Discussion and Future Work

We shall focus our discussion on the situation with 120 initial objects using search technique A (model difference measured

by predictions) and experiment generation technique C (batch

sizes of 10). The system behavior is summarized in table 4.

1" 2

nd 3

rd 4

.b 5*

Trial Trial Trial Trial Trial

True Classes 6 8 7 9 10

Found In One of

the Best Models

Class experiments 1 3 9 2

focus on True Model Found No No No No Yes

Table 4. Summary of Behavior For 120 Initial Object Case.

The ten classes in the true model are not justified by the initial data. After the first trial with 120 objects, the best models, in combination, contained the correct description and object

assignments for six of these classes. The models most

disagreed upon what class objects in the class 1 should

belonged to, more objects similar to this class were requested.

A further 4 more trials occurred before the true model was

found. Of course in our situation we know what the true model

is. It was interesting that the number of true classes found did not increase monotonically, nor that the class the models

predictions differed most on, was not the least frequent.

One of our aims was to determine the impact of searching the

model space to find the best but most different models with

respect to description and predictions. However irregardless of

the measure of difference used, similar models were found.

We feel this is due to the simplicity of the problem and most

likely this will not occur in more complex domains.

We have not made use if there exists any relationship between

the similarity of two models for their predictive capability and

descriptions. We can consider five cases:

Relationship Interpretation

^•ab(P) > ^ab(D) The models predictions are more similar

than their descriptions.

^•ab(P) » ^ab(D) The models predictions are significantly more similar than their descriptions.

^-ab(P) < ^ab(D) The models descriptions are more

similar than their predictions.

^ab(P) « ^ab(D) The models descriptions are

significantly more similar than their predictions.

^ab(P) * ^ab(D) The similarity between the models with

respect to their descriptions and

predictions are fairly equivalent.

Table 5. The relationship between measures of similarity

between a models description and its predictions.

We can diagramatically represent each situation by

considering a population of things which only has one

273
attribute, which we believe to be normally distributed. Each

model has only one class whose description is the mean and

standard deviation for that particular attribute. Figure 1

illustrate the situations for Xab(P) > ^(D). The circles represented data points. In this situation the models make

similar predictions for the current data points, but they are evidently different. Xab(P) is larger than Xab(D) because the current data points do not occur in areas where the models

predictions would differ. Using and contrasting both measures

could be of benefit.

Two Mod.li of On* Clou Willi On« Attribute

•.04

0 035

f

°"

0 0421

1

1 U*4*A

f

003 |—X—Mortal ft

f 0411 jjy • • • • \,

0.01 • • • • V ^y'' m • • •

S«B • • " • •

0

' t»r^ • • • •

j oooooooooooooooooooooooo AtlrtkHti VatMi

Figure 1.A.ab(P)> WD)

We intend to explore the annealing literature to see if any

insight can be provided to bias the search technique to better explore the model space. The lambda measures of association

used in the contingency tables whilst adequate are problematic

for skewed distributions. We intend to explore measuring the

information content of contingency tables to obtain better measures of predictability. As stated earlier we believe that using multiple models can address other questions in autonomous learning such as when to change the model space

which we plan to explore. Our clustering system can change

the model space by taking the Cartesian product of attributes and changing the probability distribution (discrete or normal)

assumed for each attribute.

7. Conclusion

We have developed a clustering system which can search the

model space for good but distinct models. The difference

between models can be measured regarding their predictions or descriptions. Using these models can provide insight into how to address questions of autonomous learning systems of

which, we have focused on the next set of experiments to conduct to better understand the domain. We have applied

this clustering system to an artificial problem where the initial

set of data is inadequate to find the true model. We explore

the idea of generating new objects where the models

predictions differ. We have shown that this approach results

in finding the true model by generating only half as many

additional objects than by using blind techniques for our problem.

8. Acknowledgments

I am most grateful to Emeritus Professor C.S. Wallace from

Monash University for his continual comment and

suggestions on this work. Professor Wallace's work is supported by ARC grants A49703 162 and A49703 170.

9. References

[I] Wallace C, Boulton D., "An Information Measure for

Classification," Computer Journal, Volume 1 1 No. 2, pp. 185-

194, 1968.

[2] Quinlan J.R. "Induction of Decision Trees," Machine

Learning, Volume 1, pp. 81-106, 1986.

[3] Rissanen J. "Modeling by the shortest data description,"

Automatica, Volume 14, pp. 465-471, 1978.

[4] Davidson I.N.P. "Clustering Using The Minimum Message

Length Criterion and Simulated Annealing," in Proceedings of

the 3

rc* International A.I. Workshop, Brno, Czech Republic

1996.

[5] Dunn G., Everitt B.S.. An Introduction to Mathematical

Taxonomy. Cambridge University Press 1 982.

[6] Michalski R.S., Stepp R.. "Learning from Observation:

Conceptual Clustering," in Michalski R.S., Carbonell J.G, Mitchell T.M. editors, Machine Learning: An Artificial Intelligence Approach, CA: Morgan Kaufmann, 1983.

[7] Clifford T., Stephenson W. An Introduction To Numerical

Classification, Academic Press, 1975.

[8] Chaitin G. "On The Difficulty of Computations," IEEE

Transactions ofInformation Theory, IT- 16, 1970, pp. 5-9.

[9] Kolmogorov A. "Logical Basis for Information Theory and

Probability Theory," IEEE Transactions of Information

Theory and Control, IT- 14, 1965, pp. 662-664.

[10] Solomonoff R. "A Formal Theory of Inductive Inference: Part

1," IEEE Transactions of Information Theory and Control,

IT:7, 1964, pp. 1-22.

[II] Wallace C.S., "An Improved Program for Classification," in Proceedings of the 9th Australian Computer Science

Conference, Volume 8 No. 1, 1986, pp. 357-366.

[12] Metropolis N., et al, "Equation of State Calculations by Fast Computing Machines," The Journal of Chemical Physics,

Volume 21 #6 June, 1953, pp. 1087-1092.

[13] Kirkpatrick S., Gelati C, Vecchi M. "Optimization by

Simulated Annealing," Science, Volume 220, 1983, pp. 671-

680.

[14] Van Laarhoven L. Theoretical and Computational Aspects of

Simulated Annealing, CWI Tract, 1988.

[15] Everitt B. Contingency Tables, Cambridge University Press, 1980.

[16] Lenat D. "AM: An artificial intelligence approach to discovery

in mathematics as heuristic search," In Knowledge-based

systems inA.L, McGrawHill, 1982.

[17] Kulkarni D., Simon H.A., Computational Models ofScientific Discovery and Theory Formation, Editors P. Langely, and J. Shrager, chapter 9, Morgan Kaufmann, 1990.

274
Agent based task viewing in telerobotic environments

Gerard T McKee, Paul S Schenker* & Bernard G Brooks

University of Reading, Department of Computer Science, Whiteknights

Reading RG6 2AY, UK. Email: G.McKee@reading.ac.uk, B.Brooks@reading.ac.uk

California Institute of Technology, Jet Propulsion Laboratory,

4800 Oak Grove Drive/MS 198-219, Pasadena, CA 91109, USA. Email: schenker@telerobotics.jpl.nasa.gov

Abstract

Teleoperation environments consist of viewing and

manipulation controls to interact with the remote

environment. Camera control distracts the operator from

the manipulation task, leading to reduced efficiency.

Releasing the operator from the camera control overhead can be achieved with the use of a second operator or by

employing an automated viewing system. In this paper we

present a model for automated camera positioning that can track a task and index a set of viewing actions, visual

acts, that in turn control camera placement. We illustrate

the use of "multi-agent" architectures to create viable

experimental environmentsfor studying automated camera

control and we present a multi-agent model we are

currently exploring for creating an automated camera

positioning support for operators in teleoperation

scenarios.

1. Introduction and Background

Teleoperation environments consist of viewing and

manipulation controls to interact with the remote cameras and manipulators respectively. Typically teleoperation

tasks can be performed in two ways. In the first case, a single operator has sole control. However, the complexity of

the controls means that typically the operator will control

either the robot manipulators or the cameras, but not be

able to control both at the same time. This means that the task of controlling the cameras tends to distract the operator from the manipulation task, and leads to significantly

reduced efficiency [11]. In the second case, the teleoperation task is performed

by two operators. The first operator controls the robot

manipulators, and the second operator controls the cameras in an attempt to provide the first operator with the visual information required to perform the task. Although this

is an improvement for the first operator, extensive operator

training may be required. One of the key challenges in this mode of working is to structure the task such that the

intentions of the first operator are signalled clearly to the

second. This is normally achieved using a pre-compiled

task script and communication between the two operators

to register their actions within the real-time setting.

The aim of automating camera control is to remove the

need for the second operator without incurring the burden

of camera control on the first operator. A secondary aim is

to reduce the complexity of the operator interface, and

wherever possible, to offer additional assistance to the operator by complementing the sensory data from the remote environment [11]. In a previous paper we proposed to use deliberative task

models and a reactive architecture to achieve these goals

[9]. The deliberative model captured the notion of a script

and the reactive model addressed the real-time environ- ment. The automated viewing system, in this context, rep- resents an "autonomous" agent acting cooperatively with

the operator. It takes away the responsibility for visual

control, leaving the operator to focus attention on the manipulation task. The success of the cooperation

depends, however, on signalling the operator's intentions

to the viewing system. In particular, it is essential that the automated viewing system remain stable and provide a

consistent quality of service to the operator. Our aim, in

particular, is for the viewing system to be "responsive" to the operator so that the operator still retains the feeling of

being in control, while remaining "stable." The actions of the operator and their concomitant

impact on the remote environment, are the prime source of

signals for an automated viewing system. However, they

may not reveal themselves without some form of coercion

during the design of the operator interfaces and the task environment. Therefore, autonomous systems need, in many cases, to be situated within an operational context. Within this context they are expected to behave intelligently. In a wider context, however, they may not display

the same level of intelligent action, and we should not necessarily expect them to do so. We should, however, expect the evolution of the auton- omous agent to follow a path of generalisation as we

develop techniques which allow us to relax the coercion.

We might actually say that this evolution may progress in tandem with our ability to discriminate signals. The hybrid

architecture we have proposed lends itself to a manmachine interface model in which manipulation actions can be enhanced to provide clear signals to the viewing

system, while retaining a manipulation focus. We have to be clear, however, that while we are granting autonomy to the viewing system, we are at the same time creating a symbiotic link which ties the autonomous agent to a spe275
cific operational context. The remainder of this report is based on work being

done in the Active Robotics Laboratory at the University

of Reading to demonstrate computer aided camera placement techniques for teleoperation. In the next section we

outline a model for automating camera placement. In section 3 we present some ideas for the simulation and implementation of this model in a real robotics laboratory, and in section 4 we present the specific model we are currently

exploring. In section 5 we draw our conclusions.

2. Intelligent Automated Camera Placement

Our model for automated camera placement makes use of a high-level task based schedule. The components of the

schedule are used simply to provide the context of a task operation. The cameras are placed under the control of a

reactive decision making system which attempts to deter- mine what the operator is "looking at" and provide suitable

views.

The task model provided is generated from prior train- ing runs. During these training runs, a sequence of high

level instructions such as "pick up bolting tool", or "place

screwdriver head in screw" can be determined. These

instructions, are then classified as generic operations, such

as "peg-in-hole", which are provided to the viewing sys- tem in the form of an operation-based schedule.

Visual Goals

Our proposal is based on decomposing task operations

into simple atomic goals [1][7][8]. These goals, which

match the model of human perception, are computed as if the operator were performing an assembly task. The notion

is to use assembly planning techniques to compute a set of

atomic geometric, kinematic or topological constraints that must be satisfied in order to perform the operation [4]. An example is the "peg-in-hole" operation (Fig. [1]). To

perform this operation, the operator must first satisfy three basic geometric constraints before inserting the peg into the hole, namely:

• Axes of peg and hole must be parallel.

• Axes of peg and hole must be coincident.

• Lower surface of peg must be flush with the upper sur- face of the hole. Each constraint is considered a visual goal, and each visual

goal has associated with it a visual act to satisfy that goal.

Since the visual goals are independent of each other, the visual acts can be performed sequentially in any order, or indeed in parallel. Constraints on the sequencing of the

visual goals are imposed by the task setting. For example,

the parallel and the coincident constraints have to be satisfied before the insertion of the peg in the hole can be completed.

A "visualisation model" for a task can therefore be

a. parallel axes b. coincident axes c. insertion

Figure 1 : The peg-in-hole operation

defined as follows: A task can be segmented into a set of

operations and a set of constraints on the sequencing of

these operations. Associated with each operation is a set of

visual goals and, implicitly, a set of constraints imposed by

the task setting.

Visual Acts

As mentioned, a visual act is the viewing action

required to satisfy a visual goal. Specifically, since it is the operator that performs the manipulative action, the auto- mated camera placement system must use the information

in the visual act to provide a set of viewing parameters for the camera system.

The camera placement system must track the operator

continually. In particular it must determine:

• Which specific action, or actions, the operator is currently trying to perform in pursuit of the task.

• As the workspace evolves, how best to set the viewing

parameters to satisfy each visual act.

Ideally, there would be no explicit communication of

the operators intentions to the automated camera positioning system. However, this is not realistic at this time since even in the dual-operator scenario, where the second operator is also an "autonomous" agent, explicit communication of intentions is required to register the manipulation

and viewing actions. Our aim is to at least retain the majority, if not all, of the operator's attention focused on the manipulation task. We are, therefore, willing to consider

additional modules or actions within the manipulation

interface which on the one hand can be motivated by the manipulation task, but which provides signals that can be

used to identify the operator's intentions.

For example, we might introduce an additional module

which allows the operator to designate task operations at various levels of abstraction. The automated camera positioning system can then takes its cue from this interface module to index the associated set of visual goals.

Within this top-down context we then propose a reactive multi-agent model [2] [12] to select and deliver task- relevant information to the operator. There are actually a number of ways in which we can deploy multi-agent models apparently to good effect. In the following section we

276
outline a number of these approaches and we describe the multi-agent environment we are currently implementing to support these.

3. Architecture

Our choice of architecture is not just an implementation

issue. With the way the problem is modelled, outlined

above, it is almost impossible to divorce the architecture of

implementation from the problem. In this section we hope

to demonstrate how our architecture permits us to implement a solution and actually assists us with that solution.

3.1 Resource Contention

The resources to support remote viewing comprise not

just of cameras, but also video displays, network bandwidth, etc. Four basic categories can be identified

• Operator console devices, including six degree of free- dom input devices, and graphics user interfaces.

• Operator output devices, including video displays, and

other devices to present data to the operator.

• Remote environment sensor devices, including cameras,

sonar, and other sensors.

• System resources, including computation and communication devices.

These resources are generally limited. Thus, the visual

acts will have to compete with each other for control of the resources. Some form of conflict resolution needs to be

adopted if contention for resources arises. This means that

it is necessary to identify how important it is to get a particular visual goal satisfied.

3.2 Multi-Agent Architecture

The problem of resolving resource contention and pro- viding views automatically to the operator cannot be realised easily using either of the extremes of current agent

architecture design. In classical planning systems, the

planner generates the plan of achieving a goal in very fine

detail before the plan can be executed. These systems rely

heavily on the assumption that the environment is static, which clearly it is not, since the operator, who is a part of

the viewing systems environment, can perform the task in any number of ways.

On the other hand, purely behaviour based reactive

architectures [2] rely on the close coupling of sensors to

effectors. With these systems goals are always represented

implicitly according to a fixed, pre-compiled ranking

scheme. They also assume that the requisite activity of the system can be implied directly from the current state of the environment [3]. Again, this architecture is not entirely

suitable since visual acts are inherently parallel, and the operator is free to execute the task in whatever order he or she decides.

The system, therefore, must maintain a concept of the

global task, but still be responsive to the operators choice.

Our solution is to adopt a hybrid multi-agent architecture

[5] [12], with each agent executing in parallel to follow the operators progress as the operation is being performed. We

use this method in order to allow the simultaneous tracking

of each visual act by the viewing system. Although each

agent embodies a single goal, they must compete for the necessary resources to achieve their goal, and any conflict

must be resolved by negotiation. To do this, each agent is required to declare a qualitative measure of their contribution to the system. This requirement forces the system to

reflect on the environment and react to the operators

actions, while still maintaining a single global task constraint.

Initially the negotiation process may be as simple as choosing to allocate resources to agents that show the most

promise of delivering a goal. However, to prevent instability, where agents oscillate between goals, or resources are switched continuously between agents, some additional

rules may have to be applied. Again, simple rules, such as retaining the status quo until a particular threshold is reached, may suffice.

In order to map the problem onto a multi-agent architecture we have identified three approaches.

Resource Centred

Using this approach, each "resource agent" is assigned

sole control over a single resource (camera, sonar sensor).

At the beginning of the task, the operation is divided into

its component visual goals (as described above), and each

visual goal is injected into a central pool.

The goals in this pool are offered to the resource agents

for "adoption". The agents negotiate with each other to decide which agent should adopt which visual goal. Once

an agent has adopted a goal, the role of that agent is to manage its resource in order to provide the information

necessary for the visual act.

In order to cope with the evolving nature of the environment, the agents are required to continue their process of

negotiation. The effect is that each resource is occupied

with providing information to the operator that most

closely matches its situation in the environment.

Requirements Centred

Since the task is decomposed into its individual visual

goals, this approach models each goal as an agent. These

"requirements agents" are solely responsible for their visual goal being serviced by the available resources (Fig.

[2]).Each agent negotiates with the others for control of the

necessary resources to achieve its goal. As with the resource centred approach, the agents continue to monitor

the progress of the operator and renegotiate for control of resources as the operator progresses through the task.

277
parallelism

agent

y

coincidence

agent

i

L " ' t

insertion agent

Figure 2: Resource agents for peg-in-hole operation

Hybrid Approach

In the "peg-in-hole" example used above, one of our

three basic geometric constraints was given as Axes of peg and hole must be coincident.

To achieve this, the operator may choose to divide this goal into yet simpler tasks X-axis of peg and hole must be coincident.

Y-axis of peg and hole must be coincident.

The operators choice on how to divide the operation fur- ther will depend on the available cameras in the environment and on any specific kinematic constraints (for

example a camera may be constrained to pan/tilt control

only).

Using the hybrid approach we consider the problem in two parts. The first stage is similar to the resource centred

approach where each resource is modelled by an agent.

The visual goals are presented to the agents which use knowledge of the environment and of their respective cameras, to propose further subdivisions of the goals. All the new goals are then injected into the central pool of visual

goals.

In the second stage, the visual goals are themselves

modelled as agents. These agents are now responsible for negotiating with each other to gain resources to achieve

their particular visual act. The advantage of this approach is to increase the sys- tems flexibility and allow it to cope with particular hard- ware constraints, or perhaps, if there is a surplus of

resources, allows the system to maximize the benefit

gained from these resources.

3.3 A Multi-Agent Implementation

Our system makes very few constraints on the nature,

implementation, or function of an agent. Agents can communicate with each other, enter into negotiations, issue

instructions to the remote environment control system,

apply for a sensor "feed" from any part of the remote environment or from each other, or perform any other action

virtually without constraint. However, an agent must embody a single goal, process

or strategy. Agents must maintain their own local information necessary to perform their task. We may relax this rule for performance reasons, although only where this is trans- parent to the function of the agent.

With the exception of agents with control over a partic- ular piece of hardware, agents have no physical properties.

The "resource agents" are given control over only one specific piece of hardware, such as a camera or sonar device.

In order for the system to perform at all, the agents must

cooperate.

Our system also makes very few constraints on the nature of inter-agent communication, or agent to remote

environment communication. In addition to traditional explicit communication channels, we expect to use

implicit communication channels. For example, the basis

of the approaches outlined above were the visual goal or resource "pools". These pools can be seen as implicit communication channels.

Our implementation of agents as individual processes, perhaps distributed across several machines, allows us to develop solutions that are truly flexible. Agents are thus

forced to use the inter-process and network communications facilities available. This approach is necessary in order to simulate the dual operator scenario, however, it does also afford several additional benefits. Clearly, two implementations of an agent, so long as they maintain the same interface, are interchangeable. We

make use of this feature to implement some of the hard- ware resources in simulation. This allows us to develop the computational agents, test them in simulation, and then

simply plug in the real hardware control agents in place of

the simulation to test our algorithms with the real robotics

hardware. Figure [3] shows how each module in the sys- tem relates to each other. The modules (such as the robot

simulation module) are implemented as an agent or set of

agents, and communicate with each other using standard

point to point, and/or shared memory communication.

Our initial experimental aims have been to measure rel- ative timings for simple teleoperation tasks using a single

and dual operator system. We have begun with a simulated

environment in order to constrain the problem and to enforce the assumptions that we have made concerning the required behaviour of the camera control system and the accuracy of the workspace model. This simulation environment is built using a multi-agent approach as outlined

above.

The Active Robotics Laboratory at the University of

Reading will form the basis of experiments using real robotic manipulators and cameras. The Netrolab environment [10] provides a set of networked robotics resources which can be configured to support diverse applications.

278
SHARED MEMORY COMMUNICATION

INTELLIGENT VIEWING SYSTEM

ROBOT

SIMULATION

generate new \ robot position ]

send controls calibrate with

to pan/tilt head pan/tilt and video

HUMAN

TELEOPERATION ENVIRONMENT

Figure 3: Multi-Agent Modules

The resources include stationary and mobile robots, laboratory viewing cameras and sonar sensors. The networked

aspect of this laboratory suits the multi-agent architecture

that we have proposed, and makes it particularly easy to plug the computational modules of the simulation directly

into the laboratory [6].

4. An Autonomous System for Camera Control

The model we are investigating for automated camera

control is based on the hypothesis that knowledge of:

• the task setting,

• the task operation being performed,

• the set of visual acts associated with task operations,

identified above,

• the "information" content of the task environment,

will provide sufficient constraints on the operator's intentions to determine his or her visual goal(s) at any instant

during the performance of the task. Following the model presented above, we assume that

the task operation is designated by the operator at the

manipulator interfaces. The task setting can be assumed to be instantiated by the operator prior to task execution and

updated in tandem with the operator's actions. We assume,

that is, that the task environment is known. The set of visual goals is assumed to be identified a priori through auto- mated task planning or manual processing of task logs.

We also exploit the state of the manipulator in the remote environment, and the control actions of the operator to change this state, in order to determine the "information content" of the task environment. Specifically, we aim

to track the level and the rate of change of the information

associated with each visual goal.

Our aim is to develop a multi-agent model which will exploit this information to identify the current visual goal.

In this model an agent will represent a visual goal, and will use the above information to "argue" its case. The agents

which dominate will determine the visual acts presented to the operator and their relative configuration in the display

interface. A number of methods for combining the infor279
mation will be explored, including rule-based, fuzzy logic

and neural network methods.

We intend to conduct two sets of experiments. The first, which we designate the "passive operator" scenario, will allow us to provide a base line model with which to compare and contrast the impact of the automated viewing sys- tem and allow us to assemble data with which to prime the

latter. In the passive operator experiments, subjects will be

"led" through a sequence of task operations according to a pre-defined script based on the visualisation model. Quantitative performance data, and qualitative observations and

reports, will be used to assess the operator's reaction to

this mode of working. We will be particularly interested to determine whether the operator feels "in control". The second set of experiments will evaluate the multiagent model within an "active" operator scenario; the operator is free to direct the progression of the task. We are keen to observe the operator's performance within this sce- nario and his or her awareness of the viewing system. We

are particularly interested in determining the operator's

willingness to adapt to the viewing system as well as the required adaptation of the viewing system to the operator.

Another area where we will pay particular attention is the situation where there is no clear winner among the agents. We expect that an inertial factor will be need to be

introduced in order to smooth the transition between visual

acts, and therefore maintaining the "stability" mentioned

earlier. These experiments are now being developed and

will be reported in subsequent papers.

5. Summary and Conclusions

In this paper we have presented a model for automating

viewing for teleoperation. We have discussed several tech- niques for realising this model using a multi-agent architecture, and have shown how this architecture can promote

a flexible solution without incurring additional cost. During teleoperation our system will track the progress of the operator and support him or her by providing views

based on the visual acts model. This model is designed

with stability as an important goal, in order that the environment remain firmly under the control of the operator.

Man-machine interface design is a key tool in providing a symbiosis between the operator and the viewing system

which maintains stability in the latter. Using the peg-in-hole example, we are currently conducting tests on both single and dual operator controlled

simulated teleoperation environments, and have identified several key aspects that warrant particular investigation.

Our laboratory, which is well equipped for teleoperation

applications, will allow us to expand our experiments to use real robotic manipulators and camera viewing systems.

References

[I] Brooks, B. and McKee, G. T. 1995, 'Towards the Implementation of Visual Acts for Automated Viewing

During Teleoperation", SPIE Intl. Symp. Intelligent Systems.

[2] Brooks, R. A. 1986. "A Robust Layered Control System for a Mobile Robot", IEEE J. Robotics and Automation, RA-2,

pp. 14-23.

[3] Ferguson, I. A. 1992. 'Touring Machines: An Architecture

for Dynamic, Rational, Mobile Agents", Ph.D. Thesis,

University of Cambridge, U.K., Technical Report No. 273,

University of Cambridge Computer Laboratory.

[4] Hirai, J., and Nagata, T. 1994. "Agent-Oriented and

Distributed Assembly Task Planning for Multiple

Manipulators", Proc. IEEE Intl. Conf. Intelligent Robots and

Systems, pp 113-117.

[5] Haddadi, A. 1993. "A Hybrid Architecture for Multi-Agent

Systems", Proc. Workshop Cooperation Knowledge Based

Systems (CKBS-SIG), pp. 1 3-25, Keele, U.K.

[6] McKee, G. T., and Brooks, B. 1996. "Interactive Robotics

Using the Internet", Submitted Intl. J. Computer Science.

[7] McKee, G. T., and Schenker, R S. 1995a. "Human-Robot

Cooperation for Automated Viewing During Teleoperation",

Proc. IEEE/RSJ Intl. Conf. Intelligent Robots and Systems,

IEEE Computer Society Press, pp. 1 24- 1 29.

[8] McKee, G. T., and Schenker, R S. 1994. "Visual Acts for Goal-Directed Vision", Proc. SPIE Conf. Sensor Fusion VII, Vol. 2355, pp. 314-322.

[9] McKee, G. T., and Schenker, R S. 1995b. "Visual Acts for Remote Viewing During Teleoperation", Proc. IEEE Intl. Conf. Robotics and Automation, Nagoya, Japan, pp. 53-58.

[10] McKee, G. T., Schenker, R S., and Fryer, J., 1995. "Networked Robotics, Cooperating Agents, and an

Application to 'Visual Acts'", IEEE Workshop on

Architecturesfor Intelligent Systems, Monterey, C.A.

[II] Schenker, P. S., Peters, S. F., Paljug, E. D., and Kim, W.

S. 1994. "Intelligent Viewing Control for Robotic and

Automation Systems", Proc. SPIE Conf. Sensor Fusion VII,

Vol. 2355, Boston, M.A.

[12] Wooldridge, M., and Jennings, N. R. 1995. "Intelligent

Agents: Theory and Practice", Knowledge Engineering

Review.

280
A Unified Approach for Fast Recognition, Learning and Interpretation

of the Environment by an Autonomous Mobile Robot

Andreas Stopp and Lars Kiittner

Daimler-Benz AG

Systems Technology Research

Alt-Moabit 96a, D- 10559 Berlin, Germany

E-mail: stopp@DBresearch-berlin.de

ABSTRACT

In this paper we briefly describe our approach to recognition and

learning for autonomous mobile systems. Our system architecture

is a multi-skill-oriented architecture. Each skill in our architecture comprises components for reflexive behavior and components for complex behavior. Complex behavior is represented by our Applied Memory-Based Reasoning approach (A-MBR). This is a

scalable algorithm for fast recognition using a large extendable database containing sparsely coded knowledge. Application of AMBR to robot navigation is explained and learning principles are

discussed. We are working on the extension to 3D recognition. We

integrate principles from geometric hashing [2] and memory based

reasoning [4] approaches known in the literature. KEYWORDS: robot navigation, system architecture,

learning, memory-based reasoning, geometric hashing.

faster and more precise model matching and simplified

model learning.

Section 2 describes the architecture as well as our framework for A-MBR. Section 3 gives a short overview of Recognition by Geometric Hashing. Section 4 is dedicated to our robot application. Subsequent sections describe recognition/learning principles and experimental results.

2. SYSTEM ARCHITECTURE

A schematic of our multi-skill-oriented architecture for learning systems is shown in Figure 1 . It is similar to the well-known reference architecture [1]. Each skill frame

contains the functional blocks planning, reflexive behavior

(RBF-like NN) and complex behavior (based on models).

1. INTRODUCTION

Autonomous systems such as robots are used for transport

and service tasks in industry, manufacturing and space missions, where they have to solve various complex problems

in the future. It will become necessary to recognize the real world, to handle large data sets, to learn unknown objects,

environments, rules and behavior. A mobile system has to behave safely and reliably and to communicate at least on an

interpretable level to make its behavior, plans and intentions

transparent to cooperating systems and humans. To improve

acceptance, the behavior should be safe and transparent to the user. The system should be able to react to unexpected

events reliably and autonomously. Intelligent systems such

as autonomous mobile robots need models for intelligent behavior besides the reflexive behavior. Applications are intelligent sensor-based control together with model-based predictive control for motion and manipulation tasks. For

intelligent control we need improved fast prediction in the

real-time range using realistic, large model bases. We need

Intelligent Autonomous System (IAS)

Jehavior

Actuators

(£> able to learning

WM World Model

Planning

Preprocessing Feature Extraction Reflexive Behavior

Complex Behavior (A-MBR)"

Decision Making

PLPP

FRB

CB

D

Figure 1 Schematic of system architecture

281
In Figure 1 some functional blocks are labeled by the capital letter L which indicates that their knowledge representations are potentially open for learning. It would not be helpful to apply learning procedures to all knowledge

representations in parallel but flexible access to all knowledge representations offers high potential for new learning

principles. In this paper, we describe some aspects of our new Applied Memory-Based Reasoning (A-MBR) ap- proach. This is our framework for handling and representing

complex knowledge. A-MBR results in more intelligent behavior. It contains numerical and symbolic data of objects,

relations, and rules. It is a large extendable database of

sparsely coded knowledge. We use principles of the

Memory-Based-Reasoning approach for handling knowledge such as relevance feedback. Data sets are derived from

world models (e.g. CAD data) and from sensor data. Incomplete knowledge can be used. A-MBR provides symbolic

and numerical entries into the database, which means at least symbolic input and symbolic output on the communication

level and numerical input and numerical output on the control level (see Figure 2 ). The semantic layer is connected

to the numerical data layer of our object model database even if planning models or planning maps are temporarily

generated. In addition, the object database contains attrib- utes such as docking points, grasping points and relations,

rules, temporal logic, etc.

MMI, Guidance Systems, Cooperating IAS's Communication —

Intelligent Autonomous System (IAS)

Input A-MBR

Symbolic Knowledge

Numerical Knowledge

fooJie Output

lumcrkal

Controller

Real World

Figure 2 Schematic of A-MBR knowledge representation

Operator commands, messages from guidance systems, or messages from cooperating autonomous systems or from

higher control levels, can be communicated to the symbolic

level and can be interpreted by the planner. Cooperative

planning is possible by communication on the common

symbolic level and mapping into the local planner of each

autonomous system, enabling consistency of a common

view. Thus, recognition results, output messages and fault messages can be interpreted on the symbolic level and can be output via MMI to an operator or via messages to the guidance/planning hierarchy for continuing control or for

fault treatment on a higher control level or for changing

cooperation among autonomous systems. Unpredictable sit- uations can be explained on the symbolic level after recognition. If the system learns, it is able to generalize learned in- formation and transform it to the symbolic level. It is an open

approach for complex task planning and execution. This in- cludes task planning for different actions, skills for manipulation, and skills for motion.

3. GEOMETRIC HASHING

In our A-MBR framework Geometric Hashing as promoted

by [3] is the preferred method for organizing the search for matches in the model-based vision system. It provides the search engine portion of the object recognition system.

A model or object is uniquely identifiable via its features. Provided that there exists an edge representation for the object, edge middle points can be taken as so-called point features. A feature may or may not possess an attached attribute

list containing items such as edge orientation, length, or color. Edge representation and feature extraction form crucial inputs to the geometric hashing algorithm. With objects

characterized through point features, the object recognition

problem is equivalent to the problem ofrecognizing patterns

of point features. An object may, however, have many features. To keep the pattern-matching task ofreasonable complexity, the novel idea suggested in this paper - as opposed

to the approach pursued by [3] - is to recognize an object on the basis of portions of an object. A portion is a fragment

of an object containing only a bounded number of edges

from a local neighborhood. The total number of different portions per object may vary but is roughly on the order of

the number of edges that make up the object.

Before the process of pattern matching can commence, the portions must be normalized. The notion of a transformation base set is central in the scope of a portion. Such a base

set uniquely determines a similarity-invariant transformation (translation, rotation, scale) with which the features of

a portion will be transformed from their local coordinate sy- stem into the global hash space. Every normalized feature contains a reference to the portion it belongs to, which in turn contains the name of the original object as well as the transformation parameters. An object is thus multiply en- coded by means of its complete set of normalized portions.

The recognition phase proceeds as follows. In a preprocessing stage, an edge segmentation algorithm is applied to the

pixel image ofthe scene as recorded by the sensor. For every

edge, the corresponding feature together with its attribute

list is calculated. Next, a portion is composed as a collection

of neighboring edges. From the portion's base set of points, a transformation matrix is determined with which all the features of this portion are normalized. This normalized portion to be recognized is now compared against all previously

normalized portions stored in hash space on a feature-byfeature basis: every feature of the portion is compared

282
against every other feature in its (hash-space) vicinity. Because noise has to be taken into consideration, the features

pre-recorded in hash space are assumed to represent the

mean value of a normal distribution N(u., 2) (with covarian- ce matrix 2) rather than an exact position. The hash space

should be organized so as to provide quick access to all the

features in the vicinity of a given point. This is achieved by

subdividing the hash space into so-called bins (a mesh of

small boxes with pointers to a list of all features that fall into

the respective bin). Every feature in the vicinity of the portion's point feature gets a vote that increases with decreasing

distance and approaches 1 as the distance approaches 0. The

following formula is introduced as a rough approximation

for the vote a single feature may contribute: v(d) = exp (- X.

d), where d is the Euclidian distance and X > 0 an adjustable

parameter. All the votes that are computed during a single

hash table inquiry are accumulated on a per-portion basis

(and not a per-object basis). The portions with the two highest accumulated votes are tracked down and compared

against each other. A positive decision about a correct match

can be made if (i) the absolute value of the vote of the top

portion and (ii) the distance between the votes of the first and

second portions exceed certain thresholds. Otherwise, a vector with the first k "promising" portions (where k may

vary according to the distribution of the top votes) together

with the votes they received is memorized, and the next hash

table inquiry with a new portion of object features extracted

from the scene is launched.

If recognition on the portion level is not possible (because

of continued ambiguities), recognition on the object level might still be possible. In order to achieve this, the votes that were memorized at the end of each hash table inquiry could

be accumulated across inquiries on a per-object basis. In the

end, one object might have received an overwhelming accu- mulated vote that distinguishes it from the others.

4. ROBOT NAVIGATION

A promising application field of our A-MBR approach is ro- botics and in particular navigation, relocation, position es- timation, recognition/learning and planning as an integrated

solution. Two examples illustrating most aspects are briefly

described in Section 6.

Figure 3 shows the schematic of robot positioning by our A-MBR procedure using laser range data by means of

known positions of objects (walls). In our first simulated

scenario there are 16 rooms of different complex structure, few rooms are similar. New rooms can be generated and re- place others. We can place the robot at any position in the

16 rooms with any direction. We start the relocation process

by scanning the environment at the start position. Cyclic

position estimation and position correction is performed by

the A-MBRrecognition (e.g. disturbances by mobile objects are tolerated up to a certain extent). Each hashed object portion knows its current position. The output is the name of the room and the current robot position (computed using recognition and current laser range data). In case of grasping or docking, we get the geometric data for the controller (grasping points, docking points) depending on the recognized object and its position.

Current robot position in an unknown

room m

IS

to

lAnuivulinne f\t rA\t£*r*i ^Pfthra A?**"'*

Recognized

and derived

position

ipr

Figure 3 Object recognition for robot relocation

5. RECOGNITION AND LEARNING

A-MBR is able to recognize known objects, rooms and environments. Robustness allows the recognition of noisy or

partially covered objects. Figure 4 shows a 2D example of

a real laser scan of our laser sensor ( 1 80 degrees). Raw input

data are preprocessed (first-step noise cancellation). Feature

extraction detects lines and other features (depending on the

283
context). In addition, features such as segmentation points

and lines and points of further interest are derived. Fig- ure 5 shows the simulated set of extracted feature data of one complete scan (360 degrees) at time t.

Recognition starts as described above with selection of in- formation portions (feature neighborhood) from the feature

data, depending on the focus of interest (e.g. object nearest

to the sensor). The input data portion is compared to the

hashed object data portions. Each portion belongs to an object concept and a well-defined name, or it belongs to a pre- liminary concept of new learned data.

3000 > 1 1 i

-6000 «000 -3000 0 3000 1 00 0 00 00 0 00 0 10000 13000

Figure 4 Example of a real laser scan

As described above, the result is the number of matches. The

further recognition process is controlled depending on the number of objects matching. Resulting answers are for ex- ample: too many, some, few, one, or no matches. If there is exactly one match wilh high probability against the rest of

the data base, it is assumed to be correct. If there is more than one match, more sensor data are needed. No match means

either the wrong model data set is used, or it is an unknown

object and a candidate for learning. If results are not clear enough for precise decision making the recognition process

continues self-controlled sensor data acquisition step by

step. In most cases only one scan is required to achieve rec- ognition under normal conditions (one-shoot recognition).

We introduced new learning procedures for A-MBR. Self- controlled data acquisition uses some preferred options for self-planned active sensing, e.g. turning/moving sensor head, moving/changing position, motion to the remaining

points of interest, etc. Figure 6 shows the summarized data

set of extracted features computed (merged) from some

scanning cycles (and recognition/learning). One can see the more complete view compared to Figure 5 . We are accu- mulating sensor data on the feature level (merging numerical and symbolic features accompanied by failure correction).

\

1

\ ^<

*\

i

1 \

—'

1 1 —-+

1 1

—

1

Figure 6 Summarized feature data of a still unknown object after a few scan cycles (memory coordinates)

Figure 5 Extracted features of one laser scan (360 degree,

robot coordinates)

284
Besides detected lines there is additional information. In

particular, the remaining points of further interest which are used for continuing recognition if needed.

If the current task is positioning or recognition, the process

is stopped after successful recognition. The result is the name ofthe object/room and the current robot position. If we

need higher reliability, or the object/room seems to be un- known, the process continues until all available sensor data

are considered. After this exhaustive process (e.g. an object/ room has been completely scanned) the system has to decide

whether the object/room has been known before to the sys- tem or not. Thus the system can store the summarized in- formation as a candidate for learning, usable as preliminary

vague data. Real learning should be accepted after verification, e.g., or entering a known area again, or after confirmation of relevance by higher-level instances. One can see

there is no difference between the robust recognition procedure using all available methods for gaining information and

the process of exploration of learning new sensor data and

adding to the world model.

The most interesting and most important task is to find the

best voting principles. This is an open research field. Differ- ent voting principles on different voting levels are applied,

supported by voting on the symbolic level and on the level of relations and task context.

For systematic investigations of new voting principles and

their recognition probability and for evaluation of robustness, we are able to tune the disturbance of the input data. With increasing disturbance the recognition/learning process becomes more uncertain. Thus, it takes more time for

reliable decision making. The result confirms the robustness

of the approach.

Concept generation (self-defined terms) for new learned

data can be performed by taking the concept ofthe most similar data of the existing knowledge and adding some comments expressing similarity, uncertainty and the recognized

main feature differences compared to the feature vector of

the selected concept. Resulting information are e.g. "unknown object, but similar to object B differing in feature c".

If there is no similar knowledge the simplest procedure is

to append data to a running numbered list of unknown objects. Renaming of preliminarily named objects has to be

done at a certain instant of time by considering more knowledge (via world knowledge) or by knowledge acquisition

via MMI (communication to humans) using the quasi-symbolic description of features. This is a goal for future re- search.

Note that learning is done via sparsely coded knowledge

data by A-MBR. Hash-table entries are generated from ac- cepted A-MBR knowledge in order to keep all data consistent.

6. SELF-CONTROLLED LEARNING

Two examples describe the problems. In the first example, an autonomous system doesn't know where it is and it has

to explore the environment in order to find any known objects or relocation points (the curious robot). If we start with- out knowledge and without GPS information it defines the

current position, or a first good position (middle), of the un- known room as the origin of exploration (learning frame,

preliminary coordinates). If a first known object/position is detected it is able to transform all learned objects/positions

to the coordinate system of the known objects (knowledge

frame, global coordinates). The learning process has to consider the transformation via coordinates of the robot and its sensors (robot frame, platform coordinates and sensor frame, coordinates of active sensor).

Figure 7 Derived planning map for exploration with the

computed path from the current position (right)

to the next point of interest (left)

A second example of a goal-oriented navigation (fire fighting robot) is not concerned with exhaustive exploration but

with fastest motion toward one or more goal positions or

centers of interest (valve, stopcock, center of fire, injured

persons) It has an orientation toward the goal and learns onthe-fly. The first priority is the fastest move to the goal, but

it leams differences of the map, closed gateways using old

maps, or assuming free space. Its start position is known,

direction or goal position is known, but the area between is unknown (destroyed).

285
Both procedures are self-planning. Figure 7 shows an ex- ample of dynamic map generation and path planning for optimized recognition/learning/exploration process. Input to the planner is the latest update of the summarized information (features). The information is used to generate a gridbased planning model of desired size, granularity and desired value of obstacle growing. The planning process is performed after every new scan to plan an efficient way to the next point of interest (point of exploration) or even with

a higher cycle rate. We integrated our planning approach [5] using a diffusion algorithm. The resulting path and laser range data are the input to the platform controller (reflexive

knowledge) for collision avoidance and for following the

path to the next point of interest. If the planner doesn't find a solution, map generation switches to the higher resolution

level. Planning works with incomplete knowledge. All actions can be supervised, interpreted and reported using symbolic knowledge.

7. EXPERIMENTAL RESULTS

Current experiments are done on a Silicon Graphics. One

complete cycle of recognition as described above takes less than one second for a normal scenario. Target hardware is

parallel digital signal processor systems and multi-PC sys- tems. Previous investigations on scalability and speed have

been done on the Connection Machine CM-5 with 32 nodes

and the data-parallel language C*. Figure 8 shows the dependency of run time for object recognition (logarithmic) on the number of objects in the database (symbolic name of

the object, here # of the object in the database) . The objects

are polygons with a distinguished edge for control. The

hashed object portions consist of 5 edges in this experiment.

—I ' r time/s

-1 1 1 1 . . 7 ' >—

# of objects time to recognition s

128 0.0073 s /

1024 0.018 s /

16384 0.27 s /

65536 i.i s y

number of objects

1 10 100 1000 10000 100000

Figure 8 A-MBR - run time measurement on a parallel computer system - the Connection Machine CM-5 with 32 nodes

8. CONCLUSIONS

The A-MBR approach is able to support recognition and

learning in a very fast and accurate way. It is an open ap- proach for handling large data sets of sparsely coded and in- complete knowledge (numerical and symbolic). Our method provides a high functionality, in particular for robust

recognition in a dynamically changing world of objects, for exploration of unknown space regions accompanied by ro- bust path planning, and for interpreting actions and events on a symbolic level. The A-MBR method is scalable. Thus,

the algorithm is simply mappable onto parallel architectures. Tests and simulations have been done on different

hardware, e.g. Silicon Graphics, Multi-DSP's, CM-5. The

target robot platform is equipped with a laser scanner (company Sick). Later, a laser image camera (a laser distance camera manufactured in our company) will be applied. We

are working on the extension ofour approach to recognition

of 3D objects. On a Silicon Graphics, recognition of a simulated 3D object takes less than one second in a scenario of

4 selected objects and a database of 1 024 objects. We intend

to increase the A-MBR database with real 3D object data in combination with symbolic knowledge. We are investigating further extensions and new learning methods and plan to integrate them in our system architecture.

9. REFERENCES

1 1] Albus, J. S., Meystel, A.M. "A Reference Model Architecture for Design and Implementation of Semiotic Control in Large and Complex Systems," in Pro- ceedings of the ISIC-Workshop on Architectures for Semiotic Modeling and Situation Analysis in Large

Complex Systems in Monterey, CA, Aug. 27-30,

1995

[2] Rigoutsos, I., Hummel, R. "Massively Parallel Model Matching," IEEE COMPUTER, Feb. 1992, pp. 33-42

[3] Rigoutsos, I., Hummel, R. "A Bayesian approach to model matching with geometric hashing," Computer Vision and Image Understanding, 62(1): 11-26,

July 1995

[4] Stanfill, C, Waltz, D. 'Towards Memory-Based

Reasoning," Communications of the ACM, Vol. 29,

Nr. 12, December 1986. pp 1213-1228.

[5] Stopp, A., Riethmuller, T. "Fast Reactive Path Planning by 2D and 3D Multi-Layer Spatial Grids for Mobile Robot Navigation," Proc. of the 1995 IEEE

Int. Symposium on Intelligent Control, Monterey

CA, Aug. 1995.

286
Learned Emergence of Functional Symbol Systems

in Adaptive Autonomous Agents,

Guided by Skinner's Analysis of Verbal Behavior

William R. Hutchison, Ph.D.

Behavior Systems LLC

2002 Linden Drive, Boulder, CO 80304

Abstract

B.F. Skinner developed a detailed analysis of how the

remarkable phenomena of language and symbol systems could

emerge from the relatively simple processes of operant

conditioning. The creation of computer models of operant

conditioning— adaptive critic agents—finally enables this controversial theory to be tested. This paper describes simulations

training such agents following procedures derived from Skinner's

analysis, similar to those used to train humans. The simulations

demonstrate several of the basic elements of symbol systems, but more importantly that they combine to produce significant

emergent performances such as following memorized rules. Two

simulations contradict one of the supposed limitations of

conditioning theories of language, that they do not produce

generalization to untrained situations. These results encourage

further research in this parsimonious theoretical direction.

Keywords: emergence of language, computer

simulations, operant conditioning, syntax, rules

1. Introduction

One of the main controversies about symbol

systems and language is whether they can emerge from

learning, and if so whether specialized brain mechanisms

are required. B.F. Skinner's book, Verbal Behavior [19],

presented an extremely detailed analysis of how an adaptive

autonomous system can learn a complex symbol system

based on selection of behavior by its consequences, i.e., operant conditioning. There are currently 800 professionals

in a special interest group applying and expanding Skinner's

analysis in research and clinical work. However, despite the

considerable productivity of this theory, it has had little impact outside the field of behavioral analysis. The author

attributes this lack of impact to the fact that verbal behavior

research of this kind with human and animal subjects is inevitably open to question for two reasons: (1) The

daunting complexity of variables cannot be reduced by

imposing experimental controls with young human subjects as is done with animals, and (2) We do not know important

properties of the system we are studying: for example, when

a subject quickly learns a verbal function in our procedures,

is it attributable to operant conditioning alone or is there

also a specially-adapted brain mechanism?

Therefore, the recent development of computer

systems that can simulate the learning processes of operant

conditioning is especially valuable. Such computer "agents"

enable us to overcome both of these problems: we can know

the exact characteristics of an agent, and we can control the

agent's environment through its entire history. At the least,

such simulations can provide sufficiency tests of hypotheses

such as Skinner's. Moreover, if the training process is similar to what humans experience, and if the acquisition

process follows patterns like those of humans, the

simulations provide a stronger argument that human verbal

behavior is learned the same way. We advocated such

research in the early days of neural networks [7,8], and have

published earlier descriptions and research in

[7,11,12,13,21,22],

This paper gives an overview of seven years of

research on the training of verbal behavior in adaptive

autonomous computer models that simulate operant

conditioning, along with more detail on three pertinent

studies. We have used neural network models of the

adaptive critic type [1,15]. The architecture is shown in

Figure 1, and detailed descriptions and source code for our system is provided in [13]. The training has closely

followed guidelines suggested by Skinner's detailed analysis,

with exact training procedures specified in computer-based

training (CBT) format. The agent and training software is written in Java and operates in environments written in

VRML 2.0, though many of the older simulations have not

yet been converted from the original Smalltalk versions.

2. Overview of Skinner's Theory

Skinner's analysis requires very limited

assumptions about the properties of organisms: that they be

capable of operant and classical conditioning. Operant

conditioning could be roughly defined as the selection of

behavior by the value of its consequences, where we assume

the primary values have themselves been selected by a

287
Body

Sensors Network

Actuators

Recurrenl

Proprioceptive

External

(incl. Primary Values)

Primary Values Current Levels

PrirnaryValues" Current Levels

Leamipg

Change

Change

nmary Value Function

Environment

Figure 1 . Agent architecture: a type of adaptive critic

genetic evolutionary process (e.g., water is reinforcing

because organisms which are so reinforceable are more

likely to survive; see [4,20]. Reinforcing events strengthen

the connections between recently-emitted responses and the

stimuli which were present. Secondary conditioning is very

important in learning, and is nicely modeled in adaptive

critic systems. None of these assumptions is very

controversial either to adaptive agent modelers or to animal

researchers. Note that the agent architecture in Figure 1 contains only elements necessary for operant conditioning,

nothing specialized for symbolic processes.

Skinner proposed several basic units of verbal

relations, and argued that the complexity of human verbal

behavior and symbol systems is produced by variations and

combinations of these units in complex environments. The

basic units are relatively simple and easily

demonstrated (see below) Therefore, the two main

open questions seem to be:

1. Do the basic units of verbal behavior

actually combine to produce complex functional

behavior?

2. Does learning generalize to untrained

situations, as it must to explain human verbal

behavior?

The basic units are the tact, intraverbal,

mand, and autoclitic, along with a closely related

unit which has been called pliance. A tact (cf. contact) is defined as a verbal response, similar to naming, controlled by environmental stimuli such

as properties of objects or events (see Fig. 2a).

Neural network researchers have easily

demonstrated similar "categorizing" responses

controlled by stimulus patterns, though the category

is generally represented simply by which output is activated rather than by more complex naming

responses. Tacts may be nouns, adjectives, verbs,

adverbs, other parts of speech or smaller units such

as the suffixes. An intraverbal (Fig. 2b) is a verbal

response to a verbal stimulus, for example, saying

"4" in response to hearing "2 plus 2 is" or saying

"Denver" in response to hearing "The capital of

Colorado is". Intraverbals are often considered

trivial, yet all explicit knowledge can be stated as

intraverbals (cf. cognitive structures or world

"models"). A mand (cf. command) is a verbal

response with a characteristic consequence, which

is therefore typically evoked by corresponding states of deprivation; e.g., asking for water when thirsty.

An autoclitic is a verbal response controlled by a combination of verbal and nonverbal stimuli, and is therefore responsible for most grammatical

structuring. Pliance (cf. compliance) is a nonverbal

response to a verbal stimulus; e.g., lifting an arm upon

hearing "Lift your arm" (Fig. 2c).

Each of these units has well-defined stimuli and

responses, and they can be easily demonstrated in adaptive

critic agents, as in the first simulation described. Many

important verbal phenomena are variations of these basic

units; for example, abstraction or analogy occurs when

subsets of properties of objects control tacts, such as "animal" or "furmture." Other phenomena occur when

variables combine in the complexity typical of the natural

environment, such as tacting "heart attack" vs. "myocardial

enfarction" depending on both the condition and the

"audience" stimuli. However, we have suggested above that

288
(a)

Tact/

"Naming"

Context

Stimuli

(b)

Intraverbal

Say

:Red"

Context

Stimuli

(c)

Pliance

Say

"Move

Back"

Context

Stimuli

Agent

Moves

Back

Figure 2. How Tact, Intraverbal, and Pliance Combine to Produce Rule-Following

the more challenging issues are whether these units combine

to produce complex language-based functioning and

whether they generalize to untrained situations. We will

briefly describe simulations that give initial affirmative answers to both of these questions.

3. Tact + Intraverbal + Pliance

=> Rule-Following

An extremely important function of language is enabling culture itself: the ability of humans to describe

useful relations or rules to others, who can then behave

effectively without having to learn personally through

extensive and often dangerous direct experience. Werbos

[24] has shown the power, and argued for the necessity, of

"world models" in intelligent agents, but like most theorists

he has created a hybrid system with a separate module for

this function. Can we simulate this functional language

using the verbal units described in a much simpler, operant

system? Our formulation is as follows: verbal relations such

as rules can be stated as intraverbals; an example we will use is "If red then move forward." For the intraverbal to be

functional, its elements must have "meaning" to the agent;

i.e. both the conditions (IF) and the actions (THEN) must

connect appropriately to the real world. Logically, we look

for two corresponding kinds of units: on the sensory side, we

need a unit with environmental stimuli as inputs and with

verbal responses as outputs; on the response side, we need a

unit with verbal inputs and with actions on the environment

as outputs. The tact meets the former requirements, and

pliance meets the latter. Figure 2 shows how these units

should fit together to produce rule-following behavior,

according to this relatively simple formulation.

Upon sensing environmental stimuli, the agent

utters a corresponding tact, which produces stimuli that

evoke the intraverbal response; the intraverbal produces

stimuli that instruct the appropriate action on the

environment. Observations of humans [6,18] suggest that

humans often behave in exactly this way when following

memorized rules. In this simulation, the two rules were "If red then

move forward" and "If green then move back." Our

objective is for the agent to memorize the rules and learn the

meanings of their elements and relations such that it can

follow the rules the first time after learning them, without

having ever done those behaviors in those conditions

previously. First, we trained a naive agent to imitate the

sounds A, B, F, G, I, M, R, and U by presenting the sounds

and giving simulated calories if the agent produced

corresponding sounds. Using those sounds as prompts

which were then faded out, we trained the agent to tact the

color of red, green, and blue objects, where saying "red"

required the agent to say "R" then "A", green was "G" "I",

and blue "B" "LP'. For example, a red object was presented

along with the sound sequence "R A", after which the

agent's correct imitation of the sounds was reinforced. The

"R A" prompt was faded until the agent could name the

color without any prompt. Similarly, prompting was used to train the agent to say "R A M F" (= "red, move forward")

and "G I M B" (= "green, move back"), with no colors

present (Note that humans typically say rules in a minimal

form without "If' or "then" [18]). Finally, we trained the

agent to move forward or back after hearing and repeating

the instructions "move forward" or "move back" ("M F", "M

B"). The detailed training procedure is described in [1 1, 12],

and the exact code for agent and training are in [13], The

training procedures are like those a behavioral trainer might

use with humans. At the end of this training, the agent

moves forward when it sees red and moves back when it sees green, the very first time it sees these colors after learning

the rules. This rule-following is mediated by the sequence

289
of verbal responses as we predicted, exactly as observed with

humans following rules.

4. Does Learned Syntax Generalize?

Two simulations have shown that, contrary to simplistic predictions ([3], but see [14,17]), this process of

learning can produce grammatical ordering that generalizes

to novel instances, as it must to explain human performance.

The first simulation shows that after learning only

a few examples of saying adjectives (color) before nouns

(based on shape), the agent will do the same in a novel case. In this simulation, the agent was first taught to tact blue,

green, and red colors with unnamed shapes, using the same

procedure as in the prior simulation. Similarly, the agent was taught to tact circle, square, and triangle shapes with

unnamed color. Of the nine possible combinations of color

and shape, eight were then trained by presenting the

combined stimulus (e.g., a red triangle) and reinforcing only

the correct sequence of verbal responses ("red triangle", or "R T" in the simplified language). It is very notable that even before the end of this training phase, the agent named

two of these stimuli correctly the very first time they were

presented. This cannot be explained by chance, since the

agent's natural tendency is to repeat reinforced responses, so

that it would say "R R" if it happened to say "R" first and

received reinforcers, as occurred at this stage of training.

When the ninth combination was presented, the agent used

the correct grammatical ordering the first time it ever encountered a red circle, even in a test when hundreds of

irrelevant responses occurred between the last training trial and the first test presentation.

Simulations enable us to analyze and understand

surprising behaviors such as this. We have found that an

extremely useful relation the agent learns is that, after

saying something, saying it again will rarely produce

reinforcement even though the conditions that evoked the

response the first time are still present (e.g., red is still

present). Not only is it generally true that listeners do not

want to hear the same information twice, but suppression

also functions as a modulator for syntax in many cases. In

the red circle case, saying "red" suppressed saying it again

so that saying "circle" would become relatively stronger.

The architecture in Figure 1 enables this to be learned by the

well-known mechanism of recurrence: the agent's responses

produce stimuli for subsequent responses. This mechanism

will show up again in the next simulation.

The second simulation addressed a more

challenging situation. Can an operant agent learn to follow

implicit grammatical rules to compose novel relational

statements describing its environment? For example, can an

agent learn to make descriptive statements of the type "X is

left of Y" when presented with pairs of objects in left-right

relations, including the very first time either of the objects

has been in that relation?

The test was for the agent to learn to say, for

example, "Carp is left of tuna" when those objects were

presented visually in that relation, even when neither object

had ever been seen in that relation before. The agent was

taught to name four visual patterns, called shark, tuna, carp, and jellyfish (named "S", "T", "C" and "J" in our simplified

language). Then these objects were presented within its

field of vision but not directly in front of its eyes, so that it learned to move its eyes to look directly at each object and

then to name it (this procedure is consistent with the concept

of "active vision" [2]). In the main training procedure, the

agent received only 18 training trials of 2 cases each, one in

which a shark was left of a tuna and one in which a jellyfish was left of a carp. The agent learned to look at the nearest

object, name it, look left or right as necessary to look at the

second object, say either "is leftOf* or "is rightOf* ("I L" or

"I R") as demanded by the situation, then to name the

second object. Correct responses were reinforced with

simulated calories. After this brief training, a test situation was presented: a carp to the left of a shark. Even though

those objects had not been seen in those positions before, the

agent correctly said, "Carp is left of shark" ("C I L S"). How

did it learn this generalized syntax after only 2 examples of

it? As in the previous simulation, an examination of its network at each point in time showed how locally-available cues were adequate. Upon seeing an object, its strongest

initial response is to orient toward it; then seeing it directly

ahead, the strongest response is to name it. Naming it produces auditory and proprioceptive stimuli that suppress

naming it again, so orienting toward the second object

becomes the strongest response. Now there are two strong

responses: one is to name the second object because the

agent is now looking directly at it, and the other response is

to say the relation "is leftOf' because of the stimuli from

having just done the corresponding orienting response. Its history of reinforcement has produced a network that gives

the relational response more strength, given this stimulus

pattern. But after stating the relation, the responseproduced stimuli suppress saying it again and the naming

becomes strongest. This is a very nice emergent solution

because the agent can learn many different relational

assertions without much mutual interference. Such control

of relational statements by stimuli from the agent's own

prior movements is quite general, according to Skinner's

[19, pp 340-343] expansion upon Tooke's [23] argument

that relational words generally have their roots in actions.

290
5. Other Verbal Phenomena That Have Been

Simulated

The following is a listing of verbal phenomena the author

has simulated, including ones described above:

Generalized echoic behavior: imitation of sounds

Generalized textual behavior: reading from text Tacting: naming objects, actions, properties of objects and

actions

Intraverbals: verbal associations, phrases, sentences, rules

Instruction-following ("Move back"-> move back)

Generalized word ordering (adjectives before nouns: "blue

circle")

Generalized relational descriptions of scenes ("Tuna is left of shark")

Generalized identification of matching vs. non-matching

pairs of objects (Are 2 objects the same?)

Same, but with delay between stimulus presentations

Sequences of verbalizations maintained by reinforcement

only at the end of the sequence

Symmetry (learn "A = B", say "B = A"

Transitivity (learn "A implies B" and "B implies C", say "A

implies C"

Generalized compliance with memorized rules when

condition is first encountered

Interplay of rule-following and direct learning from

experience

Creativity: recombine learned responses to solve problems

[9]

Rapid training of verbal responses using prompt and fade

procedures, as used with humans

Some of the verbal phenomena we would like to simulate in the near future include: using real voice input

and articulatory speech output; more complex grammar

(e.g., "The cat that ate the mouse jumped"); using larger,

English-like words; training large verbal repertoires;

generalized use of "not"; rhymes and puns; self-editing;

combining relational statements ("Frog is on log" + "Log is beside tree"); and tacting of private events such as pain.

6. Discussion

Our simulations serve as sufficiency proofs that

adaptive autonomous agents of the adaptive critic class can

learn important and fairly complex functions of symbol

systems with proper training. A critical property of this

analysis is that it brings language into a larger

biological/economic framework: Each set of behaviors

produces consequences sufficient to maintain it, or

equivalently, it contributes to the fitness of the organism.

Rule-following generally produces valuable results, since

people learn to discriminate reliable from unreliable rulegivers, as an inherent part of operant learning. In contrast,

mechanistic theories of rule-following which produce

automatic compliance fail to explain how people learn to avoid bad advice. Even more stringently than overall value,

Skinner's theory requires that every action of each agent at each point in time be learnable and sustainable by actual

consequences [19, pp. 84-90], a point emphasized in a

simulation of a two-agent ecology in [10]).

Even if the training used in these simulations is characteristic of disciplined behavioral training techniques,

some critics may object that it is uncharacteristic of human

experience. While typical caregivers are not as consistent as

professionals, observations show that humans provide

extensive language training in the natural course of

interacting with children [16]. For example, a parent might

show a child blue objects, say "Blue" to each, and show a

positive reaction to the child's saying anything

approximating "Blue." In subsequent cases, prompts will

typically be made weaker and better pronunciation will be

required.

The results of these simulations support Skinner's

analysis, while its consistency with a broad biobehavioral

perspective gives the theory further appeal. The scientific

principle of parsimony compels us to pursue the hypothesis

that symbolic language functions emerge from accepted

processes of operant conditioning without any need for

language-specific brain mechanisms.

7. References

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Intelligent Control: Neural, Fuzzy, and Adaptive

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brain theory and neural networks. Cambridge, MA: MIT

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[3] Chomsky, NA Review of Verbal Behavior, by B.F.

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[4] Donahoe, J.W., Burgos, J.E., & Palmer, DC. A

selectionist approach to reinforcement. Journal of the

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complex behavior. Boston: Allyn & Bacon.

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[7] Hutchison, W.R. Cognitive vs. Behavioral Psychology in

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Proceedings of the first international conference on neural

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behavior patterns as a function of subsistence level of

reinforcement in neural networks and animals: Necessity is the only mother. Presented at the Association of Behavior

Analysis Conference, Atlanta, May, 1995.

[10] Hutchison, W.R. Demonstration of work from the 7G

Computer Modeling of Behavior Project. Presented at the

Third Simulation of Adaptive Behavior Conference,

Brighton, England, August, 1994.

[11] Hutchison, W.R. Teaching an Agent to Speak and

Listen with Understanding: Why and How? Online

proceedings of the Intelligent Information Agents

Workshop, CDCM, Baltimore, Dec. 1-2, 1995.

http: //www. cs. umbc. edu/~cikm/iia/submitted/viewing/whutc

hi. html

[12] Hutchison, W. R. Demonstration of Training Imitation,

Language, and Cognition in a Behavior-based Agent.

Presented at the Fourth Simulation of Adaptive Behavior

Conference, Cape Cod, MA, September, 1996.

[13] Hutchison, W.R. Simulations of operant behavior;

software and documentation, v. 1.0. Cambridge, MA:

Cambridge Center for Behavioral Science, 1997.

[14] MacCorqudale, K. On Chomsky's review of Verbal

Behavior. Journal of the Experimental Analysis of

Behavior, 13, 83-89, 1970.

[15] Miller, W.T., Sutton, R.S., & Werbos, P.J. (Eds.)

Neural networks for control. Cambridge, MA: MIT Press,

1990.

[16] Moerk, E.L. A first language: Taught and learned.

Baltimore, MD: Paul H. Brookes, 1992.

[17] Palmer, D. Chomsky's nativism: A critical review. In

P.N. Chase & L.J. Parrott (Eds ), Psychological aspects of

language (pp. 49-60). Springfield, IL: Charles Thomas,

1986.

[18] Potter, W. F. Comparison of Selection-based and

Topography-based Verbal Behavior. Doctoral dissertation,

Western Michigan University, 1996.

[19] Skinner, B.F. Verbal behavior. New York: AppletonCentury-Crofts, 1957. (currently available from B.F. Skinner

Foundation)

[20] Skinner, B.F. The ontogeny and phylogeny of behavior.

Science, 153, 1203-1213, 1966.

[21] Stephens, K.R. & Hutchison, W.R. Behavioral personal

digital assistants: the seventh general of computing. The

Analysis of Verbal Behavior, 10, 149-156, 1992.

[22] Stephens, K.R. & Hutchison, W.R. Behavior analysis

and the quest for machine intelligence. Educational

Technology. 52-61, October, 1993.

[23] Tooke, J.H. The Diversions ofPurley. London, 1857.

[24] Werbos, P.J. Consistency of HDP Applied to a Simple

Reinforcement Learning Problem. Neural Networks, 3, 179-

189, 1990.

292
LIKELIHOOD, MIXTURE, SYMBOLS

TOWARDS QUANTUM FIELD THEORY OF SYMBOL

Leonid I. Perlovsky

Nichols Research Corporation, 251 Edgewater Dr., Wakefield, MA 01880

Tel. 617-246-4200, Fax 617-246-0065, E-mail nrcbmo@world.std.com

ABSTRACT: A mathematical theory of a symbol as an

adaptive process is presented. It is founded on the theory of

modeling fields, in which learning is based on adaptive

internal models. Quantum computation algorithms of the

modeling field theory are developed. I discuss computational,

philosophical, and physical aspects of the dynamic theory of

the symbol.

KEYWORDS: semiotics, symbol, computational

intelligence, quantum computation, neural networks, internal

models, learning algorithms, philosophy of mind

1. INTRODUCTION

The popularity and subsequent fall-out-of-favor of

"Symbolic AI" left many researchers with a bad taste towards

the word "symbol". But, an impression that "Symbolic AI"

represented the mathematics of symbols is very wrong. A

symbol is not a monumental piece of a bronze sitting on a foundation of stone. A symbol is a fleeting vortex of the

interacting perceptions, feelings, a priori models, adaptation,

attention, behavior and concept formation. In other words, a symbol is a process. It is a process of thought.

Semiotics is a science devoted to studying signs and

symbols. The founders of semiotics (Pierce, 1935; Morris,

1971) introduced the notion of a sign as a trilateral unity of

sign-vehicle, (the media used as a sign), designation (the

object which the sign refers to) and interpretant (or interpreter, a mind or an intelligent system, which interprets a signvehicle). The process of interaction within this triadic unity is called semiosis. Morris decomposed this process into the

three dyadic relationships-processes: syntactics (relations

among sign vehicles), semantics (relations between signvehicles and their designata), and pragmatics (relations between

sign-vehicles and their interpreters). A contemporary tendency

is to use a word semiosis for the learning process at a system

level involving multiple triadic processes. When a single

triadic process is concerned, a word sign is used in relatively

simple, non-adaptive cases of semiosis, when there is an a

priori known and fixed straightforward way of relating a signvehicle to designatum (such as a look-up table); and, a word

symbol is used in complicated cases of a single-triadic

semiosis, when an adaptive process is needed to establish the

relationship; this adaptive process of semiosis is a symbol.

According to Pribram (1971), signs within the brain are

acts of communications that are invariant to the context, while

symbols are context dependent. Signs are the results of the

associative cortex affecting the input sensory systems. These

are the a priori, less-adaptive aspects of the internal models.

Symbols, according to Pribram are the results of interaction

between frontal lobes and limbic system, they are stimulants

to actions and are sensitive to context.

In this paper, mathematical and physical theories of the

symbol are developed. They are based on the modeling fields

theory (MFT) developed previously by the author (Perlovsky,

1996; Perlovsky et al, 1997). MFT combines a priori

knowledge and adaptivity of the internal model. The global

model describing "the world" is composed of multiple "local"

models (similar to a visual field being composed of edges,

etc.). MFT establishes a correspondence between subsets of

local models and subsets of input data, while adaptively

learning models. This process is similar to a central problem

in several areas of artificial intelligence and pattern recognition

[Winston, 1984; Negahdaripour & Jain, 1991; Segre, 1992].

Traditional methods of solving problems of this kind lead to algorithms of exponential complexity, which are not

physically realizable even for problems of moderate

complexity, and which can not therefore serve as physical

models of intellect. MFT leads to algorithms of linear

complexity. A computational system of MFT is composed of

multiple interacting loops adapting individual models and

competing for evidence in the input data. Each loop involves an individual internal model, a measure of its similarity with

the data, and its adaptation mechanism that increases the

similarity. Each loop is a semi-independent intelligent agent

performing an adaptation-recognition of a category. It involves a sign-vehicle that is the category name (or internal

MFT message-code), a designatum that is a subset of input

data corresponding to the category, and interpretant that is the

MFT system that interprets and acts upon the recognized

category. Thus, MFT agents recognizing and adapting

categories are dynamic symbol-processes. The dynamics of

agent-symbols, the process of semiosis, is composed of

syntactics, semantics, and pragmatics.

Where are the dynamic symbol processes physically

realized in the brain? A traditional interpretation is that they

are realized by networks of neurons, such as described in (Perlovsky et al, 1997). An alternative interpretation is that

each neuron has a microstructure capable of performing

complicated computations. These sub-neuron computations

are hypothesized to be performed by quantum process taking

place in microtubular neuronal substructure [Hameroff &

Watt, 1983]. Keeping in mind this possibility, I describe a quantum system implementing MFT. The next Section 2

summarizes the mathematics of classical MFT. Section 3

describes quantum computation MFT algorithms, QMFT.

Section 4 discusses results and relationships between

mathematics, Kantian theory of mind, and classical semiotics.

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2. MODELING FIELD THEORY

MFT considers (1) a set of input data {X(n), n e N},

where each member is a vector in D-dimensional space, X =

{X<j, d = 1,... D}; (2) a set of adaptive categories {h € H},

which are characterized by internal parameters {Sh} and by

models of the data {Mn(Sh, n)}; and (3) a similarity measure between the sets of models and data, L({X},{M}). A set of

parameters is finite, Sh = {Sa n , a = 1,... A}, but not

necessarily limited, and a set of categories is not fixed, its cardinality H is finite, but may vary in the process of learning.

A similarity measure is designed so that it treats each model as an alternative for each piece of data

L({X},{M}) = J! I r(h) *(X(n) I h), (1)

neN heH

here /is a conditional partial similarity between data vector

X(n) and model Mh- For example, /can be selected as a probability density function. Then L is a total likelihood (this

interpretation does not require statistical independence among

data vectors n and n': dependencies can be accounted for by

considering X(n') as parameters of the models for the data

vector n).

The problem consists in concurrent recognition and

adaptation of categories. Adaptation is achieved by estimating

internal parameters S, and recognition consists in obtaining a

partition of data among categories,

{N} = {Ni IN2 I...|NH }, (2)

that decides, which model h corresponds to an observation n

(here Nh is a subset of N). The recognition and adaptation

process shall maximize the similarity (1). When likelihood is used as a similarity measure, this is a problem of the

maximum likelihood estimation.

Categories activated by high similarity values produce

actions, including generation of messages transmitted within

the intelligent system, which acknowledge the category

activation. Messages include the category name code and

model parameters. They can serve as input data for other

categories and can be used for control of actuators.

Correspondingly, data are sensory data or internal messages,

and models represent patterns of messages and sensory data.

The above mathematical framework is fairly broad and

encompasses most formulations of intelligent adaptive

systems. It includes as particular cases, statistical and modelbased pattern recognition, complex adaptive systems, neural

networks, and systems of intelligent agents. The above

formulation addresses "higher-level" intelligence functions of

recognition and adaptation. A compete intelligent system

would include lower-level drives for survival, reproduction and,

in case of an artificial system, a robot or infobot, drives for

producing specific tasks it was designed for. Each individual

model, Mh, together with the process of its adaptation and

recognition defines a symbol-process.

In case, when a set of observations, N, corresponds to a

continuous flow of signals, for example, a flow of visual

stimuli in time and space, it is convenient instead of eq.(l) to consider its continuous version,

L = exp J ln( X r(h) /(X(n) I h) ), (3)

N heH

where N is a continuum, such as time-space. In this case, models describe a continuous modeling field, conditional

partial similarities can be compared to Lagrangian, and

maximization of similarity L can be compared to minimization of action in the physical field theory.

MFT solution of this problem uses fuzzy adaptive logic

[Perlovsky, 1996]. Adaptive fuzzy class memberships f(hln),

associating each data vector n with each category h are defined

as:

f(hln) = r(h) /(X(n)lh) / I r(h') /(X(n)lh'). (4)

h'eH

In case of the maximum likelihood estimate, upon

convergence of the estimation procedure, f(h I n) can be

interpreted as a posteriori probabilities. An internal dynamics

of the Modeling Fields (MF) is given by

H

df(h I n)/dt = f(h I n) £ { [8hh' - f(h' I n)] •

h'=l

[3ln/(X(n)lh')/3Mh'] 3Mh'/3Sh' • dSh'/dt, (5)

dSh/dt = {I f(h I n) [3ln/(X(n)lh)/3Mh] 3Mh/3Sh, (6)

N

where

8hh' is 1 if h=h', 0 otherwise. (7)

Parameter t is the time of the internal dynamics of the

MF system. A theorem was prooved that equations (5)

through (7) define a convergent dynamical system of MF with

stationary states defined by maxjgjjjL. It follows that the

stationary states of an MF system give the maximum

similarity solution of the category adaptation and recognition

problem. When likelihood is used as a similarity, the

stationary values of parameters {Sh} are asymptotically

unbiased and efficient estimates of these parameters [Cramer,

1963]. A computational complexity of the MF method is linear in N,

complexity(MF) = C2H-N, (8)

where C2 is defined by the relaxation time of the MF system

and is likely to be independent of N (or depends weekly). In

this way the MF system solves the problem of the

exponential complexity associated with traditional methods.

Fuzzy class memberships f(h I n) define a fuzzy partition of set N, which can be used to define a non-fuzzy partition of the

type of eq.(4): Vn, max^ f(h I n) => n e NhMFT describes an intelligent system composed of

296
multiple adaptive intelligent agents-symbols: each categorymodel-symbol is "dormant" until activated by a high

similarity value. Every piece of data may activate several

categories-symbols, which "compete" with each other, while

adapting to the new piece of data. Adaptation and other

actions by activated symbols are largely independent from

most other symbols, except for those competing with each

other. Most important actions by activated symbols are transmission of messages and sustaining the loop of

adaptation of their own parameters. Evolutionary computation

is naturally incorporated within MFT: transmitted messages,

including category parameters and other aspects of categorymodel-symbols are strings-objects of evolutionary

computations and are employed by modeling field systems for

adaptation of its structural components that could not be

incorporated in a continuous fashion and are not the subjects

of adaptive MFT symbol-loops. The overall architecture of

MFT categories-symbols can combine heterarchical and

hierarchical organization.

3. QUANTUM MODELING FIELD THEORY

(QMFT)

It is possible that quantum processes play a role in

neuronal adaptation [Hameroff & Watt, 1982]. Therefore,

apart from implementing MF as a computer algorithm it is interesting to consider a possibility of realization of MF as a quantum system, QMF. Quantum computing received

significant attention as a potential method of breaking through

the limitations of classical computing paradigms since

Feynman [1982, 1986] draw the attention to this area of

research. The following two limitations of classical

computational systems are expected to be surpassed. First,

classical systems dissipate a finite amount of energy (~kT) per

1 bit for every operation. Second, a number of important

problems in classical computational intelligence, in the

number theory, and in other fields are very hard in that their

solutions require an exponentially large amount of

computational steps as a function of the problem complexity.

(While the MF discussed in the previous section addresses the

exponential computational complexity of the symbol

adaptation, still quantum algorithms promise tremendous

advantage in computing power). Quantum computing is expected to surpass classical computing for the following rea- sons. First, quantum computation proceeds without energy

dissipation until the process of quantum measurement, which

potentially can be postponed until the end of the computation

process. Second, a quantum system can exist in a superposition of multiple states, so that multiple computational paths (including all possible combinations of path

segments) can potentially be performed in parallel, within a

single process of quantum interference between the quantum

system states. In QMF, an internal dynamics of the symbol

adaptation occurs as a process of quantum interference (in place

of eqs.(4, 7)), and a partition similar to eq.(2) is obtained in the process of quantum measurement. Let us outline the main

characteristics of QMFT.

QMFT describes a system which is characterized by

quantum states I h > and which interacts with the external

world characterized by quantum states I n >. The entire system

including the QMF system and the external world, in the

general case, is described by a quantum state which is a superposition of states

( I h > I n > ), H

^(t)= I I Cnn I h > I n >. (9)

N* h=l

Here integration over n € N* includes spatial (and possibly

other coordinates of the external world) but excludes time, t. Because of the probabilistic nature of quantum theory, we

consider similarities given by likelihoods, and fuzzy class

memberships being probabilities. Quantum amplitudes Cnn

are related to the probabilities defined in eq.(4) according to the

rules of quantum theory

f(h I n) = I Chn I 2

(10)

Generally, the QMF system is in a mixed state and is described by the density matrix [Neumann, 1910; Sakurai,

1985],

Phl,h2(t) = 1 Ch l, n C*h2, n , (ID

N*

or, equivalently, by the density operator

H

p(t) = I Ihl>phi,h2<h2l. (12)

hl;h2=l

Equations of motion are given by a Hamiltonian,

therefore the next step is to define the Hamiltonian in such a way that the dynamics of a QMF system would lead to a solution of the considered problem of the dynamic symbol

adaptation. Two types of quantum systems are considered

below, first, a nonequilibrium quantum statistical system

evolving to Gibbs distribution and second, deterministic

Hamiltonian quantum dynamical system.

3. 1 Gibbs Quantum Modeling Field System

Consider the conditional similarities to be given by

conditional probability distribution functions, or conditional

likelihoods. Let us define the Hamiltonian so that the QMF

dynamics would lead to a Gibbs distribution with probabilities

defined by the similarity eq.(l). Following well known

principles of the quantum statistical physics [Feynman, 1972;

Zubarev, 1971], let us define the Hamiltonian through its relationship to the pdf. The dynamical variables of this

system are unknown parameters {Sh}, while the data values

X(n), n = 1,... N, are fixed, therefore the Hamiltonian,

297
H = -lnpdf({Sh } IX(1),...X(N)). (13)

Using Bayes' theorem,

pdf({Sh}l{X(n)})= pdf({X(n)}l{Sh })pdf({Sh })/pdf({X(n)}). (14)

Here pdf( {Sh} ) can be considered constant in absence of prior

information concerning values of these parameters. In this case, pdf( {X(n)} ) is also constant, because in absence of a

priori values of these parameters it has to be invariant. Thus

the Hamiltonian can be written as

H = - In pdf( {X(n)} I {Sh} ) + const. (15)

Comparing eq.(15) with eq.(l), we conclude that in absence of

a priori information on the parameter values, the Hamiltonian

is local and the Hamiltonian density !H can be introduced

H = - In (pdf(X(n))), H = j H + const. (16)

N(t)

Here N(t) stands for a set of observations available at time t. This underlines the fact that the Hamiltonian is defined using

past data only (in case when n includes time). It is a nontrivial fact that availability of a priori values for the

parameters may result in a non-local Hamiltonian.

The Hamiltonian eq.(16) defines the dynamics of the

density operator [Feynman, 1972],

p (t) = exp (- i J H ) p (0) exp ( i \ H). (17)

t t

In order to complete a correspondence between Gibbs QMF

(GQMF) and classical MF, we define an operator of internal

model parameters S as follows

S = X I h > Sh < h I. (18)

heH

Thus, the partition of the type given by eq.(4) and the values

of internal model parameters {Sh} at time t can be obtained in

the process of the quantum measurement

f(h I n) = Tr[ I h > < h I p(t) ], Sh (t) = Tr[ S p(t) ], (19)

An initial state of a GQMF system is specified according

to the initial state of the MF: one can choose initial values of

Sh based on a priori phenomenological considerations, this

leads to initial probabilities f(h I n) defined according to eq.(4),

and to initial values of the density matrix p(0) defined

according to eq.(17), (18),

Phi h2(0) = J ei<t>(hlln) + i<t,(h2ln) [f(hlln)f(h2ln)]

1/2

(20)

N*

The phases (j) in this expression are left undefined and can be

chosen to suit concrete problems at hand. One way to avoid a need to choose phases is to use an alternative initialization

procedure: define a non-fuzzy partition according to eq.(2),

leading to a diagonal density matrix, and compute initial values of the model parameters Sh from eq.(6).

In a GQMF system described above, the finite temperature

of the system (and therefore, the finite accuracy of the

computation) does not interfere with computations, but is a

part of the system dynamics. On the one hand this is a highly

desirable property for any practical implementation of a quantum computing system. On the other, interaction with a thermal reservoir leads to irreversible energy dissipating

processes involving quantum measurements. A desirable

compromise is to reduce interactions with a thermal reservoir

to a relatively rare occasion, which will ensure Gibbs

distribution and will correct accumulating phase errors, while

in between these interactions a GQMF system will evolve

according to Schroedinger equation (17) without energy

dissipation.

3.2 Hamiltonian Quantum Modeling Field System.

In this alternative approach, let us define the Hamiltonian

so that the Hamiltonian QMF (HQMF) dynamics leads to the

symbol adaptation. We will do this for a simplified case of

MF, when the conditional pdfs defining similarities are Gaussians with unit covariances. Let us emphasize, that this Gaussian-symbol model leads to the Gaussian mixture

distributions for classes described by more than one symbol,

which can model probability densities of any shape, not only

Gaussian. In this case symbol-model parameters are the

Gaussian means, Mh- The ML estimation equations for the

parameters Mh can be written as Mh = I f(h I n) X(n) / £ f(h I n), (21) n n

where the denominator has a meaning of the average number

of observations described by symbol h,

Nh = I f(h I n). (22) n

Also, in place of eq.(18) we have

M = X I h > Mh < h I. (23)

heH

An internal HQMF encoding I x(n) > of the external patterns

X(n) (equivalently, of the states I n > of the external world) is defined as,

H

I x(n) > = < n I «F(t) > = I Chn I h >. (24)

h=l

This encoding follows from eq.(9), it is a consequence of

298
interaction between the external world and the QMF system.

For a HQMF system, this interaction should be defined so that a parametric shape of the probabilities in eq.(10) corresponds

to that of the classical MF system, eqs.(4) [Perlovsky, 1996].

Note that the encoding states defined in eq.(24), in general, do

not form an orthogonal set. Using these states, the density

operator can be written as

p(t) = I I x(n) > < x(n) I. (25) n

Let us also introduce an observation operator X acting on the

encoding QMF states,

X = I I x(n) > X(n) < x(n) I. (26)

n=l

Consider eigenstates I A. > of this operator,

X\X> = X\X>, or <X\X\X> = X. (27)

Substituting eq.(26) into eq.(27),

X = X I < X I x(n) > I 2

X(n). (28)

n=l

Comparing this to eqs.(10), (21), (22), and (23), we see that X

is identified with Mh-Nh, and I X > is identified with I h >. Introducing an operator

M = X I h > Mh-Nh < h I, (29)

heH

we have the following identity for the quantum operators

M = X. (30)

This identity should be attained in the result of an internal

QMF dynamics. States I h >, which are defined as the

eigenstates of the operator 9A. should evolve (according to Schroedinger equation) into the eigenstates of X, and the

considered dynamic symbol-process, is equivalent to the

process of finding eigenstates of the operator X. A number of

algorithms exist that can be used for this purpose [Brockett,

1991; Oja, 1992; Xu & Yuille, 1995]. These algorithms

utilize unitary transformations and can serve as a basis for the

design of a quantum system. A Hamiltonian H can be defined

as

H(t) = i [M,X]. (31)

According to [Brockett, 1991], this Hamiltonian defines a dynamics that evolve eigenstates I h > of an operator M into

the eigenstates of the operator X. It might be noted that a dynamical diagonalization of an operator naturally occurs in

many quantum systems, therefore, a choice of a specific

physical realization will determine a specific realization of the

Hamiltonian.

If X(n) are vector quantities (as they usually are), then

lx(n)> are defined with a corresponding vector-index, so that X

is a vector-operator and various components of X operate on

the corresponding components of I x(n) >. Thus components

of X commute (and similarly, components of Ovt commute). If values of Nh are known, then Mh can be directly obtained

from M. When Nh values are not known a priori, eq.(19) can

not serve as a definition of the operator N, and Nh have to be

obtained similarly to Mh, in the process of internal HQMF

dynamics. By comparing eqs.(10), (12), (22), (24), and (25)

the N operator is identified with the density operator. Its eigenstates are different from I h >, N and M do not commute,

and expected values of N in ^-eigenstates Ih > are given by

the diagonal elements of the density matrix [Garvin &

Perlovsky, 1995],

Nh = < h I p I h >. (32)

The HQMF defined above evolves according to Schroedinger (Hamiltonian) dynamics without energy

dissipation. I would also note that this algorithm does not

require an exponential number of interfering quantum states, a "speed-up" relative to the classical computation occurs in the

result of interference between a number of states, which is only a linear function of the complexity of the system. It seems, however, that a required coherency (accuracy of

computation) is a constant number that does not grow with

the complexity of the problem. This is because, only few

amplitudes < h I x(n) > (few h for each n, and few n for each

h) interfere. In addition, the HQMF system has an advantage

of a relatively simple formulation, providing a foundation for

the next step of a physical realization of a quantum computer.

4. DISCUSSION

The first dynamic conception of mind belongs to Aristotle. His theory of Forms describes learning as a

realization of an a priori Form-as-potentiality. The conception

of mind as a dynamic system based on a priori categories was

further developed by Kant (1781, 1788, 1790). Kant described

working of the mind as a triadic process of UnderstandingJudgment-Reason. MFT gives the mathematical description

of this process (Perlovsky, 1998). Understanding is given by

a priori models, Judgment is given by a similarity measure,

and Reason is given by the adaptation mechanism. MFT

provides a mathematical description of both, Kantian theory of

mind and the process of semiosis. This establishes the

relationship between the two profound contributions to the

analysis of mind, Kantian theory and semiotics. The dynamic

symbol-formation loop describes Kantian triadic-mind process.

In [Dmitriev, Perlovsky, 1996], these loops were called the

vortexes of thought. The relationships among the semiotical

description of the symbol-semiosis, the Kant triadic process,

and MFT mathematical agent-vortexes will be illustrated.

Sign-vehicles are the internal model codes, objects or designata

are the incoming data, the interpretant (that recognizes sign299
models as corresponding to patterns in input data and generates

actions) is a combination of Judgment+Reason (that is, similarity+ adaptation and other actions of the activated

symbol within MFT). Syntactics is a logic governing

Understanding that is relationships among internal models.

Semantic is Judgment or similarity measures relating input

data and models. And, pragmatics includes the effects of

models on similarity and adaptation actions of Reason,

modifying the models.

REFERENCES

Aristotle, (IV BC). Metaphysics . Trans. H.G.Apostle, 1966,

Bloomington, IN: Indiana University Press. Brockett, R. (1991). Dynamical Systems That Sort Lists,

Diagonalize Matrices, and Solve Linear Programming

Problems. Linear Algebra and Its Applications, 146,

pp.79-91

Cramer, H. (1963). Mathematical Methods of Statistics. 10th

printing. Princeton University Press. Princeton, NJ.

Dmitriev, V.A. & Perlovsky, L.I. (1996). Art Form as an Object of Cognitive Modeling (Towards Development of

Vygotsky's Semiotics Model). Proceedings of the

Conference on Intelligent Systems and Semiotics '96. Gaithersburg, MD, v.2, pp. 385-389.

Feynman, R.P. (1972). Statistical Mechanics. Benjamin,

Reading, MA.

Feynman, R.P. (1982). Simulating Physics with Computers.

Foundations of Physics, 16, pp.507-31.

Feynman, R.P. (1986). Quantum Mechanical Computers.

Int. Journ. ofTheor. Physics, 21(6/7), pp. 467-88.

Hameroff, S.R. & Watt, R.C. (1982). Information Processing

in Microtubules. J. Theor. Biol., 98, pp. 549-61.

Kant, I. (1781). Critique of Pure Reason. Tr. J.M.D.

Meiklejohn, 1943. Willey Book, New York, NY.

Kant, I. (1788). Critique of Practical Reason. Willey, New

York, NY.

Kant, I. (1790). Critique of Judgment. Tr. J. H. Bernard,

1914, 2nd ed., Macmillan & Co., London.

Negahdaripour, S. & Jain, A.K. (1991). Final Report of the

NSF Workshop on the Challenges in Computer Vision

Research; Future Directions of Research. National

Science Foundation.

Neumann von, J. (1910). Nachr. Acad. Wiss., 1910, 3, pp. 228-103.

Morris C. (1971). Writings on the General Theory of Signs,

ed. Th. A. Sebeok. The Hague: Mouton.

Peirce, C.S. (1935-66). Collected Papers of Charles Sanders

Peirce. Cambridge: Harvard Univ. Press. Perlovsky, L.I. (1994). Computational Concepts in

Classification: Neural Networks, Statistical Pattern

Recognition, and Model Based Vision. Journal of

Mathematical Imaging and Vision, 4 (1), pp. 81-110.

Perlovsky, L.I. (1995). Unpublished.

Perlovsky, L.I. (1996). Mathematical concepts of intellect. World Congress on Neural Networks, San Diego, CA.

Perlovsky, L.I. (1998). Neural Networks and Physics of

Mind. Oxford Univ. Press, New York, NY.

Perlovsky, L.I., Schoendorf, W.H., Burdick, B.J. & Tye,

D.M. (1997). Model-Based Neural Network for Target

Detection in SAR Images. IEEE Trans, on Image

Processing, 6(1), pp.203-216.

Oja, E. (1992). Principal Components, Minor Components,

and Linear Neural Networks. Neural Networks, 5, pp.927-

35

Sakurai, J.J. (1985). Modern Quantum Mechanics. Addison

Wesley, New York, NY.

Segre, A.M. (1992). Applications of Machine Learning.

IEEE Expert, 7(3), pp. 14-17.

Winston, P.H. (1984). Artificial Intelligence. 2nd edition.

Addison-Wesley. Reading, MA.

Xu, L. & Yuille, A.L. (1995). Robust Principal Component

Analysis by Self-Organizing Rules Based on Statistical

Physics Approach. IEEE Trans. Neural Networks, 6(1), pp. 13 1-43

Zubarev, D.N. (1971). Nonequilibrium Statistical

Thermodynamics. Nauka, Moscow.

Acknowledgments: I am thankful to Lev Levitin and Roger

Brockett for fruitful discussions.

300
SEMIOTIC COMPOUNDS — MIXTURES OF COMPONENTS

INVARIANT UNDER SPECIFIED TRANSFORMATIONS

Roy L. Streit

Naval Undersea Warfare Center

Code 2002, Building 1171

Newport, RI 02841

streit@c223.npLnuwc.navy.mil

ABSTRACT

Semiotic compounds are mixtures of probability density

functions. They are used to formulate joint estimation

problems and methods that transcend the boundaries of the

traditional detection, classification, and state estimation

problem hierarchy. They are non-hierarchical statistical

models because they are marginal densities over alternative

hypotheses, or choices. Several novel examples of semiotic

compounds are discussed in this paper. A common thread

running through these examples is that useful semiotic

compounds often have mixture components that are related by

specific invariance transformations, that is, the components

are invariant to characteristic transformations that are determined by the application.

KKYWORDS! continuous mixtures, compound mixtures,

semiotic compounds, invariance properties, invariance,

detection, estimation, classification

1. INTRODUCTION

Traditional techniques for detection, classification, and state estimation (or localization) are typically structured

hierarchically, that is, detection is undertaken first, then

classification is performed as a post-detection problem, and

finally state estimation is conditioned on the outcomes of the

detection and classification steps. This conditioning hierarchy

is founded on natural and clear distinctions between important

statistical issues inherent in many problems and applications;

however, hierarchical conditioning may lead to performance

that is inferior to joint non-hierarchical methods when

numerous alternative hypotheses occur within the problem.

Semiotic compounds are mixtures of probability density

functions (PDFs). Each of the alternative hypotheses

contributes one component to the mixture. Semiotic

compounds are presented in this paper as the constituent

models of statistical approaches to joint detection,

classification, and state estimation (or localization)

capabilities. Joint methods and algorithms based on semiotic

compounds defy easy categorization within the traditional

hierarchical conditioning structure because of their use of

marginalization and because of their avoidance of conditioning on specific hypotheses.

Semiotic compounds vary considerably depending on the list of alternatives over which the particular marginalization, or summation, is performed. A semiotic compound takes the

form of a finite sum of PDF's if the alternatives are finite in number, and it takes the form of an integral if the alternatives are characterized by one or more real valued parameters. In the

former case the semiotic compound is called discrete, and in the latter it is called continuous. Continuous semiotic

compounds are not widely used, perhaps in part because of the

(incorrect) perception that they are merely continuous

extensions of the more widely used discrete mixtures. Infinite

discrete semiotic compounds are also potentially interesting,

but no examples of this kind are presented here.

Semiotic compounds also vary in the nature of the component

PDFs characterizing the alternative hypotheses. In this paper

it is assumed that the component PDF's have the same

parametric form, but different values of the parameters; that is, they belong to the same general parametric family Discrete

Gaussian semiotic compounds are easily the most widely used

in applications to date. Mixtures of disparate types of PDFs

are possible, but are not considered in this paper.

An important contribution of this paper lies in the importance

it ascribes to the concept of component invariance under

transformation. Recognizing the appropriate invariant

transformation can give considerable insight into the problem

under study. Invariance is not discussed in generality; rather,

it is discussed in the context of the following specific

problems (which may be read independendy):

(a) In Section 2, a generalized likelihood ratio test (GLRT)

for detecting transient and spread spectrum signals in

noise is treated using a discrete exponential semiotic

compound; estimates of both signal-to-noise (SNR)

level and bandwidth fall out as by-products of the

GLRT procedure.

(b) In Section 3, three discrete Gaussian semiotic

compounds are discussed for estimating a PDF from

sample data. Although two of these compounds are well known, the thud is new and potentially very

useful because of its numerical and statistical

robustness.

301
(c) In Section 4, a continuous semiotic compound is applied to so-called bearings-only target motion

analysis (TMA) state estimation problem.

Concluding remarks are given in Section 5.

2. TRANSIENT DETECTION

Difficulties arise in GLRT detection problems where one or more of the signal parameters requires an enumeration that is computationally intractable. In transient signal detection the

frequency characteristics of the signal are typically unknown,

so even if aggregate bandwidth is assumed, the estimation

problem intrinsic to the GLRT requires an enumeration of all possible sets of signal locations within the monitored band.

A prior distribution is imposed on the portion of the signal

parameter space that usually requires intractable enumeration.

By replacing enumeration with the problem of estimating the

hyperparameters of the model jointly with other signal

parameter, a new formulation of the problem that avoids

enumeration and is computationally feasible is possible. The

GLRT approach is not changed by this model — what is changed is the signal modal.

An observation vector X of length N is obtained by taking the

magnitude squared of the output of an FFT whose input is a broadband Gaussian time series. Elements of X are therefore

independent and exponentially distributed. It is assumed that

the exponential distributions have one of two possible means:

the larger mean, denoted by a, is the expected signal-plus-noise

power; the smaller mean, denoted by b, is the expected noiseonly power. Every element of X is assumed to contain a sample obtained under either {H: noise only} or {K: signal

plus noise}. Thus, two mutually exclusive and exhaustive

alternative hypotheses are assumed.

A Bernoulli random variate with outcomes {H, K} having

probabilities {1-q, q}, respectively, is used to model the

aggregate signal bandwidth, that is, the number of elements of

X that contain signal. In this model, N samples of the

Bernoulli variate are generated, one for each element of X.

These outcomes comprise the missing data in the sense of the

method of expectation-maximization (EM). Samples of the

FFT outputs are then drawn from the exponential density

determined by the Bernoulli outcomes. Thus, the expected

signal bandwidth is equal to qN.

The parameters {q,a,b} are unknown and must be estimated

from the data vector X using maximum likelihood (ML).

Marginalizing over the Bernoulli random deviates gives the

likelihood function L(q,a,b) as a product over the data of a two

component mixture of exponential densities,

ni=i

(1 - q^Expl-X, I b] + q-Expi-X, I a]

b a

Given current estimates {q,a,b} for the parameters, for

i=l,...,N compute the weights

wi (H) = (l-q)jExp[-Xt /b]

(1 - q^Expl-X, I b] + q-Expl-X, I a]

b a

q—Exp[-Xi la]

a

(1 - q)\Eq>[-Xt I b^q-Expl-X, I a]

b a

Updated estimates of noise power and signal-plus-noise power

are then given by the convex combinations

and

_ Er_,>"iWX;

a =

The expected signal bandwidth is given by

qN = j^wi (K).

These equations complete the algorithm statement.

The GLRT modeling philosophy requires that the final

estimates of {q,a,b} be substituted into a likelihood ratio for

testing H against K. Further details are given in [1], where

the GLRT is shown to be comparable to the best of a family

of nearly optimal power-law detectors developed for this

problem.

Extension of the Bernoulli signal model to p>2 power levels

(i.e., outcomes) requires semiotic mixtures of p exponential

PDFs; applying the method of EM leads to an ML algorithm

that is very similar to that sketched above. Further details are given in [1].

The importance of this example is two-fold. Firstly, it shows

that the detection statistic requires joint estimation of signal

and noise parameters from the data vector and that signal

bandwidth is estimated before the signal detection decision is completed. Thus, the GLRT does not fit the traditional

statistical hierarchy in this problem. Secondly, the invariant

transformation of the exponential PDFs used in this problem

is scalar multiplication. The difference between the noise and

signal models is essentially an arbitrary distinction based on

their power levels.

Straightforward application of the method of EM using the

Bernoulli signal model yields the following ML algorithm:

302
3. DENSITY ESTIMATION

Discrete Gaussian semiotic compounds are widely used to approximate an unknown PDF from which a set of

statistically independent and identically distributed (i.i.d.)

sample data have been drawn. ML algorithms are easily

derived via the method of EM for estimating the parameters of

two classes of Gaussian mixture: homoscedastic ("same

scatter") mixtures, which employ the same covariance matrix

in every component; and heteroscedastic ("different scatter")

mixtures, which use different covariance matrices in every

component. The former are robust numerically, but may

sometimes require many components to achieve good PDF

approximation accuracy. Heteroscedastic mixtures may require

fewer components for the same PDF accuracy as homoscedastic mixtures, but they may be numerically

unstable in that one or more of the covariance matrices may

become singular during iteration. Deficiencies of

heteroscedastic mixtures become very severe as the

dimensionality of the sample data PDF increases. Further

discussion of these mixture classes is given in [2] and in the

references therein.

In this paper, covariance restrictions are seen to be special cases of the general principle of component in variance under

transformation. The transformation is selected to characterize

the common semiotic content of the fundamental symbol

under study; that is, components that are identical under the

specified transformation comprise the components of the

mixture, and each component is a legitimate expression of the

same symbolic content. Thus, the mixture characterizes the

symbol.

The invariance transformation of homoscedastic mixtures is rigid translation, because components differ only in their means. For heteroscedastic mixtures, the components may be

general Gaussian PDFs, so the invariance transformation is the combined transformations of translation, rotation, and

dilation. A rotation and dilation will transform one

covariance matrix into another, as is easily seen from the

singular value decomposition (SVD).

It is clear from the above paragraph that an important class of

invariance transformations has been omitted, namely, the class

of transformation comprising translation and rotation only.

Gaussian semiotic compounds with this invariance

transformation are called herein a strophoscedastic ("twisted

scatter") compounds, and they were first discussed in [3].

Surprisingly, the method of EM yields an explicit ML

estimation algorithm, that is, the M-step of the method of EM

can be solved explicitly, just as it can in the homoscedastic

and heteroscedastic cases. Although the derivation is significantly more difficult, the resulting algorithm is intuitively reasonable in that it differs from the algorithms for

the other two mixtures simply in the amount of averaging that

is required.

Let p(x) denote the true, but unknown, PDF of the sample

data, and let d > 1 denote the dimension of the samples. The

density p(x) is approximated by a strophoscedastic mixture,

denoted by q(x), having N components. N is assumed given;

its selection is a model order selection problem and is outside

the scope of this paper. The parameters defining the

strophoscedastic approximation

p(x) = q(x) = E n„ K (x | /;„, Q'n A Qn )(i) n=l are given as follows:

(i) Mixing proportions K = {ni,---,n^} such that

7C n > 0 forn = 1, .... Nand 7Ti+ --+7t N =1,

(ii) Mean vectors \i = {fliy -,Hn} such that nn

€ R

d

for n = 1, .... N,

(Hi) Positive definite diagonal kernel matrix

A = <Duy[ah •••,ad ]eRdxd

, a, > ••• >ad >0,

(iv) Orthogonal matrices Q, = {Qi, Qn)>

Qn e R

dxd

, Q'

n Qn = Qn Q'n = I for n = 1, N.

The parameters in the list (i) - (iv) are estimated from the

sample data using the ML method. Let K be the number of

i.i.d. samples in X = {x,,x2 ,---,x K }, where x^ ERdis drawn from the distribution p(x). Using the approximation

(1) and the independence of the samples X gives the posterior

likelihood function

£(X|tc,h,A,Q,) = ft q(x k | n,\L,A,(l). (2)

k=l Applying the method of EM requires defining random

variables to characterize the so-called missing data. The

missing data are easily understood from a simulation of the

mixture q(x): Firstly, the discrete PDF defined on the set

{1,...,N} by the probability vector k is sampled to obtain a

particular Gaussian component of the mixture. Secondly, this Gaussian component is sampled to produce a vector in the

sample set X. Every sample in X is modeled as having

arisen in this fashion, so the missing data are the discrete

outcomes of the first step of the hypothetical simulation.

Using the missing data enables the method of EM to be

applied to derive a ML algorithm that is guaranteed by general

properties of the method to generate a sequence of parameter

estimates that monotonically increase the likelihood function

(2). Thus, if the likelihood function is uniformly bounded

above for any choice of parameter set, the algorithm converges

to either a local ML parameter estimate or a stationary point

of (2).

For m = 0, let 7C (m)

, n

(m)

, A

(m)

, and Q.

(m)

be initial

estimates for the parameters defining the strophoscedastic

mixture that satisfy the conditions imposed in (i) - (iv) above.

For integers m > 0, updated estimates for iteration m+1 are given by the following equations: For n = 1, N and k = 1,

.... K, compute the weights

303
w

The expected number of samples from component n, conditioned on parameter estimates at iteration m, is

K<m+1> = £ w

(m+1)

- n nk

k=l

The updated mixing proportions are given by

7C(m+l) =K(m+l) /K

n n

and the updated mean vectors by

K

(m+1) _ l

si K

(m+1) Kn k=l

The within-component sample data covariance matrices

(conditioned on parameter estimates at iteration m) are K

w

(m+1) (x.-nrx^-nr")

Compute the ordered SVD's

s

(m+l) _ |j<m+l) £(m+l) ^j(m+l)y

^ n n n n

where the matrices U^n+1

^ are orthogonal and the diagonal

elements of the matrices

I

(m+1) = 2Wa(m+1)

a

(m+1)

••• a

(m+1)

] n In ' 2n ' ' dn 1

are arranged in decreasing order. The updated orthogonal

matrices of the strophoscedastic mixture are the transposes of

the orthogonal matrices of the ordered SVD's, that is, q(m+l) _ ^m+ljy

The kernel matrix is obtained by averaging the diagonal

matrices of the SVD's over all mixture components:

A

(m+1) = £

^(m+1) s(m+l)

n=l n n

This completes the statement of the algorithm. A derivation

of the algorithm is given in [4]. ML algorithms for the three mixture classes differ only in

where averaging is applied. Homoscedastic algorithms

average the within-component sample data covariance matrices

to obtain the component covariance matrix. Strophoscedastic

algorithms average only the singular values of the withcomponent matrices. Heteroscedastic mixtures do not average

the within-component matrices at all. The presence of

averaging explains intuitively why homoscedastic and

strophoscedastic ML mixture algorithms are so reliable and

unlikely to encounter singular covariance matrices during

iteration.

4. TARGET LOCALIZATION

Classical TMA statistical models are post-detection models,

that is, they assume a priori that the measurements Z belong

to a common target having a specified parametric form (e.g.,

straight line motion). Post-detection tracking implies that

measurements are independent if they are conditioned on the

target. ML estimators thus answer the question "Given data

generated from a target track, which parameterized track besi

fits the data?" In contrast, the empirical maximum

posteriori (EMAP) estimators discussed here differ

fundamentally from classical post-detection TMA because they are joint detection-estimation methods which seek to answer

the alternative question "Does a target track of the specified

parametric form fit the data?" A generalized likelihood ratio

test (GLRT) in which track parameters are estimated and

substituted into a likelihood ratio is the EMAP answer to the

question; however, it is the estimated track — and not the

GLRT detector — which is the object of interest in this

paper.

The data {Z,X°} = {(Zn ,X°)}^=l are assumed statistically

independent because measurements are not specified a priori to belong to the same track. Independence implies that

The data {(Zn , X")}^ contribute independent probability

density assessments of "potential" target position that are valid

at the measurement times. Let X

a = {X"}^=1 denote socalled "empirical" random variables associated with potential

target location. Empirical random variables are assumed

independent when conditioned on corresponding measurements

and sensor locations; hence, the empirical target location PDF

is N

^xn |zxo ^

n

' = n^xQ |z X°

'

The empirical target likelihood function is evaluated for

specified parametric target motion models, once the

conditional density of X^ is defined.

In the remainder of this section the passive azimuthal

bearings-only TMA problem is considered; thus, it is assumed that the target lies in the x-y plane, that Z„ = 6„ ,

where 6n

is the measured azimuthal bearing from the sensor

to the target, and that X° = (x°,yl) is the sensor location

when the bearing 6n

is obtained. Target is unobservable from

a single bearing because range measurements are assumed to be unavailable from the passive sensor.

A continuous semiotic compound, or marginal integral

representation, of the PDF of the empirical state variables can

I

304
be derived by introducing the dummy random variable rn to model the "missing" sensor range measurement corresponding

to 6n

. Full details of this novel approach to target

observability difficulties are provided in [5] and are not

repeated here. Sensor and target characteristics are assumed to be such that the missing range variable lies in a known finite

range interval, r^a <rn < r^.

Let X = {X\,y\,XN ,yN ) denote the endpoint coordinates of

a target with straight line motion. Substituting this motion

model into the integral representation, and substituting the

result into the overall empirical likelihood function gives

S '"max ( j

pxa]ZX0 mx)\z,x°)= n J

Exp«

"

n=l 2r

Q =

where the quadratic form Q of the exponential function is

'a(tn )*, + P(t„ )xN - x°n - r„ cos 6, n '

a{tn )yx +P(tn )yN -y°„-rn smdn

~a{tn ) Xl + P(t„ )xN - x° - rn cos d,

' _ a(tn )yl + P(t„ )yN - y°„ - r„ sin d„

_ and the linear interpolation functions are given by

a(t)= and P(t) = ——

The covariance matrix of the quadratic form Q is given by

cosd„ sin0„"

T < o" cosdn sind„

-sin0„ cosdn 0 <_-sin0„ cosd„

2 t\ —2 where <7

n

is the variance of the bearing an

, and Kn

is the

variance of the missing range variable rn

.

By discretizing the integrals and applying the method of EM,

an EMAP estimation algorithm can be derived. It can be

shown that this algorithm is a sequence of iteratively

reweighted linear least squares problems. The variance of the

missing range measurement rn

is a free variable that can be

used to greatly accelerate the convergence of the EM

algorithm. Further details will be reported in [6].

The quadratic exponent Q of the Gaussian component of the

continuous semiotic compound is the only form satisfying a combination of geometrical and analytical properties natural to the bearings-only TMA problem. Firstly, empirical target

location is assumed to be Gaussian distributed when

conditioned on actual target location. This is a Bayesian

assumption about the empirical target, not the target.

Secondly, the marginal density over the empirical range

variable of the conditional empirical PDF is required to be

independent of actual target range. This requirement implies

that the cross-range and down-range variances must grow as

the square of target range. Thirdly, the marginal density over

empirical range is required to be a function of the difference

between the empirical bearing and the target bearing. This

requirement forces the axes of the empirical covariance matrix

to align with the cross-range and down-range directions. In summary, these requirements completely characterize the

Gaussian component density of the semiotic compound, that

is, the quadratic form Q is the unique form that satisfies these

requirements. For a detailed derivation, see [5, Appendix A].

As is seen from direct examination of Q, the components of

the continuous semiotic compound are invariant under the

combined transformations of translation down-range and

square-law spreading of the variances of its principle

components with increasing range. The resulting integral

representation of the empirical density is remarkable in that it

is very nearly constant along straight lines radiating outward

from the sensor location, and moreover it is very nearly

Gaussian along circular cuts centered on the sensor. Both

these statement are valid within the annulus with inner and

outer radii rmin + £ and — £, respectively, where e is a

small positive number.

Multitarget applications of discrete semiotic compounds are also possible. In these applications the missing data is the correct assignment of a measurement to a target. Just as in the examples above, the method of EM can be used to derive

ML estimation algorithms. Invariance transformations have

not yet been sought for these problems. See [7, 8, 9] for

further details.

5. CONCLUDING REMARKS

The common thread linking the various examples is that of an

invariant transformation. However, the appropriate nature of

the transformation depends strongly on the given application.

It also appears from these examples that semiotic mixtures of

components constructed (i.e., derived) to be invariant under a specified set of transformations may possess remarkable

properties that are important for the application. In any event,

more examples are needed to illustrate the utility of semiotic

compounds with invariance transformations for joint detection,

classification, and localization.

The method of EM is not the only available ML estimation

method, for in any problem to which EM is applicable, the

standard necessary conditions may always be derived and solved

directly. EM is merely a general procedure for deriving local

ML parameter estimation algorithms in problems whose

likelihood function is modeled as a marginal PDF over

"missing" information. Specific algorithms derived via EM

vary considerably in nature, depending strongly on the

parametric form of the particular PDF's that are used. EM

algorithms often take huge steps toward the solution in the

very first few steps (a phenomenon unaccounted for in the

305
convergence literature), but it remains a complaint that they

are asymptotically only linearly convergent. For numerical

purposes, a hybrid algorithm seems potentially useful:

initialize with EM, and finish with a quadratically convergent

method such as Newton-Raphson. Ultimately, the real value

of the method of EM may reside more in the way of thinking

and modeling that it suggests for new and challenging

problems than in any the resulting algorithm.

Implicit within the marginalization interpretation of semiotic

compounds is a randomization concept that is essentially

Bayesian in nature. Consequently, when detection,

classification, and estimation problems are undertaken in

contexts (e.g., high SNR) in which decision errors are very

unlikely, the use of the traditional hierarchical conditioning

may be satisfactory for many applications. However, when

decision errors become common, special decision support

systems (i.e., expert systems) are needed to protect against

them and to accommodate conflicting decisions. Over the last decade, Bayesian networks (see, e.g., [10]) have been proposed

and developed for reasoning under uncertainty with

mathematical guarantees of consistency. In environments

where reasoning under uncertainty is the central and pivotal

issue, semiotic compounds are potentially useful models.

6. ACKNOWLEDGMENTS

This work was supported by the Office of Naval Research.

[6] R. L. Streit, "Augmented Bearings-Only Target Motion

Analysis Problems", IEEE Transactions on Aerospace

and Electronic Systems, in preparation.

[7] R. L. Streit and T. E. Luginbuhl, "Maximum

Likelihood Method for Probabilistic Multi-Hypothesis

Tracking," SPEE International Symposium, Signal and

Data Processing of Small Targets 1994, SPIE

Proceedings Vol. 2335-24, pp. 394-405.

[8] R. L. Streit, "Probabilistic Multi-Hypothesis Tracking,"

Naval Undersea Warfare Center Technical Report 10,428,

15 February 1995.

[9] H. Gauvrit, C. Jauffret, and J. P. LeCadre, "A General

Formulation of Multitarget Tracking in the Viewpoint of an Incomplete Data Problem," IEEE Transaction on

Aerospace and Electronic Systems, to appear.

[10] F. V. Jensen, An Introduction to Bavesian Networks.

Springer-Verlag, New York, 1996

7. REFERENCES

[1] R. L. Streit and P. K. Willett, "Hybrid Bayes/GLRT

Detection of Transient Signals," Proceedings of the

Conference on Information Sciences and Systems, Johns

Hopkins University, Baltimore, MD, March 19-21,

1997.

[2] R. L. Streit and T. E. Luginbuhl, "Maximum

Likelihood Training of Probabilistic Neural Networks,"

IEEE Transactions on Neural Networks, NN-5(5), 764-

783.

[3] R. L. Streit, S. G. Greineder, and T. E. Luginbuhl,

"Maximum Likelihood Training of Probabilistic Neural

Networks With Rotationally Related Covariance

Matrices," Proceedings of the International Conference

on Neural Networks, Perth, Australia, 27 November - 1 December 1995, 300-303.

[4] R. L. Streit and T. E. Luginbuhl, "Estimation of

Gaussian Mixtures With Rotationally Invariant

Covariance Matrices," Communication in Statistics, Part A: Theory and Methods, to appear.

[5] R. L. Streit, "Bearings-Only Target Motion Analysis

With Propagation Loss Models Of Uncertain Fidelity,"

Proceedings of the Third International Conference on

Theoretical and Computational Acoustics, Newark, New

Jersey, 14-18 July 1997.

306
INFORMATION, LIKELIHOOD, AND EINSTEIN

Leonid I. Perlovsky

Nichols Research Corporation, 70 Westview Street, Kilnbrook IV, Lexington MA 02173

Tel: 617-862-9400; Fax: 617-862-9485e-mail: perlovsl@nichols.com

Abstract. A new type of statistical estimation principle is

suggested. It is based on the Einsteinian interpretation of the

spectrum as a pdf. I discuss its relations to and distinctness

from the classical estimation principles of maximum

likelihood, information, and entropy. The new principle can be interpreted as a relaxation to equilibrium of a physical

system consisting of the "world" and the estimation system.

The new estimation principle has been successfully tested in a number of applications. Performance exceeding classical

estimation principles has been indicated.

1. INTRODUCTION

Fundamental principles of statistical estimation include

maximization of likelihood, maximization of mutual

information, and related techniques. Maximization of

likelihood (ML) is a most established principle, dating to Bayes. According to the ML, unknown parameters are estimated by maximizing a probability density function (pdf)

of the available data. The ML has certain optimal properties,

it is asymptotically unbiased and efficient. The information or entropy maximization has being used since 1950s. Kullback

and Leiblerl, following Khinchin, developed a measure of

information distance, that was used to develop KhinchinKullback-Leibler estimation approaches also known as maximum entropy (ME), minimum cross entropy (MCE) and

minimum discrimination information (MDI)2>3. The ME

philosophy was formulated by Jaynes^ as: "maximally

noncommittal with regards to missing information". A related

minimum cross-entropy principle^ minimizes "information measure necessary to change a prior pdf into estimated pdf".

Of a particular interest is Shore's comment^ that the ML

estimation is justified from the basic principles only if a model

is exactly correct (for some set of the model parameters),

while MCE does not rely on this. Thus, he argued that MCE is a more general approach than ML, in that it is justified even if we know that our models are approximate.

I propose a new estimation principle, which is related to and distinct from the classical estimation principles discussed

above. Following Einstein and Hopf-\ I consider a different

type of pdf than usually considered in statistical estimation.

Since the concept of pdf is a basis for statistical estimation,

likelihood, and information measures, the new principle leads

to different results than the classical ones. A specific point of

difference is the attribution of randomness. Usually, in

statistical estimation, randomness is attributed to measured

quantities as follows. E.g., if an image is produced by the

light intensity, an intensity of the pixel is considered as a random quantity and pdf models are designed to model this

randomness. Or, if a radar measures Doppler spectra, a signal

intensity or power in a Doppler cell (a sample) is considered a random quantity, and pdf models are constructed accordingly

(say, for the spectrum it could be a density). Contrary to

this, Einstein interpreted the spectrum as a pdf of photon

frequency. That is, the Doppler cell frequency is to be

considered random, rather than the intensity or power.

I develop the Einsteinian concept further, and relate it to the type of estimation, which is usually considered in

statistical physics. Namely, I relate the new estimation

principle to the process of relaxation to equilibrium in a physical ensemble. The ML principle, when applied to "Einsteinian" likelihood, results in the same estimation

equations as the maximum entropy principle used to find the

equilibrium of a physical system. Also, the new estimation

principle is interpreted as a maximization of mutual

information in the model about the data. The "Einsteinian"

likelihood and pdf models are applicable to signals or images

formed by measuring the energy (spectrum) of

electromagnetic or acoustic waves, which are widely used

types of data.

Many statistical spectrum estimation methods are based on parametric spectrum models. This permits one to utilize

information about signal phenomenology and enables one to achieve a better accuracy than by using non-parametric

estimation approaches. A number of models have been

utilized for this purpose, suitable for broad categories of

signals, including autoregressive, moving average, their

combination, and sinusoids in noise. Also, a number of

parameter estimation methods have been developed, many of

which are based on classical ML or maximum entropy

principles^. Types of spectrum models and the estimation

technique developed here are different from those previously

discussed. In particular, they are applicable to often

encountered cases when multiple interfering phenomena are present^" 11

, an(j wnen classical techniques may be

inapplicable. Also, the new estimation technique described

here results in more efficient estimation as compared to

classical ML and ME methods, even when applied to classical

autoregressive problems^.

Section 2 discusses Einstein's interpretation of photon

spectra for electromagnetic waves, introduces a pdf model for

signal spectra compatible with Einstein's ideas, and derives the

ML estimators for the model parameters. I discuss the

relationships between the ML and the entropy or information

maximization and address specific similarities and differences

307
between the new estimation principle and the classical ones. Section 3 extends these results to images and higherdimensional cases. Section 4 contains a discussion; also, it briefly overviews and provides references to the applications

and numerical comparisons that have been implemented and

published.

2. EINSTEINIAN MODEL FOR SPECTRUM

ESTIMATION

Einstein interpreted the electromagnetic spectrum as a

probability density function (pdf) of the photon energy^. A

similar interpretation is valid for phonons of acoustic spectra

(speech, seismic signals, etc.) and for any signal field obeying

Bose-Einstein's statistics (bosons). A photon energy e is

related to its frequency co,

8= ftco, (1)

therefore, according to the Einsteinian interpretation, spectral

models, F(co), are to be interpreted as frequency pdfs, or, in other words, proportional to the number of photons with

frequency co. This interpretation requires proper

normalization; since empirical spectrum S(co) is measured in units of energy, its interpretation as a pdf requires

normalization on a photon energy. We, therefore, consider the

number of measured photons

NQ = S(co)/ftco, Z No = N.

CO

(2)

and F(co)//2CO is a model pdf for a single photon with frequency

co, that is an expected value EfNu/N} normalized as follows

2 F(co)//KO = 1, F(co)//zco = E{No/N}.

CO

(3)

We consider discrete empirical spectra and their models, so

that Nqj is the number of photons in the appropriate interval

of frequencies and F(co) is their normalized expected value.

We also assume that a small interval of frequencies around

zero is excluded, so that normalization (3) is possible. In many applications zero frequency is excluded, because the

physical carrier signal frequency is much larger than the

frequency variations of interest. In macroscopic systems,

photons are statistically uncorrelated (most often, this is also

true for microscopic systems as well). Therefore, for an ensemble of photons n = 1,..., N, the joint pdf or likelihood L

is a product over individual photons

L = n F(cOn)//icon = n [F(co)//2CO]

N(0 = n [F(co)//?co]S(CO)Mt°

CO CO

(4)

The second equality here is obtained as follows. The product over individual photons, n, is split into two terms: a product

over photons with a fixed frequency CO and a product over

various frequencies CO. There are Nqj photons with a fixed

frequency co, all distributed according to identical pdf model

F(co), this leads to the above expression. The likelihood (4)

does not account for the variability in data associated with

differences between a single realization of the empirical data

N(o and the model of its expected value. For a quantum

system containing a small number of photons this might be a

significant deficiency, but for classical systems containing

large numbers of photons, expression (4) is adequate.

According to the ML principle, the likelihood (4) or its logarithm should be maximized in the estimation process. If the number of parameters, Npar, vary in the estimation

process, the proper quantity to be maximized is called the

Akaike Information Criterion, AIC; it is obtained by

subtracting Npaj/2 from the log-likelihood

AIC = logL - Npar/2 (5)

The specific shape of the parametric model for F(co) can

be determined based on the physics of the process under

consideration^'^, or a general type of flexible parametric

model can be selected as in [6, 11] or below. Often, signals can be considered as being produced by incoherent

contributions from several sources. In such a case, the

spectrum is a sum of individual source contributions,

F(co) = X F(co|m), m= 1..... M.

m

(6)

Such a model for a pdf is called in statistics a mixture model,

and we call each mixture component F(co|m) a sub-model

corresponding to source m. Conditional pdf modeling

individual sources in many cases can be modeled using

Gaussian densities. Gaussian models are widely applicable,

because a superposition of Gaussian models can be used to model any function. The Gaussian model is given by

F(co|m) = ftco Am G(co|m) Aco, m = 1,..., M;

-1/2-1 2 2

G(colm) = (2k) (am) exp{-0.5 (co- com) /om }. (7)

In the above equations, Am is a sub-model weight, Aco is a sampling interval, com is the sub-model mean frequency and

am is the sub-model frequency standard deviation. A

multiplicative term /zco in Eq. (7) is introduced according to

the normalization requirement (3), so that [Am G(co|m)] is measured in units of a photon number, and G(co|m) is interpreted as the conditional pdf of the photon frequency from

source m. A wide applicability of the above model is due to the fact, that Gaussian functions form an overcomplete set of

functions so that any function No can be modeled using eqs.

(6), and (7).

The mixture model specified by (6), and (7) is characterized by three parameters per Gaussian sub-model: the

weight, the mean, and the standard deviation. The ML

308
estimation equations for these parameters are derived by

maximizing the likelihood L in (4), or its logarithm, LL = In L. Constraint (3) can be accounted for by using the method of

Lagrange multipliers, resulting in the following ML equations:

Am = Nm / N, Nm =2 P(mlco) [S(co)//jco],

CO N = Z S(co)//zco, (8)

CO com = Z P(mlco) [S(co)//jco] to / Nm, (9)

CO Cm

2 = Z P(mlco) [S(co)//ico] (co - toTM)

2

/ Nm. (10)

CO

The term P(mlco),

P(mlco) = F(co|m) / [ Z F(co|m') ], m' XP(mtco)= 1, m= 1....M, (11)

m

has the meaning of the a posteriori Bayes probability that a photon at frequency co has originated from the source (or submodel) m. Thus, Nm is the number of photons from the source m, and N is the total number of photons.

The ML estimation eqs. (8) through (11) do not yield an immediate estimate of the model parameters, because the

probabilities P(mlco) in the right-hand side of eqs. (8) through

(10) depend on the unknown parameter values, according to (11) . These equations can be considered as defining an

iterative system: beginning with some values of parameters,

the sub-models F(co|m) are computed and the probabilities are computed according to (11); on the next iterations, the

parameter values are recomputed according to (8) through

(10), etc., until convergence. The convergence is determined

by requiring that parameter changes are small from an iteration

to iteration. The convergence is always attained; this is a consequence of the estimation-maximization (EM)

algorithm^. If the number of sub-models, M, should be

estimated from the data, this is accomplished by maximizing

eq.(5).

It should be noted that the above Eqs. (8) through (1 1) are approximate. The approximation is in considering the

Gaussian densities to be normalized for a discrete set of

frequencies,

Z G(colm) Aco = J G(colm) dco = 1 . (12)

CO

A numerical evaluation shows that for om > 1 (in units of

sample numbers), the approximation is accurate.

Below, I discuss two alternative interpretations of the

above estimation procedure. First, the estimation is interpreted as a relaxation to equilibrium of the photon

ensemble, leading to a relationship between the "Einsteinian"

likelihood and entropy. And second, the estimation is

interpreted as maximization of the information contained in the internal model of an estimation system about the world.

Equilibrium of the Photon Ensemble.

I will demonstrate that the ML eqs. (8) through (11)

describe the equilibrium state of a system consisting of the

physical ensemble of photons and the estimation system,

which degrees of freedom are the estimated parameters of the

model. An average number of the observed photons is proportional to a number of the photon physical states. Therefore, according to Einstein's interpretation, a spectrum

sub-model F(co) is interpreted as being proportional to a number of physical states, for a single photon at each

frequency,

F(co) = const • M) • O(o . (13)

The equations of physical equilibrium in our case can be

derived by using a standard textbook procedure^, which is now briefly described (for the classical limit, when Nqj / <J> U

« 1). Since our estimation procedure deals with the fixed

observation data, the number and energy of photons is fixed,

which should be accounted for in the estimation procedure. In

statistical physics, a system with the fixed energy and number

of particles is called a microcanonical ensemble. The

equilibrium of a microcanonical ensemble is obtained by

maximizing the entropy of the ensemble, E, subject to the

constraints of conservation of energy e and photon number N.

According to eqs. (1), (2), and (3), this results in the following

constraints on our model F(co),

e = Z S(co) = N Z F(co);

co CO N = Z S(co)//2CO = N Z F(co)//zco. ( 1 4)

CO CO

The ensemble entropy, E, is a logarithm of the number of

states available to the system, T. It is a product of the number

of states available at each frequency, ru, and its computation

is a standard textbook exercise^. For Nq> photons with

frequency co, the total number of states To is

Tco = (Oco)

N(°/ (No!), (15)

where the numerator is the total number of all combinations

and the denominator accounts for the permutations of the

equivalent photons. Thus, we obtain for the entropy of the

photon ensemble,

E = lnr=lnnro) = Z Noln [ Oco/No)]. (16)

CO CO

If the number of the parameters vary in the estimation process,

the varying degrees of freedom associated with the estimation

system have to be accounted for in the estimation process.

309
I

This is accomplished by subtracting 1/2 for every degree of

freedom, this is subtracting the number of parameters divided

by two, Npaf/2 to the above expression; this procedure is a consequence from the first principles, which is well known in

statistical physics and in statistical estimation theory 14,12

Combining eq.(16) with this additional item and with eqs. (2)

and (13),

E = I [S(M)//2CD] In [ F(co) / (const-S(co))] - Npar/2. (17)

CO

Maximization of this expression subject to constraints (14) can be obtained by using the method of Lagrange multipliers. It leads to the same equations (8) through (11). Thus, the ML

estimation, using "Einsteinian likelihood" is equivalent to finding an equilibrium of the estimation system and photon

ensemble.

Information in the Model about the Data

In his classical work^, Shannon introduced a concept of

the mutual information contained in the received message

about the sent message. For our purpose, this concept can be

formulated as follows. We identify the sent message with the

measured data S(co) and the received message with the internal

model, F(co). Then, the mutual information in the model about

the data is given by (see Appendix for details)

1= Z [S(co)//zco] In [ F(ca)//KD ]. (18)

CO

Maximization of the entropy (17), for the estimation purpose,

is equivalent to maximization of the mutual information (18).

The information or entropy maximization discussed in

this paper is connected to the maximum entropy estimation

principle that has been used since 1950s. There are significant

similarities and differences between our approach and other

methods under similar names, so it is useful to provide a brief

overview of the history and literature concerning the roots of

the maximum entropy estimation in statistics. Kullback and

Leibler^, following Khinchin, developed a measure of

information distance, that was used to develop KhinchinKullback-Leibler estimation approaches also known as maximum entropy (ME), minimum cross entropy (MCE) and

minimum discrimination information (MDI)2>3 The ME

philosophy was formulated by Jaynes^ as: "maximally

noncommittal with regards to missing information". In ME

estimation, the problem is formulated as follows. Estimate a

pdf, q(n), given a set of linear constraints on q. The ME

estimation consists in maximizing the entropy defined as

maxE; E = -E q(n) In q(n). (19) n

According to the ME philosophy, ME estimates a function

q(n) by maximizing its randomness, while satisfying the

constraints. When a prior guess p(n) estimating q(n) is known

in addition to the constraints, MCE is used, which minimizes

cross-entropy CE,

min CE; CE = I q(n) In [q(n)/p(n)], (20) n

subject to the constraints. MCE minimizes "information measure necessary to change p(n) into q(n)", subject to the

constraints. Note the differences between eq.(20) and our

eq.(17): in MCE like in ME, the sum is weighted with the

sought function q(n), while in our definition, the sum is weighted with the measured numbers of photons. Shore^

emphasized that the ML estimation is justified from the basic

principles only if a model is exactly correct (for some set of

parameters), while MCE does not rely on this. Thus, he

argued that MCE is a more general approach than ML, in that

it is justified even if we know that our models are approximate. This is also true for our "Einsteinian" mutual

information: the developed method extracts maximal

information about the data, which could be extracted with a given model, even if the model is approximate.

*« 2d 1

3. EXTENSION TO 2-D AND HIGHER

DIMENSIONAL IMAGES

The Einsteinian interpretation of spectrum does not have

to be limited to the frequency-domain spectra, but is naturally

extended to intensity or power densities in any coordinates,

e.g., two-dimensional domains of time-frequency spectra,

regular angle-angle intensity imagery, or higher dimensional

domains such as time-frequency-range-angle imagery^' 10,11

The extension is a straightforward one. Let us denote the

general D-dimensional image coordinates as x, imagery data,

S(x), and image models, F(x). The "Einsteinian" likelihood

expression and the ML equations are similar to the ones in the

previous section,

logL = Z [S(x)//j(0] log[F(x)//zco]. (21) x

If the mixture model with D-dimensional Gaussian

components (sub-models) is used,

F(x) = E F(x|m) , F(x|m) = ha Am G(x|m), G(xlm) = m

(2r:)"

D/2

(detCm

)" 1/2

exp{-0.5 (x - xm)T Cm"

1 (x - xm)},(22)

Again, Am is a sub-model weight, xm is the sub-model mean

position vector and C m is the sub-model covariance,

determining the shape of the sub-model in D-dimensional x- space. The term [Am G(co|m)] is measured in units of a photon number, and G(x|m) is interpreted as the conditional

pdf of photons from source m. And, the ML estimation

equations for the model parameters are:

Am = Nm/N, Nm= £ P(mlx) [S(x)/ftco], N = £ [S(x)//jco] , x x

310
xm = Z P(mlx) [S(x)//j(0] x / Nm, x Cm = Z P(mlx) [S(x)/ftco] (x - xm) (x - xm)T

/ Nm., x

P(mlx) = F(x|m) / [ Z F(x|m') ], (23)

m'

where P(mlx) has the meaning of the a posteriori Bayes

probability that a photon with coordinates x has originated

from the source (or sub-model) m. Thus, Nm is the number

of photons from the source m, and N is the total number of

photons. As in the previous section, this set of equations

defines a convergent iterative system. While the Gaussian

mixture model described above can model any intensity

image, usually, it is practically useful for images composed of

relatively few Gaussian "blobs". More complicated models

that are required for more complicated images can be

developed and estimated by combining the new estimation

principle with a technique described in [10, 1 1, 16].

4. DISCUSSION

This paper introduced a new estimation principle based on

the Einsteinian interpretation of the spectrum as a probability

density for the photon frequency. Today, the photon

composition of light is well known, and Einsteinian

interpretation of spectrum as a frequency pdf is not surprising

and no different in principle from other distributions

considered in statistical physics. Still, my inspiration for

connecting physical estimation of state distributions with

statistical estimation came from the 1910 paper by Einstein

and Hopf, and I think that terms "Einsteinian likelihood" and

"Einsteinian information" are justified.

The new estimation principle is applicable to most regular

intensity images and signals produced by classical

(macroscopic) imaging systems. We used classical limit for

computations of the numbers of states, still, the quantum

nature of the electromagnetic (or acoustic) field determines

statistical properties of a photon (or phonon) ensemble and the

estimation procedure. This can be compared to the Plank

distribution of a classical blackbody radiation being

determined by the quantum nature of the electromagnetic field. The quantum structure of nature is utilized in the new

estimation principle for solving a particular problem of the

classical Shannon information theory. Information is defined

with respect to elementary choices among classes, or elementary states. In classical information theory, the

definition of elementary states is arbitrary. In the proposed

estimation principle, when interpreted as maximal mutual

information, the elementary states are given by the quantum

states, photons (or phonons).

This paper considered positive-valued intensity or power

signals and images. But, it seems that the developed technique can be extended to non-positive and complex-valued signals as

well. The physical field carrying the signal is composed of

photons or other particles and the phase of the signal is related

to the phase of the particles. Therefore, one may expect that

phase density models can be developed that relate the signal

phase to the photon (or phonon) density. These models will be

suitable for oscillating and complex-valued signals, and will

correspond to the estimation principle described in this paper.

The "Einsteinian" estimation principle described here has

been applied to a number of diverse applications, on a somewhat ad hoc basis. It was applied to spectrum estimation

of autoregressive signals^; numerical results for a number of

cases have shown that the new principle results in more

efficient estimators than the classical ML and ME estimators

in non-asymptotic region. Applications to model estimation

for two-dimensional time-frequency spectra of acoustic signals

also was described in [6]. Modeling of interfering phenomena

in over-the-horizon radar spectra was described in [8, 9] along

with estimation of parameters of specific events of interest due

to ionospheric disturbances. Development of concurrent

detection, classification and tracking techniques (so called

track-before-detect) based on the new principle was described

in [10] for radar and in [11] for sonar. Superior performance

to the classical techniques was indicated.

REFERENCES

1. Kullback, S. & Leibler, R.A. (1951). On information and

sufficiency. Ann.Math.Stat. 22, 76-86

2. Jaynes, E.T. (1957). Information theory and statistical

mechanics I, Phys.Rev., 106, 620-630

3. Shore, J.E. & Johnson, R.W. (1980). Axiomatic derivation

of the principle of maximum entropy and the principle of

minimum cross-entropy. IEEE Trans. Inf. Theory, IT-26 (1),

26-37.

4. Shore, J.E. (1984). On a relation between maxmum

likelihood classification and minimum relative entropy

classification. IEEE Trans. Inf. Theory, IT-30 (6), 851-4.

5. Einstein, A. & Hopf, L. (1910). Uber einen Satz der

Wahrscheinlichkeitsrechnung und seine Anwendung an die

Strahlungstheorie . Annals of Physics, 33, pp. 1096-1 104.

6. Perlovsky, L.I. (1994). A Model Based Neural Network

for Transient Signal Processing, Neural Networks, 7(3), pp. 565-572.

7. Proakis, J.G., Rader, C.M., Ling, F. & Nikias, C.L.

(1992). Advanced Digital Signal Processing. Macmillan, New

York, NY.

8. Perlovsky, L.I., Plum, C.P., Franchi, P.R., Tichovolsky,

E.J., Choi, D.S., & Weijers, B. (1995). Estimation of

Ionospheric Effects on Radar Spectra. International

Conference on Signal Processing Applications & Tecnology,

Boston, MA.

9. Perlovsky, L.I. (1996b). Einsteinian Neural Network..

Proceedings of World Congress on Neural Networks, San

Diego, CA; Lawrence Erlbaum Associates, NJ, pp. 603-606.

10. Perlovsky, L.I. (1995). MLANS Tracker. Proceedings of

ARPA Counterdrug Over The Horizon Radar Workshop,

Chesapeake, VA, pp.A147-A173.

11. Perlovsky, L.I., Schoendorf, W.H., Tye, D.M., Chang, W.

(1995). Concurrent Classification and Tracking Using

311
Maximum Likelihood Adaptive Neural System. Journal of

Underwater Acoustics, 45(2), pp. 399-414.

12. Akaike, H. (1973). Information theory and an extension

of the maximum likelihood principle. Petrov and Csaki, Eds.

Proceedings of the Second International Symposium on

Information Theory, Budapest: Akademiai Kido.

13. Dempster, A.P., Laird, N.M. & Rubin, D.B. (1977).

Maximum Likelhood from Incomplete Data via the EM

Algorithm. Journal of the Royal Statistical Society, 39B.

14. Sakurai, J.J. (1985). Modern Quantum Mechanics.

Addison Wesley, New York, NY.

15. Shannon, C.E. (1948). The mathematical theory of

communication. Bell System Technical Journal, July and

October, 1948.

16. Perlovsky, L.I., Schoendorf, W.H., Burdick, B.J. & Tye,

D.M. (1997). Model-Based Neural Network for Target

Detection in SAR Images. IEEE Trans, on Image Processing,

6(1), pp.203-216.

APPENDIX

Consider a "universe" consisting of the two interacting

systems, "world" characterized by the data {S(co)} and

"estimation system" characterized by the model {F(co)}.

Mutual information in the model about the data is given by I =

In ( p(S,F)/ p(S)p(F) ). Here, p(S,F) is the probability (or pdf)

of the data {S(co)} and estimated model {F(co)} (in the

interacting universe), and p(S) and p(F) are the probabilities

(or pdfs) for the non-interacting universe. Using p(S,F) =

p(SIF)p(F), the mutual information can be rewritten as I = In ( p(SIF)/ p(S) ), where p(SIF) is a conditional probability (pdf).

These probabilities can be computed by using corresponding

numbers of states, I = In ( FsiF /Ts ). Here, TsiF is tne number of the world states compatible with the knowledge of

the data {S(co)} given the estimated model {F(co)}, and Ts is the number of states compatible with the a priori knowledge,

"prior to interaction" between the two systems. Prior

knowledge depends on properties of the model that are known

a priori and do not change in the estimation process, this is given by N, O. By using computations similar to those in the

text, we obtain InrsiF = £ Nq In [ Om ] and lnl"s = N ln<£> CO

(in these expressions we have omitted the terms accounting for

permutations of identical photons, because, as we have seen, these terms do not depend on the model parameters and do not

affect the estimation process). Finally, we obtain for the part

of mutual information that depends on the model parameters, I = Z No ln[Oco /O] = ZN(o ln[F(co)/ftco], this gives eq.(18).

CO CO

ACKNOWLEDGMENT. It is my pleasure to thank Dr. L.B. Levitin, who read the manuscript and made valuable

suggestions.
A Symbolic Representation of Misconceptions

Benjoe A. Juliano, Ph.D.

Department ofComputer Science

Coastal Carolina University

Conway, South Carolina 29526, U.S.A.

Tel: (803) 349-2144 Fax: (803) 349-2455

E-mail: Juliano@ccucs.Coastal. edu

Abstract

An intelligent system must process information as human

beings do. A framework is presented wherein dynamic cognitive

structures called chains ofthought are used to embody the dynamic

aspects of the intentions of intelligent agents. These chains of

thought are represented as fuzzy cognitive structures. In this

particular framework, structure mapping plays an important role in

the notion of misconceptions. An expert agent has to deduce the

"private" symbolic constructs of a novice agent in order to

correctly guide the novice through a particular task. These

"private" constructs are derived from (partially) corresponding

"public" symbolic constructs that are a result of intelligent

symbolic communication between the expert agent and novice

agent. This whole process embodies what the author refers to as

cognitive diagnosis.

Chains of thought, the "private" symbolic constructs, are the

main focus of the current paper. Its applications in designing

intelligent systems and cognitive diagnosis are emphasized. The

resulting framework is also an important step towards developing

a method for evaluating degrees of intelligence and possible

comparison between (groups of) intelligent systems.

L Introduction

For an artificial system to be considered intelligent, it must

process information as human beings do. The theoretical work

presented in this paper has two major goals. First, it investigates

and describes what types of cognitive structures are used when

intelligent agents communicate with each other. Secondly, it attempts to capture the dynamics of these cognitive structures during symbolic communication between intelligent agents.

Intelligent agents express their intentions when they

communicate with one another. In order for this communication to

take place, a common vocabulary has to be used. These "public"

symbolic constructs make up speech, be it spoken or otherwise. In addition to this common vocabulary, there needs to be a correspondence between the syntax of the language used by each

participant. As noted by Kohout [2], there must also be semantic

agreement if the conversation is to be successful. Unfortunately,

the transition from "private" intentions to "public" symbolic

constructs is not always clear. This is true not just to agents

actively involved in the conversation (we shall call these

participants), but also to those agents not really involved in the

conversation: spectators (correspondingly, non-participants) just

observing the interaction.

Dynamic cognitive structures must be used by intelligent

agents to deduce and make decisions. These must also be used to express themselves. The whole process of trying to determine

what one agent is thinking, or attempting to express, based on a dialogue, their behavior, their actions, etc. is what initiated the

work presented in this paper.

This work has relatively close ties to the field of semiotics, a

discipline of combining the theory of signs, symbols, and meaning

extraction. In the next few sections, we explore the area of

intelligent tutoring systems as a foundation for the work by Juliano

and Bandler [1]. Next, the dynamic cognitive structures that Juliano and Bandler call chains of thought [1 ] are introduced. A

brief discussion of the implications of this work is presented and

further work is also proposed.

IL Tutoring Systems and Deducing Misconceptions

Intelligent tutoring systems

Intelligent tutoring systems (or ITSs) provide, perhaps, the

best ground work for investigating the cognitive structures of

interest in this study. ITSs are systems designed to aid in tutoring

students on a particular subject matter. These systems are supposed to possess some form of intelligence by having

1 . some form of model of the student; and

2. some reasoning capabilities based on this model

The most common approach in the design of an ITS is to get a

better understanding of possibly how we as humans perform in a tutoring role. In particular, we need to investigate how we

represent and process information based on the two items listed above. This entails an approximation of the thinking process using

some knowledge structure based on a system's "own" expert

knowledge structure. The process of "thinking about thinking" is what Juliano and Bandler [1] have referred to as cognitive

diagnosis, which includes any method of confirming the relative

313
position of the novice student's thinking pattern based on a corresponding idealized pattern.

The approach we take is based on cognitive diagnosis during

problem solving. In this scenario, the student is given several

problems to solve and the tutor may intervene whenever

appropriate in directing the student to understanding the concepts

involved It is during this problems solving session that a model of

the student's understanding has to be formulated and used in determining when to intervene and how to control the direction of

the session (do we present a simpler problem or do we go with one

that is a little bit more challenging?).

The process ofdeducing misconceptions

Perhaps the most important factor in successful tutoring is how

to correctly deduce student misconceptions. This is based on

information gathered during a tutoring session, most likely

consisting ofpartial or incomplete solutions to the problem at hand.

This information may also contain a lot of noise. The student may

indicate varying degrees of uncertainty (or confidence) to their

solutions. Furthermore, under most normal situations, the

information is usually available in various forms: verbal, visual

cues, scribbled computations, diagrams or doodles, etc. Clearly, all

this complicates approximating this in an artificial system.

To simplify the process, the following main assumptions are made for an underlying theory of knowledge states, which can be

conveniently represented in a computer:

1 . The knowledge of the expert agent and the knowledge of the

novice agent overlap one another.

2. A knowledge state describes a set of concepts and the set of

relations among these concepts.

3. When an expert agent approximates the knowledge state of a novice agent, this information is used to generate "lines of

reasoning", which we call chains of thought, to account for

each observed action.

The first assumption is important because it implies the view that

expertise is decomposable into independent components that may

be used to define various dimensions of knowledge. It also implies

that "subsets" inherit essential characteristics of the "full" model;

hence, the novice agent's mastery of a particular component can somewhat be deduced.

The second assumption indicates an associative

representation. Fuzzy cognitive maps are used to account for the

inherent vagueness and imprecision in most natural tutoring

environments where decisions are based on imprecise, qualitative

data. The third assumption adds an important level of detail in the

dynamics of the process of cognitive diagnosis.

This subsethood assumption between the knowledge of the

expert agent and novice agent somewhat parallels Kohout's [2] note that semantic agreement is required if a conversation between

two agents is to be successful. In his statement, he indicates that there must be some form of overlap for this to proceed.

The process by which tutoring systems deduce misconceptions

by novice agents is also similar to the way intelligent agents

perceive their surrounding environment. In the tutoring scenario,

the environment is replaced by a particular novice. The expert

agent has to adjust to each novice agent and base its actions on its current model of that agent. Similarly, intelligent agents must

adapt to changes in their environment.

IDL Approximating Chains of Thought

Fuzzy cognitive maps

As indicated in the previous section, one of the assumptions

we have is that knowledge states describe a set of concepts and the

set of relations among these concepts. The dynamic cognitive

structures we use to represent knowledge states are fuzzy cognitive

maps (or FCMs). Mathematically [ 1 ], a FCM M={CM, RM) over

a finite universe of discourse, X, is afuzzy graph that is a 2-tuple

where:

CMe [0, 1]* is a fuzzy concept space of X (l)

and

Ru

=

(rm . rm » - . Ru ) >s a fuzzy multirelation (2)

Each R* (where 1 <> k <, rM) is afuzzy relation on the fuzzy concept

space CM For more details on the mathematics, operations, etc. on FCMs, refer to [1].

FCMs are ideal representations of knowledge states not just

because they capture the essence of the first two assumptions listed

in the previous section. They are ideal also because they can be

encoded from the communication between two intelligent agents.

This gives us a means of possibly representing "private" symbolic

constructs to correspond to an agent's expertise or knowledge, or

as an approximation of what another agent is trying to say.

Chains ofthought

Knowledge states alone are not sufficient in capturing the three

assumptions we laid out To represent lines of reasoning, there has

to be a way to move or transform from one knowledge state to

another. This requires a formal representation of chains of thought.

Mathematically [1], we can define a chain-of-thought structure on

a universe ofdiscourse,Xtobea5-tuple T = (C,/?, Y, S>, 6)

where the pair C and R define a FCM structure based on (1 ) and

(2), respectively, and

*P e [0,1]* is a knowledge state space (3)

$ e [0,1]* is a valid input space (5)

5:? X $-T is a transition function (6)

Notice that these definitions have some similarities to the formal

definition of a finite-state sequential machine. For more details on

the mathematics, operations, etc. on chains of thought, refer to [1].

314
Knowledge communication and cognitive diagnosis

What are the distinct processes involved in approximating

chains ofthought? We shall consider two intelligent agents, A and

B, although this could be extended to more than two agents.

Without loss of generality, let us assume that A is the expert agent

and B is the novice agent in a tutoring environment. Initially, we

start off with the arrangement given in Figure 1 below.

Figure 1 Initial phase of the interaction

The shaded region in each agent denotes domain knowledge.

Recall that in our first assumption, the overlay principle

(subsethood property) actually holds between agents.

Agent B's knowledge is then communicated to agent A in

some manner, possibly during a problem solving task. This is

depicted in Figure 2.

A B

Figure 2 Communication from the novice agent

Whatever was expressed by novice Agent B now has to be encoded

by expert Agent A. This is done by Agent A to either develop or update a model of what Agent B is thinking. This is illustrated in

Figure 3.

A B

Figure 3 Encoding and model generation/updating

by the expert agent

After expert Agent A has generated and/or updated its model

ofwhat Agent B is expressing (or thinking), the next step is model

interpretation. In [1], Juliano and Bandler propose the use of a discrepancy operator to identify misconceptions, if any, indicated

by the model ofthe novice. Whatever type of operator is used, this

is applied to the expert's domain knowledge and the current model

of the novice. This is depicted in Figure 4.

A B

Figure 4 Model interpretation by the expert agent

Whatever interpretation is derived by expert Agent A, this has to be

conveyed back to novice Agent B in some form. This is illustrated

in Figure 5. Hopefully this information will direct Agent B to the

ideal chain of thought.

A B

Figure 5 Expressing misconceptions identified

by the expert agent

Next, notice that the novice Agent B now undergoes a process

similar to that depicted in Figures 3 and 4. Communication from

expert Agent .4 has to be encoded and this information interpreted

and possibly assimilated into Agent B's current knowledge

structure. Thus, this model has a fairly general application for

intelligent agents and the modeling of some underlying cognitive

processes.

IV. Discussion

The model for cognitive diagnosis outlined in the previous

section warrants elaboration. Firstly, the appropriateness of using

FCMs to represent knowledge states is emphasized by two factors

in the model. Knowledge communication, the act of expressing

one's knowledge (see Figures 2 and 5), is primarily fuzzy in nature. One can observe how to express most everyday reasoning and

common sense knowledge - these are conveyed imprecisely. When

it comes to approximating this in a machine, this is where the

expressiveness of fuzzy set theory steps in. Furthermore, the

transformation of spoken (or otherwise) language into an internal,

"private" model as in Figure 3 is inherently noisy and imprecise as

well. Again, fuzzy set theory can capture this imprecision.

The use of fuzzy graphs, called FCMs, also facilitates modeling of the operation(s) depicted in Figure 4. In [1],

operations forfuzzy difference andfuzzy discrepancy between two

315
FCMs are defined. In a tutoring scenario, these can be used by an

expert agent to approximate any deviations by the novice agent

from an ideal cognitive structure. This ideal, of course, is based on

and limited by the expert agent's own domain knowledge.

FCMs also facilitate the formal definition of a chain of thought

structure. Figure 4 was meant to depict operations on either

knowledge states (using FCMs) or operations on lines of reasoning

(using chain of thought structures). Again, in [1], a formal

definition for chain ofthought homomorphisms was defined that includes both structure preserving and transition preserving

constraints.

Perhaps the biggest concern here is on the encoding scheme.

This is depicted in Figure 3 as the transformation from

communicated language to model generation or updating. To

achieve semantic agreement, a limit can be placed on the

communications bandwidth through the design of the

corresponding user interface for the system under consideration.

For example, in designing an intelligent tutoring system for

elementary genetics, a graphical user interface can be designed to include such tools as a calculator, icons depicting various species

to "breed", Punnet squares, etc. The interface can be designed so

that the use of each tool corresponds to the expression, as in Figure

2, of a novice's knowledge in FCM (or chain of thought structure)

form Ofcourse, this does not guarantee that all the necessary tools

will be used in attempting to solve a problem, but this is merely

part of the imprecision and noise inherent in the task at hand.

With this in mind, the expression of misconceptions depicted

in Figure 5 can be done in the reverse transformation. The correct use ofthe tools provided by the interface can be emphasized. This,

in conjunction with the elaboration of any other corrections to misconceptions (most likely at the knowledge state level) can

account for a fairly powerful tutoring tool.

The framework presented here does not only apply to the area

cognitive diagnosis in intelligent tutoring systems. The panoply of

operations and relations on the cognitive structures listed in [1],

some of which are presented in this paper, also provides an

important step towards developing systematic methods for

evaluating degrees of intelligence between intelligent agents. This

will also be useful in comparing (groups of) intelligent systems.

V. Summary and Conclusions

What was presented in this paper is a continuation of the ideas

presented in [3] with emphasis on the dynamics of the chain of

thought structure. The focus was on the idea that misconceptions can be symbolically represented by FCMs at the knowledge state

level, or by chain of thought structures at the reasoning level. The

area of cognitive diagnosis lends itself to other areas similarly

characterized by decision making in complex systems with

uncertainty. This uncertainty may be in the form of incomplete,

incorrect, contradictory, misleading, or even noisy information.

Chains of thought, used to represent the "private" symbolic

constructs of intelligent agents, facilitate the identification and

symbolic representation of misconceptions. This is an important

step in the design of intelligent systems; in particular, systems

where cognitive diagnosis is a significant function.

References

[1] B. A. Juliano and W. Bandler, Tracing Chains of

Thought: Fuzzy Methods in Cognitive Diagnosis,

Heildelberg: Physica-Verlag, 1996.

[2] L. J. Kohout, A Perspective on Intelligent Systems: A

Framework for Analysis and Design, London: Chapman

and Hall, 1990.

[3] L. J. Kohout and B. A. Juliano, "Dynamic aspects of

interpretation of symbolic constructs," presented at Intelligent Systems and Semiotics - International

Multidisciplinary Conference, National Institute of

Standards and Technology, Gaithersburg, MA 1996.

316
SEMIOTICS OF TEXTS AND IMAGES

MATHEMATICAL ASPECTS OF CYBERAESTHETICS

Leonid I. Perlovsky

Nichols Research Corporation, 70 Westview Street, Kilnbrook IV, Lexington MA 02173

Tel: 617-862-9400; Fax: 617-862-9485e-mail: perlovsl@nichols.com

ABSRACT: Cyberaesthetics addresses an emerging

integrated multi-disciplinary approach to the development of

intelligent systems: combining cybernetics, semiotics and

aesthetics. The paper describes a mathematical apparatus of

intelligence related it to Kantian philosophy, which has a room for the concept of beauty.

1. INTELLIGENCE AND AESTHETICS.

Robots that can read and enjoy literary texts are not yet at hand. Notwithstanding, there is a growing understanding

among engineers and mathematicians, that intelligent systems

of tomorrow will have to be able to perceive the meaning and

intentions of concepts, scenes, and texts, depending on

situations and contexts. And, in order to achieve this, robots

must be endowed with emotions and aesthetics. The term

"robot" we use broadly as an intelligent system, an "infobot".

The term "aesthetics" we use in the Kantian sense as a science

of feelings and feeling perception, a science of emotions. In western cultural tradition, there is a long-standing opposition

between thinking and feeling. And often, we tend to forget

that this is a highly abstract, refined, top level view of our psyche. Actual human processes of intellection are complicated interwoven interactions, vortices of multiple

neural processes, involving various parts of the brain and

various conscious, unconscious, and instinctual levels. A

historic view of rationality as limited to Aristotelian-Godelian

logic is too narrow and is being rejected today. A new

understanding of rationality emerges as a hierarchical goaldirected functioning, which involves internal and external

actions; actions within the mind of an intelligent system and

into the outside world. This new understanding emerges

concurrently in multiple fields dealing with phenomena of

intelligence: in philosophy, cognitive sciences, art and art criticism, education, mathematics and engineering.

If you pinch your finger, it hurts, and an ability to feel the pain is obviously an a priori faculty, which is necessary

for survival to such an extent that it is shared throughout the

entire animal kingdom. This "lower" origin of feelings

separates them from our higher cognitive abilities. And, there

is a long-standing line of thought that separates and counterposes feelings and thinking, emotions and intellect. Is there

any ground for their unification? Neural and cognitive sci- ences have been concerned with relating emotions to material

neural and bodily physiological functions. For example, neural pathways have been found from hypothalamus (brain areas associated with emotions) to viscera. The popular known

connection between fear and upset stomach could possibly be

understood as a survival mechanism regulating interactions between fear and hunger. This is another example of the "lower"

aspect of emotions. Brain research relating emotions to higher

intellectual functions is yet in the incipient stage. Interactions

between cortical systems (associated with high cognitive functions) and hypothalamus is hypothesized to be mediated

through amygdala. The high degree of reciprocal anatomical

connections found among these neural structures suggests existence of information processing loops involving emotional

and cognitive functions. Our knowledge of the brain structure

is insufficient for deducing the mathematical theory of

"higher" emotional functions, and many believe that even if the entire wiring diagram of the brain were available, it still would not be possible to deduce its main mathematical concepts. Neural and psychological data have to be combined

with philosophical analysis and physical intuition in order to develop mathematical theory of higher emotions.

In 1787 in a letter to his friend, Kant wrote that he discovered a new type of a priori principle, the feelings of plea- sure and pain, which he found to be a necessary part of our intellect. Kant came to a conclusion that our Judgment faculty

is based on the feeling of pleasure caused by the harmony or correspondence between our internal representations-concepts

and empirical phenomena. The new principle governs "intellectual emotions". These "higher" emotions are not separated

from thoughts, but they are combined together in a dynamical

process described by Kant in his three volumes that overturned our understanding of the entire history of the philosophical

analysis of the "mind-body problem" [1781; 1788; 1790].

The present paper describes mathematical aspects of

Cyberaesthetics, combining mathematics with Kantian theory

of mind. The next Sect. 2 overviews a mathematical apparatus of the modeling field theory (MFT), suitable for describing higher emotions and providing a foundation for the mathematics of mind in which a concept of beauty could be in- cluded. Sect. 3 briefly reviews Kantian theory and establishes

connections with MFT. Sect. 4 discusses a possibility for

Emotional Machine and outlines directions of future research.

2. MODELING FIELD THEORY

2. 1 Systems with Adaptive Intelligence

Consider (1) a set of input data (X(n), n e N}, where each

member is a vector in D-dimensional space, X = {X<j, d = 1,... D}; (2) a set of categories {h e H}, which are characterized by

internal parameters {Sh} and by models of the data {Mh(Sh,

n)}; and (3) a similarity measure between the sets of models

and data, L({X},{M}). A set of parameters is finite, Sh =

{S a

h, a = 1,... A}, but not necessarily limited, and a set of

categories is not fixed, its cardinality H is finite, but may vary

319
in the process of learning. A similarity measure is designed so

that it treats each model as an alternative for each piece of data

L({X},{M}) = EI I r(h) /(X(n) I h), (1)

neN heH

here / is a conditional partial similarity between data vector

X(n) and model Mh- For example, /can be selected as a

probability density function. Then L is a total likelihood (this

interpretation does not require statistical independence among

data vectors n and n': dependencies can be accounted for by

considering X(n') as parameters of the models for the data

vector n).

The problem consists in estimating internal parameters S

and in making a choice of the categories (or classification),

that is, in obtaining a partition

{N} = {NilN2 l...|NH}, (2)

that decides, which model h corresponds to an observation n (here Nh is a subset of N), by maximizing the similarity

eq.(l). When likelihood is used as a similarity measure, this

is a problem of the maximum likelihood estimation.

Categories activated by high similarity values produce

actions, including generation of messages transmitted within

the intelligent system, which acknowledge the category

activation. Messages include the category parameters. They

can serve as input data for other categories and can be used for

control of actuators. Correspondingly, data are sensory data or

internal messages, and models are patterns of messages and

sensory data. The above mathematical framework is fairly

broad and encompasses most formulations of intelligent

adaptive systems. It includes as particular cases, statistical and

model-based pattern recognition, complex adaptive systems,

neural networks, and systems of intelligent agents. The above

formulation addresses "higher-level" intelligence functions of

recognition and adaptation. A compete intelligent system

would include lower-level drives for survival, reproduction and,

in case of an artificial system, a robot or infobot, drives for

producing specific tasks it was designed for. In case, when a set of observations, N, corresponds to a continuous flow of signals, for example, a flow of visual

stimuli in time and space, it is convenient instead of eq.(l) to consider its continuous version,

L = expj ln( X r(h) *(X(n) I h) ), (3)

N heH

where N is a continuum, such as time-space. In this case, models describe a continuous modeling field, conditional

partial similarities can be compared to Lagrangian, and

maximization of similarity L can be compared to minimization of action in the physical field theory.

2.2 Multiple Hypothesis Testing

A standard method of solving the above problem

[Winston, 1984; Segre, 1992] consists in (1) considering all

possible partitions eq.(2) (within certain a priori established

limits), (2) obtaining an estimate of the parameters Sh for

each partition by maximizing similarity,

max{ sh }[pdf({X(n),neN})l{Ni I N2 I ...

| NH}] (4)

and (3) choosing the most similar partition. Obviously, a computational complexity of this algorithm is at least on the

order of the number of partitions ~ H^, and denoting a complexity of maximization of the eq.(4) by CI, a complexity

of the MHT algorithm can be written as

complexity(MHT) = C1HN

(5)

Newly emergent mathematical methods of solving the

problem of intelligence while avoiding the combinatorial

complexity of MHT include multiscale hierarchical

organization and evolutionary computation.

2.3. Fuzzy Partitions and Modeling Field Theory (MFT)

A new proposed method of solving this problem utilizes

fuzzy adaptive logic [Perlovsky, 1995; 1996]. Let us introduce

fuzzy class memberships f(hln), associating each data vector n with each category h:

f(hln) = r(h) *(X(n)lh) / X r(h') /(X(n)lh'). (6)

h'eH

Eq.(8) looks like the Bayes formula for a posteriori

probabilities, and f(h I n) can be interpreted as probabilities, if likelihood is used as a similarity measure and when the

parameters of the models are accurately estimated. Upon

convergence of the estimation procedure described below, f

converge to the estimated probabilities. Let us specify an

internal dynamics of the Modeling Fields (MF) as follows,

H

df(h I n)/dt = f(h I n) X { [°hh' " f( h'

1 n)l

'

h'=l

[3ln/(nlh , )/3Mh'] aMh'/aSh' • dSh'/dt, (7)

dSh/dt = {J f(h I n) [3ln/(nlh)/3Mh] 3M'h/3Sh,(8)

N

here

5hh' is 1 if h=h', 0 otherwise. (9)

Parameter t is the time of the internal dynamics of the MF

system. The following theorem was prooved.

Theorem. Equations (7) through (9) define a convergent

dynamical system MF with stationary states defined by

max {Sh} L.

It follows that the stationary states of an MF system give

the maximum similarity solution of the model-based pattern

recognition problem. When likelihood is used a similarity,

the stationary values of parameters {S n } are asymptotically

unbiased and efficient estimates of these parameters [Cramer,

320
1963]. A computational complexity of the MF method is

linear in N,

complexity(MF) = C2HN, (10)

where C2 is defined by the relaxation time of the MF system

and is likely to be independent of N (or depends weekly). In

this way the MF system solves the problem of the

exponential complexity associated with the MHT method,

eq.(5). Fuzzy class memberships f(h I n) define a fuzzy

partition of set N, which can be used to define a non-fuzzy

partition of the type of eq.(4): Vn, max^ f(h I n) => n e NhMFT describes an intelligent system composed of

multiple adaptive intelligent agents: each category-model is "dormant" until activated by a high similarity value. Every

piece of data may activate several categories, which "compete"

with each other, while adapting to the new piece of data.

Adaptation and other actions by activated categories are largely

independent from most other categories, except for those

competing with each other. Most important actions by

activated categories are transmission of messages that include

category parameters and sustaining the loop of adaptation of

their own parameters. Evolutionary computation is naturally

incorporated within MFT: transmitted messages, including

category parameters and other aspects of category-models are

strings-objects of evolutionary computations and are employed

by modeling field systems for adaptation of its structural

components that could not be incorporated in a continuous

fashion and are not the subjects of adaptive MFT loops. The

overall architecture of MFT categories can combine

heterarchical and hierarchical organization.

3. MFT AND KANTIAN THEORY OF MIND

3.1. The Role of Kant's Theory

What is intelligence? It is still shrouded in mystery.

A lot is understood, but much still is unknown and, most

likely, will remain unknown for a while. Intelligence is attributed to natural and artificial systems and some of these

systems are very simple, while others are very complex. At

lower levels, intelligence is an ability to sense the

environment and to control the body (machinery) toward

achieving few predetermined goals. At higher levels

intelligence includes abilities of thinking, including

recognition and formation of concepts, developing complicated

internal representations of the outer world and self,

understanding, language ability; planning behavior, including

direction of attention, definition of goals and subgoals and the

ways to achieve them; acting within itself and in the outer

world; an ability of judgment, including feeling and emotions;

abilities of intuition, learning, consciousness, creativity, and a mysterious feeling of freedom of will. Kant overturned the understanding of the relationship

between the mind and world by considering the specific a

priori contents of mind that enable its functioning. He

brought the philosophy of Pure Spirit close to the scientific

method. He developed a rational explanation of mind as a

system, if not in its entirety, still in its most interesting

"higher" intellectual abilities. Many aspects of Kant's theory were further developed by a number of philosophers and

psychologists, including Shopenhouer, Hegel, Nietzsche,

Freud, Jung, Bergson, Jaspers. Still, the original theory of

Kant remains unsurpassed in its comprehensive treatment of

mind as a system. And, mathematical theories of intellect

have remained far removed from the penetrating depth of his

understanding and are inadequate for coming even close to the

width of his analysis. This does not have to be so, for Kant's

analysis is rational and therefore can perfectly serve as a foundation for developing the mathematical theory of mind. A

first step toward rectifying this deficiency of the mathematical

theories of intellect is undertaken here. In three volumes on Critique of Pure Reason, Critique of

Judgment, and Critique of Practical Reason, Kant explained a wide variety of intellectual experiences based on three

fundamental abilities or faculties of mind: Understanding,

Judgment, and Reason. Each is based on a specific a priori

principles or instincts contained in mind: concepts,

correspondence between concepts and manifold of sensory data,

and will or desire. Understanding is a faculty of concepts, a source of general notions. Judgment is an ability to see that a

particular case comes under the general rule. And, Reason is an ability to draw conclusions that is to generate behavior.

(The most important type of behavior, interwoven with higher

intellectual abilities and emotions, Kant considered to be the

behavior of learning.) These three abilities correspond to the

three main modes of consciousness: knowledge (of concepts),

feeling (of correspondence between concepts and outer world),

and desire (to act). Even so Kant devoted a separate book to each ability, they should be combined within a dynamical

system constantly exercising all three abilities in their

interaction. This paper makes a step toward developing a mathematical apparatus of Kantian theory. We will see that

MFT contains seeds of mathematical modeling of the three

main elements of intelligence identified by Kant. MFT carries

Kantian analysis further: it is a dynamical system, in which

the three abilities identified by Kant exist in the process of

constant interaction, as it were in a "vortex". This vortex

models learning of a category as a dynamical formation of a symbol. I overview some of the higher intellectual abilities,

along with attempts at their rational explanation and

mathematical modeling.

Emotions and perception of beauty are fundamental to human mind, alike in everyday life, arts, and sciences. Still,

the concept of beauty is mystifying. The first step towards

mathematics of beauty is made here. It is founded on the

relationship between MFT and Kantian theory of mind.

MFT's will for learning, according to Kant, is the most

important will, which serves as a basis for emotional

intellectual abilities, for beautiful and sublime.

3.2 Understanding Is Based on Internal Models

An internal model is a basis of intelligence. Even at the

lower levels, say, of a lobster sensing and grabbing food, with

the axons of sensing cells "wired" directly into the neurons

321
that control muscles, we can talk about internal model.

Because, the signal that a "food-sensing" neuron sends to "muscle-neuron" indicates an internal lobster's representation

of food. There is no such thing as "food" in the ocean, "food"

is a dynamic process of interaction between an object in the ocean, sensing neuron (that forms an internal representationsignal), grabbing neuron, and other relevant neural aspects of

the lobster's experience. A lobster's mind has literally few

neurons, and if our final goal would be modeling of a lobster's mind, we will directly proceed to studying its wiring diagram

without such nebulous and not obviously useful concepts as

lobster's internal models.

Our aim, however, is to understand and model higher

levels of intelligence. At higher levels, a complete "wiring

diagram" of a neural system, even if available, would be so complicated that it does not furnish an understanding of the

basic principles of mind. A significant part of the brain is involved with internal models (storing, updating, and using

them). Our ability to recognize concepts, even simple ones, such as objects, is due to internal models or representations of

concepts. Understanding, first of all, consists of concepts in our mind along with their interrelationships. Higher levels of

understanding, such as understanding of meaning, involve a complicated internal model composed of a large number of

submodels-concepts with multiple interconnections among

them. Possibly, every particular phenomenon of

understanding-meaning only exists within a limited domain,

within a certain situation or with regard to a certain goal.

Then, meaning of a concept is modeled by including this concept within a set of situationally relevant other concepts

and goals. Meaning requires a hierarchical system: the

understanding of a meaning of a concept requires a point of

view from the next levels in a hierarchy, above the level of the

concept's inner model and its recognition. Thus, the meaning

of a lower level concept is included into a higher level

concept. However, relationships among levels are not rigidly

fixed: formation of certain concepts involves multiple

hierarchical levels, and relative position of concepts in the

hierarchical levels might be situationally dependent. Thus,

heterarchical hierarchy might be a better term. Explanation of

mind as based on a priori inner models ascends to Plato and

Aristotle. Kant identified a priori inner models as a separate

faculty of mind that he called Understanding. Mind's

operations with a priori concepts Kant calls the domain of

Pure Reason.

The main question that the analysis of Pure Reason shall answer, according to Kant, is "How are synthetic judgments a

priori possible?" This ability Kant identified as a specific a

priori faculty of pure reason. In our theory of mind, this specific faculty is represented in hierarchical models: next

levels in a hierarchy contain synthesis of the lower level

concepts. This synthesis is of the a priori nature, because the

hierarchical structure of the internal model is of the a priori

origin. Thus, development of hierarchical models is a key to mathematical modeling of the Understanding and Pure Reason.

Making this hierarchy adaptable and situationally dependent is an additional challenge.

Explanation and modeling of the phenomena of meaning

and understanding requires also including them within behavior

generation and acting of an intelligent system. The acting

could be inside, within an intelligent system, or outside of the

intelligent system, into the outer world. Actions,

corresponding to the goal or situation (internal or external),

constitutes a part of meaning. There is also another aspect of

acting out in the external world noted by Freeman, who

introduced a concept of external representations in the world.

Our external acts and their results (being perceived by

ourselves and others) from gestures and utterances to our entire

culture, as it exists in the outside world, are external

representations. To the extent that external representations are included into the Kantian cycle of category formation, they can be viewed as parts or extensions of our internal models.

Computer simulations are a perfect example of such

extensions of internal models.

According to Kant, Logic gives laws of understanding, or laws of relationships among a priori categories. Here, in the

world of Ideas, there is a significant domain of applicability of

the Aristotelian logic. For example, an internal model

category of an object is either that of target or not, according

to the Aristotelian logic law of excluded third (and this logic is different from fuzzy logic of judging which real signal belongs

to which category ). This domain of the Aristotelian logic

encompasses non-adaptive aspects of the a priori models. To

the extent that the a priori models can adapt, they are fluid, non-Aristotelian, fuzzy. Development of adaptive hierarchies

of models is a challenge for future research.

To summarize the MFT relationship to Kant's

Understanding: MFT ability for Understanding or forming

concepts is due to a priori internal models, and an ability for

synthetic judgments a priori is due to an a priori hierarchy of

models and relationships among them.

3.3 Judgment Is Based on Similarity Measures

For internal models or concepts to be useful, there should

be a way of relating them to experience. In other words, we

should be able to recognize individual phenomena according to general concepts and to decide which empirical facts correspond

to which concepts. Kant called this ability Judgment and

considered it as one of the three main abilities of mind.

Judgment is an ability to see that a particular case comes under

the general rule. In MFT theory, Judgment is mathematically

represented by similarity measures. MFT contains a measure

of similarity between the internal model and the world, as well

as between each submodel-concept-agent and a particular

subset of input data. This is an a priori property of MFT and,

according to Kantian analysis it is an a priori property of our mind.

Kant differentiates determinant and reflective aspects of

Judgment. Finding particular subsets of sensory data

corresponding to a specified concept-submodel is the

determinant Judgment. And, finding the concept

corresponding to the data is the reflective Judgment. MFT

contains mechanisms of both, determinant and reflective

Judgment. Within the iterative loop of MFT adaptation,

322
determinant Judgment is given by the association

(segmentation) of data with submodels, and reflective

Judgment is given by selecting the concept-submodel most

similar to the data segment (subset). In MFT both are given

by the fuzzy associations, f(kln), with n designating data and k

designating the concept-submodels.

Why is the Nature in its manifold knowable to our mind?

Is it due to a specific property of Nature, or due to a specific

property of mind? In other words, what makes it possible for our Understanding and Judgment to function in the way

described above? Kant's answer is that this possibility is due

to a special a priori property of our mind. This property is the

purposiveness of our internal representations (models).

Understanding and Judgment are so constructed that internal

representations of empirical events and objects appear to us as purposive (the purpose includes first, a correspondence

between our internal representations and the world, and second, an ability to learn or to improve this correspondence). This

purposiveness provides a foundation for the development of

higher faculties of mind including higher emotions, and the

notions of beautiful and sublime.

A reader might wonder if this discussion is too

philosophical and irrelevant to a mathematical theory of mind?

The relevancy of this discussion is in that it guides us in constructing internal models, measures of similarity, and in developing evolutionary theories explaining these abilities. The models and similarities are constructed so that they have a purpose or meaning within the intelligent system, which is the mathematical description of the intentionality of the

intellect. This intentionality includes the correspondence to the world and adaptivity that provides for learning. And, it is needed so that the "lower level" instincts for survival, for

performing specific tasks, etc. can be more efficiently satisfied

(by a living being or a robot). Intentionality provides a background for a mathematical theory of higher faculties of

mind, including a possibility for mathematical treatment of

beautiful and sublime. And, an evolutionary theory have to lead to these abilities. To summarize the MFT relationship to Kant's Judgment:

MFT ability for Judgment is due to similarity measures and

fuzzy category memberships, which select data corresponding

to the categories of Understanding and select categories

corresponding to the data, in iterative cycles of every MFT

loops-agents.

3.4 Reason Is Based on Similarity Maximization

Judgment mediates between concepts of Understanding and

concepts of Reason (will, and freedom). In particular,

reflective Judgment ascends from particular to universal, from

sensory data to concepts. Its principle is an ability to learn,

which Kant called the purposiveness of intellect towards the

object. This ascendance from data to concepts is practically

realized by Reason. In MFT functioning, finding a submodel

corresponding to a piece of data (Judgment) is followed by

adaptive modification of the model, which is the act of will

according to the learning principle (law) of Reason. Reason

provides laws for behavior, and MFT paradigms considered in

previous chapters were concerned with one type of behavior:

learning behavior as adaptation of the internal model.

Modification of models in MFT is governed by the principle

of maximum similarity between the model and data. The

MFT parameter-adaptation equations maximizing the

similarity give the laws of Reason. Thus, MFT provides for a mathematical description of a will for learning, a will for

improvement of its internal representations of the world and

the laws of Reason governing this will.

Kant emphasized a fundamental nature of the antinomy

between causality and freedom and severely criticized

philosophers, who underestimated the difficulty of the

causality-freedom antinomy. And, his criticism still applies

to a researcher, who is too cavalier about resolving this

antinomy. The fundamental source of difficulty is in that

freedom is an opposite of randomness. Freedom supposes

causality. If there is no causality, there could be no freedom.

But if the world's laws are causal, how the freedom could be

explained? Kant made a step towards resolving this antinomy.

He assigned the concept of causality to Understanding, where

causality is an a priori concept of understanding the nature, the

world of phenomena. And, he assigned the concept of freedom

to Reason, where it is an a priori concept governing human

desire and will. According to Kant, freedom belongs to a noumenal world, it originates from the unknowable nature of a

human-in-itself. A next step toward resolving this antinomy

should be attempted by identifying the unknowable human-initself with our unconscious and developing a physical theory

of conscious and unconscious aspects of mind.

4. EMOTIONAL MACHINE (TOWARD

MATHEMATICS OF BEAUTY)

In 1787 Kant discovered a new type of a priori principle,

which led to his formulation of Judgment faculty that unified

his philosophy. Kant came to a conclusion that Judgment is based on the feeling of pleasure caused by the harmony or cor- respondence between our internal representations-concepts and

empirical phenomena. The new principle governs "intellectual

emotions", which are not separated from thoughts, but are combined together in a dynamical process of Kant-MFT loopagents. Mathematical apparatus describing Judgment in MFT

are given by similarity measures. And, a thought process is a

loop, a vortex of concepts, emotions, and adaptation actions.

Higher emotions are related to an ability for the perception of beauty, which is a universal and fundamental property

of human mind. It is important not only in the field of fine

art, but it pervades human experience. And, there are well

known statements by famous scientists, explaining that the

first and foremost test of a scientific theory is its beauty. But,

mathematical attempts to model mind, so far, have not

touched the subject of beauty, and the directions along which

this could be attempted seem to be hidden in mystery and not

accessible to scientific investigations. Here, I attempt a first step in this direction. In this, I have found that I am greatly

added most of all by Kant, who with scrupulous detailness an- alyzed rational mechanisms of beauty and other higher emotional faculties.

323
When designing an intelligent system, say a robot, we decide what kinds of objects the robot should be able to recognize and we supply the robot with the internal models of these

objects. From robot's perspective, only those types of objects

exist which it can recognize. Every object has a purpose of

being recognized (in addition to any other purpose, the robot

may put this object for). A universal purpose of any object is

its concept: for an object to have any purpose for a particular

intelligent system, the object's concept has to exist in the sys- tem. This is a design principle of any intelligent system.

And, this design principle is applicable to us: the evolution

(or God) designed us so that we can find our ways around those

objects which we recognize in the nature. The basic principle

of the design is that the nature appears to us as purposive. The

purposiveness of nature is the a priori part of our representations and it harmonizes nature with our desire for knowledge

and produces the feeling of pleasure (or pain, if chaos is encountered).

Knowledge about objects comes from experience and from

the a priori concepts (Understanding). The role of Judgment in

this process was discussed in the previous section: it is an objective, or cognitive aspect of Judgment. In this section, we

concentrate on the subjective aspect of Judgment, that relates

to the subject and not to the object. This subjective aspect is the satisfaction and feeling of pleasure that is bound with the

harmony between our internal representations and an object.

Kant calls this aesthetical aspect of Judgment, because it relates more to emotions than to cognition (even so all aspects

are combined in every act of perception and cognition). This

aesthetical aspect of Judgment is related to the "pure" purposiveness of our representations, which is separate from any

specific purpose that an object can be used for, and includes

only the knowledge itself. Thus, android-robots capable of

self-learning have to be designed so that they have an aesthetical affinity to knowledge. In MFT this is given by the similarity, l(XIM), that relates a particular case X to the general

concept M, without any further specific purpose the object can be used for. To the extent that the purposiveness is felt in its pure

form and is bound to its a priori nature, the object is called

beautiful. The nature of beauty is related to an interest not in the object, but in the subject: what I make out of this

representation in myself. Beautiful is what coincides with the

purpose of acquiring more knowledge and improving the

harmony between the internal representations and Nature.

Kant discusses two higher intellectual aesthetical abilities: feelings of beautiful and sublime. Beautiful involves the

relationship between Judgment and Understanding and Sublime

involves the relationship between Judgment and Reason. The

feeling of Sublime moves the Reason to act toward

improvements of internal representations. MFT provides a foundation for the mathematical description of these abilities: similarity performs both of these functions, it establishes

relationships among data and models (concepts of

Understanding), and it activates actions of adaptation toward

improving the harmony between the models and nature.

Is it possible to write an equation of beautiful? And

should it be the goal of our study? Could there be an equation

that tells the difference between Rembrandt, Warhol, and a

causal recreational artist? Of course not. The purpose here is to demonstrate that there is a possibility for a mathematical

theory of mind, in which concepts of emotion and beauty have

place. But then, why not proceed directly to producing by

means of MFT even a simplest example of something

beautiful? Where is the difficulty precluding us? The

difficulty is in an adaptive nature of beauty. Kant got himself

in trouble with later readers and admirers, by his attempts to provide examples of what is beautiful and what is not. His

examples (such as e.g., that drawings could attain pure beauty

and paintings do not) were immediately criticized and he was

branded as having undeveloped aesthetical taste and worse. One of the reasons is that what was beautiful thousands years

ago is not necessarily beautiful today. Concepts of

Understanding evolve, and those concepts that were useful

sometimes ago, in that they captured important aspects of

nature and provided an evolutional advantage to those who

possess them, are not necessarily useful any longer, they lost their purposfulness. Within our evolving internal models,

some concepts may become commonplace, outdated, empty of

useful contents, and contradictory to newer, better adapted

concepts. Since mathematically, beauty is related to the

harmony between the internal model and nature, it is changing

with time. What is an excellent harmony between an adaptive

model and data in an engineering system, such as considered in [Perlovsky, 1994; Perlovsky et al, 1997], is a very simple

construct, unworthy of the word "beauty" in the context of our mind. In order to design android-robots capable of the humanlevel perception of beauty, even at a rudimentary level, their

internal models have to be much more complicated than

currently used in engineering applications. But this quickly

changes. And, possibly, we will see complicated robots,

which would have to learn for many years, like human do,

acquire individual subjective experience, and their perception of

beauty will acquire human-like, individual features.

REFERENCES

Kant, I. (1781). Critique of Pure Reason. Willey, NY.

Kant, I. (1787). Letter to Reingold. In Tractats and Letters,

1980, Interscience, Moscow.

Kant, I. (1788). Critique of Practical Reason. Willey, NY.

Kant, I. (1790). Critique of Judgment. Tr. J. H. Bernard,

1914, 2nd ed., Macmillan & Co., London.

Perlovsky, L.I. (1994b). A Model Based Neural Network for

Signal Processing, Neural Networks, 7(3),pp. 565-72.

Perlovsky, L.I. et al (1997). Model-Based Neural Network for

Target Detection in SAR Images. IEEE Trans. Image

Proc. 6(1).

Segre, A.M. (1992). Applications of Machine Learning.

IEEE Expert, 7(3), pp. 31-34.

Winston, P.H. (1984). Artificial Intelligence. 2nd edition.

Addison-Wesley. Reading, MA.

324
Semiotics and Modeling Computer Classification of Text with

Genetic Algorithm : Analysis and first Results

Vincent Rialle*, Jean-Guy Meunier**, Sofiane Oussedik*, Georges Nault**

* Laboratoire TIMC-IMAG, UMR CNRS 5525, University Joseph Fourier, Grenoble.

E.mail : Vincent.Rialle@imag.fr. ** Laboratoire d'Analyse Cognitive de l'lnformation (LANCI). Universite du Quebec a Montreal.

Abstract. Computer engineering proposes the

construction of complex systems by dynamic

prototyping (Buddie and Bacon, 1992). But this prototyping cannot be inductive and purely considered as a trial an error process. To be successful, one must

possess an underlying hypothetical model (Marr, 1982)

of what are the functions of the system. If these

functions relates to physical tasks, such as sensing

temperature, manipulatiing objects, etc., the desired

behavior can be observed, and a model can be built. Conversely, if the functions of the system are to be

applied to semio-informational tasks, such as language

translation, information retrieval, hypertext navigation,

text generation, etc., the interpretative behavior is not readily observable. Now, as any other computer

systems, these systems are symbol manipulation

machines (Newell ,1980). They must also manipulate

input and outputs, but, in themselves, these data are semiotic objects, and not physical ones. These systems

manipulate objects that have to be interpreted by some

cognitive agent. In other words, systems that

manipulate physical objects require a model of the

physical word, while systems that manipulate

informational objects require a semiotic model. In this paper, we illustrate how a semiotic model can help in the conception, the modeling, and the experimentation

of a semiotic behavior such as Computer Assisted

Reading and Analysis of Text (CARAT), and how this model has called upon the Genetic Algorithm (GA)

theory to realize some of its aspects.

I. Presentation of CARAT

1.1 General presentation

Computer Assisted Reading and Analysis of Text is the computer technology that offers readers an

asssistance in attaining some aspects of the

informational or semiotic content of a text (discursive,

lexical, hypertextual, thematic, stylistic, etc.). So,

CARAT definitely relates to interpretative actions.

There is in no way a robot that reads or understand a text by itself. One the classical models of text interpretation is the philological one 1

. Through the centuries, thousands of

readers, exegetes, and interpreters have practiced this method. Because of the quality of its principles, it has

acquired compelling recognition, and the weight of its

1 A certain number of researchers using information

technologies are beginning to place themselves in this philological perspective (cf. Thrane et ai, 1992).

experience. The basic principle of philological

perspective is that one can construct relatively

systematic procedures capable to ensure rigor in text interpretation. As a matter of fact, philology is an

instanciation of an interpretative semiotic process

applied to the processing of textual signs. It takes sets of signs (a text) as its input, then classifies, categorizes

them, explores and selects them, and produces a new set of signs - the commentaries - as its output. This

interpretation process can be translated functionally in terms of (a) inscription, (b) classification, (c)

exploration, and (d) configuration, of information

(Seffah and Meunier, 1994). In its principles, three

important dimensions can be emphasized : text reading

and analysis is a systematic, dynamic and plastic

behavior. Systematicity pertains to the controlled

processing of information; dynamicity concerns the

interaction of the analyst with the text; and plasticity

allows the constant renewed interpretation of the text.

In order to respect this particular type of

interpretation process, a computer model must rely on

an open architecture. It must allow an information

processing flow that is systematic dynamic, and plastic.

Each processing will be built out of interactive advances

and restarts which sometimes are autonomous,

sometimes are interrelated, but which all aim at assisting the reader and analyst in penetrating the

content of the information. Hence, again a CARAT

system is not a robot reader, but a faithful assistant in reading and analyzing texts. In this perspective CARAT

is defined as the set of serial or parallel operations

which, with the assistance of the computer, construct

interpretative paths in which each moment produces a new textual object to be classified, explored and

configured.

1.2 CARAT and classification

There exists an infinity of possible CARAT

processing flow. Each text, for each person, can be read

and analysed in so many ways. One can, for instance,

inquire on a particular theme, paraphrase and summarize

a specific segment, study the lexicon, evaluate the style,

retrieve information, build a thesaurus or an index of the content, and so forth. Among all the operations at work

in each of these processing, we will study more

particularly the classification process. This process is important since interpretation always requires some type

of classification of the incoming signs, symbols or

information.

In the field of text processing, there exists many

strategies of classification. Some classical strategies : a)

325
are of logico-symbolic type (eg (Hobbs, 1993; Sowa,

1991) or semantico-linguistic (Rastier, 1987, BertrandGastaldy et ai, 1987, 1993). Others are statistical (Church and Hanks, 1990; Reinhert, 1994; Lebart and

Salem, 1994; Pustejovsky, 1991; Wilks, 1996; Salton,

1989; etc.). Albeit very systematic these approaches

lack dynamicity and plasticity. Learning is limited, and

they are very weak on processing a constantly ever- changing informational input, as it is often the case with textual data (for instance on the World Wide Web).

Finally, some can be referred to as "emergent

computation" models (Forrest, 1991). They include

Markovian fields (Kindermann and Snell, 1980;

Bouchaffra and Meunier, 1995), connectionnism

(Rumelhart, 1986; Salton and Buckley, 1994), and

Genetic Algorithms as shown in this article. Besides

their properties of statistical strength and generalization,

they are systematic like any other clustering strategies,

dynamic and plastic (learning is possible).

Our purpose here, is mainly to show how the

Genetic Algorithm approach to classification can be

applied to the problem of semiotic interpretation of text, and most of all in the context of CARAT technology.

Although validation and experimentation of the GA

approach is not the main purpose of this paper, which is modeling, some initial experiments will be reported.

II. Genetic Algorithms

II. 1 General presentation

The GA approach takes its inspiration from research

done on adaptive systems. This research sees such a type

of system as an agent that applies to a domain (called

the environment) specific operations which allow him

to act upon it in the most efficient manner . This

principle is of course based on the assumption that an adaptive system is able to detect, or extract, from its heteroclite domain any regularities which concern it, and

vis-a-vis which it must construct a plan of adaptation.

"The adaptive plan determines just what structures arise in response to the environment, and the set of

structures attainable by applying all possible operator

sequences marks out the limits of the adaptive plan's

domain. "(Holland 1992:4)

In other words, a strategy of adaptation is the best

plan of action that a system could put into place in order

to identify the structures of its environment. In a more

traditional sense, it uses some type of pattern

recognition strategy in order to adapt. When applied to the field of genetic reproduction of species, this strategy

of adaptation consists in finding, for a given

environment, groups of individuals chromosomically

best adapted. When constructed in a formal model, this strategy translates into an algorithmic model called

genetic algorithm. The notion of genetic algorithm,

presented for the first timeby John H. Holland in 1975

(Holland, 1975; Holland, 1992), was considerably

developed during the 1980's and 1990's (Goldberg, 1989;

Rawlins, 1991; Varela and Bourgine, 1992;

Michalewicz, 1994).

The main function of this algorithm is the

production of a population of individuals, out of an

original population, best adapted to an environment

which represents the constraints and particularities of the problem dealt with. The degree of adaptation is evaluated

by means of a fitness function /. So, the GA is based

on:

- an incoding of information, situations, problems

and solutions, in the form of strings of building blocks,

each string being able to be broken between each block,

in the exact image of chromosomes which constitute

veritable lists of characteristics of an individual. This

incoding usually takes the form of a highly structured

binary string, of a fixed or variable length according to the type of problem;

- the capacity to reproduce such strings in large

number, which metaphorically relates to the sexual

reproduction;

- the existence of a faculty of adaptation (simulated

by the function /) which permits the evaluation of the

quality of each individual created by the algorithm.

II. 2 Basic cycle of a GA

In practice, a population P° of potential solutions

(the chromosomes) to the problem to be treated is generated at the initialization step. Then the following

standard cycle, also called genetic search, is reapplied : INITIALIZATION

If (stop test not verified) then

begin

EVALUATION ; SELECTION ; REPRODUCTION ; REPLACEMENT

end

At any given moment t, the population is: P

l = { a[ , . . . , aj, }, where a) stands for the candidate

solution a; at cycle number t. The main steps can be

briefly described as follows :

1) EVALUATION: The elements of P

1 are rank

ordered from the most to the least fitted according to the

selection probability Probs:

P Probg (a})=/(a|)/(£/(aj))

2) SELECTION: The elements which best satisfy

the constraints or characteristics of the solution sought

are selected according to the selection probability, and

arranged by couples in order to prepare the next step.

3) REPRODUCTION: genetic operators are then

applied to this population of elites, called parents, in order to obtain an intermediary population P' 1

. These

operators permits the creation of new strings, among

which some should have better fitness properties than

their parents. Two genetic operators are generally

employed: crossing-over, which allows the production

of two new elements from two parent elements (Fig. 1), and mutation, which allows the creation of new

solutions that would have been impossible to obtain by

simple crossing. Mutation consists of a random

selection of one of the bits of the chromosome, and to change its value with a pre-defined probability

(probability of mutation) (Fig. 2).

4) REPLACEMENT: This is the generation of a new population by replacing the worst elements of the previous population P' by the best of P'1

. This new

326
population possesses at least as many and sometimes more of the characteristics of the solution than the

preceding generation.

10 1 10001 01 10 1000 00101 10100 0 0

01 1010001 1 101001 j 01 1000101 101

Before cross-over

10 1 1000101 10 1000 iOI 1000101 101

01101000 11101001 | 00101 10100 0 0

After Cross over

Fig. 1. Diagram of crossing-over

1000 1 1 1 0 1 0 1 1 0 1 1 000 10 110 1 0<-L>l

p = 0,0001

Fig 2. Mutation

This cycle is iterated a lot of times until a generation

of optimal solutions is obtained, and from which only

the bests will be retained. In certain contexts it is the

entire population which stands in lieu of the solution.

III. Genetic Algorithms and CARAT

III. 1 The object of the model

As previouly said, CARAT can fan out in many

different processing flows. In this section, we propose a modeling, by means of a genetic algorithm, of the

classification moment of two specific processing flows

: the first flow aims at giving the reader hints on the

semantics contexts of particular words ; the second flow

aims at automatically suggesting hypertext links

among segments of texts. So, the main concepts that define GAs will be translated in the terms of classifying

segments of texts, and this theoretic expose will be

followed by a presentation of some experimental

results.

In the CARAT context, genetic algorithms consists

of finding, amongst different segments of a text, which one offer some regular structures or form classes of

regularities. The GA is seen as a process of

classificatory treatment which identifies segments of

text containing some identical "type" of information.

These segments are most often pages, and contains

unifs (for units of information), which are simple or compound words, lexemes, etc. The determination of

unifs and segments can be done by means of specialized

computer text analyzing programs such as SATO,

BOOKMANAGER, SPIRIT, OPEN TEXTE,

NATUREL, etc. Here one creates a lexicon, a linguistic

markup, a tagging, etc.

So, the original text is transformed into an set of

segments containing only a balanced and controlled

choice of units of information. A procedure identifies the presence or absence of each unif in each segment,

and builds the following matrix (Tab. 1) of n segments

by m unifs. unif 1 unif 2 unif m

seg. 1 Pre(l,l) Pre(l,2) Pre(l.m)

seg. 2 Pre(2,l) Pre(2,2) Pre(2,m)

seg. n Pre(n.l) Pre(n,2) Pre(n,m)

Table 1. Matrix segments-unifs

One particular segment is represented by a line vector of

binary numbers given by the predicate Pre(i, s) : 0 for absence, 1 for presence.

111. 2 Genetic classification

The object of the model is to assign each segment

to a specific and unique class. The assignment of a segment to a class is called classing, and uses a

classifier, whereas the process of research of the best

classing (i.e., the best classifier) should be called

induction of classification.

111. 3 Set definition and initial population

In order to introduce, in the context of CARAT, the concept of population of individuals (Fig. 3), and

particularly the one of initial population, we must

appeal to three important sets :

a) the set T corresponds to the set of segments of

the text. Let T = {S\, . . . , S n }

b) the set K of classes. Let K = {C\ CndC)

Where NbC represents the number of classes. A

class is a set of segments which are not too distant one from another according to the function of adaptation

defined below. At the initialisation setp, the number of

classes is arbitrarily chosen large (it is equal to the

number of segments n) in such a way as to give the

process the freedom to construct as many classes of

segments as possible. It is the purpose of the function

of adaptation to reduce, during the genetic search, this number to an optimal value. The number of cycles is also arbitrarily fixed at a fairly large value, in the order

of one thousand cycles. Finally, the interpretation of

each class is devolved upon the user.

c) The set (or population) P of the individuals (Pl

represents the state of the population at time t. It contains a fixed number p of individuals). The elements

of P are called classifier-vectors, and represents the

candidate classifiers, i.e., the potential solutions to the problem of the best classing. In other words, an

individual encodes a tentative solution for classing

segments. The size of the classifier-vectors is n ; the

position number i corresponds to the i-th segment in the text, and contains an integer equal to the number of

the class to which the segment belongs.

At the outset, the classifier-vectors are randomly

built to produce the initial population P^.

Si s2

T 1 T

Cn Cl2 Cln

I

Cp, S2 *-pn

Fig. 3- relations of sets T, K and P. The genetic search has the task of carrying out a considerable number of modifications to the classifier- vectors, such as recombinations and mutations, in an

attempt to find the best one according to the function of

adaptation.

327
The j-th individual of P corresponds to the vector : Vj = (Cji Cjn ),Cjie K

An individual or chromosome could, as well, be

seen as a set of couples which associates each segment

to a unique class. The individual represents also a function which plunges the set T of segments into the

set K of classes. Example :

Let T = {Si, S2, S3, S4 } ; K = {Ci, C2 , C3 } Example of classifier- vector : V = (2, 1, 3, 2)

Interpretation: the first segment belongs to the class C2,

the second to the class Cj, the third to the class C3, and

the last one to the class C2.

III. 4 The function of adaptation

I11.4.1 Finality

The function of adaptation must evaluate the

intrinsic value of an individual, and hence the quality of

the classing that it codes. This function is defined over

the set of individuals and gives a real value.

In an ideal classifier a, segments are grouped into

compact classes. This quality is characterized by the fact that displacing a segment i from one class to another

(i.e., changing the class number located at position i in the classifier-vector) could result only in a decreased

value of f(a). The individuals selected for reproduction

are those which posses the best values by /. Therefore,

this function directs the entire process of the genetic

search, and the quality of the whole GA model depends

essentielly on it.

III. 4. 2 Choice of a criterium of similarity

It behoves the GA designer to conceive the most

efficient function of adaptation . In particular, this function must be most discriminating. This

discriminating feature involves two complimentary

aspects :

- the evaluation of internal cohesion of classes, i.e., the degree of similarity of segments within each class;

- the evaluation of the differentiation between

classes of the classifier- vector, i.e., the degree of

contrast existing between classes. The function of adaptation we propose is based upon

the score of Jaccard as criterium of similarity. This

score uses only the property of presence or absence of

unifs in segments, and constitutes a common measure

for evaluating the similarity of textual documents in the case of information research. It has been used notably

for indexation (Gordon, 1988). However, there do exist a few other criteria (Salton, 1989).

The Jaccard score of a couple of segments (Xj, Xfc),

notated Sim (Xj, X^), is equal to the proportion of unifs

common to both segments (notation : IXj n Xk l)

relatively to the total number of unifs present in the two

XjnXk

segments: Sim (Xj, Xk) = XjUXk

where : IAI represents the cardinal of the set A.

- the internal cohesion of a class is evaluated by a

coefficient of internal cohesion noted as IC(Cj). The

coefficient is the balanced sum of the similarity of

segments taken two by two in this class. It is defined

by:

1 lC(Ci)=—— x X Sim(X.,Xk ) N(i)

CI(Ci) = N(i)

Xj,Xk eCi

x I

Xj,X K 6Ci

Xj n Xk

XjUXk

N(i) is the number of combinations of the segments

of the class Cj taken two by two.

- the differentiation of the classsing is evaluated by

the coefficient of external dissimilarity, noted as ED(Cj), and computed for a class Cj in relation to all other classes. It is defined as follows:

ED(Ci) = 1 -

1 NC(i)

XSim(X,,Xk ) Xj6C,,X k eCCj

= 1 — x X NC(i) XjeC^XkeCq

XjnXk

XjUXk

CCj is the complimentary set of Cj. This set contains all of the segments that do not belong to Cj.

NC(i) is the number of couples (Xj, Xk), Xj belonging

to Cj > and Xk belonging to CQ.

Finally, the function of adaptation / is equal to the sum of these two coefficients.

/(individual) = Y (IC(Cj) + EC(Q))

ie[l,NbC]

All the inter-segment similarities are computed at the initialisation step, before the GA search. To summerise. The genetic search runs a number of

cycles equal to the maximum number of cycles

determined at the start-up of the GA. When the cyclic

processing has finished, the resulting population

represent the best classifiers that the GA could produce.

The last step is to select from this population the

classifier- vector which gives the greatest value for /. At

the end of the algorithm, a certain number of classes are empty. This is both expected and hoped since the

number of classes was arbitrarily fixed at a high

number. Thanks to the function of adaptation, the

algorithm converges towards an optimum number of

non-empty classes.

III. 5 Experimentation results

The experiment was carried out on a textual sample

drawn from Spirale, a Belgian review on Education

Sciences. The GA was developed using Matlab, and was

integrated into a software platform, Aladin (Seffah and

Meunier, 1995), developed at LANCI for the CARAT

approach.

The probability of crossing-over was fixed to 0.8,

and the one of mutation to 0.05. The number of

328
individuals in the initial population was 100, and the

number of generations (or iterations) was 300.

The text was partitioned uniformly into 54

segments of 50 words each, the end of a segment being

determined as follows: fifty words are counted from the beginning of the segment and then any words remaining

up to the next point are added to the initial fifty words

to constitute the whole segment. We had at our

disposition a lexicon composed of 1701 words of which

the number was restricted to 1360 roots after a preliminary process of lemmatisation. So, the size of

the text matrix was (1360 x 54).

The genetic search decreased the number of classes

from 54 to 24. Here is a short sample of interpretable

results. For instance, Class 4 contains the following

segments 8 and 21, in whicn underlined italic words are common unifs determined par the GA : Segment 8 : « At last, Joelle Delatte is grappling

with the problem of books for blind and sight-impaired

children , which would seem to be the preoccupation of

at least some editors who have recently proposed

specially designed albums for them. This production is characterized by a certain diversity if however unified by

the prudence of their approach : Children's literature

does not represent all the. reading nor all the literature. but it does exist with a sufficiently rich past and

present. »^.

Segment 21 : « To the teacher convinced of the

importance of reading literature there exists a question of

choice of texts and how to transmit them. There exists

at this level no ministerial propositions nor lists of lists of books as there are for colleges; nor a specialized

university teaching tradition to define the methods; the

initial and ongoing training is incongruous and left largely to one's.own initiative. In effect, the teacher who

chooses his own texts and his own course of action,

wittingly or not, is putting into action his personal

conception of the culture and the role of the school in the education of the child. »3.

Within these two segments, three unifs have been

included in the same class : child, literature, reading.

This result might facilitate the work of a user facing the

1 « Enfin, Joelle Delattre aborde le probleme des livres pour enfants aveugles et malvoyants, dont certains 6diteurs semblent d'ailleurs se preoccuper en proposant maintenant

des albums sp6cialement concus pour eux. comme on le voit, une certaine diversity caracterise cette livraison, mais

son unite nous semble r6sider dans la prudence des

approches : La literature de jeunesse ne repr^sente ni toute

la lecture ni toute la literature , mais elle existe, avec un

present et un pass6 suffisamment riches. »

~i « Se pose alors, a l'enseignant convaincu de ['importance

de la lecture litteraire . la question du choix des textes et des modalit6s de transmission. En effet, il n'y a a ce niveau ni propositions minist6rielles de listes d'ouvrages, comme le college ; ni tradition d'enseignement universitaire

specialise' pour d6finir de m6thodes ; la formation initiale et continue est disparate, largement laiss6e a l'initiative de

chacun. En fait, l'instituteur, qui choisit ses textes et ses demarches, sciemment ou non, met en jeu toute sa conception personnelle de la culture et du role de l'6cole dans la formation de l' enfant . »

problem of reading and analysing a large text, by

suggesting a precise relation between the segments. A

more in-depth analysis of the results would of course

require the help of a terminologist or a specialist of the

field. Such help is just as indispensable at the moment

of preparation of the text matrix as it is at the end for the analysis of the results.

So, the genetic algorithm has built classes that

classifies segments of text that offer some lexical

similarity. It has done this in a systematic, dynamic and

plastic manner. From these classes of segments the

processing flow can then whether choose a particular

word and see the class of similar segments in which it operates (its particular semantic contexts) or choose to

built a hyperlink between two similar segments.

Conclusion

The use of the genetic algorithm that we have

applied to the analysis of a text is still at the

experimental observation stage. But it is, however a very promising territory and very flexible, which

combines coding, the processing of data, computation

of probabilities, artificial intelligence, and the genetic

mode of evolution. The variants of the model presented

are numerous and are linked to the diversity and richness

of the genetic operators, to the multiple ways of coding

the solution, and to the conception of the function of

adaptation.

Research perspectives are situated around the most

in-depth study of the genetic algorithm applied to CARAT and to the comparison of results obtained with

other classifying systems that are presently being

developed, such as simulated anealing and the ART

neural network.

We believe that the modeling of CARAT by genetic

algorithms allows us to foresee solutions to a certain

number of problems of processing textual information

that require classification tasks. On the one hand,

classification allows regrouping the segments of a text

in terms of an optimization of the similarity level for relating segments of information. On the other hand, by

the nature of its mathematical structure of the

topological type, the GA permits the processing of a body of text that is in constant evolution.

This algorithmic strategy is applicable to diverse

types of textual information processing systems, such

as terminological classification, thematic extraction in

text. Automatic generation of hypertextuel relations. Thanks

The present work is part of a Franco-Quebecois

project "Les classifieurs emergentistes et le traitement

de l'information" under the tutelage of, for France, le Minisere de l'Enseignement Superieur et de la Recherche (MENESRIP, Delegation a L'information

Scientifique et Technique, programme "Ingenierie

linguistique et de la connaissance"), and le Ministere des

Affaires Etrangeres; for Quebec: Gouvernement du

Quebec - Ministere des relations Internationales. We

extend a special thanks to these trustees for work and

cooperation that they have permitted.

We would also like to thank the entire team at LANCI and in particular M. Nyongwa and I. Biskri for

their advice and technical support.

329
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330
Dynamic Word Meaning Representations

and the Notion of Granularity.

Text understanding as meaning constitution by SCIPS.

Burghard B. Rieger

Dept. of Computational Linguistics - Fachbereich II: LDV/CL

University of Trier, D-5428, TRIER, Germany

E-Mail: riegerQldv.Uni-Trier.de

Abstract

Semiotic Cognitive Information Processing Systems (SCIPS) are inspired by information systems

theory. In a rather sharp departure from CL and AI approaches, Computational Semiotics (CS)

modelling neither presupposes rule-based or symbolic formats for linguistic knowledge representations, nor does it subscribe to the notion of world knowledge as some static structures that may

be abstracted from and represented independently of the way they are processed. Consequently,

knowledge structures and the processes operating on them are to be modelled procedurally and

implemented as algorithms. They determine SCIP systems as a collection of cognitive information processing devices whose semiotic character consists in a multi-level representational system

of (working) structures emerging from and being modified by such processing. Corresponding to

these levels of emerging structures are different degrees of resolution [1] that account for varying

levels of representational granularity [8]. The emergence of semantic structure as a self-organizing process is studied oil the basis of word

usage regularities in natural language discourse, whose linearly agglomerative (or syntagmatic)

and whose selectivelyinterchangeable (or paradigmatic) constraints are exploited by text analysing

algorithms. These accept natural language discourse as input and produce—via levels of intermediate representationand processing—a vector space structure as output which may be interpreted

as an internal (endo) representation of the SCIP system's states of adaptation to the external (exo)

structures of its environment as mediated by the discourse processed. The degree of correspondence between these two is determined by the granularity that the texts provide in depicting the

exo-view, and the resolution that the SCIP system is able to acquire as its endo-view of it in the course of processing the discourse.

The SCIP system's architecture is a two-level consecutive mapping of distributed representations of

systems of (fuzzy) linguistic entities. Being derived from usage regularities as observed in texts,these

representations provide for the aspect driven generation of formal dependencies and their interrelations in a format of structured stereotypes. Corresponding algorithms select and represent fuzzy

subsets (word meanings) as dispositional hierarchies that render only those relations accessible to

perspective processing which can—under differing aspects differently—be considered relevant. Such

dynamic dispositional dependency structures (DDS) have proved to be an operational prerequisite

to and a promising candidate for the simulation of content-driven (analogically-associative) instead

of formal (logically-deductive) inferences in semantic processing ([2], [3], [4]). Considered as states

which the SCIP system can enter, certain properties of these structures can be identified as results

of symbolic functions which were shown to correspond to basal referencial predicates ([5], [6], [7]).

Thus, the dynamics of semiotic knowledge structures and the processes operating on them es- sentially consist in their recursively applied mappings of multilevel representations resulting in a

multiresolutional granularity of fuzzy word meanings which emerge from and are modified by such

textprocessing. Test results from experimental settings (in semantically different discourse environments) are produced to illustrate the SCIP system's granular language understanding and meaning

acquisition capacity without any initial explicit syntactic and semantic knowledge.

331
[1] A. Meystel: Semiotic Modeling and Situation Analysis: an Introduction. (AdRem Inc,) Bala

Cynwyd, PA, 1995.

[2] B. Rieger: Unscharfe Semantik. Die empirische Analyse, quantitative Beschreibung, formale

Reprdsentation und prozedurale Modellierung vager Wortbedeutungen in Texten. (Peter Lang),

Frankfurt a. Main/ Bern/ Paris, 1989.

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332
CYBERAESTHETICS IN LIGHT OF ZOOSEMIOTICS

Victor Dmitriev*, Leonid I. Perlovskyt

*Department of Foreign Languages and Literatures, Oklahoma State University,

victor@osuunx.ucc.okstate.edu.

fNichols Research Corporation, 70 Westview Street, Kilnbrook IV, Lexington MA 02173

Tel: 617-862-9400; Fax: 617-862-9485; e-mail: perlovsl@nichols.com

ABSTRACT: Semiotic analysis of text and

aesthetic literary criticism are brought closer together

by considering a human reader as an intelligent

symbolic system, between the kingdoms of animals

and pure spirit. A science integrating aesthetics,

cybernetics and semiotics we call cyberaesthetics. It

is a philosophical and mathematical theory of

intelligence related to Kantian philosophical

aesthetics and the dynamical concept of symbol.

Phenomenology of literary text and its perception is

used to compare concepts of cyberaesthetics and

zoosemiotics.

In his book, "Sign and Its Masters", Thomas

Sebeok tells the following story. Once Sigmund

Freud entered an auditorium with a huge cigar in his

mouth. Students questioned the respected professor

if this cigar didn't remind too much of a phallic

symbol. Freud responded: "Sometimes a cigar is

just a cigar". No doubt, students laughed, but it is

quite possible that someone was pondering a question: "Just sometimes?" Not in vain, we

remembered this joke.

Lev Tolstoy wrote a story, "After a Ball". The

essence of this story is as follows. A young man

was dancing at a ball in the home of his beloved one,

whom he was about to propose. The ball was

gorgeous. The young man especially remembered

one moment when his beloved danced with her

farther, a regiment commander, a tall and powerful

man, who looked like the emperor, Nicholas the

First. After the ball, the young man could not sleep,

he was excited by just experienced happiness, and in

the morning, walikng around the town, coming by

the plaza, he saw that there was going on a punishment of a soldier: he was bitten by . An

officer commanding the procedure was the very

same colonel that the young man had admired just

few hours ago. Here, at the plaza, the very same

man was cold and unforgiving. And, bumping at his

future son-in-law and looking straight into his face,

the colonel did not even recognize him, even so he

was smiling at him and so gently at the ball, just

hours ago. After this terrible scene, the young man

could not even think about marrying the colonel's

daughter, so terrified he was by the man.

So, what is this story about? Possibly, that even

when blinded by love, a human being can not loss

the compassion to another human being. The

violence is deeply repugnant to us; even to the extent

that it can overpower the love. Where the violence

reins, happiness is impossible, and it is the

happiness that we are looking for in love. It is

important to remember that the story was written by

a writer, who was at the time an active proponent of

the idea that evil should be opposed without

violence. The young man did not become a revolutionary, did not attack the colonel, but could

not become his son-in-law.

Sigmund Freud was not surprised at his

student's question, because he taught them to ask

such questions. As far as Lev Tolstoy is concerned,

he possibly would be much surprised if he learned

about one contemporary American Slavic scholar's

idea. According to this scientist, the young man in

the story did not want marry the tall and powerful

girl, because unconsciously, her body frightened

him. The young man was searching for a reason to

avoid the marriage. Cruelly bitten, blooded body of

the soldier, looking like a piece of meet, got

associated in young man's mind with vagina, which

he despised a priori. According to the author of this

conception, at the moment of creating this story,

Tolstoy was writing folk tales, was enmeshed into

Russian folklore, with its popular motif of "vagina

with iron teeth". Also a popular image is one of

Kastchey Undead, an old voluptious evildoer. The

conclusion: colonel dancing with the daughter at the

ball got associated in young man's mind with

Kastchey Undead in a ritual dance with a future prey

of his violence.

Here is not a place to argue with this

interpretation or its legitimacy. It transforms a writer

Tolstoy into a folktale teller, destroys the Christian

pathos of the story and replaced it with an openly

paganistic canvas. Even so, the very existence of

333
this interpretation is sufficient to explore the criteria

for a valid interpretation. Which version is true? The

one that tells about confrontation of good and evil,

love and violence, or the other that tells about the

disgust to the woman body, despite the sublime

passion? If both interpretations are true, than, purely

artistically, either they are incompatible, or they

provide a foundation for another interpretation. The

physiological is telling about itself through the

spiritual, making fun of it. And making fun of the

writer, who think that he inspires the reader by

socio-humanistic pathos. Similar to student's

interpretation being catastrophic to Freud, and to all

smokers of cigars along with him, the interpretation

of Professor Zolkovsky is catastrophic to the story, or more accurately to the way that Tolstoy saw it. Tolstoy intended to struck a catastrophic blow to

the idea of government violence. The developed

contemporary culture revealed the internal

catastrophisity of this very intent. New, searching

readers pointed out to Tolstoy the true nature of his

humanistic pathos: his disgust to woman Tolstoy

veiled with a socially and ethically noble fable.

What is of interest to us in this situation? That it evolves in the aesthetic space, in a non-spatial

interpretive field of the text. Relationships among its elements are not temporal, because they are already

accomplished, they are prior to our analysis.

Apriority is timelessness. Cybernetics of aesthetical

is the nonspatial and atemporaneous relationship of

elements, which are being defined by this very

relationship. This is a definition of a literary, or in

general, artistic image. An image is always a manifold, that is, it consists of other images, it is a

virtual manifold of relationships. What is a mechanism of inter-relationship between an image

and text? How is it possible to relate a text, which is a spatio-temporal object to an image which is an

aesthetical space object? Text, in principle, contains

no catastrophe that is a property of the aesthetic

space.

The first theory of mind that combined its higher

intellectual abilities with emotions and developed a

rational theory of aesthetics, including the concept of

beauty, belongs to Kant (1781; 1788; 1790). His

theory is based on three fundamental abilities or

faculties of mind: Understanding, Judgment, and

Reason. They are related to specific a priori

principles or instincts contained in the mind:

concepts, correspondence between concepts and

manifold of matter, and will or desire.

Understanding is a faculty of concepts, a source of

general notions. Judgment is an ability to see that a

particular subset of the manifold comes under the

general rule. And, Reason is an ability to draw

conclusions that is to act. The most important type

of actions, interwoven with higher intellectual

abilities, with beautiful and sublime, Kant

considered to be the acts of learning. These three

abilities correspond to the three main modes of

consciousness: knowledge (of concepts), feeling (of

correspondence between internal concepts and outer

world), and desire (to act). While Kant devoted a

separate book to each ability, they ought to be

combined within a dynamical system constantly

exercising all three abilities in their interaction.

Cyberaesthetics provides the mathematical

apparatus of Kantian theory (Perlovsky, 1996;

1997). It carries Kantian analysis further: it is a dynamical system, in which the three abilities

identified by Kant exist in the process of constant

interaction, as it were in a "vortex". The judgment

evaluates a similarity between an a priori conceptmodel and input data (sensory data, or lower-level

concepts). A high judgment-emotion activates the

learning-adaptation action modifying the conceptmodel. And, the modified model changes the

judgment-emotion. The vortex of conceptsemotions-actions proceeds until an equilibrium is

reached: from a split-second, in a case of a simple

less-adaptive sign, it extends to generations in case of learning new cultural paradigms. The mind is a system of interacting vortexes, competing for the

evidence in the manifold of matter. Each vortex is a process of semiosis, a process of the dynamical

formation of a symbol. Perception of beauty is

related to the ability of complex adaptive symbolic

systems to perceive a similarity between the internal a priori model and outer world beyond any specific

purpose and related exclusively with a will for

learning, that is a will for improving ourselves, our

internal representations of the reality.

"The connection of ideas does not imply the

relation of cause and effect but only a mark or sign

with the thing signified. The fire which I see is not

the cause of the pain I suffer upon approaching it, but the mark that forewarns me of it (Berkeley).

That, which Berkeley calls here "the mark" is an

internal sign. An internal, because it is inside of my

body, inside myself. It is a sign of the fire, which

obviously does not burn. It is a semiotical aspect of

experience. An aspect that was isolated, emphasized

and analyzed by semiotics. We see the sign of fire,

because we look inside of ourselves, and we look

not with eyes, but with all our body, with its

biophysical memory, which all are a part of our

334
internal concept-model of fire. When we imagine

something, like approaching fire, we do it with all

our body.

This is why, the Freudist interpretation of the

Tolstoy story is not illegitimate. This is an

interpretation made by the body. Therefore, this

interpretation could be much more dangerous for its creator, than for Lev Tolstoy. But what could be

said about our interpretation, which seems to us to

be so humane, sublime, spiritual, etc.? It is also a body's interpretation. The covered with blood body

of the soldier associated in young man's mind with

his own body. He saw himself in the place of the

soldier, and because he was not a sadist nor

masochist, he was terrified. His actions are

affective, that is undifferentiated, highly singleminded. Multi-minded functioning, differentiation

of thoughts and feelings is an aesthetical

phenomenon, belonging to the realm of higher

emotions that do not deterministically control our

behavior through ancient affective systems, but are an integral part of the intellect. A scientific approach

to nature is an aesthetic one, since it assumes

differentiation, multi-minded functioning, and

multiple methods. A human being is capable of

avoiding determinacy. This capability is a manifestation of a cyberaesthetic "energy", a psychic

energy that is non-deterministically concentrated. An

adaptive logic of cyberaesthetics assumes freedom

with respect to space-time, freedom of

consciousness towards itself. The difference

between a symbol-image and non-adaptive sign is

that the image is fuzzy, it "knows" of its nonidentity

with itself, which is manifest in its adaptivity, an

inherent property of the dynamical symbol of

cyberaesthetics. A bee functions in an image-reality

which is visible to our mind, but invisible to the bee.

A bee is a pure sign that is a pure text, the writing

itself, while a human being, in addition, is also an

author of the writing; a human exists as a will that

moves the hand.

Professor Sebeok quotes an important citation

from Peirce: " ...thought is not necessarily connected

with a [human] brain. It appears in the work of

bees, of crystals, and throughout the purely physical

world... Not only is thought in the organic world,

but it develops there [and] there cannot be thought

without Signs" [Peirce, 1935]. Evidently, here

Peirce talks about the universal organizing principle,

the universal spirit of Hegel that through the

Schellingian Absolute ascends to the philosophy of

Jacob Behme. A human being is a manifestation of

this universal spirit like a bee or a crystal. But, what

is not touched upon by Peirce is a human being as an

internal catastrophe of the spirit, an internal freedom

in which the universal spirit does not know itself.

This is the "space" or realm that we call aesthetics.

Origins of aesthetics and semiotics are complementary. Aesthetical realm is a thought

without sign. Semiotical realm is a signs without

thought. In this regard, zoosemiotics differs from

antroposemiotics just quantitatively, by the number

and configurations of signs. The purpose of the

semiotical is to point out its aesthetical meaning, its

self-other, where signness disappears yielding to

functionality. The meaning is a function of the sign.

But, as a function, the sign is an element of the

aesthetical realm, it virtualizes, dissolves in the

image. Cybernetical aesthetics is a science of control

of the sign-realm, a control that transforms signness

into the psychic energy of combined sign and its

apriority, into the vortex of thought.

Here we would remind you of the most

idiosyncratic zoosemiotical example ever discussed

by philosophers. We are talking about the Ludwig

Feierbach's cat, which instead of scratching out its

own eyes still jumps at the mouse and eats it up. In

this way Feierbach argued against berkelians,

hegelians, and other idealists whom he broke off

with. From the cyberaesthetical point of view,

jumping at the mouse, the cat indeed scratching out

its own eyes, the very same eyes that it saw the

mouse with. The cat, as it were, puts in itself a new

eye, it changes the space of its functioning,

transforms it, for now it obeys a will of the third, of

some true interpretant. Within the will of this

interpretant, the cat and the mouse are just but

elements of some whole system, elements whose

continuous transformations are the conditions of the

system's existence. To cut it short, the mouse is a

self-interpretation of the cat. Without the "mouse",

the cat would be something else. We came to the

notion of a system, which can not be understood as a

sum of individual objects. The understanding can

not proceed through the differentiation alone, but

requires a next step, the synthesis. Similarly, every

instinct is a manifestation of a cyberaesthetical

phenomenon, a sign expression of the beyond-sign

reality.

In professor's Sebeok book there is a story of

the honey-guide bird, which guides people to the

bee-hive with honey. It is not clear, what causes this

bird kindness, for seemingly, it gains nothing. It does not eat honey, nor has any use for wax,

because it does not build nests: it put its chicks into

others nests. While telling us about this one more
example of zoo-utilization of signs, professor

Sebeok's role is that of a semioticist. But, when

asking: what is behind this bird's actions? - he leaves

the realm of semiotical and enters the

cyberaesthetical, the realm of meaning, where the

bird as such does not exist. Semiotics is, as it were,

a Wilson camera collecting the traces of the

aesthetical. Let us assume some interpretation, for

example, that the bird "put" a human into the

beehive, similar to putting its own progeny into

other's nests. So, if we assume that all the altruism

of the bird is dictated by its inborn "meanness", we

enter the realm of aesthetical. The mechanism of our

analysis is the very cybernetical of cyberaesthetical,

this is our attempt to bring the elements into

interaction in such a way that the purposiveness of

one is seen through the purposiveness of the other.

This is the principle of any discovery, an artistic or

scientific one. From the semiotical point of view the bird is a

sign vehicle that is waiting for its interpretant. But

what the interpretant is about to interpret? If an

object exists before the interpretation, this means that

it has already been interpreted. So, purely

semiotically, the bird itself is not a puzzle. It is a puzzle aesthetically, for in this way, the bird indeed

is "a trace of a bird", a trace of a yet unknown

situation, in which the bird-human-beehive are combined in some whole, which configuration is not

yet manifest. An assumed self-regulation of these

elements we construct so that the configuration is

consistent, isomorphic with our experience. This is

the "mechanism" of any scientific discovery, any

discovery whatsoever. Thus, the growth of our

knowledge in some way is similar to that of a

crystal, it takes care of the homogeneity of its

structure, reminding us of the universal spirit.

A very interesting story is told by professor

Sebeok about a difficult life of male-fireflies of the

genus Hilara sartor. A male kills an insect and with

this "wedding gift" flies to a female, who eat the gift

during the intercourse. If it eats up the entire gift too

fast, it starts eating its beloved one right during the

intercourse. This love story may seem repugnant to

some of us. Especially to those, whose imagination,

like that of the young man in the Tolstoy story, let's us identify our body with the body of a male Hilara

sartor. This feeling of disgust is our affective bodily

reaction. And, what about the beauty that, according

to Kant is related to the perceived purposiveness of

the object? Does Kantian theory support such a relativism of beauty? The behavior of the Hilara

sartor female is quite purposive: she takes care of

producing offspring. Then, why it might be

impossible to some of us to perceive beauty in this

case? Kant explains that beauty is related not to any

purposiveness, but to the purposiveness of the object

with respect to our internal models, independent of

any utilitarian goal. Apparently, our models of love

are more purposive to us than what we see among

Hilara sartor. Even so our models are not as directly

utilitarian as theirs, some of us do not feel that our

models can improve by watching them. So, this

genus does not look beautiful to some of us. But,

are we really that different from Hilara sartor?

Aren't their relationships all too similar to human

relationships? "Dowryless" husbands and wives

often feel quite bad, especially after the romantic part

of relationships is over. If the husband does not

bring money home, the wife "eats him" in many

different ways. If the Hilara sartor male not always

can buy himself off from sexual appetites of his

partner, so among human this is also quite possible.

The ideal of beauty does not always matches the

reality, so some of us may enjoy observing Hilara

sartor relationships, if not for improving our ideals

of beauty, then at least for improving our model

adaptivity to some immediate situations in life. The above analysis is an aesthetical one, not

semiotical. An art of comparison, discovering

isomorphisms'among phenomena, is a dramatic one,

in that semiotic signs, passive objects which are predestined to remain objects of interpretation,

acquire a tendency to transform into another

category, to become a mechanism of cognition,

mechanism of isomorphism, mechanism of

transformation. To achieve this, a sign has to relieve a transfiguration first, it has to dye and risen.

Relative to the semiotic space, the aesthetic one is

like a black hole, an annihilating antimatter. Our

taboo are borders keeping us from getting too close

to these black holes, to its annihilating nature. Every

science is filled with these taboo as well as any

sphere of human activity.

Ants of genus mirmekaphilus confuse the rear

side of other ants with the front part of their own

kind, and make an intercourse "erroneously". "The

multiple resemblance between this icon and the

object for which it stands are so striking, subtle, and

precisely modulated that they can hardly be explained

away as an evolutionary coincidence" [14]. If an

evolution follows a definite logic, there would be no

room for the black holes of aesthetical in this

semiotic kingdom. There would be no freedom, no

catastrophicity. Professor Sebeok explains indecent

behavior of ants by confusion due to resemblance in

336
appearances of various genus, but then, how to

explain a similar behavior of more advanced species,

when there is no confusion at the level of signappearances? If there is a "confusion", it occurs in

aesthetical space, where the meaning of signs is

formed and where a familiar sign may acquire a new

meaning. Semiotics emphasizes apriority,

considering it as an imperative, which can only be

violated erroneously: if not for a confusion of

appearances, the ant would be more decent.

Cyberaesthetics equally supports a very different

point of view, natural imperatives that evolved in the

course of evolution are of a relative, adaptive nature.

And, in particular, sexual drives are directed at more

than just one definite utilitarian goal of gene

propagation. They also could be affine to a wider

purposiveness having no specific utilitarian goal, and

they are hostages of camouflages and

countermeasures evolved throughout evolution.

And, sexual drive may burn the organism in the fire

of isomorphisms.

Returning to the Tolstoy's story, we conclude

that both, "humanistic" and "Freudian"

interpretations contain elements of truth. Still

another interpretation seems more interesting: the

young man identified his relationships to his beloved

one and her farther, and being disappointed in one,

he lost his love to the other. Thus, a much more

refined isomorphism of sublime ideas seems to take

place in the aesthetical space of the story. When a

"Freudist", looking at a smoking man, sees "the

marks" that dissolve the smoker, his perception is

short-circuited through the "marking" semiotic

system directly to the bodily functions. Similarly a building perceives bricks it is build of. We can not

but quote Carl Jung: "I remember one Indian coming

up softly behind me while I was looking at the

mountain over the pueblo, and saying quite suddenly

in my ear, 'Don't you think all life is coming from

the mountain?' It was just in that way that Freud

talked about sexuality" [Schoenl, 1996].

A widow of one famous theologist was in rage,

when after the death of her husband, instead of

uncompleted manuscripts, she found in his desk

pages teared from erotic magazines. Naive woman

was under a spell of an opposite extreme, she

thought that all life is coming not from the mountain

but from the Mountain sermon. Erotic interests of

her husband she perceived as an error commensurate

with an ant, not a great theologist. It is a purely

semiotical error, that a great mind can not mix up

sinful with sacred. In order to overcome the

gravitation of a zoosemiotic realm, one need all its

energy. Cyberaesthetics is a philosophy and science

of combining emotional with conceptual, a theory of

control of the invisible energy of the visible.

REFERENCES

Dmitriev, V.A. & Perlovsky, L.I. (1996). Art

Form as an Object of Cognitive Modeling

(Towards Development of Vygotsky's Semiotics

Model). Proceedings of the Conference on

Intelligent Systems and Semiotics '96.

Gaithersburg, MD, v.2, pp. 385-389.

Kant, I. (1781). Critique of Pure Reason. Willey,

NY.

Kant, I. (1787). Letter to Reingold. In Tractats and

Letters, 1980, Interscience, Moscow.

Kant, I. (1788). Critique of Practical Reason.

Willey, NY.

Kant, I. (1790). Critique of Judgment. Tr. J. H.

Bernard, 1914, 2nd ed., Macmillan & Co.,

London.

Perlovsky, L.I. (1996a). Fuzzy Logic ofAristotelian

Forms. Proceedings of the Conference on

Intelligent Systems and Semiotics '96.

Gaithersburg, MD, v.l, pp. 43-48.

Perlovsky, L.I. (1996b). Mathematical Concepts of

Intellect. Proceedings of World Congress on

Neural Networks, San Diego, CA; Lawrence

Erlbaum Associates, NJ, pp. 1013-1016.

Perlovsky, L.I. et al (1997). Mathematical aspects

of cyberaestetics. ISAS'97.

Schoenl, W. (1996). Major issues in the life and

work of C.G. Jung. Univ. Press of America,

Inc. Lanham, New York, NY (p. 10).

Sebeok, T. (1979). Sign and Its Masters. Univ. of

Texas Press, Austin, TX.

337
THE HOLE IN THE SYSTEM

Floyd MerrcJl

Purdue University

as if it were

Abstract Physicist John Archibald Wheeler's concept

of the "boundary of boundaries" that lies at the heart of

what customarily goes as our physical world finds resonance with Charles S. Peirce's notion of semiosis.

which includes the categories of Firstness, Secondness,

and Thirdness. possible, actual, and potential signs, the

sign components (reprcscntamcn, object, interpretant),

and the oomplementaritv between sign

overdetermination and sign underdetermination.

If Charles S. Peirce's semiosis is process, figs,

signs becoming signs, the question inevitably surfaces:

What where, when, how, are signs, when considering

body as well as mind, self as well as other, sign as well

as interpreter, individual as well as his/her community

and the world 'out there'

?

In desperation, wc may happen to run onto that

Indian counterpart to Heraclitus. Nagarjuna, who

counsels that body, mind, self, world, are signs all. The

query To sign or not to sign" is thus no query at all, for

all that is, is sign Which is to say that (1) the sign i£. but also, (2) it is not, for there is no nonsign against

which to gauge it as a sign; in such case (3) it is both

sign and nonsign, but if that is the case, then (4) it is neither sign nor nonsign. And yet, if we arc to know

signs, all four of these possibilities are to be negated!

Nagarjuna brings about such a negation. All is no more

than appearance, but it is more than appearance, for it

is,, but if it is, then it is not, and we find ourselves on the

merry-go-round once again. The very possibility of

negation is negated, which gives rise to affirmation, but

since there is nothing to affirm, then what was affirmed

is negated, so it is impossible either to affirm or to negate, which is to say that there is bpjh affirmation and

negation and at the same time there is neither

affirmation nor negation. In other words, in a manner

of speaking there is only 'emptiness'. 'Emptiness' is not a matter of two unthinkables making a thinkable,

much as two Hegelian negations make an affirmation.

No. For, there is nothing, no-thing that is cither one

thing or the other thing. There is just 'emptiness'.

Where is all this jabber about 'emptiness'

taking us, perhaps, is toward what physicist John A.

Wheeler dubs the 'boundary of the boundary', which is another way of saying 'emptiness' Yes, the secret lies in the 'boundary of the boundary' The boundary,

Wheeler implies, is tantamount to the square root of

minus one. V-l, the function of which is found in logic,

in mathematics and chaos theory, in computer

engineering, and in quantum mechanics and relativity

theory. V-l is in a sense everywhere and nowhere. It is

emptiness' realized, paradoxically The

boundary of the boundary, the sign of itself, the hinge

that allows for all the action: it's from there that the

whole show gushes forth. Wheeler, the quantum physicist, tells us that a

boundary at its simplest best and at its confoundingly

worst begins with a solitary 'direct or "oriented" line—a

one-dimensional manifold' that has for its boundary 'the

starting point and the terminal point, both zero- dimensional' [7], Such a boundary is a hole cut out of a

sheet of paper with a pair of scissors. It consists of a

two-dimensional manifold, the cut itself defined as a one-dimensional manifold. So. where is the boundary?

At the edge of the paper What is the boundary, that is, of what does it consist? Why. nothing at all. It is zero! Zero, 'whatever the point at which wc consider that line

to have started, that is also the point at which the line

terminates' [7], A debt is incurred at the starting point

when the scissors penetrate the two-dimensional

manifold, and then that starting point is annihilated,

consumed, eaten up. Which is to say, if in our threedimensional world we were to carve out a cube, then,

like a square hole marring a Flatlandcr's twodimensional existence, there would be a section in our world that would not hold water, or anything else for

that matter. Moreover, our cube separating our space

from 'nothingness', from 'elsewhere', would be a

boundary consisting of twelve lines (onc-dimcnsional

boundaries) and six planes (two-dimensional

boundaries) making up a three-dimensional region, and

that the sum of these boundaries is zero! Nothing. A

nothing that separates what is 'herc-now' from mere

'emptiness'

Wheeler demonstrates his point with the image

of a cube. Each of its six faces has an orientation in

three-dimensional space. Three spaces give the cube's

position, and three more give its movement along its timc-linc, its world-line. In addition, each face of the

cube inherits from the interior an orientation, a swirl, a

direction of spin as it moves along its time-line toward

the future (in contemporary physics no moving body

faces forward and forward only, nor is it Janus-faced,

but in constant oscillatory, vibratory, undulatory,

gyration)., The one-dimensional boundary of one of the

faces of the cube is given a swirl by a line and an arrow. There is a start, wherever that is, and an ending, but the

ending ends up at the starting point, and the starting

point is the ending, so they cancel each other out: zero

dimensions. But isn't the line a boundary? That's one

dimension, isn't it? But the line begins eating its own

tail, finally leaving nothing, Total washout. Kaput.

338
Actually, wc cut the sheet of paper, a twodimensional universe, with three-dimensional scissors

from within our three-dimensional vantage point. The

question is, then; What kind of scissors could we

possibly use to cut a cube out of our own threedimensional space from within a fourth dimension?

Why, four-dimensional scissors, of course. A big

problem. Where do we get them and how can we use them? We don't, and we cant, short of our playing the

impossible role of a Maxwell Demon and a Laplace

Superobserver all wrapped up into one. So wc donl,

and we cant. Yet, let's see how far we can go. If twodimensional space is subject to one-dimensional

boundaries and three-dimensional space to twodimensional boundaries, then it stands to reason that

four-dimensional space must be subject to threedimensional boundaries. Wheeler depicts the whole

shebang as a 'hypercube'. The four-dimensional block

of spacctime at the center is bounded by eight threedimensional cubes according to the orientations of those

surrounding the block. Each cube sports six twodimensional faces, and each face is bounded by four

lines Yet in the final analysis it's the same story: these

lines cancel themselves out, leaving zero. By the same

token, we would suppose that in four-dimensional space

the planes, serving as boundaries in our threedimensional space, would likewise annihilate each other

to yield 'nothingness'.

In a desperate attempt to get a better handle on

all this, let us turn our attention to Ludwig, an

imaginary four-dimensional demon, Ludwig would

essentially dwell in the central 'hypercube' with a vantage point allowing him to peer into our innards and

view a stomach ulcer, a kidney stone, some lung crud,

and whatever other personal secrets wc have stashed

away in that blemished temple, our body. How can wc

possibly identify and empathize with Ludwig? We can't, or at least it is well nigh impossible to do so. So we

must concede that while prolonged contemplation of

Ludwia would be interesting enough, plenty of meat for a Ray Bradbury story, wc really should be addressing

ourselves to signs of the sort we can sink our teeth into

A difficult task, for if we ask ourselves what there is in

terms of signs, our signs, ourselves as signs, the answer must be: Not much, really. We and our signs are

virtually infinitesimal in comparison to the entire realm

of the possible. In fact, we and our signs are hardly

anything at all. On the other hand, we are in a certain sense virtually everything. We begin with 'emptiness',

zero, lhere in the 'center', wherever that is. Nothing

preceded it and it has no boundaries. Then we move on

to the equivalent of the 'empty set', a sort of 'noticed

absence', the absence of something that might have been

there but is not, with certain tentatively defined

boundaries, or of something that was never there, yet

there is at least the suggestion of boundaries, since the

set is 'empty'-there is some domain that can possibly be

filled by something.

Then we move on to the first sign consisting of

the Firstness (qualisign, quality, mere feeling without

consciousness of the feeling as such) of the

representamen (sign manifestation) of the semiotic

pbjgct, and of the interpTetant (roughly, the sign's

meaning), This consists of R-Q-J relations in tripod

fashion about the 'axis' or 'node' of 'emptiness' such

that R is related to O in such a manner in which they are both brought together by the mediation of I at the same

time that I is brought into relation with g. and Q in the

same way that they are brought into relation with it. The relations are properly triadic, for each pair of terms

depends upon the existence of the third term through the

existence of the 'node'. We have moved somewhere

along the infinitesimal thin plane within that fathomless

cube, our four-dimensional spacetime continuum. But

whatever this most elementary sign is. it is not for us, not yet at least. That is, we are not yet conscious of it as

sentient and self-conscious semiotic agents poised and

ready to puj, whatever there is into the service of the

semiosic stream within which we happen to find

ourselves at the moment. Such consciousness gf must

await further sign development. So we move on, somewhere within the vast expanse of the cube, Then

we become aware of the sign as something other, and we

have gravitated toward the Secondness of the sign as something 'out there' related to something that is the

object of our attention and that it must have some

meaning of some sort or other. This relation between

ourselves and the sign is at this moment no more than

Secondness. ourselves in contrast to some other. We see the sign, and sense that it must be related to something

else and that that relation in its relation to us must bring

about the emergence of some meaning, some

intcycr&eJant Then, an idea comes to mind, and we arc

in Thirdness. and 'Lo and behold!', there is a world 'out

there' awaiting our interaction and participation with it in its and our self-organizing unfolding. Then wc

exercise a move toward more developed signs: language

eventually comes issues forth, then dialogue, narrative,

discourse.

But somewhere along the line our signs cannot

help becoming self-reflexive, a mirror of themselves, As

mirroring themselves, ad infinitum, they can never be

final. For, in Pcircc's words:

what anything really is, is what it may finally

come to bo known to be in the ideal state of

complete information, so that reality depends on the ultimate decision of the community,...

In this way, the existence of thought now,

depends on what is to be hereafter; so that it

339
has only a potential existence, dependent on the

future thought of the community.

The individual man, since his separate

existence is manifested only by ignorance and

error, so far as he is anything apart from his

fellows, and from what he and they are to be, is only a negation [4]

The process of knowing is ongoing, future oriented;

knowledge in the full sense is always in the future and

not for us in the 'here-now' Consequently, the

'individual man' (or 'self. Peirce's terms), is

4 only a

negation'. Onlv a negation? Weil, yes. In a manner of

putting it. Perhaps there's no other way adequately of

putting it. The negation is the negation of a boundary,

which boundary is an infinitesimal line, nothing,

'nothingness'. 'emptiness'. Sheer emptiness

So we are back to that again. But our condition

is not as dire as it might appear. We might hope for

Peirce's envisioned 'ideal state of complete information'

as the community consensus that would finally be

arrived at in the long run of things. However, it seems

that our hopes arc shattered anew, for, according to Peirce, that community consensus will never come to

fruition short of infinite lime and an infinitely extended

community (i.e. it is a converging series). Yet whatever

knowledge can be had, however limited, and whether

consciously and willfully expounded or tacitly displayed,

must be the product of a collective effort, through

community practice and dialogue.

Speaking of language and dialogue, let us

return to physics.

BACK TO THE FUTURE, THEN?

The crisis in physics during the first quarter of

the present century and shortly thereafter brought on an

unexpected and unwanted crisis of language. The chief

problem, Htisenberg [2] writes, was that 'no language

existed in which one could speak consistently about the

new situation'. The language available at the time 'was

based upon the old concepts of time and space and this

language offered the only unambiguous means of

communication'. It was a matter, Heisenberg [2] goes

on, of waiting 'for the development of the language,

which adjusts itself after some time to the new

situation'. Heisenberg sees Niels Bohr's

'complementarity principle' as encouragement 'to use an ambiguous rather than an unambiguous language, to use the classical concepts in a somewhat vague manner

in conformity with the principle of uncertainty, to apply

alternatively different classical concepts which would

lead to contradictions if used simultaneously' [2]. In other words, an electron could be described either as a

particle or a wave in classical language, but both

descriptions could not be used in the same context

without falling into contradictions. So whatever sort of

language was to be used in describing this new situation,

it must be relatively loose and vague.

Heisenberg's words appear strange, coming

from a physicist. But when compared to the way

language is actually used, they are as natural as can be.

Peirce, in this vein, was also an ardent proponent of the

need for vague and ambiguous signs (of Firstness) as

well as logically precise language (of Secondness and

Thirdncss). For this reason he promised-though he

never delivered the finished amcle-a 'logic of

vagueness' as an alternative to the classical principles of

identity, noncontradiction, and the excluded-middle. A

vague and ambiguous language contains, within itself,

contradictory and incompatible principles. Such a

language offering the possibility of various alternatives,

some of them mutually exclusive, can be labeled

overdetermmed, In order to talk coherently, we must

attempt to differentiate between incompatibles, saying

either one thing ox the other, but not both in the same

breath. But if something contains the possibility of

being two or more distinct things, when we can see it and say it as now one thing, figw, the other thing The

two seeingg and savings are alternatives, and either

might be effective in one context while the other is more

effective in another context: differem alternatives

actualized at different times and different places, all of

them construed to be valid in their own right, are

characteristic of an underdetermined system.

Wittgenstein's rabbit-duck drawing is ambiguous in terms of its Secondness: it is actualizes as

generally either one thing pj the other. Within the

sphere of Firstness, however, it is vague, both the one

and the other, though it remains as no more than a

possibility: it is ovcrdetcrmined, Within the sphere of

Thirdness, on the other hand, it contains the potentiality

for actualization as neither the one nor the other but

something else, in fact, many possible other things. It can be imagined as the map of an island, it can be a masked person at the Mardi Gras, it can be a strangely

shaped cloud, or it can be just squiggles. In this sense it

is underdetermined. According to Bohr

complementarity, an electron behaves like a particle

under one set of circumstances and like a wave under

another set of circumstances. Expressing the electron as now one thing, now another, is revelation of language's

underdetermination. Of course, it is from another view

both a particle ajjd. a wave (overdetermined). though it cannot manifest both of those characteristics in

simultancity-nor could we be aware of both

characteristics at once even if they could be so

manifested. We have also seen this use of language in

the above comments by Heisenberg, especially in his

observation that 'the situation of complementarity is not

confined to the atomistic world alone' but is also found

in the arts and in everyday life situations 12],

340
Actually, wc cut the sheet of paper, a twodimensional universe, with three-dimensional scissors

from within our three-dimensional vantage point. The

question is, then: What kind of scissors could we

possibly use to cut a cube out of our own threedimensional space from within a fourth dimension?

Why, four-dimensional scissors, of course. A big

problem. Where do we get them and how can we use them? We don't, and we can't, short of our playing the

impossible role of a Maxwell Demon and a Laplace

Supcrobserver all wrapped up into one. So we don't,

and we cant. Yet, let's see how far we can go. If twodimensional space is subject to one-dimensional

boundaries and three-dimensional space to twodimensional boundaries, then it stands to reason that

four-dimensional space must be subject to threedimensional boundaries. Wheeler depicts the whole

shebang as a 'hypercube' The four-dimensional block

of spacetime at the center is bounded by eight threedimensional cubes according to the orientations of those

surrounding the block. Each cube sports six two*

dimensional faces, and each face is bounded by four

lines. Yet in the final analysis it's the same story: these

lines cancel themselves out, leaving zero. By the same

token, we would suppose that in four-dimensional space

the planes, serving as boundaries in our threedimensional space, would likewise annihilate each other

to yield 'nothingness'.

In a desperate attempt to get a better handle on

all this, let us turn our attention to Ludwig. an

imaginary four-dimensional demon. Ludwig would

essentially dwell in the central 'hypercube' with a vantage point allowing him to peer into our innards and

view a stomach ulcer, a kidney stone, some lung crud,

and whatever other personal secrets we have stashed

away in that blemished temple, our body. How can vvc possibly identify and empathize with Ludwig? We cant,

or at least it is well nigh impossible to do so. So we

must concede that while prolonged contemplation of

Ludwig would be interesting enough, plenty of meat for a Ray Bradbury story, we really should be addressing

ourselves to signs of the sort we can sink our teeth into.

A difficult task, for if we ask ourselves what there is in

terms of signs, our signs, ourselves as signs, the answer must be: Not much, really. We and our signs are

virtually infinitesimal in comparison to the entire realm

of the possible. In fact, wc and our signs arc hardly

anything at all. On the other hand, we are in a certain sense virtually everything. We begin with 'emptiness',

zero, there in the 'center', wherever that is Nothing

preceded it and it has no boundaries. Then we move on

to the equivalent of the 'empty set', a son of 'noticed

absence', the absence of something that might have been

there but is not, with certain tentatively defined

boundaries, or of something that was never there, yet

there is at least the suggestion of boundaries, since the

set is 'empty'-there is some domain that can possibly be

filled by something

Then we move on to the first sign consisting of

the Firstness (qualisign, quality, mere feeling without

consciousness of the feeling as such) of the

represeniamen (sign rnanifestation) of the scroiotic

gbjgcj, and of the interpretant (roughly, the sign's

meaning). This consists of &-Q-I relations in tripod

fashion about the 'axis' or 'node' of 'emptiness' such

that g. is related to Q in such a manner in which they are both brought together by the mediation of I at the same

time that I is brought into relation with R and Q_ in the

same way that they are brought into relation with it. The relations are properly txiadic, for each pair of terms

depends upon the existence of the third term through the

existence of the 'node' We have moved somewhere

along the infinitesimal thin plane within that fathomless

cube, our four-dimensional spacetime continuum. But

whatever this most elementary sign is, it is not for us, not yet at least. That is, we are not yet conscious of it as

sentient and self-conscious semiotic agents poised and

ready to pu| whatever there is into the service of_ the

semiosic_stream within which we happen to find

ourselves at the moment. Such consciousness of must

await further sign development. So we move on,

somewhere within the vast expanse of the cube. Then

we become aware of the sign as something other, and we

have gravitated toward the Secondness of the sign as something 'out there' related to something that is the

object of our attention and that it must have some

meaning of some sort or other. This relation between

ourselves and the sign is at this moment no more than

Secondness. ourselves in contrast to some other. We see

the sign, and sense that it must be related to something

else and that that relation in its relation to us must bring

about the emergence of some meaning, some

lntexptetant. Then, an idea comes to mind, and we are

in Thirdness. and 'Lo and behold)', there is a world 'out

there' awaiting our interaction and participation with it in its and our self-organizing unfolding. Then we

exercise a move toward more developed signs, language

eventually comes issues forth, then dialogue, narrative,

discourse.

But somewhere along the line our signs cannot

help becoming self-reflexive, a mirror of themselves. As

mirroring themselves, ad infinitum, they can never be

final. For, in Peirce's words:

what anything really is, is what it may finally

come to be known to be in the ideal state of

complete information, so that reality depends on the ultimate decision of the community;...

In this way, the existence of thought now,

depends on what is to be hereafter; so that it

341
has only a potential existence, dependent on the

future thought of the community.

The individual man, since his separate

existence is manifested only by ignorance and

error, so far as he is anything apart from his

fellows, and from what he and they are to be, is only a negation [4 J The process of knowing is ongoing, future oriented;

knowledge in the full sense is always in the future and

not for us in the

l here-now'. Consequently, the

'individual man' (or 'self, Peirce's terms), is 'only a

negation' Only a negation? Well, yes. In a manner of

putting it. Perhaps there's no other way adequately of

putting it. The negation is the negation of a boundary,

which boundary is an infinitesimal line, nothing,

'nothingness', 'emptiness' Sheer emptiness

So we are back to that again. But our condition

is not as dire as it might appear. We might hope for

Peirce's envisioned 'ideal state of complete information'

as the community consensus that would finally be

arrived at in the long run of things. However, it seems

that our hopes are shattered anew, for, according to

Peirce, that community- consensus will never come to

fruition short of infinite time and an infinitely extended

community (i.e. it is a converging series). Yet whatever

knowledge can be had, however limited, and whether

consciously and willfully expounded or tacitly displayed,

must be the product of a collective effort, through

community practice and dialogue.

Speaking of language and dialogue, let us

return to physics.

BACK TO THE FUTURE, THEN?

The crisis in physics during the first quarter of

the present century and shortly thereafter brought on an

unexpected and unwanted crisis of language. The chief

problem, Heisenberg [2] writes, was that 'no language

existed in which one could speak consistently about the

new situation'. The language available at the time 'was

based upon the old concepts of time and space and this

language offered the only unambiguous means of

communication', It was a matter, Heisenberg [2] goes

on, of waiting 'for the development of the language,

which adjusts itself after some time to the new

situation'. Heisenberg sees Niels Bohr's

'complementarity principle' as encouragement 'to use an ambiguous rather than an unambiguous language, to use the classical concepts in a somewhat vague manner

in conformity with the principle of uncertainty, to apply

alternatively different classical concepts which would

lead to contradictions if used simultaneously' (2]. In

other words, an electron could be described cither as a

particle or a wave in classical language, but both

descriptions could not be used in the same context

without falling into contradictions. So whatever sort of

language was to be used in describing this new situation,

it must be relatively loose and vague.

Hcisenberg's words appear strange, coming

from a physicist. But when compared to the way

language is actually used, they are as natural as can be.

Peirce, in this vein, was also an ardent proponent of the

need for vague and ambiguous signs (of Firstness) as well as logically precise language (of Secondness and

Thirdness). For this reason he promised-though he

never delivered the finished article—a 'logic of

vagueness' as an alternative to the classical principles of

identity, noncontradiction, and the excluded-middle. A

vague and ambiguous language contains, within itself,

contradictory and incompatible principles. Such a language offering the possibility of various alternatives, some of them mutually exclusive, can be labeled overdetermined. In order to talk coherently, we must

attempt to differentiate between incompatibles, saying

either one thing or the other, but not both in the same

breath. But if something contains the possibility of

being two or more distinct things, when we can see it and say it as now one thing, flew, the other thing. The

two sccings and savings are alternatives, and either

might be effective in one context while the other is more

effective in another context: different alternatives

actualized at different times and different places, all of

them construed to be valid in their own right, are

characteristic of an underdetermined system.

Wittgenstein's rabbit-duck drawing is ambiguous in terms of its Secondness: it is actualizes as generally either one thing pi the other. Within the

sphere of Firstness. however, it is vague, bojji the one and the other, though it remains as no more than a

possibility : it is ovcrdetermined. Within the sphere of

Thirdness, on the other hand, it contains the potentiality

for actualization as neither the one nor the other but

something else, in fact, many possible other things. It can be imagined as the map of an island, it can be a masked person at the Mardi Gras, it can be a strangely

shaped cloud, or it can be just squiggles In this sense it

is underdetermined. According to Bohr

complementarity, an electron behaves like a particle

under one set of circumstances and like a wave under

another set of circumstances. Expressing the electron as now one thing, now another, is revelation of language's

underdeterrnination . Of course, it is from another view

both a particle and. a wave (ovcrdetermined), though it cannot manifest both of those characteristics in

simultaneity—nor could we be aware of both

characteristics at once even if they could be so manifested We have also seen this use of language in

the above comments by Heisenberg, especially in his

observation that 'the situation of complementarity is not

confined to the atomistic world alone' but is also found

in the arts and in everyday life situations [2],

342
In other words, when physicists use ordinary

language, they are forced to talk about electrons and

quarks in about the same way as they talk about

anything else And talk, well, it's just talk. Particles

and waves, black marks on white making up a book,

squiggles forming a rabbit or a duck, and so on, are

alternate ways of talking about our various 'semiotic'

worlds Ultimately, in this respect, what the physicist

studies 'is not nature in itself, but nature exposed to our method of questioning it. Our scientific work in physics

consists in asking questions about nature m the

language we possess and trying to get an answer from

experiment by the means that are at our disposal' [2],

For Bohr himself, it is wrong to suppose that the task of

physics is that of saying what the world is. More

adequately stated, physics is concerned with what the

physicist can say about the world. In response to the

argument that the world precedes and is more

fundamental than language, Bohr once quipped: 'We

are suspended in language in such a way that we cannot

say what is up and what is down. The word "reality" is also a word, a word wc must leam to use correctly' [5]. Bohr's suggestion is that no matter how we talk about

the world, language ends up saturating it, and in the

process we finally end up talking about talk itself. 'Stand for', 'reference', and 'representation', like

'reality', are also words, and to assume our words 'stand

for', 'refer to', or 'represent' something beyond them in

the big, wide world are of the substance dissolved

dreams are made of. Talk is ultimately related to talk

and if it is also somehow related to the world, so much

the better. But we should be mindful that this

relationship will more often than not come as a hopeful

byproduct of the talk. This is interesting in light of Wheeler's postEinstein 'physics of meaning' The 'physics of

meaning' stipulates that without the scientist's asking

questions of the universe, talking to it. observing it, interacting with it, it simply is: it has no significance

for physics. Thus the physicist her/himself is a

participatory semiotic agent, a sign her/himself,

interacting with the entire range of possible signs,

initially actualizing them as signs, and pushing them

along the road towards their fulfillment as genuine signs

with fully developed interpretants. In fact, the entire

community to which the physicist belongs is involved.

Implicit within the process of the physicist's interaction

with the universe is the injunction, do such-and-such.

which entails participation with what there is. This is germane to Bohr's complementarity principle. In both

cases participation of the semiotic agent is a must, and

by means of such participation signs become full-blown

signs, in the process taking on meaning.

The story goes something like this. A set of

signs, most effectively put in the form of a sentence, is

taken as an assertion that such-and^s_uch is the case. It

is at the same time an injunction, either implicit or

explicit, to consider the practical effects the assertion

might conceivably have with respect to the act of

following the injunction. For example, if you say 'My

speakers can take a 90 watt blast'. I might take it that I am invited to subject them to the full volume of the

amplifier. If I do so. and if they withstand the pressure,

then we know. If they don't, we still know-and you

turn on your word processor, intent on writing a letter to

the manufacturer regarding their warranty. So 'My

speakers can take a 90 watt blast' is not thoroughly

meaningful until we put it to the test. In other words, in

Wheeler's 16] terms, we must put the signs (or

phenomena) to use, whether they be sign-events, in the case of conceivable and actual physical effects, or

thought-signs, in the case of fictions, purely hypothetical

situations, or 'thought-experiments

1

. This is comparable to Bohr's theory of meamng

emerging from his complementarity principle [3]. Is an

electron a particle or a wave? Since it cannot be a

panicle and a wave simultaneously, one might surmise

that it is neither a particle nor a wave, or that it is bjjjh a

particle and, a wave In the first case, one does not

commit oneself, but holds out for a more general

concept of 'particle' and 'wave'; in the second case, one

embraces a contradiction at the expense of admitting a cloud of vagueness into one's purview. For Bohr,

neither case is adequately meaningful: 'an electron as

particle' is meaningful under certain actualized

conditions, and 'an electron as wave' is meaningful

under other complementary conditions. The conditions

must be actualized before the signs in question become

genuine signs. Meaning is a matter not of what we can know about the 'real world' but what we can do with

signs in such a way that we can say more about the

'semiotically real' objects surrounding us. In a Peircean vein, the notion of bp_th a

'particle' anj2 a 'wave' exists in the overdc.term.tned

sphere of possibilities (Firstness), neither a 'particle' nor

a 'wave' at the same moment has citizens rights to the

underdetermined sphere of generalities (Thirdness),

ordained by convention, habit, and an incessant

movement towards an expansion of one's conceptual

grasp. In contrast, Bohr's fipjy. a 'panicle', now a

'wave' (or either a 'particle' or a 'wave') holds true to

classical logic and the tenets of physical existence

(actualities. Secondness). It has to do with the things we

can do with signs and the things they do to us. Quite

obviously, Firstness and Thirdness break out of the

fetters imposed on them by classical logic, for

contradiction and excluded middles are allowed, while

Secondness, the master of our physical world as we

would like to perceive it and conceive it, generally

remains faithful to classical principles So a sign can be

343
drawn from a massive range of possibilities to become

an actual sign, which can then be meaningful in terms

of its practical consequences-its interrelation in the

world of actual signs But its meaning will remain

incomplete, for between the neither and the ngr (or the

either and the oj) other signs always stand a chance of

popping up to alter whatever meaning was to be had.

WHAT MORE CAN WE DO?

The initiation of semiosic flow, I would submit,

is graphically depicted in the central portion of Figure 1, where there is nothing more than an infinitesimally thin

plane or boundary separating nothing from anything

else: it is mere 'nothingness', 'emptiness', no more

than folds and warps, topological distortions.

mac ocean:

FIGURE 1

Yet this 'nothingness' or 'emptiness' contains, 'within'

itself, the sphere of possibilities that can give rise to the

emergence of everything that is in a particular

'semiotically real' world. We could say of scmiosis

what Wheeler says of geometrodynamics.

This great world around us~how is it put

together? Out of gears and pinions? By a oorps of Swiss watchmakers? According to some multifaceted master plan embodying an

all-embracing corpus of laws and regulations?

Or the direct opposite? Are we destined to find

that every law of physics, pushed to the extreme

of experimental test, is statistical—as heat isnot mathematically perfect and precise? Is physics in the end 'law without law', the very

epitome of austerity? [7]

Now, what can Wheeler possibly mean by 'law

without law'? That the boundary is where the action is. And what is the boundary'? Once again, zero, zilch,

nothing at all. It is a fold, that which is folded within

itself, like a cavity that is a cavity of itself, like the

origami fold, the paper of which is superfluous, for what

is important is the fold itself, a fold of space that is at the same time an enfolding and an unfolding. A

hurricane of incessant unfolding of the enfolded and

enfolding of the unfolded, At this level, there is no

distinction between organic and inorganic matter,

between the living and the dead. Thus wc are now told

by Ilya Prigogine, fractal geometers, and chaos

mathematicians, that all is self-organizing (codependent

emergence), like the self-organizing universe itself. A

geological formation is enfolded into a vein of gold,

sheaves and shears of tectonic plates press plants into

black carboniferous matter and ultimately enfold that

into a diamond, an enfolded chick embryo or an acorn

unfolds onoe. twice, thrice, and virtually countless times.

But please don't get me wrong. The unfolding

of the enfolded and vice versa is not simply a matter of

tension release and tension build-up, nor is it dilation

and contraction, but rather, it is evolving and involving,

developing and enveloping, convolution and involution.

A living organism's organs are involved, enveloped,

contracted folds that got that way after generation upon

generation of evolution, development, and dilation and

displaying of what was there all along as a possibility.

And now. they are there, within the organism, in the

process incessantly of enveloping, involving, enfolding,

implicating matter and energy from the outside in order

that they may sustain life: that is their charge and their

purpose in and for the organism A cell is the product of

one-dimensional engenderment according to a few

letters and an algorithm in three-dimensional space to create something 'here' that is distinguished from

everything 'there

1 by a two-dimensional wrap, a

relatively smooth fold, a boundary. The entire surface of a living organism takes up a minute piece of threedimensional space, and at the same time that surface is a boundary in four-dimensional spacetime in the sense of

Wheeler.

'This won't do the trick,' someone retorts. 'You must really be more explicit.' However, how can we say what there is in that 'emptiness

1 which allows of no saying at all? How can we say, really say, what there

is within the center of the Figure 1 cube where

everything is enfolded and nothing unfolded?

Impossible! As impossible as geometrodynamic field

equations 'saying' how mass-momentum and energyget a grip on spacetime at the boundary of the boundary.

It can be described through equations but hardly said

clearly and distinctly in natural language [7], You

simply can't describe the enfolded point, the center,

which is the equivalent of Wheeler's zero moment of

rotation. How can anything be of zero rotation in a

universe in which all movement depends upon frames of

reference? Assume we place a cube of ice with a small

buck-shot frozen in its center-like Figure l~on a

skating rink floor. Wc rotate the cube, which is a quite

effortless task since there is little friction between ice

cube and icy surface. The cube being well-nigh

symmetrical, and all other things being equal, we look at the buck-shot and observe that it appears to be

motionless. As a virtually infinitesimal point it has zero moment of rotation. Everywhere else there is force

imparted with a certain amount of energy, but this

central point has no energy and it exercises no force. It

344
is comparable to the hub of the Buddhist wheel. It is the

'image' of 'emptiness'!

'But', someone retorts, 'what we have here is a mere point, clearly and distinctly 'nothingness'-if not to say "emptiness" You should really get back to the idea

of boundary, which cannot be explained away in such

sophomoric fashion'. O.K. Assume we have a Lmelander gliding happily along her two-dimensional

strip-world one extremity of which is given a twist and

connected to the other extremity to form a Mobius-strip.

Easy enough. She is a onc-dimensional being residing on a two-dimensional sheet curved and doubled back on

itself in three-dimensional space, In essence, she

inhabits three dimensional space. Now suppose she

stretches herself out along the strip until she encounters

her hind quarters and latches onto them. She has

become a circle. As such, she is finite but unbounded.

Unbounded? Of course. She is apparently a ring, an unbounded boundary that bisects the M8bius-strip,

separating it into two worlds, this one and jjjai one, the one that is first 'above' and then 'below', and the other one that is first 'below' and then 'above' Now that is a boundary we can identify with. Is it not? We have a

one-dimensional line, or Firstness, that, in relationship

with its other, the two-dimensional strip, brings about a

'cut' in order to construct a binary relationship of

Secondness. all by means of the mediating capacity of

Thirdness from our three-dimensional view wherein the

Mobius-strip could become a legitimate M6bius-strip,

Let us suppose we bisect our Lmelander by

taking our scissors and cutting the strip in two pieces

precisely where she is lying in apparently so relaxed and

carefree a position. Now we should have two Mttbiusstrips separated by our erstwhile Linelander. To our

surprise, however, the stnp isn't bisected at all. It remains intact. But it is definitely not the same strip.

No, that's not correct, not exactly. It is now half as wide

and twice as long as it was, and it sports two twists

instead of one. Zero sum game again! Then it is the

same strip, only evincing a different form. What did our Lmelander-boundary separate anyway? 'Nothing' from

'nothing'. The boundary was a zero boundary. While

wc were cutting the strip, there was a direction, and time

passed, irreversible time, But when we finish we realize

that there had been no line that separated something

from something else, no direction, no irreversibility, and

no indication of time. There was no other, nothing

distinguishing this from Qg&,

Now, essentially the whole strip is indivisible if we cut it along its elongated surface. In this sense, it is, most properly speaking an icon, self-contained, selfreferential, unary (it is chiefly of Firstness). The strip

itself, then, is indcxical insofar as it is capable of

incorporating two-dimensionality, directionality,

binanly (it is chiefly of Secondness) And the line is

symbolicity in the sense that it entails one-dimensional,

linear eneendcrment of signs (it is chiefly of Thirdness).

However, the fact remains that the strip as icon in the

pure sense is indivisible. Try to sever it with images,

relations, and words, and it remains as it is, though of a

slightly to radically different countenance. Yet virtually

nothing has changed. The sum of all changes is no

change—as the French say, the more things change the

more they stay the same. Now, what happens if we apply our Linelander

within her Flatland to our own sphere of existence? We

take the cube of Figure 1, metaphorically tantamount to our three-dimensional universe, and we stretch the

nght-hand side of it out, give it a twist, and bring it back

to its left-hand side and connect it. What wc have is a

rectangularly shaped sort of skewed torus. Now suppose

we split our angular, twisted torus in half along the

shaded plane in Figure 1. We now know what the yield

will be. We are left with a torus half as thick and twice

as long as it was. Zero change once again! Total

change is no change at all. The iconicity of the whole

remains intact. What are we. within this whole

concoction, but, ourselves, minuscule twists, tiny warps,

skewed spots, in four-dimensional space?--we are like

the buck-shot in Figure 1, which, if stretched out when

the oubc is topologically transformed into a M6biustonis, becomes a line, a boundary that separates

'nothing' from 'nothing'.

So much for stories and boundaries. What we

are left with is a flow of interdependent, interrelated,

merging, diverging and converging, signs. Signs all! Semiosis: the becoming of signs fjgj us vyithin our

world-line.

REFERENCES

[1] Baer, Eugen (198S). Medical Semiotics. Lanham:

University Press of America.

[2] Heisenberg, Werner (1958). Physics and

Philosophy. Ann Arbor: Michigan UP.

[3] Murdoch, Dugald (1987). Niels Bohr's Philosophy

of Physics. Cambridge. Cambridge UP.

[4] Peirce, Charles Sanders (1931-35), Collected Papers

of Charles Sanders Pence, C. Hartshorne and P. Weiss (eds.), vols, 1-6, Cambridge: Harvard UP.

[5] Petersen, Aage (1985), 'The Philosophy of Niels

Bohr.' In Niels Bohr: A Centenary Volume. A.

French andP Kennedy (eds.), 299-310. Cambridge:

Harvard UP,

[6] Wheeler, John Archibald (1980). 'Law Without

Law ' In Structure in Science and Art. P. Medawar

and J. H. Shelley (eds ). 132-68) Amsterdam:

Excerpta Medica.

[7J Wheeler, John Archibald (1990). A Journey into

Gravity and Spacctime. New York: Scientific

American Library.

345
i
XIII MULTIDISCIPLINARY

APPLICATIONS OF SEMIOTICS

Control Mechanisms for a Nonlinear Model

of International Relations

Aron Pentek, Jim Kadtke

Institute for Pure and Applied Physical Sciences, University of California at San Diego, La Jolla, CA 92093-0360

Suzanne Lenhart

Mathematics Department, University of Tennessee, Knoxville, TN 37996-1300

Vladimir Protopopescu

Computer Science and Mathematics Division Oak Ridge National Laboratory, Oak Ridge, TN 37831-6364

ABSTRACT

Some issues of control in complex dynamical systems are considered. We discuss two control mechanisms, namely: a short

range, reactive control based on the chaos control idea and a long-term strategic control based on an optimal control algorithm. We apply these control ideas to simple examples in a

discrete nonlinear model of a multi-nation arms race. KEYWORDS: chaos control, optimal control, arms

race

1. INTRODUCTION

The field of nonlinear dynamics offers the possibility to

describe high dimensional complex systems - which hitherto have only been modeled stochastically or heuristically - in terms of nonlinear low dimensional deterministic models. The appeal of such models stems from

two apparently opposing features. Indeed, on one hand

the models - described by a system of either coupled

maps (discrete evolution) or ordinary differential equations (continuous evolution) - are simple enough to warrant a rigorous and extensive analysis while on the other

hand they display an extremely rich dynamical behavior

that captures some of the complexity of the systems they

are supposed to model. Due to these features, low dimensional nonlinear models have been extensively applied to

ecologic, neuromorphic, societal, and military systems.

Recently the focus of these applications has shifted from

analysis and exhaustive exploration of the phase and parameter spaces to control and prediction [15].

In this paper we discuss the application of two conceptually different control mechanisms to simple discrete dynamical systems of Richardson type used to model arms

races. [5,8,13]. A short description of these models will

be given in Section 2. In Section 3 we present our first control strategy to arms races and international relations,

namely a short range, reactive control designed to react to changes in international relations based on immediate

feedback utilizing the natural dynamics of the system. In

this case policy changes are typically planned only one

(time) step ahead. At each time step control is revised

based on some feedback that reflects the actual state of

the system and does not take into account any long term

strategic thinking. The main advantage of this short term

crisis management is that typically it requires only very

small changes in the system parameters. Indeed, due to

the inherently nonlinear and potentially unstable character of the dynamics, this control is based on a chaos

control algorithm [12-14] and it is used to stabilize unstable periodic orbits or fixed points of the dynamics by

applying only small perturbations to (one of) the system

parameters. The basic idea is to perturb the system in

such way to drive it to the unstable manifold of the desired orbit. On this manifold the natural dynamics of the

system will bring the trajectory closer and closer to the

desired fixed point or limit cycle.

The second procedure, called long range, strategic control reflects a longer term planning of policy changes that

are implemented consistently throughout the whole evolution. The long term strategic control is achieved by an

optimal control algorithm [6] that we briefly discuss in

Section 4. In the optimal control framework the perturbations (controls) are evaluated in order to minimize or maximize some objective functional that depends on the

state and the controls. The actual form of this functional

essentially depends on the goal we want to achieve and

explicitly includes the reward and cost of that goal. The

main advantage of such planning is that the changes one

has to implement are known over the whole time span of

the system's evolution and provide an optimal solution

(an optimal cost effectiveness is realized for attaining the

desired goal). The basic disadvantage of this method

is that modeling errors, inherent perturbations, and unforeseen factors will usually lead to a trajectory different

from the planned one.

2. MODIFIED RICHARDSON MODEL

To illustrate the control algorithms we choose a very

simple example related to the socio-political field. Re349
cently, Miller, Sulcoski, and Farmer have presented a

modification of the Richardson model (MRM) describing an iV-nation arms race, in the form of a discrete, nonlinear set of coupled dynamical equations [8]. This complex spatio-temporal system can be simply represented

by a coupled map lattice (CML). Specifically, the model

is given by

fcis = hi = 0.4, xm 0 6 x

2 1.5, x

3max

xi+l — xi + ( x

amax x1) kaa(xmin Xi ) + ^ab xi

(1)

where x

a

is the "total military capability potential"

(TMCP) of country a at time i, xmax and xmin are maximum/minimum values for the TCMP sustainable

by the respective country a, and kaa and kat, are coupling constants, representing internal threats and external alliances, respectively. The internal instability in- dex Ia = 2kaa/(xmax ~ xmin) determines whether country a behaves like a democratic (Ia > 0) or totalitarian (Ia < 0) nation [8]. Another interpretation classifies these countries as non-militaristic and militaristic,

respectively. For

particular parameter values, iteration of this mapping

produces a 2D landscape ( 1 spatial, 1 time) whose topology describes the qualitative dynamics of the political sit- uations of the N countries. Being globally coupled and

nonlinear, this model has the potential for rather rich

behavior, and so far there have identified stationary, periodic, and chaotic parameter regimes. The relevance of

this model, as for the original Richardson model, is that

it may have solutions which yield considerable insight

into the possible dynamical regimes for the current

multi-sphere world order, allowing qualitative analysis

and prediction.

Case A) A four-nation model, consisting of a weak

democratic nation (1), a weak totalitarian nation (2), a stronger totalitarian nation (3), and a strong democratic nation (4). These countries form two alliances,

between the totalitarian and democratic nations, respectively, which are relatively strong. The parameter values

are: kn = 1.0, k22 = -0.1, k33 = -0.3, kM = 2.0,

ki2 — k2 i = 0.1, fci3 - &3i = 3.0, ku - hi = -0.1,

k23 = ^32 = -0.1, k2i = k42 = 0.1, k34 = fc43 = 0.1, — 1-5, xmax X = 0-7, Xmax — 2.0, max = 0-7, Xmax —> •"rnax ' "max = 0.2, xmin = 0.5, x'T 0.3, xmin = 0.5. As

initial conditions (armament levels) we choose Xq = 0.4,

x\ — 1.4, Xq = 0.6 and x% = 1.6. Figure 1(a) shows the

resulting time evolutions of this system which indicate

exponentially

growing behavior (which is artificially truncated after

some time for illustrative purposes).

Case B) A three-nation model, with the following parameter values: k\\ = 0.1, £22 = —0.9,

k33 = 0.3, k12 = k21 = 0.4, k23 = k32 = 0.7,

0.7, x

lmin = 0.2, x2min = 0.3, x

3min = 0.5. As initial

conditions (armament levels) we choose Xq = 0.3, Xq =

1.1, and Xq = 0.4. This corresponds to a system with

two weak democratic nations (1 and 3) and a stronger

totalitarian nation (2) which is destabilized by an internal

security threat. The resulting complex time evolution of

this system is shown in Fig. 2(a), which indicates chaotic

evolution of the totalitarian nation's TMCP.

The instabilities in the MRM leading to fast oscillations or chaotic evolution of the TMCP may be interpreted as a transition to war or insurgency [7] (c.f. Figs. 1(a), 2

(a)). The basic question we try to answer in

the next Section is whether or not such instabilities arising at some stage of the dynamics of the interaction of

the nations can be controlled, by actively changing the

international or internal relations, and thus avoiding the

onset of "war". The question is difficult and here we

only address some simple examples. We will examine

the MRM dynamics and sketch some conclusions about

controllability, as follows from the MRM (1).

For this discussion, we assume that the model equations and most estimated coefficients are known, and the

only parameters that can be effectively changed are those

related with internal affairs (A;aa ) and international relations (kab). Interpreted in the context of international

relations, we assume that a given government can at- tempt to strengthen or weaken its military potential by

changing the internal relations within its own country, or by carefully tailored international alliances with any of

the other countries. The other parameters of Eq. (1), the

maximum and minimum sustainable capability £max and

xmin , are assumed difficult to change on short time-scales

as they reflect economic structure, culture, demographics, technological development, governmental structure,

etc.

3. SHORT RANGE REACTIVE

CONTROL

Recently nonlinear dynamics has provided us with a series of methods designed to control unstable saddle points

of complex systems, with only small

changes in one or a few of the experimentally accessible parameters. These methods assume an active monitoring of the system and evaluation of the new control

parameters at each time step based on the actual state

of the system (active feedback, "closed-loop control").

Although here we assume perfect knowledge of the governing equations, in practical cases this is neither realistic nor necessary, as most of the information needed to control the system can be extracted by observing the evolution of the system and the effect of parameter variations

(c.f. Ref. [12,13]). We have to emphasize that such an

approach to stabilize international relations may not be

350
regarded as a long-term solution, but rather as a short

term crisis management.

Here we will consider the method of Ott, Grebogi and

Yorke [12], which is one of the most widely accepted chaos

control algorithms, and which has already been applied

to a variety of physical systems, such as magneto-elastic

ribbon, chaotic laser, semiconductor devices, chemical re- actions etc. The method applies only small perturbations

to drive the system to the curve in the phase space along

which the saddle point can be exactly reached, called the

stable manifold. Thus it takes advantage of the naturally attractive dynamics along the stable manifold. The

reader is referred to Ref. [12,13] for a detailed description

of the method as well as to Ref. [14] for an extension to

higher dimensional systems.

2 -

1.8 -

1.6 -

1.4 -

1.2 -

a.

0.8 -

0.4

0.2 -

0

I 1 1 1 i 1 ' ' ' 0 5 10 15 20 25 30 35 40

time 2 -

1.8 -

time

FIG. 1. Time evolution of the TMCP for the uncontrolled

(a) and controlled (b) case. Here the short range reactive control have been employed. Fig. (c) shows the time evolution of

the control parameter. Note that the except the first timestep

the applied perturbation is very small.

Our main conclusions about controllability can be

summarized as follows: a) although in the mathematical model the control can be sustained for arbitrary long

time with only small perturbations, in practical cases this

procedure may fail after some time as the model may become invalid; b) with the exception a few special cases it

is not possible to control nations at their maximum ca- pability potential; c) when the nations are strongly coupled and have nontrivial fixed points one has to employ a

higher dimensional control algorithm, and the controllability condition should be also tested in a higher dimensional framework as presented in Ref. [14].

This control crisis management is most effective when

at least two of the nations have saddle points that differ from their maximum sustainable potential. Such an example is provided by Case A. This model results in a

fixed point at r* = (0.6422,1.5,0.7,0.5779). This shows

the presence of two strongly democratic nations, one of

them at the edge of internal stability (J4 = 1.5), (similar behavior is observed at slightly lower I4 values). The

strongly democratic nation has a large maximum sus- tainable potential (x^aa. = 2.0) but has a low armament

level. Figure 1(a) shows the time evolution with initial

TMCP values x\ = 0.5, x

20 = 1.5, x% = 0.7 and x% = 0.6. One can observe that while the weak democratic and the

totalitarian nations quickly reach a steady TMCP level,

the strong democratic nation's TMCP oscillates periodically after some chaotic transients. Our strategy is now

to actively change one of the coupling coefficients between the two democratic nations. Figure 1(b) shows the

time evolution during the control procedure and Fig. 1(c)

the evolution of the corresponding coupling parameter

4. LONG TERM STRATEGIC

CONTROL

This approach is based on the optimal control method

applied to discrete systems [6]. The optimal control

method can be simply summarized as follows. The system is described by a scalar or vector state function depending on a number of independent variables that take

values in the phase space of the system. The state satisfies a (usually nonlinear) dynamical scalar or vector

equation that depends also on some parameters that take

values in the parameter space. One or more of these parameters are considered external controls to be adjusted

at will. The goal is to optimize a given objective functional that depends on the state and on the control (s).

351
Prom the state equation and objective functional one constructs, in a canonical way, a non-homogeneous adjoint

equation for a (scalar or vector) adjoint variable. The

original state equation together with the adjoint equation

form the optimality system (OS). The optimality condition yields an explicit, analytical formula for the optimal

control in terms of the solutions of the OS. By replacing

this expression of the control in the OS and solving it, one obtains the optimal state and adjoint variable and

therefore the optimal control. The general framework

for optimal control for general nonlinear systems as developed by J.-L. Lions [9] was recently applied to competitive systems of social and military interest [10,11].

As an example for this control strategy we chose the

three-nation model of Case B described in Section 2. The

overall goal is to minimize the oscillations of the totalitarian nation's TMCP by changing his internal stability

coefficient (£22)- Also we want to achieve this goal at an optimal cost, and by simultaneously keeping the the

democratic nations stable. The corresponding choice of

the cost function is

a.o

1 (b)

(

' n

time

time FIG. 2. Time evolution of the TMCP for the uncontrolled

(a) and controlled (b) case. The long range strategic control

is applied to minimize the oscillations of the totalitarian nation's TMCP (*) at a minimal cost. The parameters used are

a\ = 0.2, a,2 — 1.0,a3 = 0.2 and 7 — 0.01. Fig. (c) shows the

time evolution of the control parameter.

G=Ei=A 01 (*i - *!-i)

2 + «a (*? - A-xf +

a3 (xf -4-i)2 -7*Mt <] (2)

where 01,02,03 and 7 are positive constants weighting

the relative importance of the "goals" and the "cost",

respectively. In this example we choose a N — 3 time

step planning, an correspondingly the control will be also

projected three time steps ahead reflecting a longer term

strategical objective. Fig. 2(a) shows the uncontrolled

trajectory, while Fig. 2(b,c) the controlled version and

the variation of the control parameter, respectively. According to the choice of the cost function the oscillations

in the totalitarian nation's TMCP have been minimized

at optimal cost.

5. CONCLUSIONS

In principle, each of the above control methods can be

used to achieve either stabilization or destabilization of

the dynamics of MRM. The choice between the two methods is not merely a political decision. In some cases one

or another method may be more efficient, or one of these

methods may not be suitable at all. One simple example

is the problem of destabilizing stable fixed points of the

dynamics. If the fixed point is elliptic, the short range re- active control does not work because small perturbations

applied to the system are unable to perturb the trajectory

from the elliptic point's neighborhood. In general, short

range reactive control is better suited when the model of

the system is incomplete and cannot take into account

all relevant factors. Hence it is a good choice when one

does not have a well-defined overall goal or strategy and

in unforeseen crisis situations. The long range control

is better suited when one has a good idea about global

strategic objectives, the costs involved and, one wants to

achieve a well-defined goal. Since the role of the user is essential in deciding what control strategy to use we see here an excellent example of applied semiotic analysis to international relations.

ACKNOWLEDGEMENTS

The authors wish to thank M. Sulcoski, L.D. Miller,

G. Mayer-Kress, and Z. Toroczkai for very useful discussions. This work was partially supported by a grant from

the Office of Naval Research, from the National Ground

Intelligence Center and from the US-Hungarian Science

and Technology Joint Fund under Project JF No. 501.

A. P. wishes to thank partial support from the Hungarian

Science Foundation under Grant Nos. OTKA T17493,

F17166. V.P. was partially supported by the Office of

Basic Energy Sciences of the U.S. Department of Energy

under contract No. DE-AC05-96OR22464 with Lockheed

Martin Energy Systems, Inc.

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196-202.

[2] Crutchfield, J., and McNamara, B., "Equations of motion

from a data series." Complex Systems 1 (1987): 417-452.

352
[3] Cremers, J., and Hubler, A., "Construction of differential

equations from experimental data." Z. Naturforsh. 42A

(1987): 797-802.

[4] Kadtke, J. B., and Kremliovsky, M., "Estimating Statistics for Detecting Determinism Using Global Dynamical

Models", preprint (1996).

[5] Richardson, L. F., Arms and Insecurity. Pittsburgh; Boxwood, 1960.

[6] Fan, L.-T., and Wang, C.-S., The Discrete Maximum

Principle. New York; John Wiley & Sons, 1964.

[7] Saperstein, A. M., "Chaos - a model for the outbreak of

the war." Nature 309 (1984): 303-305.

[8] Miller, L. D., Sulcoski, M. F., and Farmer, B. A., "Dis- crete Richardson Model: A Paradigm for International

Relations?", preprint(1996).

[9] Lions, J.-L., Optimal Control of Systems Governed by

Partial Differential Equations, New York; Springer Verlag, 1971.

[10] Lenhart, S., and Protopopescu, V., "Optimal Control

for Competitive-Cooperative Systems: Modeling Flexible Coalitions in Tomorrow's Competitive World" , paper

presented at the 61st MORS Conference, Dayton, Ohio,

June 22-24, 1993.

[11] Lenhart, S., Protopopescu, V., and Szpiro, A., A., "Optimal Control for Competing Coalitions", to appear in Nonlinear Analysis: Theory, Methods, and Applications.

[12] Ott, E., Grebogi, C, and Yorke, J. A.,

"Controlling Chaos." Phys. Rev. Lett. 64 (1990): 1196-

1199.

[13] Kadtke, J., Kremliovsky, M., and Pentek, A., "Dynamical Classification and Control of a Nonlinear Model of In- ternational Relations", in Proceedings of the 1996 Inter- national Workshop on Complex Systems: Issueas of Measurement and Semiotic Analysis, 8-12 December 1996,

Las Cruces, New Mexico.

[14] Pentek, A., Kadtke, J. B., and Toroczkai, Z., "Stabilizing

chaotic vortex trajectories: an example of

high-dimensional control." Phys. Lett. A in press (1996).

[15] Coombs, M., and Sulcoski, M., eds. Proceedings of the

1996 International Workshop on Control mechanisms for

Complex Systems: Issues of Measurement and Semiotic

Analysis, 8-12 December 1996, Las Cruces, New Mexico.

353
GALEN IN MEDICAL SEMIOTICS

Thomas A. Sebeok

Indiana University

Ullmann (1951: 161) distinguished among four

juxtaposed branches of word-study: "(1) the science

of names (lexicology if synchronistic, etymology if diachronistic); (2) the science of meanings

(semantics); (3) the science of designations

(onomasiology); (4) the science of concepts

(Begriffslehre)." Although the distinction between

designation and meaning, particularly as displayed in the works of German and Swiss semanticists (of the

sometimes loosely, as well erroneously, called TrierWeisgerber School) is far from consistently drawn or pellucid, I take it that this alterity depends on

whether one's starting point is the name, the lexeme,

or, more generally, the sign; or whether it is the

concept or, more generally yet, the object, i.e. the

constellation of properties and relations the sign

stands for. If the former, the analysis should yield a semiotic network responsive to the question: what

does a given sign signify in contrast and opposition

to any other sign within the same system of signs? If the latter, the analysis should reveal the sign by

which a given entity is designated within a certain

semiotic system. According to Ullmann, the second

inquiry "is the cornerstone of Weisgerber's structure" (1951), but I believe that the two questions are

indissolubly complementary. In any case, the whole

enterprise critically hinges upon how the investigator

parses the sign/object {aliquiaValiquo) relation, and

what the conjunctive stands for, in the judgment of

the investigator, entails. The probe becomes at once more intricate, but

also more intriguing, when the lexical field

(Bedeutungsfeld? Sinnfeld? Wortfeld?) being

explored happens to be reflexive, that is, self- searching. Such is the ease of symptom (Sebeok

1986:45-58), an ancient technical term in both

semiotics and medicine. Thus its examination may

begin in the inner realm of the lexicon, if viewed as a name, or in the outer realm of clinical experience,

if viewed as sense. One may properly inquire: what does the lexeme

symptom mean in language L\; or what does the

same lexeme designate, or reveal as a diagnostic

intimation, with respect to, say, an actual quality of

"diseasehood" (Fabrega 1974:123), that F.G.

Crookshank (in Ogden and Richards 1938:343)

foresightedly portrayed as "a mysterious substantia

that has 'biological properties' and 'produces'

symptoms"? In the end, the results of such

dichotomous inquiries amalgamate in a common

dialectical synthesis. For the purposes of this

exposition, Li is American English. However, the

semantic field of "medical discourse," which is typically nested within wider sets of concentric

frames (Labov and Fanshel 1977:36f.), is here

assumed to be, mutatis mutandis, very similar to that

in every other speech community committed to the

paradigm of medical theory and practice "in the

context of the great tradition" (Miller 1978:184) of

thinking marked by a continuity that links modern

clinicians with the idea of isonomia launched by the

brilliant Alcmaeon of Croton during the first half of

the fifth century. This heritage was further

consolidated by Hippocrates — arguably considered,

at one and the same time, the "father of medicine"

(Heidel 1 94 1 :xiii), and the "der Vater und Meister

aller Semiotik" (Kleinpaul 1972:103) -- and Plato,

Aristotle, and the Alexandrian physicians of the

fourth century B.C. (Manetti 1987:57-134). Equally

perceptive studies of symptom have, in fact, cropped

up in the semiotic literature (e.g., Baer 1982, 1986,

1988) and in the medical literature (e.g., Prodi

1981), undertaken by savants who mutually know

their way around the other field as well as their own

(see also Staiano 1979, 1982). One should, however,

continue to be ever mindful of the admonition of

Mounin (1981) against a mechanical application of

semiotic (especially linguistic) concepts to medicine

(especially psychiatry).

Symptom always appears in conjunction with

sign, but the precise nature of the vinculum is far

from obvious (as in MacBryde and Blacklow 1970

or Chamberlain and Ogilvie 1974). The basic

semiosic facts were perspicuously depicted by

Ogden and Richards: "If we stand in the

neighbourhood of a crossroad and observe a pedestrian confronted by a notice To Grandchester

displayed on a post, we commonly distinguish three

important factors in the situation. There is, we are

sure, (1) a Sign which (2) refers to a Place and (3) is being interpreted by a person. All situations in which

Signs are considered are similar to this. A doctor

noting that his patient has a temperature and so forth

is said to diagnose his disease as influenza. If we talk

like this we do not make it clear that signs are here

also involved. Even when we speak of symptoms we

often do not think of these as closely related to other

groups of signs. But if we say that the doctor

interprets the temperature, etc. as a Sign of

influenza, we are at any rate on the way to an inquiry

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as to whether there is anything in common between

the manner in which the pedestrian treated the object

at the crossroad and that in which the doctor treated

his thermometer and the flushed countenance"

(1938: 21).

The relation of sign to symptom involves either

coordination or subordination. If the distinction is between coordinates, what matters less than their

inherent meaning is the mere fact of the binary

opposition between the paired coordinate categories.

This was nicely brought to the fore in a report of an

investigation of the symptom "fatigue" by two

physicians, Shands and Finesinger: "The close study

of.. .patients made it imperative to differentiate

carefully between 'fatigue,' a feeling, and

'impairment,' an observable decrement in

performance following protracted effort. The

distinction comes to be that between a symptom and

a sign. The symptom is felt, the sign observed by

some other person. These two terms cover the broad

field of semiotics; they are often confused, and the

terms interchanged [at least in L] without warning"

(Shands 1970:52).

This passage underscores the importance of

separating the "private world" of introspection

reported by the verbal description or nonverbal

exhibition of the symptoms on the part of the patient

from the public world of signs reported by the

description of status or behavior observed on the part

of the physician. As I had written earlier: "It is a

peculiarity of symptoms that their denotata are generally different from the addresser, i.e. the patient

('subjective symptoms,' confusingly called by many

medical practitioners 'signs') and the addressee, i.e. the examining physician ('objective symptoms,' or simply 'symptoms')" (Sebeok 1976:181). Note that

only a single observer — to wit, oneself — can relate

symptomatic phenomena or events, whereas an

indefinite number of observers — including oneself —

can observe signs. Accordingly, within this

framework the fact of privacy looms as a criterial

distinctive feature that demarcates any symptom

from any sign (Sebeok 1991:36-48). Symptoms

could thus be read as recondite communiques about

an individual's inner world, an interpretation that

sometimes acquires the status of an elaborate occult

metaphor. For instance, the eating disorder anorexia nervosa would appear to be reasonably decipherable

as "I am starving (emotionally) to death." Its symptoms are sometimes believed to result from

disturbed family relationships and interpersonal

difficulties (Liebman, Minuchin, and Baker 1974a,

1974b). One palpable sign of this ailment is, of

course, weight phobia, measurable as a decrement in the patient's mass. The crucial distinction between fatigue and

impairment is "similar to that between anxiety as a

felt symptom and behavioral disintegration often

exhibited in states of panic. The latter is a sign, not a symptom" (Shands 1970). The dissemblance

exemplified here is obviously related to Uexkiill's

(1982:209) notion, maintained both in the life and

the sign science, of "inside" and "outside." I take the

pivotal implication of this to be as follows:

"Something observed (= outside) stands for

something that is (hypothetically) noticed by the

observed subjects (= inside). Or something within

the observing system stands for something within

the observed system" {ibid.). For any

communication, this complementary relationship is obligatory, because the organism and its Umwelt

together constitute a single system. The shift from

physiological process to semiosis is a consequence

of the fact that the observer assumes a hypothetical

stance within the observed system

{Bedeutungserteilung / Bedeutungsverwertung).

For symptom (in L\), there exists an array of

both stricter and looser synonyms. Among the

former, which appear to be more or less commonly

employed, Elstein et al. solely but extensively use

cue. Although they do so without a definition, their

import is made quite clear from passages such as "cues were interpreted by physicians as tending to confirm or disconfirm a hypothesis, or as noncontributory" (1976:279). Fabrega, on the other

hand, seems to prefer indicator, but he uses this

commutably for either symptom or sign; and when

he remarks that "all indicators may be needed in order to make judgments about disease" (1974:126),

he surely refers to both categories together. The

word clue, on the other hand, is a looser synonym

for symptom: generally speaking, where symptom is used in medical discourse, clue is found in the

detectival sphere (Sebeok 1981a, Eco and Sebeok

1983).

In the minimalist coupling, sign / symptom are

equipollent; both are unmarked vis-a-vis one another

(Waugh 1982). Sometimes, however, symptom

encompasses both "the objective sign and the

subjective sign" (cf. Staiano 1982:332). In another

tradition, symptom is a mere phenomenon "qui

precisement n'a encore rien de se miologique, de

semantique," or is considered falling, for instance, in the terminology of glossematics, in the area of

content articulation, la substance du signifiant, an

operationally designated figura that is elevated to

full semiotic status only through the organizing

consciousness of the physician, achieved through the

mediation of language (Barthes 1972:38f).

However, still other radically different sorts of

arrangements occur in the literature. In Biihler's

organon model (see Sebeok 1981b), symptom

constitutes but one of three "variable moments"

capable of rising "in three different ways to the rank

of a sign." These include signal, symbol, as well as symptom. Biihler (1965:28) specifies further that the

355
semantic relation of the latter functions "by reason of

its dependence on the sender, whose interiority it expresses." He clearly subordinates this trio of words

under one and the same "Oberbegriff 'Zeichen'," then

goes on to ask: "1st es zwakmassig, die Symbole,

Symptome, Signale zusammenzufassen in einem

genus-proximum 'Zeichen'?" It should also be noted

that Buhler's first mention of symptom is immediately followed by a parenthetic set of

presumed synonyms: "(Anzeichen, Indicium)."

(Note that the German verb anzeigen bears an ominous secondary judicial connotation, "to denounce somebody" [see Sebeok 1981b:228f.)

Thus, in acknowledging the importance of the

notion of privacy as an essential unmarked feature of

symptom, Biihler also recognizes that, while it is coordinate with two other terms, it is also

subordinate to the (unmarked) generic notion of

sign, namely, that kind of sign that Peirce earlier, but

unbeknownst to Biihler, defined with much more

exactitude as an index (Sebeok 1991:128-143).

Despite his extensive knowledge of medicine

(Sebeok 1981a:37), Peirce did not often discuss

symptom (nor anywhere, in any fecund way,

syndrome, diagnosis, prognosis, or the like). For

him, a symptom, to begin with, was one kind of sign. In a very interesting passage, from the dictionary

lemma "Represent," he expands: "to stand for, that

is, to be in such a relation to another that for certain

purposes it is treated by some mind as if it were that other. Thus, a spokesman, deputy, attorney, agent,

vicar, diagram, symptom, counter, description,

concept, premise, testimony, all represent something

else, in their several ways, to minds who consider

them in that way" (2:273).

For Peirce, however, a symptom was never a

distinct species of sign, but a mere subspecies,

namely the index — or secondness of genuine degree

(in contrast to a demonstrative pronoun, exemplifying secondness of a degenerative nature) — of one

of his three canonical categories. But what kind of

sign is this? Peirce gives an example that I would

have preferred to label a clue: "Such, for instance, is a piece of mould with a bullet-hole in it as sign of a

shot; for without the shot there would not have been

a hole; but there is a hole there, whether anybody has

the sense to attribute it to a shot or not" (2.304). The

essential point here is that the indexical character of

the sign would not be voided if there were no

explicit interpretant, but only if its object were

removed. An index is that kind of a sign that

becomes such by virtue of being really (i.e.

factually) connected with its object. "Such is a symptom of disease" (8.119). All "symptoms of

disease," furthermore, "have no utterer," as is also

the case with "signs of the weather" (8.185). We

have an index, Peirce prescribed in 1885, when there

is "a direct dual relation of the sign to its object

independent of the mind using the sign... Of this

nature are all natural signs and physical symptoms"

(3.361).

A further detail worth pointing out is that Peirce

calls the "occurrence of a symptom of a disease. ..a legisign, a general type of a definite character," but

"the occurrence in a particular case is a sinsign"

(8:335), that is to say, a token. A somewhat cryptic

remark reinforces this: "To a sign which gives

reason to think that something is true, I prefer to give

the name of a symbol; although the words token and

symptom likewise recommend themselves" (MS 787,

1896). Staiano is undoubtedly correct in remarking

that "the appearance of a symptom in an individual

is thus an indexical sinsign, while the symptom

interpreted apart from its manifestation becomes an

indexical legisign" (1982:331).

Symptoms, in Peirce's usage, are thus unwitting

indexes, interpretable by their receivers without the

actuality of any intentional sender. Jakobson

likewise includes symptoms within the scope of

semiotics, but cautions that "we must consistently

take into account the decisive difference between

communication which implies a real or alleged

addresser and information whose source cannot be

viewed an addresser by the interpreter of the

indications obtained" (1971:703). This remark

glosses over the fact that symptoms are promptings

of the body crying out for an explanation — for the

construction, by the self, of a coherent and

intelligible pattern (which of course may or may not be accurate; cf. Polunin 1977:91).

Pain comprises one such symptom that

embodies a message compelling the central nervous system to influence both covert and overt behavior

to seek out signs of pain, throughout phylogeny,

ontogeny hie et ubique. Miller befittingly expands:

"From the instant when someone first recognizes his

symptoms to the moment when he eventually

complains about them, there is always an interval,

longer or shorter as the case may be, when he argues

with himself about whether it is worth making a complaint known to an expert.... At one time or another we have all been irked by aches and pains.

We have probably noticed alterations in weight,

complexion and bodily function, changes in power,

capability and will, unaccountable shifts of mood.

But on the whole we treat these like changes in the

weather.... (1978: 45-49).

Peirce once particularized the footprint that

Robinson Crusoe found in the sand to be an index

"that some creature was on his island" (4:351), and

indeed an index always performs as a sign the

vectorial direction of which is toward the past, or, as Thorn put it, "par reversion de la causalite

generatrice" (1980:194), which is the inverse of

physical causality. Augustine's class of signa

naturali, defined — in contrast to signa data — by the

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relation of dependence between sign and the things

signified (De Doctrina Christiana II. 1.2), beside its orthodox sense (such as a rash as a symptom of

measles), is also illustrated by footprints left by an animal passed out of sight. It may thus be regarded

as encompassing a portent, or in the most general

usage, evidence (for instance, as a south-westerly

wind may both signify and bring rain, i.e., give rise to its significatum). Thus symptoms, in many

respects, function like tracks -- footprints,

toothmarks, food pellets, droppings and urine, paths

and runs, snapped twigs, lairs, the remains of meals,

etc. -- throughout the animal world (Sebeok

1976:133), and in hunting populations, where

humans "learnt to sniff, to observe, to give meaning

and context to the slightest trace" (Ginzburg 1983).

Tracks, including notably symptoms, operate like

metonyms. This trope is also involved in pars pro

toto, as extensively analyzed by Bilz, who spelled

out its relevance: "Auch eine Reihe korperlicher

Krankheitszeichen sog., funktioneller oder organneurotischer Symptome, haben wir unter den

Generalnenner der Szene gebracht, einer

verschutteten Ganzheit.... Hier ist es...eine

Teil funktion der Exekutivc.wobei wir abermals

auf den Begriff der Parsprototo stiessen" (1940:287).

It is, of course, Hippocrates who remains the

emblematic ancestral figure of semiotics — that is to say, semiology, in the narrow, particularly Romance,

sense of symptomatology ~ although he "took the

notion of clue from the physicians who came before

him" (Eco 1980:277). Baer alludes to a "romantic

symptomatology," which he postulates may have

been "the original one," carrying the field back "to an era of mythical consciousness" (1982:18).

Alcmaeon remarked, in one of the scanty fragments

of his book: "As to things invisible and things

mortal, the gods have certainties; but, so far as men

may infer...," or, in an alternative translation, "men

must proceed by clues..." (Eco 1980:281), namely,

provisionally conjecture. And what is to be the basis

of such circumstantial inference? Clearly, the

concept that has always been central is symptom

(semeion; Ginzburg 1983).

While Alcmaeon is commonly regarded as the

founder of empirical psychology, it was Hippocrates,

a clinical teacher par excellence (Temkin 1973), who

broke with archaic medical practice where the

physician was typically preoccupied with the nature

of the disease, its causes and manifestations,

refocusing directly upon the sick person and his/her

complaints —in brief, upon the symptoms of disease:

"Nicht so sehr die Krankheit als das Kranke

Individuum" (Neuburger 1906:196).

For Hippocrates and his followers symptoms

were simply "significant phenomena" (cf. Heidel

1941:62). Their consideration of symptoms as

natural signs — those having the power to signify the

same things in all times and places — was of the

most comprehensive sort. An early discussion of this type is found in Hippocrates' Prognostic (XXV):

"One must clearly realize about sure signs, and about

symptoms generally [peri ton tekmerion kai ton allon

semeion, that in every year and in every land bad

signs indicate something bad, and good signs

something favourable, since the symptoms semeia

described. ..prove to have the same significance in Lybia, in Delos, and in Scythia. So one must clearly

realize that in the same districts it is not strange that one should be right in the vast majority of instances,

if one learns them well and knows how to estimate

and appreciate them properly."

I have previously recalled an enduring example

of his method, the detailed description of the famous

fades hippocratica (Sebeok 1979:6f); another

example may here be cited from Epidemics I: "The

following were the circumstances attending the

diseases, from which I formed my judgments,

learning from the common nature of all and the

particular nature of the individual, from the disease,

the patient, the regimen prescribed and the prescriber — for these make a diagnosis more favorable or less; from the constitution, both as a whole and with

respect to the parts, of the weather and of each

region; from the customs, mode of life, practices and

age of each patient; from talk, manner, silence,

thoughts, sleep or absence of sleep, the nature and

time of dreams, pluckings, scratchings, tears; from

the exacerbations, stools, urine, sputa, vomit, the

antecedents of consequents of each member in the

succession of diseases, and the absessions to a fatal issue or a crisis, sweat, rigor, chill, cough, sneezes, hiccoughs, breathing, belchings, flatulence, silent or

noisy, hemorrhages, and hemorrhoids. From these

things we must consider what their consequents also

will be" (Heidel 1941:129).

In The Science of Medicine, Hippocrates also

stated: "What escapes our vision we must grasp by

mental sight, and the physician, being unable to see

the nature of the disease nor to be told of it, must

have recourse to reasoning from the symptoms with

which he is presented." The means by which a diagnosis may be reached "consist of observations on the quality of the voice, whether it be clear or

hoarse, on respiratory rate, whether it be quickened

or slowed, and on the constitution of the various

fluids which flow from the orifices of the body,

taking into account their smell and colour, as well as

their thinness or viscosity. By weighing up the

significance of these various signs it is possible to deduce of what disease they are the result, what has

happened in the past and to prognosticate the future course of the malady" (Chadwick and Mann 1950:

87-89).

However, it was Galen, whose one and only idol was Hippocrates, and whose medicine remained (on

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the whole) Hippocratic, who attempted to provide

prognostics, wherever feasible, with a scientific

underpinning, i.e. to base his forecasts on actual

observations. This he was able to do because he

practiced dissection and experiment: whereas

Hippocrates studied disease as a naturalist, Galen

"dared to modify nature as a scientist" (Majno 1975:

396; cf. Neuburger 1906:385). "Empirical method was first formulated in ancient medicine," as systematic and detailed expression in the

Hippocratic corpus (De Lacy 1941:121), and became

a part of the theory of signs of the Epicureans and

Sceptics, in opposition to the Stoic rationalistic

position. Philodemus' fragmentary treatise (circa 40

B.C.) is by far the most complete discussion of a thoroughgoing methodological work uncovered (in

the Herculean library) and extensively elucidated to date. Galen, despite all of his Platonic training, was

later "forced by his profession to be more empirical"

(Phillips 1973: 174), even though this open-minded

investigator, who continued to speak with the voice

and authority of a man of science, did gradually turn

into something of a dogmatic mystic (Sarton 1954:

59). He can therefore be regarded as a subtle founder

of clinical semiotics. As such, his work therefore

constituted something of a watershed, since "die

galenische Semiotik verwertet die meisten

Beobachtungs- und Untersuchungsmethoden die das

Altertum ausgebildet hat" (Neuburger 1906: 385).

Although Galen can, very likely, be reckoned

the first "scientific" semiotician, philosophy and

medicine are, as well, consistently conjoined in his

writings. Barnes (1991:50) recently reminded us

that, according to Galen, "The best doctors. ..are also

philosophers," and that he even wrote a pamphlet to show how a competent physician "possesses all the

parts of philosophy — logic, natural science, ethics,"

to which one may dare add: semiotics, or logic in its most technical Peircean sense; (on Galen's logic, see Barnes 1991:54-56 et passim). Galen counted

himself among "those who teach the greatest and

finest human achievements — the theorems which

philosophy and medicine impart." No wonder that

the Emperor Marcus Aurelius, as Galen himself

informed us, referred to him as "the first among

physicians, unique among philosophers" (quoted

ibid.). He was irjdeed the first to explicitly articulate, as far as we know, the kind of medical semiotics put

in practice by his most eminent predecessors — in

fact, he deemed this to have been a platitude in the

Hippocratic tradition — and, having reaffirmed it, emulated by a veritable legion of professional

successors in and beyond his craft. Particularly intriguing is Galen's usage of the

term endeixis — roughly: "indication" — in medicine

and logic, as most recently, and very revealingly (if not exhausively) reviewed by Kudlien (1991) (with

added commentary on its prehistory and Medieval

Latin renderings, by Durling [1991]). This important

term, so cherished by Peirce, is very seldom found in the Hippocratic Corpus and then never in a technical sense or in the sense, or rather the broad spectrum of

senses, employed by Galen. Kudlien rightly

emphasizes that doctors then, as now, do not

deem"indication" to be a "a mere 'sign'," but rather, as puts it, an action: that is, a sign which points

(usually) to the treatment of certain symptoms, or

the syndrome, of the disease being diagnosed

(Kudlien 1991 : 103f.). According to him, the

evidence confirms that "it was Galen, above all, who

used the word in the modern sense" {ibid. 104),

along with such derivatives as endeiktikos,

endeiknynai, synendeiknysthai, antendeiknysthai,

and the like. In brief, for Galen, endeiktikon is by no means the same as semeion or symptomata. His own

usage was quite different from those of the adherents

of the Empiricist or again the Methodist schools of

physicians (he counted himself a member of the so- called Dogmatist school of medicine). "When

seeking for the true 'endeixis', the Dogmatist would

not observe all possible signs/symptoms as such (as

the Empiricist does), but select only those that are

'indicative of the cause (sc. of the disease)..."

(Kudlien 1991:106). In brief, in Galen's writings,

true endeixis is always something "logical." As he

clearly remarked: "One must also use the logical

[viz., semiotic method to recognize what all the

diseases are, with regard to species and kinds, and

how, for every disease, one must take an 'endeixis' of

the therapeutical measures ('iamata')" (quoted in Kudlien 1991:107).

Galen's pen was as busy as his scalpel. In the course of his exceptionally bulky writings, he

classified semiotics as one of the six principal

branches of medicine {mere iatrikes ta men prbta

esti, to te phusiologikon, kai to aitilogikon e pathologikon kai to hugeinon kai to semiotikon kai

to therapeutikon [XIV:689]), an ordering that had a

special, indeed, critical importance for its "effect on

the later history of medicine" (Phillips 1973:172).

The strength of Galenism, as Temkin (1973:179)

also emphasized, "reposed in no small measure in having provided medical categories. ..for relating the

individual to health and disease," including

"semeiology (the science of signs)."

Of semiotics, Galen further specified: Semeidsis

de dai eis therapeia men anakaia, all' ouk estin aute he therapeia. Dia gar tes hules he therapeia

sunteleitai kai to men hulikon aneu therapeias ouden

heteron sumballetai. To de semeioikon kai aneu

therapeias anankaion pros to eidenai tina

therapeutika kai tina atherapeuta kai periistasthai

pros to eidenai tina therapeutika kai tina atherapeuta

kai periistasthai auta, hopos me epiballomeomenoi

adunatois sphalldmetha (XIV:689). At the end of

this same chapter, Galen then divided the field into

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three enduring parts: in the present, he asserted, its concern was inspection, or diagnosis, in the past

cognition, or anamnesis (etiology), and in the future

providence, or prognosis (diaireitai de kai to se- meiotikon eis tria, eis te epignosin ton pareleluthoton

kai eis ten epikepsin ton sunendreuont on kai eis

prognosin ton mellonton") (XIV:690). His clinical

procedure was depicted by Sarton (1954:6) thus:

"When a sick man came to consult him, Galen...

would first try to elicit his medial history and his manner of living; he would ask questions concerning

the incidence of malaria and other common ailments.

Then the patient would be invited to tell the story of

his new troubles, and the doctor would ask all the

questions needed to elucidate them and would make

the few examinations which were possible." Galen

regarded "everything unnatural occurring in the

body" as a symptom (VII:50, 135; also X:71ff), and

an aggregation of symptoms (athroisma ton

symptomaton) as a syndrome. He was fully aware

that symptoms and syndromes directly reflected

clinical observation, but the formulation of a diagnosis required causal thinking (cf. Siegel 1973).

He was the master of foretelling the course of

diseases: Galen "pflegtc.die Prognostik in

besonderem Masse und nicht den geringsten Teil

seines Rufes als Praktiker dankte er richtigen

Vorhersagungen" (Neuburger 1906: 383). Although

his prognostications rested essentially and loyally

upon the Corpus Hippocratum, his own anatomical

knowledge and exactitude of mind predisposed him

to build up his prognoses from a cogent diagnostic

foundation.

It would not appear unreasonable to expect a finely attuned reciprocal conformation between

internal states and "reality," between an Innenwelt

and the surrounding Umwelt, or more narrowly,

between symptoms and their interpretations as an outcome over time, in evolutionary adaptation —

prodotto genetico, in Prodi's succinct formulation

(1981:973) — that benefits an organism by raising its "fittingness."

But such does not reflect the state of the art of

diagnosis. The probabilistic character of symptoms

has long been realized, among others, by the Port- Royal logicians (Sebeok 1976:125); the often vague,

uncertain disposition of symptoms was clearly affirmed by Thomas Sydenham, the seventeenth

century physician often called the "English

Hippocrates" (Colby and McGuire 1981:21). This

much-admired doctor, held in such high regard by

his brother in the profession, John Locke, was also

known as the "Father of English medicine" (Latham

1848:xi). Sydenham was noted for his scrupulous

recognition of the priority of direct observation. He

demanded "the sure and distinct perception of

peculiar symptoms," shrewdly emphasizing that

these symptoms "referred less to the disease than to

the doctor." He held that "Nature, in the production

of disease, is uniform and consistent; so much so, that for the same disease in different persons, the

symptoms are for the most part the same; and the

self-same phenomena that you would observe in the

sickness of a Socrates you would observe in the

sickness of a simpleton" (Latham 1 848: 1 4ff.). This

assertion of his was, of course, quite mistaken,

although the medical-student jape referred to by

Colby and McGuire "that the trouble with psychiatry

is that all psychiatric syndromes consist of the same

signs and symptoms" (1981:23), appears to be

equally exaggerated. There are, to be sure, certain

diagnostic difficulties inherent in the similarities

between the symptomatology of functional

syndromes and of those of the organic maladies. The

marginal, or supplementary, symptoms of the former

can, however, be assimilated according to specific

criteria, such as are set forth, for instance by Uexkiill

(1979).

This set of strictures leads me to a consideration

of an aspect of symptom that is seldom mentioned in the literature but that I have found both fascinating

and, certainly for semiotics, of broad heuristic value.

This has to do with anomalies, a problem that was

considered, in a philosophical context, especially by

Peirce. According to Humphries (1968:88), a naturally anomalous state of affairs is such "with

respect to a set of statements which are at present

putatively true," or, putting the matter in a more

direct way, "any fact or state of affairs which

actually requires an explanation can be shown to be

in need of explanation on the basis of existing

knowledge" (1968:89). The enigmatic character of

semiotic anomalies can especially well be illustrated

by clinical examples, where few existing models are capable of accounting for a multitude of facts.

Medicine may, in truth, be one of the few disciplines

lacking an overarching theory, although local,

nonlinear, and hence restricted and over-simple

paradigms, such as the "theory of infectious

diseases," certainly do exist. Take as a first approach to the matter of

anomalies the spirochete Treponema pallidum. This

virus, in its tertiary phase, may manifest itself

("cause") aortitis in individual A, paretic

neurosyphilis in individual B, or no disease at all in individual C. The latter, the patient with

asymptomatic tertiary syphilis, can be said to have a disease without being ill. Note that a person may not only be diseased without being ill, but, conversely,

be ill without having a specifically identifiable

disease. What can we say, in cases such as this,

about the implicative nexus conjoining the

"proposition," i.e. the virus, with its consequent,

expressed in some tangible manner or, on the

contrary, mysteriously mantled? Are A, B, and C in

complementary distribution, and, if so, according to

359
what principle — the constitution of the patient, or some extrinsic factor (geographic, temporal, societal,

age- or gender-related, and so forth), or a coalition of

these? The influence of context, one suspects, may

be paramount. This becomes overriding in the matter

of hypertension — not a disease at all, but a sign of

cardiovascular disorder (Paine and Sherman

1971:272) — which is realized in one and only one

restricted frame: within that of patient/physician

interaction, assuming the aid of certain accessories,

such as a sphygmoscope. Semiosis is, as it were,

called into existence solely under the circumstances

mentioned; otherwise there are no symptoms (the

asymptomatic, or so-called silent, hypertension lasts, on average, fifteen years) — there are no signs, and

there is, therefore, no determinate — i.e. diagnosable - object.

Studies have shown that the majority of people

who have gallstones -- about fifteen million or probably many more Americans among them — go

through life without palpable problems. The

presence of these little pebbles of cholesterol that form in a sac that stores digestive juice can clearly

be seen on X-rays: the shadows are the "objective

signs," but most of them never cause pain, or any

other symptom. They remain mute. They are, in other words, diagnosed only in the course of detailed

checkups, and thus require no surgical intervention.

Sensory experiences, at times, lead to semiosic

paradoxes, such as the following classic

contravention. A hole in one of my teeth, which feels mammoth when I poke my tongue into it, is a subjective symptom I may elect to complain about to my dentist. The dentist lets me inspect it in a mirror,

and I am surprised by how trivially small the

aperture — the objective sign — looks. He lets me

inspect it in a dental mirror, and I am surprised by

how trivially small the aperture — this objective sign — looks. The question is: which interpretation is "true," the one derived via the tactile modality or the one reported by the optical percept? The felt image

and the shape I see do not match. The dentist is, of

course, unconcerned with the size of the hole, filling

the cavity he/she beholds.

It is a common enough experience that the

symptom (for reasons ultimately having to do with

the chance evolutionary design of the human central nervous system) refers to a different part of the body

than where the "damage is actually situated. "The

pain of coronary heart-disease, for example, is felt across the front of the chest, in the shoulders, arms

and often in the neck and jaw. It is not felt where the

heart is - slightly over to the left" (Miller 1978:22).

Such a misreport is unbiological, in the sense that a lay reading could be fatal. An even more outlandish

symptom is one for which the referent is housed

nowhere at all, dramatically illustrated by a phantom

limb after amputation. Miller writes: "The phantom

limb may seem to move — it may curl its toes, grip

things, or feel its phantom nails sticking into its phantom palm. As time goes on, the phantom

dwindles, but it does so in peculiar ways. The arm

part may go, leaving a maddening piece of hand

waggling invisibly from the edge of the real

shoulder; the hand may enlarge itself to engulf the

rest of the limb" (1978:20). What is involved here is an instance of subjective — as against objective —

pain, a distinction introduced by Friedrich J. K.

Henle, the illustrious nineteenth century German

anatomist and physiologist, and generally

perpetuated in classifications of pain ever since (e.g.,

by Behan 1926).

Subjective pain is described as having "no

physical cause for existence," i.e. there is no organic

basis for its presence (indeed, with respect to a limb

unhinged, not even an organ): it results "of

impressions stored up in the memory centers, which

are recalled by the proper associations... aroused"

(Behan 1926:74f.), which is to say that the pain

remains connected with a framework of signification

dependent upon retrospective cognizance. Referred

pain and projection pain are closely allied; the latter

is a term assigned to pain that is felt as being present

either in a part that has no sensation (as in locomotor

ataxia) or in a part that because of amputation no

longer exists.

Certain symptoms — pain, nausea, hunger, thirst,

and the like -- are private experiences, housed in no

identifiable site, but in an isolated annex that humans

usually call "the self." Symptoms such as these tend

to be signified by paraphonetic means, such as groans or verbal signs, which may or may not be

coupled with gestures, ranging in intensity from

frowns to writhings. An exceedingly knotty problem,

which can barely be alluded to here, arises from the

several meanings of self and how these relate to the

matter of symptomatology. The biological definition

hinges on the fact that the immune system does not respond overtly to its own self-antigens; there are

specific markers that modulate the system generating

antigen-specific and idiotype-specific cell lines — in

brief, activate the process of self tolerance. Beyond

the immunological self, there is also a "semiotic

self," which I have discussed severally elsewhere

(cf. Sebeok 1991, Chaps. 3 and 4, and 1992).

Another diacritic category of symptoms

deserves at least passing mention. A linguist might

be tempted to dub these "minus features," or

subtractive symptoms. Here belong all the numerous

varieties of asemasia (Sebeok 1976:57, 1979:58)

such as agnosia, agraphia, alexia, amnesia, amusia,

aphasia, apraxia, etc., as well as "shortcomings" like

blurred vision, hardness of hearing, numbness — in short, symptoms that indicate a deficit from some

ideal standard of "normality."

360
In any discussion of symptoms, it should be

noted that even a syndrome, or constellation of

symptoms — say, of a gastronomical character

(anorexia, indigestion, hemorrhoids) — may not add

up to any textbook disease labeling or terminology.

Ensuing treatment may, accordingly, be

denominated "symptomatic," accompanied by the

supplementary advice that the patient remain under

continuing observation. In some circumstances, "the

syndrome might be ascribed to psychologic

etiology" (Cheraskin and Ringsdorf 1973:37). What

this appears to mean is that the interpretation of

symptoms is often a matter involving, over time, a spectrum of sometimes barely perceptible

gradations, entailing a progressively multiplying

number of still other symptoms. It is also worth

remarking that, temporally, or for predictive purposes, symptoms generally precede signs, which is

to say that the orderly unfolding of evidence may be

termed prognostic.

No one at present knows how afferent neuronal

activity acquires meaning, beyond the strong

suspicion that what is commonly called the "external

world," including the objects and events postulated

as being contained in it, is the brain's formal

structure (logos). For all practical purposes, we are ignorant about how the CNS preserves any structure and assigns a meaning to it, how this process relates to perception in general, and how it induces a response. Implicit in this set of queries is a plainly

linear model: for example, that fear or joy "causes"

increased heart rate. Not only does such a model seem to me far too simplistic, but there is not even a shred of proof that it exists at all. The future of symptomatology will clearly rest with program developments using computer

techniques derived from studies of artificial

intelligence. These are intended to mime and

complement, if not to replace, human semiosic

processes, such as judgment based on intuition (in one word, abduction). Such automated diagnostic

counselors are already operational, as for example

the program termed Caduceus (McKean 1982). In the simplified example illustrated in Fig. 1, this

program "examines a patient with fever, blood in the

urine, bloody sputum from the lungs, and jaundice.

The program adds together numbers that show how

much each symptom is related to four possible

diagnoses -- cirrhosis of the liver, hepatitis,

pneumonia, and nephritis — and picks pneumonia as top contender. The runner-up in score is hepatitis.

But because hepatitis has one symptom not shared

with pneumonia (blood in the urine), Caduceus

chooses cirrhosis as first alternative. This process,

called partitioning, focuses the computer's attention on groups of related diseases" (McKean 1982:64).

[Fig. 1]

The craft of interpreting symptoms has a

significance far exceeding the physician's day-to-day

management of sickness. As Hippocrates had

already anticipated, its success derives from its psychological power, which critically depends on the

practitioner's ability to impress his/her skills on both

the patient and their joint environment (the audience

gathered in this workshop, which may consist of the

patient's family and friends, as well as the

physician's colleagues and staff). Dr. Joseph Bell, of

the Royal Infirmary of Edinburgh, attained the knack

with panache, leaving his imprint not just on clinical

practice but, famously, on the detective story,

following in the footsteps of his pupil's, Dr. Arthur

Conan Doyle's fictional realization, Sherlock

Holmes (Sebeok 1981a, Ginzburg 1983). According

to recent medical thinking, the contemporary

preoccupation with diagnosis — that is, the doctor's

perceived task, or pivotal drive, to explain the

meaning of the patient's condition — rests in the final

analysis with the doctor's self-assigned role as an

authenticated expositor and explicator of the values

of contemporary society. Disease is thus elevated to the status of a moral category, and the sorting of

symptoms had therefore best be viewed as a system

of semiotic taxonomy — or, in Russian semiotic

parlance, a "secondary modeling system."

Lord Horder's dictum — "that the most important

thing in medicine is diagnosis, the second most

important thing is diagnosis and the third most

important thing is diagnosis" (Lawrence 1982) -- must be true, because medical knowledge has risen

to the status of a means of social control.

Symptomatology has turned out to be that branch of

semiotics that teaches us the ways in which doctors

function within their cultural milieu.

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NOTE

This article has had an involuted publishing

history, which I need to record along with my

acknowledgments.

In 1982, I wrote a paper titled "Symptom" for

delivery at a Symposium on New Directions in

Linguistics and Semiotics, convened at Rice

University at the initiative of Professor Sydney

Lamb. That paper was published, in much expanded

form, in a book bearing the same Symposium title, edited by James E. Copeland (Houston: Rice

University Studies, 1984), pp. 21 1-230. A somewhat

revised version appeared thereafter in my own book,

/ Think I Am a Verb: More Contributions to the

Doctrine of Signs, pp. 45-58 (New York: Plenum

Press, 1986).

On October 19, 1992, 1 then presented, under the

new title "Medical Semiotics: The Legacy of Galen,"

at the 4th Congress of the Hellenic Semiotic Society,

at the University of Thessaloniki, Greece, by

invitation of the co-organizers, a substantially

reworked but still necessarily abridged variant based on my earlier paper. That version will be eventually

be published among the voluminous Proceedings of

the Congress.

In November, 1992, while I was both a Visiting

Professor of Semiotics at The University of Toronto

and a Senior Fellow in residence at Massey College,

I wrote the latter further elaborated version,

incorporating added materials, particularly on Galen.

I want to thank Professors Alexandras Lagopoulos

and Karin Lagopoulou for their generous hospitality

in Athens, Iracleo, and especially in and around

Thessaloniki. I would also like to record my deep

appreciation to Professor Marcel Danesi, of The

University of Toronto, for providing me with the

opportunity to lecture for a month in Ontario and

elsewhere in Canada, and to write at leisure in the

stimulating environment of Massey College.

The present version is a still further expanded

variant of my Greek Congress paper, which is to appear, due to local technical considerations, only

after much delay, in 1996 or 1997.

363
INTRODUCTION IN PHYSICS OF OPEN SYSTEMS

Main Principles. Diagnostics on the "S-Theorem" Criterion. Norm of Chaos.

Degradation and Self-Organization. Phase Transitions

Yu.L.Klimontovich

Physical Faculty

Moscow State University

117234 Moscow Ruaaia

E-mail: ylklim@hklim.phys.msu.su

(12 - 1997)

The aim of this Report to give the short representation of some ideas, methods and results of the statistical theory of

open systems.

I. PREFACE

Let us begin by quoting from the Preface to the author's Statistical Physics (Moscow, Nauka, 1982; Harwood Academic Publishers, New York, 1986) [1]: "My God! Yet another book on statistical physics!

There's no room on my bookshelves left". Such emotion are quite understable. Before jumping to conclusion,

however, it would be worthwhile to read the Introduction

and look through the table of contents. Then the reader

will find that this book is totally different from the existing courses, fundamental and concise" "The author

certainly does not wish to exaggerate the advantages of

the book, considering it as just the first attempt to create a textbook of a new kind"

.

The second step in this direction was the author's

Turbulent Motion and the Structure of Chaos (Moscow,

Nauka, 1990; Kluwer Academic Publishers, Dordrecht,

1991) [2]. This book is subtitled A New Approach to the Statistical Theory of Open Systems. Naturally, "the

new approach" is not meant the defy of course the consis- tent and efficient methods of the conventional statistical

theory of the nonequilibrium processes. "The new approach" is based on a judicious combination of "the old"

and "the new"

.

The following and the radical step was in the last author's book Statistical Theory of Open Systems. Volume I: with the subtitle A Unified Approach to Kinetic

Description of Processes in Active Systems, published

by "Yanus", Moscow 1995; Kluwer Academic Publishers, Dordrecht, 1995 [3]. Now it is almost ready the

manuscript of the following Statistical Theory of Open

Systems. Volume II: Part 1 New Approach in the Plasma

Kinetic Theory (Myth on Collisionless Plasma); Part 2

Kinetic Theory of Second Order Phase Transitions [4]. The author hopes that will be prepared and the next

book Statistical Theory of Open Systems. Volume III: Quantum Open Systems [5]. We must try to give now the answer on the question:

What means the notion "Physics of open systems?.

II. PHYSICS OF OPEN SYSTEMS

"Physics of open systems" is an interdisciplinary field of science [1-5]. Here is a brief list of key words and notions to characterize it: Chaos and Order; Open systems;

Criteria for the relative degree of order in open systems;

Norm of chaos; Degradation and self-organizing; Synergetics; Diagnostics of open systems; Semiotic control;

Constructive role of dynamic instability of atomic motion; Transition from reversible to irreversible equations;

Kinetic and hydrodynamic description of nonequilibrium

processes taking into account the structure of continu- ous medium; Nonequilibrium process in active media;

Equilibrium and nonequilibrium phase transitions; Unified kinetic description of laminar and turbulent motions;

Quantum open systems.

Certainly, many of these concepts are not at all 'new'. The purpose of "Physics of open systems" is to elaborate

ideas and methods for the integrated description of this

broad class of problems.

Open systems can exchange energy, matter, and (last

but not least) information with the environment. We

shall consider only open macroscopic systems. They are composed of many objects, constituent structural ele- ments. These elements may be microscopic, e.g. atoms

or molecules in physical and chemical systems. They

may be small but macroscopic such as macromolecules

in polymers or cells in biological structures. Due to the

complexity of open systems, they may host a variety of

structures. Dissipation plays a constructive role in the

formation of these structures. At first sight, this seems

surprising because the dissipation concept, is associated

with the attenuation of various forms of motion, energy

scattering, and the loss of information. It is extremely

essential, however, that dissipation is necessary for the

formation of structures in open systems. To emphasize

this, I Prigogine has coined the term "dissipative struc- tures" [6,7]. This comprehensive and exact term covers

all sorts of structures: temporal, spatial and time- space

structures. The latter are exemplified by autowaves.

The complexity of open systems provides an ample opportunity for cooperative phenomena to occur. In order

364
to emphasize the role of collective interactions in the formation of dissipative structures, H. Haken has introduced

the term 'synergetics', that means joint action. The objective of synergetics is to reveal common ideas, methods,

and laws in totally different fields of natural science, so- ciology, and even linguistics [8,9].

Moreover, synergetics is an area where various special

disciplines cooperate. The scope of synergetics is illus- trated by a series of books under the common title of

Synergetics published by Springer Verlag. The last issue

in this series is volume 67 [10].

Synergetics stems from thermodynamics and statistical

physics. This accounts for the word Physics being the

first in the title of this Section. Thereby, it is emphasized

that the theory of open systems is virtually based on fundamental physical laws

All systems that we are going to deal are macroscopic.

This means that they consist of a large number of ele- ments. This allows in many cases to treat such systems

as a continuous medium. Such convention change dramatically the nature of the system. In order to avoid the

potential problems, it is necessary to use a physical definition of continuous medium rather than a formal mathematical definition. This requires a concrete definition

of physically infinitesimal time and length scales in term

of characteristic parameters of system. The corresponding physically infinitesimal volume is the equivalent as a

physical "point".

III. PHYSICALLY INFINITESIMAL INTERVALS

(SCALES) OF LENGTH AND TIME IN A

RAREFIED GAS AND A RAREFIED PLASMA

[1-3,11]

A. Rarefied gas. Kinetic level of description.

Thus, a rarefied (Boltzmann) gas and a rarefied (Debye) plasma are characterized by the dimensionless density and plasma parameters:

* 1 £ = nrg«l, ^<1 (3.1) nrD

These parameters determine and the connection between infinitesimal scales Tph and lp h with the corre- sponding relaxation ("collision") parameters r = rrei and

/ = l re i of the Boltzmann gas and the Debye plasma.

We denote by Np h = nVph the number of particles

in the physically infinitesimal volume Vp h- By definition

of physically infinitesimal scales, the number of particles

within Vph is large (that is Np h ^> 1), and the scales rp h and / p h are small compared to the characteristic scales

T and L (r and / for the Boltzmann gas and the Debye

plasma)

Tph « f, lp h « L, Nph » 1. (3.2)

The definition of physically infinitesimal scales is not be

universal: it will depend on the adopted level of description on nonequilibrium processes (kinetic, hydrodynamic,

diffusion).

Boltzmann gas. The following relationships between

characteristic lengths hold for a rarefied gas:

r0 «ra„<<C/, e = nrg«l. (3.3)

The time of transition to local equilibrium is determined by the "collision time"r. The relevant length scale

is the mean free path /. So, for the kinetic stage of relaxation we set in formulas (3.2):

T->r, I-W. (3.4)

At first sight, this attempt to regard a rarefied gas as a continuous medium may seen paradoxical. To show that

this is not so, we proceed as follows.

Divide the value of r, which is average time interval

between two consecutive collisions of a given particle,

into the number Np h = nVp h- The resulting value is the

time between consecutive collisions of an single particle

contained within physically infinitesimal volume Vp h- It would be natural to take this for the definition of Tp h- Using the relationship rv h — Iph/^T for the kinetic stage

of description, we obtain two equations ,

~TT ~ -73- = Tph; Tph = . (3.5

Nph nlfh vT

Hence, making use of the definition of / and e ,we obtain concrete estimates for physically infinitesimal scales:

Tph ~ \Rt < t, lph ~ y/el < /, and Np h = -4= » 1.

(3.6)

In hydrodynamics the relaxation times are expressed

in terms of the external parameter L, and one of the

three dissipative coefficients: diffusion D, viscous fric- tion v, and thermal conductivity x- All these dissipative

processes are of diffusion type; accordingly, the "coefficient of diffusion" is represented by one of the coefficient

D, 1/, and \- Then the time of relaxation by diffusion is

L

2 td = —, whereD = D , v or^. (3.7)

For diffusion processes the linkage between physically in- finitesimal scales is given, instead the "kinetic relationship" Tp h = lph/vT, by the corresponding "gasdynamic

("G") relationship

(ig\

2

Tph = ^-^ where D = D,or ,v, or \. (3.8)

Observe, that by this definition, "traces" of diffusive

(hydrodynamic) motion are preserved also within the

365
physically infinitesimal volume Vp h - in a "point" of con- tinuous medium.

Hence, making use of the definitions (3.7), (3.8), we

obtain the concrete estimates of physically infinitesimal

scales for the gasdynamic level of description:

G

Tph ~

TP

N2/< < TD , I ph #1/5 C L, N,Ph N

2 ' 5 > 1.

(3.9)

Here we have used equation nL3 = N.

We see that, unlike the case of (3.6) for the kinetic description, now the physically infinitesimal scales depend

on the external parameter L. This is a clear indication

that the definition of physically infinitesimal scales for

the Boltzmann gas depends on the adopted level of description.

Naturally, the gasdynamic descriptions is rougher than

the kinetic one, and so the "point" of continuous medium

in hydrodynamics is larger, that is, Vph < VpG

h

. The transition from the kinetic equation to the more "rough" gasdynamic description can be made in the following manner. For this transition it is usually uses the perturbation theory on Knudsen number (methods of Hilbert,

Chapmasn-Enscog and Grad).

Kn = j

(3.10)

However, in this way we meet serious difficulties in applying the pointed perturbation theory. They are due to the fact that parameter Kn does not reflect the structure

of the "continuous medium".

Instead of Knudsen number it is more natural to use the "physical Knudsen number". For the kinetic level of

description it is defined by the expression:

KPh =

ph Iph

I

1 (3.11)

The smallness of this parameter is ensured by condition

Np h » 1. In the limit of free molecular flow -"collisionless flow",

when the characteristic length L (for instance, the diameter of pipe) is much smaller than the free path /, the approximation of continuous medium may be used

as long as

lP h < L < /. (3.12)

In the case of hydrodynamic description, the physically

infinitesimal scales are defined by expressions (3.9), and

the physical Knudsen number is

lx ph —

l ph

L

1 1/2- (3.13)

The smallness of this parameter is ensured by condition

N?h » 1-

For the unified kinetic and gas-dynamic description the

size of a "point" is defined by relations:

I ph l ph

ph

ph

(3.14)

We see that the minimum length Lmin - the minimum

size of point, for which the traces of diffusive motion are

still retained and the gasdynamic description is still feasible, is less than mean free path / and greater than the

kinetic physically infinitesimal scale lp h- So, a unified description of kinetic and hydrodynamic processes is possible in a broad range of Knudsen numbers without using

perturbation theory.

The relevant characteristic time is defined as

(r

pG

h) D

y/er Tph (3.15)

and is of the order of physically infinitesimal time interval

for kinetic description. We shall need this result for the

generalization kinetic equation for unified description of

kinetic and gasdynamic processes in rarefied gases and

plasmas.

The above obtained relationships allow making esti- mates for the number of particles within a "point":

nLi -5/4

(3.16)

Hence, at normal conditions, when e ~ 10

-4

, the number

of particles within a "point" is 7Vmin « 10 5. Rarefied Coulomb plasma (Debye plasma) For a

rarefied plasma the possibilities of the unified description

kinetic and hydrodynamic processes are more justified,

than for a rarefied gas. It is the cause due to collective

character of charged particles interaction.

For a rarefied plasma there are two possibilities for the

definition of the physically infinitesimal scales. The former is similar to one that we meet in the kinetic definition

(3.6) for a rarefied gas. However, for a plasma it is a more natural to adopt

the following definition of physically infinitesimal scales:

ph D

D ~ vjl. (3.17)

Here, as for a rarefied gas, three kinetic coefficient: dif- fusion D, viscous friction v, and thermal conductivity \ , are equal. We see that now the connection between physically infinitesimal scales is defined by the "gasdynamical

relation"

Tph

I 2

l ph_

D

(3.18)

Thus, for a rarefied plasma there is a wide region of

parameters (more wide than for a rarefied gases) for the

unified description of kinetic and gasdynamical processes

Now the role of the length Lmm plays the Debye radius.

366
The physical Knudsen number and the maximal usual

Knudsen number for a plasma the following formulas are defined as:

Kph =

l-f~r-^, (tf„) max = — = -»l- (3.19)

The last inequality opens a possibility for the unified

description of kinetic and hydrodynamic processes in a

rarefied plasma on scales L > ro. We have now enough information about the structure

of a rarefied plasma as a continuous medium in order to

construct the corresponding kinetic equations.

IV. RELATIVE ORDERING CRITERIA IN OPEN

SYSTEMS [1-5,12]

A. Degradation and self-organization in evolution

Evolution is the process of changes and development

in nature and society. Worded in this manner, it is a

very general concept. In physically closed systems, evolution in time results in the equilibrium state to which

maximum entropy and the maximum degree of chaos cor- respond.

In open systems, it is possible to distinguish two classes

of evolutionary processes:

(1) Development in time towards the nonequilibrium

stationary state

(2) Evolution via a series of nonequilibrium stationary

states of an open system. The latter process is due to

variation of the so-called control (governing) parameters.

Darwin's theory of evolution is based on the principle of natural selection. Thus, evolution can either lead

to degradation or represent a self-organization process

during which more complex and sophisticated structures

arise. Can selforganization be the unique outcome of evolution? The answer is negative because neither physical nor even biological systems display an "intrinsic drive"

towards selforganization. Therefore, evolution may also

lead to degradation. A physical example is evolution to

the equilibrium state, the most chaotic one, according to

Boltzmann.

Thus, selforganization is only one of the possible routes

of evolution. Criteria for selforganization are needed to answer the question along which route a process will develop, but such fundamental concepts as degradation and

selforganization are not necessarily to be defined. This

is very difficult to do, laying aside the ambiguity of such

definitions. Of much greater importance is the comparative analysis of the relative degree of order (or chaos) in

different states of the open system being examined. Only

such analysis can answer the question whether the open

system undergoes selforganization or degradation.

We have already emphasized the concepts of chaos and

order. Now, what distinguishes order from chaos?

There are cases when the difference between them is

clear. However, it appears from the comparison of laminar and turbulent flows that a seemingly obvious infer- ence may turn out to be incorrect. Quantitative criteria

for the relative degree of order (or chaos) in different states of open systems allow a more reliable conclusion

to be obtained.

The results of such analysis are objective and provide

additional information which constitutes the basis for the

establishment of the " norm of chaos" and helps to reveal

two- side deviations from the norm under the influence

of various impacts. In biology, for instance, all kinds of

stress may cause deviations in the degree of chaos from

the norm. Deviations on either side suggest "pathology",

i.e. represent the process of degradation.

Therefore, a statement (based on a selected criterion)

of the impaired degree of chaos does not necessarily mean

that selforganization occurs and vice versa, an increase in

the degree of chaos is not always identifiable with degradation. Such a conclusion is valid only for those physical

systems where thermal equilibrium may be taken as the

reference point for the degree of chaos. For example, in

such, an open system as a generator of electrical oscillations, the equilibrium state is that of zero feedback when

only thermal fluctuations exist in the electrical contour.

Since an organism normally functions only if a certain

norm of chaos is available, corresponding to an essentially

nonequilibrium state, the above reference point is nonexistent. This accounts for the lack of objective information about variation of the degree of chaos in biology as

well as in economics and sociology which hampers distinguishing between self-organization and degradation in

such systems.

However, another classification is equally relevant. The

norm of chaos being determined, deviations on either

side may be regarded as "pathology", i.e. degradation.

Therefore, it is possible to monitor the choice of "therapy". Here, a criterion for the relative degree of or- der is at stake again. If the 'treatment' normalizes the

state of the open system, in terms of this criterion, self- organization occurs. Otherwise, "therapy" leads to further degradation.

The difficulty in introducing the relative measure of

order (or chaos, for that matter) in open systems is in the first place due to the absence of definitions for

the initial concepts: chaos, order, degradation, and self- organization. It has already been mentioned that the definitions of these concepts are to a great extent arbitrary.

We have just noted that the transition to a more chaotic

state should not necessarily be regarded as degradation.

It is essential to consider deviations from the norm of

chaos.

In this context, it appears useful to consider the principal concepts at greater length in order to formulate the

criterion for the relative degree of order without which

the notions of degradation and self-organization actually

remain void of meaning.

367
B. Physical and dynamical chaos

Although "chaos" and "chaotic motion" are fundamental physical concepts, their precise definitions are lacking,

according to Boltzmann, motion in an equilibrium state

is most chaotic. However, motions far from equilibrium

are also called chaotic. Such is the "motion" in noise

generators intended for signals suppression.

Normally, different forms of turbulent motion in gases

and fluids are also described as chaotic, e.g. turbulent

motion in pipes which arises from laminar motion when

the pressure difference at the ends of the pipe is suffi- ciently large. It seems natural to conceive turbulent motion as being more chaotic than laminar motion. However, such a view largely stems from the confusion of the

concepts of complexity and chaos. Observation of tur- bulent motion primarily reveals its complexity, whereas

additional analysis is needed to estimate the degree of

chaos and appropriate criteria to quantify it. Of late, the concept of "dynamical chaos" has been

extensively exploited to characterize complex motions in

relatively simple dynamic systems. The word "dynamic"

implies the absence of fluctuation sources, that is sources

of disorder.

For this reason, the "dynamic system" concept is a some- what idealized one. A more real chaotic motion,

with random sources taken into account, might be called

"physical chaos". An example is the chaotic motion of

atoms and molecules in equilibrium. The mathematical

notion of "dynamical chaos" can be traced back to the

works of H. Poincare and A N Kolmogorov.

The main feature of dynamical chaos is dynamic instability of motion. It is expressed as strong (exponential)

divergence of the originally close trajectories and leads

to their mixing.

A major contribution to the investigation into the re- lationship between the dynamical and statistical descriptions of complicated motion was made by the prematurely deceased N.S.Krylov [13]. He was the first to raise

the question of the role of dynamic instability and mixing as the basis of statistical physics in his posthumously

published book Works on the Foundations of Statistical

Physics (1950).

C. Constructive role of dynamic instability of motion

Relatively simple dynamic systems can give rise to very

complicated motions perceived as chaotic. This was the reason for the introduction of such new concepts, as the

strange attractor and dynamical (or determined) chaos.

As a rule, the word "chaos" has negative connotations

in physics, biology and economics. However, the concept

of chaos is a many-faceted one. For example, life can exist

neither in complete chaos nor in perfect order. A normal

organism needs a certain norm of the degree of chaos

which can be estimated on the criterion of the relative

degree of chaos.

Given an opportunity to measure the relative degree

of chaos, the word requires no additional attributes. It is therefore appropriate to ask whether the term "dynamical chaos" is relevant. In fact, it was coined to characterize the complex states which arise from dynamic instability, i.e. exponential divergence of trajectories at a minor change of the initial conditions. However, this

term is somewhat in conflict with the fact that the tra- jectories computed from dynamic equations can be re- produced based on the initial data in a numerical experiment. Moreover, dynamic instability can play a constructive role in the physics of open systems..

Indeed, dynamic instability of motion, i.e. exponential

divergence of the trajectories leads to mixing of trajectories in phase space. This accounts for the possibility of

smoothening at physically infinitesimal scales and introducing the concept of "continuous medium" to pass from

reversible microscopic equations of motion for gas particles to irreversible kinetic and hydrodynamic equations

for macroscopic functions of the continuous medium.

In this approach, the atomic structure of a system

is taken in account to define "a point of continuous

medium". This requires that physically infinitesimal

time and length scales be defined as well as the corre- sponding physically infinitesimal volume which actually

stands for the "point" of a continuous medium.

Naturally, it is desirable that such definitions agree

with the definition of the minimum mixing region and

the minimum time for the development of dynamic in- stability.

D. Criterion for the relative degree of order.

S-theorem

Of all macroscopic functions, only entropy S possesses a combination of properties that allow it to be used as a measure of uncertainty (chaos) in the statistical description of processes in macroscopic systems.

Boltzmann gave a statistical definition of entropy for

both equilibrium and nonequilibrium (irreversible) processes and proved the famous H-theorem.

It states: The entropy of a system tending to an equilibrium state grows and remains unaltered after equilibrium is attained. According to Boltzmann, the degree of

chaos monotonically increases during evolution and has

the maximum value at equilibrium, entropy being a measure of uncertainty (chaos).

In this context, it is essential that during the evolution of a closed system to equilibrium in compliance with

the Boltzmann equation, the average energy (E) remains

constant. This means that fluctuations of energy are al- lowed. This to internal non-clossedness of the Bolt zmann

gas system. It is due to the existence of an infinite (in the

thermodynamic limit) buffer of internal degree of free- dom. Boltzmann's kinetic equation only contains a small

368
fraction of total information about the system. However,

conservation of average energy in course of evolution is not a common property of all kinetic equations.

It is only natural that the criterion for the relative degree of order needs to be universal. There is no reason it should be applicable only to a class of systems where av- erage energy is conserved during evolution. Which route

may lead to the solution of this problem?

Entropy being the sole function with the properties of a measure of chaos, there is but one option. It is necessary

to redefine entropy so that the average energy remains

constant in the course of evolution.

We shall consider the evolution of stationary states

in open systems at slowly changing governing parameters. It is for this type of evolution, that the criterion

for the relative degree of order in various states of open

systems will be introduced below. This criterion was for

the first time formulated by the author and called the

"S-theorem".

Let us consider the evolution of stationary states of an open system at a varying control parameter a. Let us further assume the existence of two states with the control

parameters a — 0 and a — a\, e.g. the stationary states of

the Van der Pol generator at different values of the feedback parameter. Of course, the description of generation

should take into account both current and charge fluc- tuations. Then, thermal fluctuations of the current and

the charge in the electrical contour correspond to the

former parameter value, when feedback is absent. The

developed generation state, with the feedback parameter

considerably exceeding the threshold, corresponds to the

latter value.

In the general case, the degree of order of the distinguished states differs, which accounts for one of them

being more chaotic than the other. Let us term it "physical chaos". As a rule, this state is nonequilibrium and

more ordered than the equilibrium state. However, in

the case of a generator with a — ao, it coincides with the

equilibrium state. Let us denote the macroscopic characteristic of the sta- tionary state as X. The role of X for a generator can be

played by the oscillation energy E. Let us further denote

the distribution functions of two distinguished states as

/o,/i and the corresponding entropy values as So, S\.

In the general case, there is no such notion as energy

for an open system and only the effective energy can be

introduced. It may just as well be termed the effective

Hamilton function and denoted as He ff. It is defined

by the distribution function of the physical chaos state

He j f = — In /o and as a rule vanishes with a change of the

control parameter. For this reason, functions substituted

by the corresponding new values /o,So , if the entropy

difference So — Si needs to be used as a measure of the

relative degree of order in the distinguished states. These

new values are determined from the equality condition

for the examined states of the average effective Hamilton

function.

When the physical chaos state coincides with the equilibrium state, as is the case with the Van der Pol generator, renormalization is carried out by substituting temperature T by the new value T. It is determined ^from

the solution of the equation which describes the equality

condition for the average effective Hamilton functions in

the two states of interest. This equation has the form:

J

Heff fo(X,a = a0 )dX = j

Hef f fi(X, a = a x )dX.

(4.1)

Given the correct choice of the 'physical chaos state',

the solution of this equation has the form:

f(a)>T. (4,2)

The sign of equality is relevant at a = ao, i.e. for the

state of physical chaos. Evidently, the state "0" should

be 'heated' to equalize average energies. As the comparison is now made at identical values of the average

effective energy, the entropy difference So, Si can serve

as a measure of the relative degree of order in the distinguished states. The renormalized distribution function may be presented in the form of the canonical Gibbs distribution:

i(j) a ,SafibMl. ( 4.3)

The corresponding expression for the BoltzmannGibbs- Shannon entropy is derived from the equation

So = -J

In (/oPO) f0 (X)dX. (4.4)

Now, let us turn back to the equation (4.1). If the

"0" state is coincident with equilibrium, its solution has

the form (4.2), with T standing for the temperature. In the general case, the "0" state, i.e. the state of physical

chaos, is a nonequilibrium one. The distribution (4.3)

includes effective temperature which is equal to unity for

the physical chaos state. Therefore, the solution (4.2)

should be written in the form

f{a) > 1. (4.5)

Here, the sign of equality also corresponds to the state of

physical chaos. However, both effective temperature and

free energy are now dimensionless. If the inequality (4.5)

is valid at control parameter values a > ao, the choice of

the condition "0" in the form of physical chaos is correct , and the relative degree of order in the distinguished states

is defined by the difference between the corresponding

entropies.

Using the expression (4.3) for the distribution function

fo(X) and the constancy condition for the average effec- tive Hamilton function, the expression for the entropy

difference may be presented as the inequality:

369
S0 -S = J

(lnijl^/xpOo^O. (4.6)

on the condition that

(He jf) = const. (4.7)

The known inequality lna > 1 — 1/a at a — /i//o is used

to derive the formula (4.6).

To summarize, the result of computing the relative

degree of order in the two distinguished nonequilibrium

states is represented by two inequalities. One (4.5) confirms the correct choice of the "0" state as presenting

physical chaos. Given the opposite inequality, physical

chaos would be represented by the state "1". The formula (4.6) provides a quantitative measure of the relative

degree of order in the distinguished states. The above calculations were made for the case of one

a parameter. When several control parameters are available, it is possible to optimize the search for the most

ordered state. Let us now apply the "S-theorem" to estimate the rel- ative degree of order upon the transition from laminar to turbulent flow.

E. Relative ordering of laminar and turbulent flows

[2,3,14]

Calculations based on the S-theorem allowed the general results (4.5), (4.6) to be specified for the case of

transition from the laminar flow in a pipe to the steady

state turbulent flow.

It will be clear from the forthcoming discussion that

laminar flow may be assumed to represent the state of

physical chaos. The role of the effective Hamilton function is played by the average kinetic energy of the laminar

flow. For the equality of this energy in both laminar and

turbulent flows to be true, the laminar flow should be

"warmed up"

:

kB Tlam = kB Tturb + j({Su) 2

) > kB Tlam . (4.8)

The temperature difference is defined by the sum of

squared diagonal elements in the Reynolds stress tensor. Reynolds' stress representing collective degrees of free- dom, the equality (4.8) may be interpreted as indicating

that a part of thermal (chaotic) motion is replaced by

the collective degrees of freedom during the transition

from laminar to turbulent flow. This justifies the choice

of the Reynolds stress tensor as the order parameter of

the turbulent flow.

The result (4.6) which in the present case defines the

relative degree of order in laminar and turbulent flows

has the form:

Til 11 T(Slam - Sturb ) = — ((Su) 2

) > 0. (4.9)

Thus, the entropy of the turbulent flow is lower than

that of the laminar one. This implies a higher degree of

order in the turbulent flow. Here, the role of the control parameter is played by the pressure difference at the

ends of the pipe. At its zero value, the fluid is in an equilibrium state characterized by the maximum degree of

chaos. This is another important example of a physical

system in which the equilibrium state is taken as the ref- erence point for the degree of chaos. One more example

is the Van der Pol generator.

When the pressure difference is other than zero, all states are better ordered. This adds weight to the argument, in accordance with what is said in Section 4.4, that

the transition from laminar to turbulent flow is an example of the selforganization process. However, this does

not mean that the degree of order grows monotonically

with increasing Reynolds number.

A higher degree of organization of the turbulent motion

compared with that of the laminar one is also apparent

as demonstrated below.

The momentum transfer between layers in a laminar

flow is mediated through a molecular mechanism which

consists in independent changes of momenta of individual

gas particles.

Conversely, in the case of a turbulent flow, the momentum transfer from one layer to another is a collective

process. It other words, individual disorganized motion

in a laminar flow changes, upon transition to the turbulent flow, into collective (hence, more organized) motion.

This results in the turbulent viscosity coefficient being much higher than the corresponding parameter for a laminar flow.

A higher degree of order in turbulent motion is also

confirmed by calculations of entropy production.

F. Estimation of the relative degree of order from

experimental data

Practical application of the S-theorem implies that the

effective Hamilton function is known. It is easy to find

provided a mathematical model of the process in question

is available. In many cases, however, there are no adequate mathematical models for open physical systems.

This problem is even more complicated as far as biological, social, and economic entities are concerned.

Therefore, it is sometimes necessary to be able to determine the relative degree of order in open systems directly from experimental data. This can be achieved in

the following way:

1. By selecting control parameters for a given system,

e.g. two states of the system with control parameters ao and ao + Aa.

2. By experimentally obtaining sufficiently long temporal realizations for the chosen values of the governing

para- meters.

X0 (t,a0 ), X(t,a0 + Aa). (4.10)

370
These data are loaded into a computer and used to construct the corresponding distribution functions:

fo(X,a0 ), f(X,a0 + Aa). (4.11)

The two distributions are normalized to unity.

Further operations are as above.

G. Diagnosis of medico-biological objects [3,12]

Let us consider some applications of the S-theorem for

the purpose of medico-biological diagnostics. Investigations into this problem were initiated in Kiev and Moscow

in 1990, using both mathematical models and experimental data. In 1994, the first results of the analysis of car- diograms based on the S-theorem were obtained by the

joint efforts of biologists and clinicians in the Laboratories of Nonlinear Dynamics at the Saratov and Potsdam

Universities.

Biological experiments reported by T. G. Anishchenko

from Saratov university revealed significant differences in

the responsiveness of male and female rats to the noise

stress. Biochemical studies have demonstrated opposite

changes in the behaviour of the two sexes. This finding

provided the basis for a study of men and women's behaviour in response to stress. The evaluation was also

made using the S-theorem.

Two cardiograms were obtained from each subject included in the study, one before and the other after identical stress impact (a shrilly acoustic signal).

Two cardiograms being available from each subject,

this allowed a change in the relative degree of order to be

individually estimated using the S-theorem. The experiment has demonstrated opposite changes in the degree of

order in men and women, the former showing a decreased

degree of chaos, while in the latter it increased.

In both cases, there was a deviation from the "norm

of chaos" suggesting "pathology". It is for physicians to

decide which "disease" is more dangerous.

The return to the "norm of chaos" may be spontaneous. Then, the "recovery" occurs unaided, with time

serving as the control parameter.

If the patient's conditions are normalized by drug therapy, its efficacy is possible to evaluate using the same

criterion.

Naturally, each doctor has his (her) own criteria unrelated to the S-theorem. However, it may be equally

useful to take advantage of the additional objective in- formation derived from the analysis of the relative degree

of order as described above.

V. WHAT IS SELF-ORGANIZATION? [12]

Two classes of systems were outlined in a previous Section.

One of them includes many physical systems exemplified in the foregoing discussion by two cases. To begin

with, it is a Van der Pol generator in which losses (of

electrical resistance) are first compensated as the feedback parameter grows while its further rise results in the

transition to the developed generation region. According

to the S-theorem, this is a case of selforganization. This

process starts from equilibrium, that is, thermal fluctuations in an electrical contour in the absence of feedback.

This leads to the conclusion that the process of selforganization may be defined as the transition from a most

chaotic (equilibrium) state to a more ordered one (generation).

The situation is similar in the transition from lami- nar to turbulent flow in a pipe with increasing pressure

difference (a higher Reynolds number).

Here, the reference point for the degree of chaos is also

the equilibrium state of a fluid in the absence of pressure

difference, that is at the zero control parameter. In this case, hydrodynamic motion is lacking and only chaotic

motion of molecules occurs. Evidently, this state is most

chaotic.

Again, the process of self-organization is the transition from a more chaotic to a less chaotic state. Is this

the universal definition of self-organization? It can be

inferred from the previous section that the process of

self-organization is not necessarily associated with an in- crease in the degree of order.

Indeed, there is a broad class of systems (in the first place, biological systems) for which neither the state of

complete chaos (thermodynamic equilibrium) nor that of

ideal order can be realized. Biological systems would not

function under such conditions.

A more fundamental notion for such systems is the

"norm of chaos" which has been used more than once in

the previous discussion. This notion is compatible with

that of "health". Then, selforganization is the process of

reconvalescence.

Now, let us turn back to the studies on the responsiveness of men and women to stress. Earlier, we have

agreed to regard post-stress conditions as "pathology".

This means that the transitions to the "norm of chaos"

in women is actually the "recovery" referred to above as selforganization, i.e. the transition from a more chaotic

to less chaotic state. Conversely, the stress-induced state for men is "illness"

which corresponds to a more ordered state. Hence, the "recovery" (self-organization)for men is the

transition from an ordered state to a more chaotic one. Thus, the concepts of self-organization and degradation in biological systems cannot be unequivocally related

to an enhanced (self-organization) or impaired (degradation) degree of order respectively.

A more fundamental notion for such systems is the

"norm of chaos" which can be estimated from empirical

data using the 'S-theorem'.

To summarize, it appears from the above analysis that

in certain cases selforganization is easy to observe, e.g.

371
the generation developing in a Van der Pol system with an increasing feedback parameter. Other well-known ex- amples are the appearance of a new structure (Benar

cells) at the liquid surface heated from below and Taylor vortices between rotating coaxial cylinders. Using the

most fortunate term "dissipative structures" coined by I Prigogine, the selforganization process may be described

as the spontaneous occurrence of structures in nonlinear

dissipative open systems, e.g. temporal dissipative struc- tures in the Van der Pol generator and spatial dissipative

structures exemplified by the Benar cells and Taylor vortices. Elimination of the control parameter (feedback,

temperature gradient, etc.) in all these cases results in a "system at rest", i.e. one in the state of thermodynamic

equilibrium.

Such understanding of the term "self-organization" underlies the theory of formation of dissipative structures. The first systematic exposition of this range of problems

has been given in the well-known book of I Prigogine and

G. Nicolis. The starting point was Prigogine's ideas on thermodynamics of irreversible nonequilibrium processes.

Haken's theory of self-organization is based on the appearance of structures due to collective interactions. In other words, cooperative processes are posited as being

of primary importance. This prompted H. Haken to use

the term "synergetics" for this new interdisciplinary field

of research. In more complicated cases such as transition from one

turbulent motion to another, in biological systems, it is possible to distinguish between the processes of degradation and self-organization based on the criterion "Stheorem" . In such cases, the understanding of self- organization as the appearance of new structures or the

transition from less to more ordered states becomes insufficient.

This inference is valid for all systems in which the

equilibrium state can not serve as the reference point

for the relative degree of chaos (or order). Here, the

"norm of chaos" concept is of greater importance and, in

the general case, certainly applies to the nonequilibrium

state, with the transition from "pathology" to "health"

corresponding to self-organization. Since deviation from

the norm is possible in two directions (towards a greater

or smaller degree of chaos), the self-organization process

may in the general case also proceed in two directions.

Therefore, the traditional definition of

self-organization as the spontaneous formation of struc- tures in dynamic nonlinear dissipative open systems is too "narrow". A more comprehensive description of self- organization processes, even their mere identification, is feasible by the methods of the statistical theory of open

systems.

The term "self-organization" is actually rooted deep

in ancient thought. This is a very interesting question

worthy of illustration by the following facts. In 1966, the book on "Principles of Self-Organization" was published in the Russian language. It is a collection

of reports delivered to a Symposium at the Illinois State

University, USA, in 1961. Here is a quotation from the

Preface to the Russian edition by A Lerner, the editor:

"Despite the marked prevalence of self-organizing sys- tems and persistent attempts of scientists to understand the phenomena occurring in such systems, self- organization has in a way remained for many centuries

perhaps the most mysterious phenomenon, the most in- timate of nature's secrets" . The Preface goes on to state:

"... the reader will hardly find here a report which would

not claim to disclose the mystery of selforganization"

.

Heinz von Foerster, the editor of the American publication, writes in the Introduction with reference to a

story by Plato, a famous Greek philosopher:

"The house of Agathon was the place where the first memorable symposium was held on the problems lying at the junction of different sciences, attended by

philosophers, statesmen, dramatists, poets, sociologists,

linguists, doctors and students learning various trades".

The report by Y. Eshby, a known expert in the field,

contains a statement to the effect that the word "self- organization" can also mean "transition ^from bad to good organization", even though the author does not

explain how to distinguish between "bad" and "good".

An approach to this problem is illustrated by the abovementioned analysis of cardiograms which allowed to dif- ferentiate between "health" and "pathology". Such a distinction is also possible based on the above criterion for

the relative degree of chaos in different states of open

systems.

Naturally, there are more diagnostic criteria to evaluate the state of biological systems. However, the comparison of different diagnostic tools is a matter which

requires special attention.

VI. PHYSICS OF OPEN SYSTEMS FOR

SOCIOLOGISTS AND ECONOMISTS

H. Haken has reported one of the earliest applications

of synergetics to sociology. The expedience of applying

synergetics for this purpose is due to the important role

of collective effects in social processes. Specifically, they

are to a great extent involved in shaping public opinion even though separate acts of choice are, by necessity, individual. A model survey of social systems was carried out

by the group of W. Weidlich who suggested simple models for the description of the formation of public opinion,

population migrations, and urbanization.

At present, methods of synergetics are extensively employed to simulate economic processes. Economics is an

ancient science with deeply rooted traditions and advanced methods of qualitative and quantitative description of various processes. Nevertheless, there is a wealth

of unresolved problems challenging the physics of open

systems to apply its methodology in this field. A substantial part of these problems is related to the

optimization of the relationships between production,

372
distribution, and consumption based on the criterion for

the relative degree of order in open (social or economic)

systems. Such an approach may hopefully provide additional information necessary to monitor the efficiency of

the assumed control parameters, to estimate the 'norm

of chaos', and to "treat the disease", that is a deviation

from the 'norm of chaos' on either side. In case of spontaneous "recovery", i.e. without interference from the outside ("medication"), "reconvalescence" may also be regarded as a self-organization process. Certainly, similar to the situation with biological

systems, the equilibrium state cannot serve as the refer- ence point in estimating the relative degree of chaos in

social and economic systems. Only the state corresponding to the "norm of chaos" may be used for this purpose.

Identification of such a state is the principal task which

can be accomplished using criteria for the relative degree

of order in physics of open systems.

A few years ago, G. Cagliotti [15], an Italian investigator, published a popular-science book under the title of

Dynamics Ambiguity. One of the first pages in the book

reads as follows: "A study of perception may reveal integrating factors. That is, originally disordered sensory

stimuli become correlated and organized in the brain into

ordered coherent structures which are then converted to a thought" . In other words, the transition from perception to idea is the transition from a less to more ordered

state of the brain.

True, this is a very beautiful picture of the birth of an

idea. The question is how close it is to reality. The book

gives no answer since it does not consider the criteria for a relative degree of order in open systems which would

allow for the distinction between 'order' and 'chaos'.

Doubtless, some information about the modulation of or- derliness accompanying the generation of an idea can be

obtained from the analysis of brain activity using en- cephalograms and the above criteria from the physics of

open systems, specifically the 5-theorem.

Such an approach implies a series of experimental studies designed to elucidate "the thought production rate",

its difference in men and women, the influence on artistic performance, etc. Naturally, joint efforts of specialists

representing different scientific disciplines are necessary

to solve such a difficult problem.

Finally, all this his brings to mind the famous book of

Erwin Schrodinger What is Life? published in English in

1944 and in Russian in 1947. We shall refer to only one

fragment directly related to the present discussion.

Very interesting statement which Schrodinger makes

in the final chapter of his book is worth citing:

"An organism's astonishing gift of concentrating "a

stream of order" on itself, and thus escaping the decay

into atomic chaos of "drinking orderliness" from a suitable environment seems to be connected with the pres- ence of the "aperiodic solid" , the chromosome molecules,

which doubtless represent the highest degree of wellordered atomic association we know of - much higher

than the ordinary periodic crystal...".

This is truly a remarkable thought, but it cannot be

considered here at greater length. Suffice it to answer the

following question: "Is the degree of order in an aperiodic

crystal higher than in an usual periodic one, in terms of

the above theory?" There is every reason to argue that

the answer must be in the affirmative!

Indeed, there is an analogy with the relative degree of

order for laminar and turbulent flows. It seems natural to

identify a laminar flow with a periodic crystal and a tur- bulent one with an aperiodic crystal. The thermal atomic

motion in periodic crystals may be assumed to represent

the state of physical chaos. Hence, collective degrees of

freedom in aperiodic crystals are of greater importance

than in periodic ones. This suggests, in conformity with

the S-theorem, a higher degree of order in an aperiodic

crystal than in a periodic one. This inference, however,

remains to be quantitatively confirmed.

VII. KINETIC DESCRIPTION OF THE SECOND

ORDER PHASE TRANSITIONS

In this part the kinetic method of physics of open sys- tem for description of phase transitions in ferroelectrics

is considered [16].

A. Kinetic equation

Let us X(R,t) is the local value of a relative displacement of crystal lattices of a ferroelectrics. In the Landau

theory for the nonsymmetrical phase it shall be play the

role of the local order parameter.

Following the Landau theory [17-20] we introduce the

effective Hamilton function. For the ferroelectrics model

the effective Hamilton function he f j for the one particle

is defined by expression [21,16]

heff = mu(l-as )+

l-bX'< (7.1)

m is the mass of atom, and ttvJq is the hardness, and

Wo is the proper frequency of the atoms vibration. The

parameter a/(T) defines the influence of the Lorentz ef- fective field on the hardness. This parameter depends on the temperature. In the region of the critical point,

following the Landau Theory this dependence is defined

by the expression

1 - af T-Tc Tr

(7.2)

Here Tc is the critical temperature.

To obtain a qualitative representation about the behavior of the system for all temperature it is possible to

represent the function aj(T) by the following expression:

1 — a.f = tanh

T-Tc AT (7.3)

373
Here AT is the "temperature width" of the transition

region.. The parameter 6 characterizes the role of nonlinearity.

For kinetic description of the second order phase transitions we shall be to use the kinetic equation for a distribution function f(X,R,t) not only internal variable X,

but also and coordinates R of bistable elements [3,4,16]:

df{X, R,t) d_

dt ~dX

df 1 dheff (X,a f ) D^dx + 7^ dx f + D

d

2 f

(7.4)

It contains two dissipative terms, which are determined

by redistribution of bistable elements in space R with the

diffusion coefficient D, and redistribution in the space

X with the diffusion coefficient D(x ), accordingly.. For

simplicity we assume lower that two diffusion coefficients are equal. The equilibrium solution of the kinetic equation for the homogeneous distribution coincides with the

Boltzman distribution

fB {x,af ,T) = exp

J- —U J—. (7.5)

The Hamilton function /i e // depends on temperatures

and, as consequence, the additional thermodynamic

"thermal force" appears:

Ftk(T) = -j dHeff

d

{T

X' T)

f(X,af ,T)dX. (7.6)

This leads to the change of the thermodynamic relations. In particular, the known Helmholtz relation has now the

form

dF(T)

dT = -SefJ (T)-Fth (T). (7.7)

Here F(T) is the Gibbs free energy , the effective en- tropy Se f / (T) for all system is defined by the Boltzmann

distribution fs {X, a,f,T).

B. Thermodynamic functions in Landau theory

In the Landau theory thermodynamic functions are defined through the most probable values Xmp, for the distribution function

Xm.p. = 0 a t > 0; Xm.p, = ±\f\r\ b a r < 0.

(7.8)

In the critical point there is a place the jump of heat

capacity:

kB T

moj 2

• (7.9)

We see, that in the Landau theory the peak of the function C(T) is absent. For the Boltzmann distribution the

heat capacity is defined not by the Boltzmann entropy,

but by the thermal force. Thus the Helmholtz relation is replaced by the following expression:

dF(xmp.,T)

dT = - Ft h{xm.p.,T), Sgff(xm. p ,T) - 0.

(7.10)

The Boltzmann entropy on this level on the description

is not taking into account.

C. The first-moment approximation. Monodomain

state

On a basis of the kinetic equation we can obtain

the chain of equations for moments (Xn

). In the self- consistent approximation, when {Xn

) = {X) n

, we receive

closed equation for the first moment (X) . In the approximation the distribution function f{X, R,t) is possible to represent in the form:

f(X,R,t,) = S(X-X(R,t,)), (X) = X(R,t) (7.11)

The kinetic equation is reduced in this case to the

reaction-diffusion equation for first moment - the function X(R,t) [20,22]:

dX{R,t)

dt

Il+bX2 (R,t)

dR?

(7.12)

It differs from the corresponding Ginsburg-Landau equation by the structure of dissipative terms.

With the help of this equation it is possible to describe, for example, the structure of domain walls in fer- roelectrics In the stationary one-dimensional state (R is parallel y) the solution is defined by the expression:

X(y) =

Tc -T

tanh y

Tc b I d'

The width of a wall is defined by the formula:

(7.13)

d = XT 2

Tr'T

kT

(7.14)

The ratio of the thickness of the wall d to the "amplitude"

at X(y — —oo) is defined by the expression

d

X(y = -oo) = {2X$bf'2 Tc -T (7.15)

At approach to a critical point this ratio increase by the

Curie law. In the critical point this solution loses sense. On the basis of the kinetic we can evaluate this ratio and

in a critical point.

374
In order to describe kinetic fluctuations, we shall use

the kinetic equation with the Langevin source. The intensity of a noise is defined by a sum of "reaction" and

diffusion terms.

By solving this linearized equation (7.12)for region T >

Tc , we get the following expression for space-time spectral

density of fluctuations SX(R, t) : m'^ JX^->m- (716)

We used here the designations for the "reaction" dissipative coefficient 7^) at T > Tc and for dispersion {(8X) 2

) for the Boltzmann distribution in Gaussian approach

7(»)

7

Tc mu/j T — Tc — Xt T-Tc

(7.17)

In the expression (7.16) on the equal rights are taking

into account both dissipative terms. In the consequence

of this the spatial density of fluctuations and the spatial

correlation functions are defined by formulas:

(5X5X) k = i ((8X)2 ) ; {5X8X) R>RI = ± {{SX)2 ) 6(R - R').

(7.18)

Thus the spatial correlation function is now not defined,

as in the Landau theory, by the Ornstein-Zernike (0-

Z) formula. The dispersion (SX8X) R=RI differs from

zero only in a volume of a point of continuous medium

(in physically infinitesimal volume Vp h), as the function

6(R— R') \jt-fti= V~h

x

. For one-point correlator ((8x) 2

) we have, in result, the expression:

1 {8X8X) R=RI = —((8X) 2

) ph

(7.19)

Here Np h = nVph is a number of particles in a physically

infinitesimal volume. Thus the dispersion of fluctuations

are smoothed on a volume of "point" is in Np h times less,

than for the Boltzmann distribution.

The 0-Z formula is connected now, not with the integral for the spectral line on frequency ui, but with a

spectral line for zero frequency u> = 0. After the integration over the wave number we get:

1 , r „ 2 Tc (8X8X)u=0,r7(x) = -{(8X)2 )

1 ' \ 2 v2 exp( ); rc = XT

-

VIII. APPROXIMATION OF THE SECOND

MOMENT. POLYDOMAIN FERROELECTRICS

Let us the system has the polydomain structure and

the first moment (X(R,t)) — 0. In this case it is more

natural to use the self-consisting approximation for the

second moments (X2m

) -- (X2

)

n = (E) which leads to the reaction-diffusion equation, but now for the function

(X2

) = (E) = E(R,t) we have the following equation:

T-Tc

(7.20)

We see that the meaning of the formula O-Z in theory

of phase transitions is changed. ' We can now to enter new correlation parameter K,

which is analog to the Ginsburg parameter Gi:

K ^

r - ( ^^rrr 1

'

. (7.21) X2m.p nr? \\T-TC \

In the kinetic theory it is possible to give the definition

for the correlation parameter for all values of temperature

(see below).

dE(R,t) , dt

' d(x) - r (^YT + bE{R' °) E(R' t]

\ + D

d

2 E{R,t)

dR?

(8.1)

The stationary solution for the homogeneous state is determined by the equation:

(X2

) +

~ / y2\ _ XT

E(R,t) = (X2 ). (8.2)

For tree selected states: X2 Tr. TT-TC (X2

) = x^

Tr-T

Tc b

(x?f)

1/2

T> Tc T = TC T<TC

(8.3)

We see that the second moment plays for the nonsymmetrical phase the role of the order parameter. In the

critical point it has a finite value. Above the critical

point the function (X2

) coincides with the dispersion for

the Boltzmann distribution.

For the calculation of fluctuations for the approximation is considered in the kinetic we can carried out the

replacement:

1 dhejj {X,a} ) m-y dX X T-Tc + b(X2 fj (8.4)

As a result the kinetic equation has the form:

df_ _d_ df ^(T -Tc dt

+ dX d(x) gr + r ^ + bE(R, 0) Xf + D

d

2 f

dR2

'

(8.5)

Together with the equation (8.2) it consists the closed

system of equations for function f(X,R,t) and average

energy E(R,t).

We shall see that there are two type of fluctuations:

"fast" and " slow " . The fluctuations of energy are fast ones. To describe its we can use the closed equation

(8.1) for energy's fluctuations. The slow fluctuations are described by the last equation with mean energy is determined by stationary equation (8.2). In this approximation the kinetic equation (8.5) can be represented in

the form:

df

dt

_d_

dX D(x) df D

+

ox (x2

) xf + D

d

2 f

dR2 (8.6)

375
The equilibrium solution is the Gaussian distribution

X2 f(X) = (2n(E))- 1/2

exp (- (8.7) 2(X2

) Now we can proceed to the calculation of fluctuations

IX. FAST AND SLOW FLUCTUATIONS AT

PHASE TRANSITIONS

The equation for the Fourier components of energy

fluctuation 5E(R,t) is:

at T{E)

(9.1)

The relaxation time is defined by the following formula

for all temperatures

1 = A{E) (k)=2T(^^ + 2b(X 2 ))+Dk2 (9.2)

T(E)

The average energy (A' 2

) = (E) is defined by the solution

of the equation (8.2).

For calculation of a slow fluctuations we shall use

the kinetic equation (8.6) with an appropriate Langevin

source. In result, the equation for a Fourier components

of the function X(R, t) has the form:

—iu +

1

T(X)

X{u,k) - y(x)(w,A;) (9.3)

with the appropriate width of a spectral line:

= A X - —jT(X) (X s

) + Dk2 = D

(l+r2

c k

2

). (9.4) (X2

)

The appropriate response on the Langevin source y[ui, k)

is defined by the expression:

and therefore

1 -^ + ^(1+^2)' (9.5)

X(x)W = 0,k = 0) =

(X2

) _ 1 (X2

) D r x2 (9.6)

All received characteristics can be determined in a critical

region for all values of temperature including and the

critical point.. Their behavior in a symmetrical phase

qualitatively same, as and in the Landau theory. In the

nonsymmetrical phase, however, its are essentially other

from known ones. The susceptibility increase on the Curie law only at approach to the critical point from the side of a symmetrical phase. At approach to critical point from the side

of low temperatures the susceptibility decrease. It give

the reason to speak about of existence of the "jump for

susceptibility"

:

X(x)\tc -t>at - X(x)\t-tc >at =

p

y2~7,

^

f

• ( 9 - 7 )

Remark, that this formula is like to the one for the jump

of the heat capacity in the Landau theory. Similar behavior of a dielectric susceptibility is observed in some

kind of ferroelectrics. Exists also and the "jump of a

relaxation time"

.

At last, the correlation radius is defined by the expression

r

2 D (X2) r x2 Dt,(X) (X2

) (9.8)

^From it follows that exists and the " jump of square of a correlation radius"

.

So, the square of r

2c > X\ for all T < Tc and, as consequence, for T < Tc the spatial coherence exists.

For slow fluctuations the Ornstein-Zernike formula also

take place only for the temporal correlator on zero fre- quency. This means, that in nonsymmetrical phase the

interaction at temperature T < Tc

is collective. This re- sult allows to enter the finite dimensionless correlation

parameter for all values of temperature.

The heat capacity at the phase transition is defined by

the formula

C(T) = ^sN^r

and in the critical point

C(T = Tc ) = \kB N-

' X2 b

(9.9)

(9.10)

We see, that now the jump of the heat capacity is equal to zero and the function C(T) is the symmetrical function

of temperature with a finite value in the critical point.

Thus, for polydomain systems the jump has a place

not for the heat capacity, but for a susceptibility and for

characteristics is connected with it. The similar behavior was pointed characteristics observe on experiments.

X. SHORT CONCLUSION

We represented here some illustration of ideas, methods and results of the modern statistical theory of open

systems - systems capable of exchanging matter, energy

and information with the surrounding world. No doubt

that the notions "norm of chaos" or "norm of order" were

introduced above allow to differentiate the degradation

and self-organization processes in Intelligent Systems and

Semiotics [23,24].

REFERENCES

376
1. Yu.L.Klimontovich. Statistical Physics (Harwood

Academic Publishers, New York, 1986); ("Nauka",

Moscow, 1982 (In Russian)).

2. Yu.L.Klimontovich. Turbulent Motion and the

Structure of Chaos (Kluwer Academic Publishers, Dordrecht, 1991); ((in Russian) "Nauka", M.,1990).

3. Yu.L. Klimontovich. Statistical Theory of Open Systems (Kluwer Academic publishers, Dordrecht, 1995);

((in Russian) "Janus", M.,1995).

4. Yu.L. Klimontovich. Statistical Theory of Open Systems. Vol. II. Part 1. Alternative approach in the Kinetic Theory of

Plasma.

Part 2. Kinetic Theory of Phase Transitions.

Manuscript.

5. Yu.L. Klimontovich. Statistical Theory of Open Systems. Vol. III. Physics of the Quantum Open Systems. (In work).

6.I.Prigogine. From Being to Becoming (Freeman, Sun

Francisco, 1980).

7.I.Prigogine, I.Stengers. Order out Chaos (Heinemann, London, 1984).

8.H.Haken. Synergetics (Springer, Heidelberg Berlin

New

York, 1978).

9 H.Haken. Advanced Synergetics (Springer, Heidelberg Berlin New York, 1983).

10. H.Haken. Principles of Brain Functioning (Springer,

Heidelberg Berlin New York, 1996).

11. Yu.L. Klimomtovich. Physics of collosionless

plasma. (Uspechi Fiz. Nauk 167 (1997) 23-55).

12. Yu.L. Klimomtovich. Relative ordering criteria in

open systems (Uspechi Fiz. Nauk 166 (1996) 1231-1243).

13. N.S.Krylov. Works for the Foundations of Statistical Physics ("Nauka" Moscow, 1950 (in Russian)).

14. Yu.L. Klimomtovich. Is turbulent motion chaos of

order? Is the hydrodynamic or the kinetic description of

turbulent motion more natural? (Physica B 228 (1996)

51-62).

15. G.Cagliotti. Dynamics of Ambiguity (Springer,

Heidelberg Berlin New York, 1992).

16. Yu.L. Klimontovich. Two alternative description of

second order phase transitions-- the Landau and the self- consistent approach. (Physics Letters A 210 (1996) 65-

70).

17. L.D. Landau and E.M. Lifshitz, Statistical Physics

(in Russian) (Nauka, Moscow, 1976).

18. H.E. Stanley, Introduction to Phase Transition and

Critical Phenomena (Clarendon Press, Oxford, 1971).

19. B. Strukov, .P.Levanuk. Physical Foundations

of Segnetoelectrics Phenomena in Cristalls ("Nauka",

Moscow, 1995 (in Russian)).

20. A. Z. Patashinskii and V.L. Pokrovskii, Fluctuation

Theory of Phase Transitions (Nauka, Moscow, 1982) (in

Russian).

21. V.L.Ginzburg. (Sov.Phys.Uspekhi, 1949, v.38,

p.490; 1962, v. 77, p. 621).

22. E.M. Lifshitz and L.P.Pitayevsky. Physical Kinetics

("Nauka", Moscow, 1979 (in Russian)).

23. M.Coombs, M.Sulcoski (Eds) Control Mechanism

for Complex Systems. Las Cruces, New Mexico, 1996.

24. A.Meystel. Semiotic Modeling and Situation Analysis (AdRem, Inc, 1995).

377
Non-Equilibrium Thermodynamics

Explains Semiotic Shapes:

Applications to Astronomy and to

Non-Destructive Testing of Aerospace Systems

Roberto Osegueda, Carlos Ferregut, Mary J. George,

Jose M. Gutierrez, and Vladik Kreinovich

FAST Center for Structural Integrity of Aerospace Systems

University of Texas at El Paso, El Paso, TX 79968, USA

emails osegueda@utep.edu, ferregut@utep.edu, mjgeorge@utep.edu,

jmgutie@sandia.com, and vladik@cs.utep.edu

ABSTRACT

Celestial bodies such as galaxies, stellar clusters, planetary systems, etc., have different geometric shapes (e.g.,

galaxies can be spiral or circular, etc.). Usually, complicated physical theories are used to explain these shapes;

for example, several dozen different theories explain why

many galaxies are of spiral shape. Some rare shapes are

still difficult to explain.

It turns out that to explain these "astroshapes" , we do not

need to know the details of physical equations: practically

all the shapes of celestial bodies can be explained by simple

geometric invariance properties. This fact explains, e.g., why so many different physical theories lead to the same

spiral galaxy shapes.

This same physical idea is used to solve a different problem:

the optimal sensor placement for non- destructive testing of

aerospace systems.

KEYWORDS: astrogeometry, semiotics, symmetry

groups, non- equilibrium thermodynamics, non-destructive

testing, aerospace structures

1. SEMIOTIC SHAPES

IN ASTRONOMY: FORMULATION

OF THE FIRST PROBLEM

From the computer viewpoint, an astronomical image is a

set of pixels of different brightness. However, astronomers

traditionally interpret these images in terms of certain ge- ometric shapes, usually, described in semiotic terms (by

words and symbols). For example, they talk about spiral or elliptical galaxies, etc. This language is very productive, because it enables astronomers to predict new results.

However, the very origin of these shapes remains somewhat

a mystery.

To be more precise, there are several dozens theories that

explain, e.g., the spiral galaxy shape (see, e.g., [2,9,10]),

but the very fact that there are so many different theories for explaining the same observations probably means

that the physical details involved in these theories are not

needed, and these shapes can follow from fundamental principles. In this paper, we show that that this is indeed the case: we

can explain these shapes by using the fundamental physical

ideas of symmetry and non- equilibrium thermodynamics.

2. MAIN PHYSICAL IDEA

The initial state of the Universe was highly symmetric. To find out how shapes have been formed, let us start from the beginning of the Universe (for a detailed

physical description, see, e.g., Zeldovich and Novikov [13]).

The only evidence about the earliest stages of the Universe

is the cosmic 3K background radiation. This radiation

is highly homogeneous and isotropic; this means that initially, the distribution of matter in the Universe was highly

homogeneous and isotropic. In mathematical terms, the

initial distribution of matter was invariant w.r.t. arbitrary

shifts and rotations.

We can also say that the initial distribution was invariant

w.r.t. dilations if in addition to dilation in space (i.e., to changing the unit of length), we accordingly change the

unit of mass.

In the following text, we will denote the corresponding

transformation group (generated by arbitrary shifts x —

x + a, rotations, and dilation x — X x) by G.

378
Dynamic equations are also symmetric. On the as- tronomical scale, of all fundamental forces (strong, weak,

etc.) only two forces are non-negligible: gravity and elec- tromagnetism. The equations that describe these two

forces are invariant w.r.t. arbitrary shifts, rotations, and

dilations in space. In other words, these interactions are invariant w.r.t. our group G.

The problem: our world should be symmetric, but

it is not.

• The initial distribution was invariant w.r.t. G;

• the evolution equations are also invariant;

hence, we will get G—invariant distribution of matter for

all moments of time. But our world is not homogeneous.

Why?

Solution: spontaneous symmetry violation. The

reason why do not see this homogeneous distribution is that this highly symmetric distribution is known to be unstable: If, due to a small perturbation, at some point a

in space, density becomes higher than in the neighboring

points, then this point a will start attracting matter from

other points. As a result, its density will increase even more, while the density of the surrounding areas will decrease. So, arbitrarily small perturbations cause drastic

changes in the matter distribution: matter concentrates

in some areas, and shapes are formed. In physics, such

symmetry violation is called spontaneous.

Non-equilibrium thermodynamics explains why

perturbations usually preserve some symmetry.

What kind of perturbations are possible? In principle, it

is possible to have a perturbation that changes the initial

highly symmetric state into a state with no symmetries at

all, but statistical physics teaches us that it is much more

probable to have a gradual symmetry violation: first, some

of the symmetries are violated, while some still remain;

then, some other symmetries are violated, etc. (Similarly, a (highly organized) solid body normally goes through

a (somewhat organized) liquid phase before it reaches a

(completely disorganized) gas phase.) At the end, we get

the only stable shape: rotating ellipsoid.

This idea leads ot an explanation of all possible

astroshapes. Before we reach the ultimate ellipsoid stage,

perturbations are invariant w.r.t. some subgroup G' of

the initial group G. If a certain perturbation concentrates

matter, among other points, at some point a, then, due to

invariance, for every transformation j G G',we will observe

a similar concentration at the point g(a). Therefore, the

shape of the resulting concentration contains, with every

point a, the entire orbit G'(a) — {g(a)\g £ G'} of the

group G' . Hence, the resulting shape consists of one or

several orbits of a group G'

3. THE RESULT OF

PHYSICAL ANALYSIS:

DESCRIPTION OF ASTROSHAPES

In view of the above analysis, to describe all possible shapes

of celestial bodies, it is sufficient to describe all possible orbits of subgroups G' of the group G (= all shifts, rotations,

and dilations). In this paper, we will show that this description really describes all known astroshapes. (Some of

these results were first announced in [3-5,6-8].)

A word of warning: geometric shapes are only approximate. Objects of nature can only approximately be

described by geometric figures. Correspondingly, in our

physical explanation, perturbations are only approximately

invariant w.r.t. G'. The farther away from the point a, the

less similar is the point g(a) to the point a. Therefore, in

reality, we may observe not the entire orbit, but only a

part of it.

Possible orbits. 0—, 1 — , and 2—dimensional orbits of

continuous subgroups G' of the group G are easy to describe:

0: The only 0— dimensional orbit is a point.

1: A generic 1—dimensional orbit is a conic spiral that

is described (in cylindrical coordinates) by the equations z = kp and p = Roexp(c<p). Its limit cases

are:

• a logarithmic (Archimedean) spiral: a planar

curve (z = 0) that is described (in polar co- ordinates) by the equation p = Roexp(cip).

• a cylindrical spiral, that is described (in appropriate coordinates) by the equations z = kip,

p - Ro-

• a circle (z = 0, p = Ro);

• a semi-line (ray);

• a straight line.

2: Possible 2-D orbits include:

• a plane;

• a semi-plane;

• a sphere;

• a semi-plane;

• a circular cylinder, and

• a logarithmic cylinder, i.e., a cylinder based on

a logarithmic spiral.

379
I

!

i

Possible orbits are exactly possible shapes. Comparing these orbits (and ellipsoids, the ultimate sta- ble shapes) with astroshapes enumerated in VorontsovVeliaminov [12], we conclude that:

• First, our scheme describes all observed connected

shapes.

• Second, all above orbits, except the logarithmic

cylinder, have actually been observed as shapes of

celestial bodies.

For example, according to Chapter III of VorontsovVeliaminov [12], galaxies consist of components of the fol- lowing geometric shapes:

• bars (cylinders);

• disks (parts of the plane);

• rings (circles);

• arcs (parts of circles and lines);

• radial rays;

• logarithmic spirals;

• spheres, and

• ellipsoids.

The only orbit-originated shape that is not in this list is logarithmic spiral. It is easy to explain why logarithmic

cylinder was never observed: from whatever point we view

it, the logarithmic cylinder blocks all the sky, so it does not

lead to any visible shape in the sky at all. With this explanation, we can conclude that we have a perfect explanation

of all observed astroshapes.

Comment: we can also explain dimcult-to-explain

disconnected shapes. In the above description, we only

considered connected continuous subgroups G' C G. Connected continuous subgroups explain connected shapes.

It is natural to consider disconnected (in particular, discrete) subgroups as well; the orbits of these subgroups

leads to disconnected shapes. Thus, we can explain these

shapes, most of which modern astrophysics finds pathological and difficult to explain (see, e.g., Vorontsov-Veliaminov

[12], Section 1.3).

For example, an orbit O of a discrete subgroup G" of the 1- D group G' (whose orbit is a logarithmic spiral) consists of

points whose distances rn to the center forms a geometric

progression: rn — ro-kn. Such dependence (called TitziusBode law) has indeed been observed (as early as the 18th

century) for planets of the Solar system and for the satellites of the planets (this law actually led to the prediction

and discovery of what is now called asteroids). Thus, we

get a. purely geometric explanation of the Titzius-Bode law.

Less known examples of disconnected shapes that can be i explained in this manner include:

• several parallel equidistant lines

(Vorontsov-Veliaminov [12], Section 1.3);

• several circles located on the same cone, whose distances from the cone's vertex form a geometric pro- j gression (Vorontsov-Veliaminov [12], Section III. 9);

• equidistant points on a straight line (VorontsovVeliaminov [12], Sections VII.3 and IX.3);

• "piecewise circles" : equidistant points on a circle; an j example is MCG 0-9-15 (Vorontsov-Veliaminov [12],

Section VII.3);

• "piecewise spirals": points on a logarithmic spiral whose distances from a center form a geometric j progression; some galaxies of Sc type are like that i (Vorontsov-Veliaminov [12]).

Not only shapes can be this explained. This idea

'

also explains relative frequency of different shapes, the di- | rections of rotation and magnetic field, possible evolution

of geometric shapes, etc. (see, e.g., [5]).

4. ALTERNATIVE EXPLANATION:

OPTIMIZATION UNDER

UNCERTAINTY AND

CORRESPONDING OPTIMAL SHAPES

There is an alternative way of analyzing the shapes, that

does not refer to physics at all, but is instead looking for

the best approximations of (unknown) actual shapes.

If we use this idea, we face the problem of selecting the best | family of images for use in extrapolation under an uncer-

| tain optimzality criterion. How can we solve this problem? | It turns out that for every optimality criterion that satisfies ! the natural symmetry conditions (crudely speaking, that

the relative quality of two image reconstructions should

not change if we simply shift or rotate two images), the

j extrapolation shapes that are optimal with respect to this | criterion can be described as orbits of the subgroups of the

corresponding symmetry group.

As a result, we get exactly the shapes used in astronomy i (such as spirals, planes, spheres, etc.) The details of this

description are given in [3,4].

5. OPTIMAL SENSOR PLACEMENT

FOR NON-DESTRUCTIVE TESTING OF

AEROSPACE SYSTEMS: THE SECOND

PROBLEM

Testing is extremely important. Structural integrity

is extremely important for airplanes, because in flight, the

380
airframe is subjected to such stressful conditions that even

a relatively small crack can be disastrous. This problem

becomes more and more important as the aircraft fleet ages.

Sensors must be placed. At present, most airplanes

do not have built-in sensors for structural integrity, and

even those that have such sensors, do not have a sufficient

number of them, so additional sensors must be placed to

test the structural integrity of a airframe.

Each integrity violation (crack etc.) starts with a small disturbance that is only detectable in stressful in-flight conditions. Therefore, to detect these violations as early as possible, we should complement on-earth testing by in-flight

measurements.

Optimal sensor placement: a problem. Sensors at- tached outside the airframe interfere with the airplane's

well-designed aerodynamics; therefore, we should use as few sensors as possible. The problem is, given the number

of sensors that we can locate on a certain surface of an airframe, what are the optimal placements of these sensors,

i.e., locations that allow us to detect the locations of the

faults with the best possible accuracy.

For future aircraft, we have a similar problem of sensor placement. The ideal design of a future airplane should

include built-in sensors that are pre-blended in the perfect

aerodynamic shape. Each built-in sensor is expensive to

blend in and requires continuous maintenance and data

processing, so again, we would like to use as few sensors as possible.

This optimality problem is difficult to formulate in

precise terms. Both for aging and for the future aircraft,

the ideal formulation of the corresponding optimization

problem is to minimize the average detection error for fault

locations. However:

• this ideal formulation requires that we know the probabilities of different fault locations and the probabilities of different aircraft exploitation regimes.

• In reality, especially for a new aircraft, we do not

have that statistics, and for the aging aircraft, the

statistics gathered from its earlier usage may not be

applicable to its current state.

Therefore, instead of a well-defined optimization problem,

we face a not so well defined problem of optimization under uncertainty. Since the problem is not well defined, we

cannot simply use standard numerical optimization techniques, we must use intelligent techniques.

Geometric approach. The problem of choosing an optimal sensor placement can be formulated in geometric

terms: we need to select points (sensor placements) on a

surface of the given structure.

To solve this problem, we use the experience of solving

similar symmetry-based geometric problems of optimization under uncertainty in image processing and image ex- trapolation (see above). Since the basic surface shapes are symmetric, a similar symmetry-based approach can be applied to the problem of optimal sensor placement. For the

simplest surfaces such as planes, cones, etc., this general

approach describes several geometric patterns that every

sensor placements which is optimal with respect to reasonable (symmetric) optimality criterion must follow.

The use of neural networks. We then use neural net- works:

• first, to confirm that these placement patterns indeed

lead to better fault location, and

• second, to select a pattern that leads to the best

results for each particular problem.

Discussion about the results. The resulting placements are different for different problems: For example,

• when we test on-earth, then our main goal is not to

miss the crack; as long as we detected it, we can al- ways perform additional measurements to determine

its location with any desired accuracy.

• In flight, however, detecting the crack is not enough;

in a fly-by-wire aircraft, we may need to adjust the

control algorithm so as not to stress the faulty surface. For that, we need to know where exactly this

fault is located.

Space structures: a similar problem. A similar problem of optimal placement of sensors for non-destructive

testing can be formulated and solved for space structures.

Acknowledgment. This work was partially supported

by NSF Grant No. EEC-9322370 and by NASA Grant No.

NCCW-0089.

6. REFERENCES

[1] Arnold, V.I. Mathematical methods of classical mechanics, N.Y.: Springer, 1978.

[2] Binney, J. "Stellar dynamics", in: Appenzeller, I., Habing, H.J., and Lena, P. (eds.), Evolution of galaxies: astronomical observations, Springer Lecture Notes in

Physics, Vol. 333, Berlin, Heidelberg, 1989, pp. 95-146.

381
[3] Finkelstein, A., Kosheleva, O., and Kreinovich, V. "Astrogeometry, error estimation, and other applications of

set-valued analysis" , ACM SIGNUM Newsletter, 1996, Vol.

31, No. 4, pp. 3-25.

[4] Finkelstein, A., Kosheleva, 0., and Kreinovich, V. "Astrogeometry: towards mathematical foundations", Inter- national Journal of Theoretical Physics, Vol. 36, No. 4,

pp. 1009-1020, 1997.

[5] Finkelstein, A., Kosheleva, O., and Kreinovich, V. "Astrogeometry: geometry explains shapes of celestial bodies", Geombinatorics, Vol. VI, No. 4, pp. 125-139, 1997.

[6] Kosheleva, O.M., and Kreinovich, V., Astrogeometry,

or geometrical investigation of forms of celestial bodies,

Technical Report, Center for New Information Technology

"Informatika", Leningrad, 1989.

[7] Kosheleva, O.M., Kreinovich, V., and Finkelstein,

A.M., "Group-theoretic approach to foundations of spacetime theory," in Proceedings of the Symposium on Global

Geometry and Foundations of Relativity, Novosibirsk,

1982, pp. 76-78 (in Russian).

[8] Kreinovich, V. Referee's comments in a review of V.

A. Dubrovin, Novikov, S.P., and Fomenko, A.T. Modern

Geometry, Moscow: Nauka, 1980, Zentralblatt fur Mathematik, Vol. 433, pp. 295-297, 1981.

[9] Strom, S.E., and Strom, K.M. "The evolution of disk

galaxies", Scientific American, April 1979; reprinted in

Hodge, P.W. (ed.), The Universe of galaxies, N.Y.: Free- man and Co., 1984, pp. 44-54.

[10] Toomre, A., and Toomre, J. "Violent tides between

galaxies", Scientific American, December 1973; reprinted

in Hodge, P.W. (ed.), The Universe of galaxies, N.Y.: Free- man and Co., 1984, pp. 55-65.

[11] Thorn, R. Structural stability and morphogenesis,

Reading, MA: Benjamin Cummings, 1975.

[12] Vorontsov-Veliaminov, B.A. Extragalactic astronomy,

Chur, Switzerland, London: Harwood Academic Publishers, 1987.

[13] Zeldovich, Ya.B., and Novikov, I.D. Relativistic Astrophysics. Part 2. The structure and evolution of the Universe, Chicago and London: The University of Chicago

Press, 1983.

382
Towards Computers of Generation Omega —

Non-Equilibrium Thermodynamics, Granularity, and

Acausal Processes: A Brief Survey

M. KOSHELEV AND V. KREINOVICH

Department of Computer Science

University of Texas at El Paso, El Paso, TX 79968

email mkosh@cs.utep.edu

ABSTRACT

Nowadays, we are using mainly computer of fourth generation, and we are designing fifth-generation computers. It

is reasonable to ask: what is the perspective? What will

the computers of generation omega look like?

• As the speed of data processing increases, we face a natural limitation of causality, according to which

the speed of all processes is limited by the speed of

light.

• Lately, a new area of acausal (causality violating)

processes has entered mainstream physics.

This area has important astrophysical applications. In this

paper, we show:

• how non-equilibrium thermodynamics makes these

processes consistent,

• how these processes can be used in computations,

and

• how the very possibility of these processes lead to the

granularity of the physical world.

KEYWORDS: computer generations, granularity,

non-equilibrium thermodynamics, quantum computing,

acausal processes

1. GENERATIONS OF COMPUTERS:

WE NEED FASTER AND FASTER COMPUTERS

No matter how fast modern computers are, there are still problems that take too much computational time and,

thus, cannot yet be handled by modern computers. To

solve these problems, we must design faster and faster computers. So far, the speed of the computers has been doubling every few years. Can we keep up with this increase?

According to special relativity, all velocities are bounded

by the speed of light; thus, to make computer elements

faster, designers try to decrease the size of these elements.

Every hardware technology eventually reaches its limit,

1. e., the smallest element size that this technology can

achieve; after that, to decrease the size further, we need

to invent a new technology. Computers that use this new

technology are usually called computers of a new generation.

The existing 4th generation computers are based on VLSI

technology. At the current speed-up rate, this technology

will soon exhaust its potential. Physicists and engineers

are therefore working on new technologies for fifth, sixth,

etc., generations of computers. Vague ideas are proposed

for technologies suitable for even further generations. (The

further generation, the more vague the ideas.)

It is therefore desirable to get a clear view of the computers

of the very distant future generations. We will call these

computers generation omega after the notation "omega"

(uj) for the first infinite ordinal number proposed by Cantor, the founder of set theory (the first consistent theory

of infinite objects).

2. COMPUTER GENERATIONS AND

QUANTUM PHYSICS: GENERAL DESCRIPTION

To get faster computers, we must decrease the size of the

elementary processing elements.

As the size of an object decreases, quantum effects become

more and more essential in its description:

383
• for macro-size objects, quantum effects are rare (e.g.,

in lasers), small, and difficult to measure;

• in chemistry (which studies molecules) quantum effects are often important;

• for elementary particles, quantum effects are so overwhelming that their non- quantum description is practically impossible.

Therefore, as the size of the computer elements decreases,

we need to take quantum effects into consideration to a

larger and larger extent.

To take these effects into consideration, we must use quantum physics. In general, a physical theory describes how

particles and fields interact in space-time. Therefore, in

the ideal quantum physical theory, particles, fields, and

space-time structures must be considered from the quantum viewpoint. In practice, the effects of their quantization is different, so, some of these quantum effects can

often be neglected:

• the largest quantum effects are related to objects

that have been known and analyzed for the longest

time, i.e., particles;

• the next quantum effects are related to newer objects: fields;

• and finally, the smallest quantum effects are due to quantization of space-time physics, physics whose ex- perimental effects are still on the edge of modern observation abilities.

The smaller the objects, the more effects we need to consider. At first, we have to use traditional quantum mechanics (also called first quantization), in which fields (and

space-time structures) are described by non-quantum for- mulas, but the particles' quantum behavior is taken into

consideration. This quantum mechanics describes atoms,

quantum chemistry, etc. Modern engineering research into

quantum dots as computer units and modern theoretical

research into quantum computing, with its exciting potential ability of solving such hard-to-solve problems as factoring large integers (see, e.g., [2,3,6,7,29,30]), is at this

quantization level.

• From the practical viewpoint, quantum dots will have

a huge potential of further miniaturizing computers,

so, if this project is successful, we will not need to worry about it for at least a few decades.

• However, from the fundamental viewpoint of a more

distant future, we need to look further.

To describe even smaller objects, we need to use second

quantization (or quantum field theory (QFT)), in which

both particles and fields are quantized, and the fully quantized theory, in which space-time is quantized as well.

3. ENTER ACAUSAL PROCESSES

In general (curved) space-time, the maximum possible

communication speed (i.e., the speed of light c) is determined by the metric tensor field gij; see, e.g., [15].

• In non-quantum theories, this field is smoothly depending on coordinates and therefore, the corre- sponding maximal speed is slightly changing in space

and time (and is practically constant for small areas).

• Quantization of space-time means, in particular, that

the metric tensor field undergoes quantum fluctuations, and, as a result, the actual maximal speed

at any given point is randomly larger or randomly

smaller than c. Since the average deviation must be

0, this means, roughly speaking, that in half of the

cases, the maximal possible speed is larger than c, and in half of the cases, it is < c.

An object of finite size is influenced by the "average" field

in the area that this object occupies.

• If the object is large enough, then the random fluctuations "average out", and the object moves as if in a space where the maximal speed is the macro-world

speed of light.

• However, if we consider much smaller objects, then

these objects can actually feel the local fluctuations.

Therefore, if this tiny object moves (and transfers information) at a maximal local speed, and this local speed, due

to a fluctuation, is larger than c, then we get a microobject

that, without violating causality, is able to transfer information at a speed v that is larger than the macro-level

speed of light c. The smaller the object, the larger this potential speed v

(it can be, actually, as large as possible).

As a result, we have an unexpected additional boost in computer performance:

• we considered smaller and smaller processing ele- ments because the smaller these elements, the faster

the computer;

• it turns out that if these elements are small enough

to take into consideration full quantum theory, then

not only their size gets smaller, but also the actual

speed of communication transfer can be made faster

than the macro-level speed of light; thus, computers

become even faster.

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4. ACAUSAL PROCESSES IN PHYSICS

AND BIOLOGY: A BRIEF HISTORY

Traditional physics is causal in the sense that future events

are determined by the past state of the Universe. This

dependence can be deterministic (as in classical, prequantum physics), or stochastic (as in quantum physics).

There have been for some time an idea of the possibility

of acausal processes, in which the influence can go in the

opposite direction: future can influence the past. Such

processes are called acausal.

The idea that the speed of all particles cannot exceed the

speed of light (and that, therefore, it is impossible to influence the past) was one of the main ideas of Einstein's

Special Relativity Theory.

In quantum mechanics, due to its probabilistic character,

many deterministic restrictions of pre-quantum physics

become somewhat "blurred" in the sense that they are no longer prohibiting some events completely, but simply

telling that these formerly prohibited events have small

probability. For example, in classical physics, a particle

cannot penetrate the potential barrier if the energy of this

barrier exceeds the initial energy of the particle; in quantum physics, however, it is quite possible (although not

highly probable) that a particle "tunnels" through this

barrier and end up on the other side of it. This is not

simply a theoretical conclusion, this "tunnel effect" is the

basis of "tunnel diodes" that are extensive used in nowadays electronics.

Uncovered possibility that quantum mechanics can make

pre-quantum restrictions "soft" lead to a possibility that

causality may also be violated in quantum processes. Such

violations were first discovered by Einstein, Podolsky, and

Rosen in their famous paradox (physicists call it EPR paradox for the first letters of the authors' names; for details, see [32]). Einstein, who was not a great fan of quantum

mechanics, proposed this paradox as a way of disproving

this theory. (It is worth noticing at this point that all experiments so far seem to confirm quantum mechanics.)

EPR paradox does not lead to a real time travel: it simply

shows that in the resulting quantum formalism, the future state influences the past one; however, all attempts to

extract a real time travel from it turned out to be futile because, crudely speaking, the resulting influence on the past

is so small that, when we try to measure it, it "drowns" in

the inevitable quantum uncertainty of measurements.

This fact does not mean that causality is true in quantum physics. In the last decade, several more sophisticated

schemes have been proposed that, in principle, can lead to

the actual time travel [33-35].

In addition to physical arguments in favor of possible

causality violations, there exist biological motivations for

such processes: Rosen [25] suggests that the living beings can use physical processes that influence the current events

depending on the future ones (he calls such acausal processes anticipatory; see also [24-28].

Until 1988, acausal processes has been mainly considered

as one the many possibilities, not the most probable possibility, and not part of the mainstream physics. In 1988, the

physicists' attitude to acausal processes changed when Kip

S. Thorne, the world's leading astrophysicist, published

several papers in the leading physical journal Physical Reviews in which he showed that within the existing quantum physics and cosmology, acausal processes are highly

probable; these publications lead to several other serious

research results [1,9,17,18,20-22,31]. As a result of this re- search, three basic types of acausal processes have been

discovered; these processes are summarizes in Thome's

monograph [32] (for more popular expositions, see, e.g.,

[4,5,12,13,19,23,36].

5. PARADOXES OF ACAUSALITY AND

HOW NON-EQUILIBRIUM THERMODYNAMICS CAN SOLVE THEM

The idea of acausal processes was, for a long time, mainly

part of science fiction, because this idea is paradoxical.

The most well known father paradox is most convincingly

described in terms of the actual time travel (travel to the

past):

The time traveler paradox occurs when a time traveler goes

to the past and shoots his own father to death before he

himself was conceived. Then:

• On one hand, the time traveler is still alive, because

he was alive before the killing, and he did not harm

himself in any way.

• On the other hand, since his father has died, he could

not have conceived the time traveler, and hence, the

time traveler cannot be born. So, he is at the same

time not alive.

A similar paradox occurs if we cannot actually travel to

the past, only influence it; also, it occurs even if we have no human beings at all, simply physical processes. The

reason why we (and other authors) present this paradox in

its time-traveler form rather that in the form of differential

equations of physics is that when we have a problem with

differential equations, there can be many reasons for that

(wrong equations, wrong method of solution, etc.), while

the time-traveler paradox reveals the paradoxical character

of acausal processes themselves.

For clarity of exposition, we will describe the current so- lution of the paradoxes of acausality on the same timetraveler example as we described the paradox itself. Of

385
course, similar to the fact that the paradox occurs even when there is no time traveler at all, the described solution is also applicable to the case of purely physical acausal

processes. This solution is described in [8,10,11,14,16].

Since the time traveler is alive at the time when he starts the shooting, this means that he was conceived after all, and therefore, that his attempt to kill his father has failed.

Why could it have failed? Well, the gun may have malfunctioned, or he might have missed, or a brick (or a meteorite)

might have fallen on the time traveler's head at the very

moment when he was ready to shoot, or a policeman of

the past has stopped him, etc. Some of these possibilities are quite realistic, some (like a meteorite) have an extremely low probability. The time

traveler can prepare for some of these possibilities: he can check his gun before going to the past, use automatic

weapons, wear a hard hat against falling bricks, a fake police uniform to prevent an interference of the past's police,

etc. In principle, whatever possibility we describe, the time

traveler can take care of it. However, he cannot take care of them all: for example, in principle, the gun can malfunction simply due to some unexpected (but probable)

random Brownian motion of its molecules.

If the time traveler takes care of all possibilities with rea- sonable (sufficiently high) probability, this still leaves other

possibilities, with extremely low probability, that normally

do not occur, but that would have to occur because otherwise, we would have a paradox.

Summarizing: if an acausal process is possible, then some

events will take place, whose probability is normally ex- tremely low to prevent this acausal influence from happening. This conclusion is true not only for a time traveler,

but for an arbitrary acausal process.

6. COMPUTERS THAT USE ACAUSAL

PROCESSES

According to the above analysis, the very possibility of an acausal process leads to the implementation of highly

improbable events. Let us assume that we have organized

such an acausal process in such a way that if we switch it on, it will lead to an implementation of a highly unprobable

event with a probability po <C 1 Let us show how this device can be used to solve a typical hard-to-compute problem of propositional satisfiability: given a Boolean (propositional) formula F{x\, . . ., xn ) with n Boolean variables x\, . . . ,xn , find the values (if any)

for which the resulting formula is true. This problem can be easily solved by trying all 2" possible combinations of n "true" and "false" values. Unfortunately, this exhaustive search becomes non-feasible even for n « 300, when

the resulting computation time exceed the lifetime of the

Universe. It is known that this problem is computationally hard (the precise term is NP-hard) in the sense that

if we can solve it in reasonable time (i.e., time bounded j by a polynomial of n), then we would be able to solve all problems from a large class (called NP) in reasonable time,

and this most computer scientists consider impossible.

To find the values X{ using acausal processes, we can set up n quantum random number generators that generate n random bits. Then, we check whether the results

x\, . .

. , xn of these bits satisfy a given formula. If they

do, these values are the desired answer; if they do not, we I switch the above-mentioned acausal process on. Nature i has two choices:

• It can generate the desired solution in the random

generators. If the formula has only one satisfying

combination of variables (out of 2"), the probability

of this event is 2 -n .

• It can also generate a vector that does not satisfy the

given formula. In this case, the switched-on acausal i process makes the nature implement the highly un- probable event, with probability poi Therefore if po <C 2~n

, it is much more probable that j Nature will prefer the first alternative.

This idea was announced in [11,14] and described in detail

in [10],

7. ACAUSAL PROCESSES LEAD TO

GRANULARITY OF THE PHYSICAL

WORLD

In the previous section, we applied the idea of acausal pro- j cesses to computations, artificially designed computations. j However, we can also apply it to nature itself.

i • In traditional causal physics, whatever initial conditions x(to) we set at the initial moment of time to, we

can always integrate the equations and end up with

the state of the Universe x(t) = F(t,x(to)) for all i consequent moments of time t > to (here, the func- >

tion F describes the dynamics of the system). In this

case, initial conditions are arbitrary and therefore, we

have a continuous set of possible states.

• If there is an acausal process present, then the initial

^ condition cannot be arbitrary: if, e.g., we have an

acausal process that transforms a part p(x(t)) of a , state at moment t into a moment of time t' < t, then, j in addition to the dynamical equation that connects

x(t) and x(t') with x(to) must have an additional t condition p(x(t)) = p(x(t')). Therefore, the initial

condition x(to) must satisfy the additional equation

p(F(t,x(to)) = P(F(t',x(t0 )).

How does an additional equation restricts the set of all possible conditions? For the case of one variable, a linear

386
equation has a single solution, a quadratic equation has,

in general, two solutions, etc. The more complicated the

equations, the more granular is the set of its solutions.

Since the dynamic equations are, usually, very complicated, we naturally expect that the additional equations

caused by acausal processed lead to a high granularity of

Universe.

8. ASTROPHYSICAL APPLICATIONS

OF ACAUSALITY

A general idea of these applications. As we have mentioned, acausal processes lead to highly unprobable events.

According to statistical physics, if Nature has a choice, it would rather prefer situations where these highly unprobable events do not occur. Therefore, if there is a random

(statistical physics-type) process that can either lead to an acausal process or not, then, the actual probability of

this process resulting in acausality is very low, much lower

that it would have been if we did not take the possibility

of acausal processes into consideration (practically, thermodynamically impossible).

In this paper, we only show this idea on one possible applications, whose description enables us to avoid technical details; other applications are also possible (see, e.g.,

[8,11]).

Example: The isotropization of the Universe. One

of the main problems of modern cosmology (see, e.g., [32])

is that the Universe is too isotropic. On large scale, in

all directions in which we look, we see the same statistical

distribution of matter. The initial state of the Universe

was, according to the modern physical viewpoint, random,

and therefore, far from being isotropic. Hence, the observable isotropization is due to some physical processes.

Many physical processes shuffle matter around and thus,

contribute to the isotropization, but calculations show that

during the lifetime of our Universe, these processes are not

sufficient to explain the current isotropy; to be more precise, for random initial conditions, the probability of the

initial conditions that lead to the observed isotropy is very

low.

The explanation of this phenomenon in acausal physics is as follows: Anisotropy means that different distant areas

of the Universe will have radically different matter densities. For acausal processes, there is no speed restriction;

therefore, since there is an excess of matter in one area and

abundance in another area, acausal processes will re-shuffle

the matter from the dense area to the area where matter

is scarce. Such a process is, as we have mentioned, thermodynamically unprobable and therefore, it is much more

possible that the random initial conditions are chosen in

such a way that prevents these acausal re-shufflings, i.e., that the initial conditions lead to the observable isotropic

Universe.

What this explanation does is shows that the probability

of an initial state of the Universe leading to isotropization, the probability that is small if we do not take acausal

processes into consideration, becomes much larger if we

consider the possibility of acausal processes.

Acknowledgment. This work was partially supported

by NSF Grant No. EEC-9322370 and by NASA Grant No.

NCCW-0089. The authors are greatly thankful to Kip S. Thorne for his inspiring talks, papers, and books, and for

his interest.

REFERENCES

[1] Allen, B., and Simon, J. "Time travel on a string",

Nature, Vol. 357, May 7, pp. 19-21, 1992.

[2] Bernstein, E., and Vazirani, U. "Quantum complexity

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i

i
SEMIOTICS OF OPEN SYSTEMS
I
'Seeing' the Battlefield through Virtual and Constructive

Simulation

Ken Hunt

Mounted Maneuver Battlespace Lab

Ft. Knox, KY 40121-5000

ABSTRACT

Determination of terrain-based decision drivers

operative in enabling the tactical commander 'to see'

the battlefield represents a critical objective for

soldier training as well as implementation of

autonomous land traverse systems. At process level,

the effort unveils obtained waypoints in the

development dynamic for knowledge evolution.

Based on manipulation of distance factors among

maneuver (combatant) elements and terrain features

in a mission execution context within a simulations

arena, an aggressive methodology is uncovered for

extracting participatory knowledge elements, and a

differentiation scheme is disclosed for realizing

(reporting) pattern-element significance applicable in

tactical decision development. A resource is suggested for detailed analysis of 'deep' decision

factors and their scheme of application in land

traverse and tactical maneuver situations.

KEYWORDS: tactical decision logic, virtual

simulation, constructive simulation, JANUS,

Distributed Interactive Simulation (DIS)

1. INTRODUCTION

To 'see' the battlefield represents a critical

capability for the tactical commander as well as,

in today's technologically advanced culture, for

autonomous systems intended to maintain pace

with or substitute for manned land traverse systems. To 'see' the battlefield is to grasp not

just the presence and location of unfolding

elements in an immediate field of view but, for

the tactical commander, to appreciate the

relevance of near and remote terrain features for

tactical advantage and identify zones of

potential action and denial areas for enemy

activity. It is to mentally prepare for emerging

events by identifying the utility of successive

terrain features to achieve reduction of risk,

extended optimization of element positioning,

and expeditious accomplishment of the mission.

The projected research explores the elements of awareness implicit in 'seeing' the battlefield

under alternative tactical conditions.

In approaching decision logic elements for

'seeing' the battlefield, the projected effort turns

to simulation capabilities for circumstance

creation and observation of battle commander

behaviors imposed during review of displayed

evolving events. In this combination, the

research discloses a methodology for using

simulation to identify 'deep significance' among

terrain details for tactical maneuver and soldier

preparation, and specifically, focuses interest on

the impact of providing virtual-simulation

terrain detail to tactical commanders and staff

during JANUS constructive-simulation exercises

(see system description below), while probing

the relevance of entity (terrain feature or tactical

element) separations for situational-awareness

during those exercises. The interaction of

JANUS constructive-simulation technology with

DIS (Distributed Interactive Simulation) virtual

simulation lies at the heart of the investigative

approach.

2. SYSTEM DESCRIPTIONS

The JANUS model is a man-in-the-loop, forceon-force, stochastic model which provides

schematic representation of the battlefield to unit staff members who control the action from

individual display consoles. Terrain

representation is limited to contour indicators

overlaying a latitude-longitude grid and shaded

with colored areas indicative of vegetation,

water, and urban development. Roads, rivers,

obstacles, and man-made features are portrayed,

as are tactical vehicle icons. Terrain elevation

profiles along single selected axes can be

displayed successively in a superimposed

window.

391
Virtual imagery at the Battlefield Distributed

Simulation - Developmental (BDS-D) facility

offers an out-the-window representation of

tactical and environmental features in a man-inthe-loop, force-on-force context. Battlefield

entities are portrayed in a contextually accurate

fashion relative to size, range, orientation,

intervisibility, and relative spatial separation.

Displayed fields of view and entity state modifications are operator controlled through

representational mechanisms reflecting actual user equipment.

Despite the JANUS capability of portraying

profile arrays along selected terrain azimuths in a superimposed display window, staff training

with such resources provides no direct view of

the relevant terrain from selected viewing points

(vehicles). This denies appropriate staff officers

terrain-use details potentially beneficial to the

operation, and limits investigation of tactical

decision logic to broad force-maneuver concerns

exclusive of terrain-characteristics-driven

tactical movement issues. Through linkage of

constructive schematic displays and virtual

tactical arrays in a mission execution context,

analysis of the 'deep significance' of

confrontational and cooperative terrain details

for tactical maneuver and soldier preparation is operationalized.

3. EXPERIMENTAL CONCEPT

Through linked virtual and constructive

simulation technologies including mannedsimulators, semi-automated force generators

(ModSAF systems), and JANUS workstations to represent an indirect-fire-supported, staff- supported mounted maneuver element

advancing toward a designated objective,

exploration of knowledge elements operative in

'seeing' the battlefield will be undertaken at the

Mounted Warfare Test Bed (MWTB), Ft Knox,

Ky. Staff officers at JANUS workstations

representing 'global' tactical events and

augmented with virtual terrain imagery

synchronized for current battlefield conditions

and provided through imagery transmissions

from manned-simulator-based maneuver

elements will direct maneuver and fire support

activities for an advancing armor force, while

vehicle commanders in manned tank-simulators

with access to schematic JANUS arrays

participate as maneuver elements. In each

exercise, the maneuver force supported by

ModSAF-generated additional support units (an

artillery firing battery) for tactical realism will

advance over European terrain as JANUS-based

staff officers (a battalion commander, an

operations officer [S3], and a fire support officer

[FSO] ) direct tactical support for the mission.

7. Tactical Context.

With poor threat intelligence, BLUFOR (i.e., the

friendly maneuver force) will advance across a

well-vegetated hilly European environment,

maintaining maximum use of concealment and

relying primarily on indirect fire (artillery) to respond at threat encounters. The remotely

located BLUFOR battalion staff will provide

axis-of-advance and fire-support information to the BLUFOR maneuver commander,

designating determined terrain advantages for route selection and indirect-fire attrition zones from provided displays. BLUFOR vehicle

commanders will fashion and execute micro- maneuvers based on JANUS and virtual

representations, disclosing across scenarios,

terrain-interpretation strategies for local maneuver demands. BLUFOR will encounter

OPFOR [i.e., opposing force or Threat] at

selected, test-directorate-controlled

BLUFOR/OPFOR distances from appointed

terrain features, to assess 'distance participation' as a contextual factor in decision logic. Interest in why an action is selected based on aggregated

'distance' factors, as opposed to how an action is performed, underlies the inquiry.

2. Execution.

Each scenario will be performed twice, once

with virtual and constructive screen- augmentation at respective locations and once

without. Training effectiveness and decision

logic will be explored under each condition in

the series of scenarios portraying alternative

inter-feature and inter-combatant distances as primary decision-drivers. Achievement of this

disclosure will be done by comparing BLUFOR

leader-directives developed with JANUS

schematics (regarded as aggregates of distances,

locations, and features), and those provided with

JANUS schematics synchronized with virtualarray 'intervention elements' descriptive, in an

'aspected' array, of spatially serial features to be

392
dealt with (disruptive [obstacles] and desirable

[concealment] ) on the represented terrain array

(battlefield). 'Seeing the battlefield', currently

addressed through relevant feature/combatant

separations, will be examined through

directorate-imposed distances among display

elements. (OPFOR elements will emerge from

selected hidden start-points under the direction

of test directorate personnel to create BLUFOR

decision circumstances consistent with study

objectives. BLUFOR display options will reflect associations of BLUFOR remoteness-to-terrainfeatures relative to OPFOR-remoteness-toadditional-[or the same] -features, and will serve

as the basis for knowledge-element

characterization effective in bringing about

commander decisions.) Performance will be

examined for the 'intervention logic' applied at the S3, the battalion commander, the FSO, and

the maneuver commander duty positions.

Training enhancements will be assessed through

performance comparisons across early and late

trials with both JANUS and JANUS-augmented

display data. With OPFOR elements reflecting

ground and air units moving along single,

multiple, and air corridors in separate events,

with various delays, distances, and locations

relative to BLUFOR, at BLUFOR threat

observation, data loggers will capture objective

data for a variety of tactical circumstances.

3. Player FunctionalityBattalion Staff. BLUFOR battalion staff personnel will direct maneuver and fire direction in geographically similar but tactically

diverse operational situations. Battalion

commanders will formulate orders positioning

friendly forces against observed threat elements

based in part on 'intervention' configurations;

S3s will fabricate traverse and kill-zone

guidelines, also from 'intervention'

configurations ('traverse logic'); and FSOs will

fashion fire support and kill-zone alternatives

again in part from 'intervention' logic. From

displays descriptive of designated distances

among terrain features and combatant forces,

staff personnel will exercise the option

(decision) to apply or bypass terrain features for

tactical advantage, and investigators will be

provided a metric (distance at which

circumstance-import changes from beneficial to detrimental) by which interpretation strategies can be specified. Early-late comparisons of

identical tactical configurations will address

training benefits associated with display

augmentation.

Vehicle Commander Operations. Maneuver

commanders serving as a platoon leader and his

'wingman' will advance using maximum

concealment (to enhance survivability) on a

designated objective in each of the tactical

scenarios. At threat observation, BLUFOR

initially will request indirect fire to suppress the

OPFOR and will maneuver to achieve terrain

advantage for a possible subsequent direct fire engagement. Commanders again will use

'intervention' details provided in virtual and

JANUS displays to select and execute micromaneuvers, and will disclose, through display

options, the relevance of pertinent distance

factors for movement decisions. This will

provide investigators additional metric insights

for interpretation strategies at the site level of maneuver operations.

4. PROJECTION

Assessment of terrain-detail significance for

tactical maneuver and soldier training through

simulation technologies and controlled

stimulation events unveils an exciting and

robust procedure for 'deep significance'

determination at multiple levels of concept

formation and in diverse operational

circumstances. Though currently structured for

distance relevance extraction in platoon

maneuvers, the present application, and each

succeeding application, essentially serves as a

solitary designation in the larger requirementsdetermination quandary for autonomous

behavior, and conveys receptivity to easy

reconfiguration, by echelon, combat activity,

battlefield resources, support activity, threat

activity, or other decision drivers, to assess distance relevance impacted by additional

factors in platoon/unit maneuvers. The

significance of abundant sub task-level decisions

which necessarily underpin mission

performance, and the importance and complicity

of seat-specific, soldier decision logic and input,

which again underlie duty performance, also are highlighted in the approach.

Given the methodology as a convincing solution

for extracting and characterizing significance/

393
meaning from observed circumstances, the

approach, through combined virtual and

constructive simulation application, ultimately

provides the critical element of authenticity to the development of significance-measures,

essentially through analysis in a mission

execution context. In capturing such measures

in this manner, a broad operational context is allowed to function as backdrop and source of

serial and spatial depth for more effective

assessment of proximal and distal significance

operators.

394
TVA's Kingston Unit 9 Distributed Control System (DCS) Retrofit

Benefit Documentation

Dennis Linkins, TVA Technology Advancement

David Lewis, TVA Kingston Fossil Plant

Rob Frank, EPPJ I&C Center

Joe Weiss, EPRI

ABSTRACT

Many utilities have been contemplating a control

system retrofit for their fossil power plants.

However, in many cases, the benefit justification

has been lacking. Consequently, EPRI and TVA

formed a tailored collaboration project to quantify

the benefits of implementing a distributed control

system (DCS) retrofit in a 1955-vintage coal-fired

power plant. TVA's Kingston Fossil Plant Unit 9

was the selected unit for the project. A

comprehensive benchmarking program was

established before the changeout and is continuing.

This paper provides a complete detailing of the

retrofit and the documentation of benefits to date.

Benefits documented to date include reduced

emissions (NOx and C02), heat rate improvement, reduced unburned carbon, improved

dispatch capability, maintenance cost reduction,

and other factors. To date, heat rate, unburned

carbon, dispatch improvements and NOx

reduction appear to be significant.

BACKGROUND

Fossil plant operation is changing. This includes

the move from base load operation to cycling

operation and meeting the emission requirements

of the Clean Air Act Amendments. Many utilities are implementing Distributed Control System

(DCS) retrofits to meet these new challenges.

Many other utilities have been seeking

cost/benefit data to justify a control retrofit. To

date, most of the economic justification for

control system retrofits has been heat rate improvement. However, a DCS should be able to

provide other benefits including improved plant

reliability/availability, improved dispatch

response, reduced emissions, salability of wastes,

and more. Additionally, since control retrofits

usually occur during an outage when other

improvements/modifications also are being

performed (e.g., turbine modifications), it has been

difficult to estimate the direct benefits from the

control retrofit. The purpose of this project was

to provide a comprehensive benchmarking of

control retrofit benefits including all potential

plant improvements. Kingston Unit 9 is a 200

MW, CE-tangential-fired, twin-furnace boiler; a

typical 1950's vintage coal-fired plant with

electric analog controls which is currently being

dispatched by Automatic Generation Control

(AGC).

APPROACH

EPRI and TVA studied the feasibility of

retrofitting all nine of the Kingston plant control

systems with DCSs. The feasibility study included

evaluating the existing instrumentation, actuators,

and plant support systems as well as the control

system. EPRI Controls Retrofit Guidelines were

used in the feasibility study. Subsequent to the

feasibility study, it was decided to retrofit only one

of the units (Unit 9) and compare the benefits of

the retrofit to the other eight non-retrofitted

units.

SCOPE OF WORK

As a result of a study, several TVA Task Teams

identified the need for a state-of-the-art control

system upgrade at the Kingston Fossil Plant.

Through a Tailored Collaboration (TC)

agreement, TVA and EPRI planned for the

395
installation of a full Distributed Control System

(DCS) for Kingston Unit 9, the I&C Center to be

established at the Kingston Plant, the installation

of a high fidelity simulator within the center for

training and advanced control system algorithm

development, and the documentation of benefits

as a result of the retrofit. Another project

deliverable was the detailed documentation of the

project benefits.

PROJECT DESCRIPTION

The project was done in three phases. The Phase

I study was performed by Gilbert Commonwealth

under contract with TVA's Fossil Engineering

Services (FES) group. Overall project

management for Phase I was provided by TVA's

Technology Advancement (TA) organization

which at the time was called Research &

Development. The objective of Phase I was to develop a conceptual state-of-the-art design basis

and cost estimate. Phase I was completed in

February 1994. The Phase I study provided a

detailed scope of work and an estimate for Phase

II. Phase II was the detailed engineering and

design of the project and procurement of the DCS

system. During this phase of the project,

specifications were prepared by the project team

for the DCS, simulator and long-lead items. The

DCS contract and a contract for design were

awarded to Foxboro. Detailed design was

performed and long-lead items were procured

during this phase. During Phase III, the DCS

upgrade was performed on Unit 9, the unit was

commissioned and testing was performed to gather

the data needed to document the benefits.

The Unit 9 controls upgrade consisted of a complete renovation of the control room and the

installation of a CRT-based control room

environment. The bench and vertical boards,

including the annunciators, were removed and the

floor openings filled. The control room was re- designed to accommodate the CRT concept. All

field sensors, actuators, and several of the valves were replaced, including field cables. Flame

scanners, high energy ignitors, and a new oil

supply system were installed to provide additional

safety and turndown capability. Secondary air

damper actuators were installed to provide the

capability to adjust the fuel-air ratio at the burner

nozzle area for NOx control. The DCS system was

designed to include network communications with

the TVA network to facilitate access to the unit

performance and statistical data from the plant

network. An EPRI Performance Monitor

Workstation (PMW) was installed to provide realtime performance evaluation for the unit. The

majority of phase III activities were completed by

the time the unit was restarted in December 1995.

The post baseline test was performed to observe

the improvements due only to the DCS upgrade.

In addition to the baseline test a series of

parametric tests were performed to begin

optimizing the unit. An experimental design was

used to determine the combinations of conditions

for NOx optimization testing.

The EPRI I&C Center was established during this

project. Construction of the I&C Center was

completed in August of 1995. The I&C Center

was dedicated on February 29, 1996. The new

simulator was available for operator training

during the Unit 9 outage for the installation of the

new controls, and all Unit 9 operators went

through a 5 week training course prior to startup.

The simulator is housed in the I&C Center

building.

PROJECT RESULTS

Listed below are the major results of the DCS

retrofit on Kingston Unit 9. These benefits were

primarily derived by two methods; baseline testing

and comparative before and after operational data.

There were three baseline test performed. The

first test performed was a true baseline in that no

retrofit work or pulverizer improvements had

been implemented prior to the test. The second

baseline was performed after extensive fuel

balancing work and pulverizer blueprinting work

had been performed. The final baseline test was

performed after the controls retrofit was

completed. The benefits listed here are the

benefits obtained solely from the DCS retrofit and

independent of other plant modifications (e.g.,

pulverizer and turbine modifications), i.e. the delta

between the second and final baseline test.

396
The heat rate has improved by 250

BTU/KWH as a result of the controls retrofit

due in part to the following:

• a 1.47% boiler efficiency

improvement

• an LOI reduction from ~ 6% to ~ 3%

• improved steam temperature controls

• a reduction in station service usage

• reduced excess air (enabled by better

02 control)

• closed loop primary air control.

This project demonstrated that this unit and

similar ABB CE units can be retrofitted with a DCS and tuned to reduce NOx emissions by

approximately 25%.

Due to tighter steam temperature controls, the

Plant Forced Outage Rate is projected to be

reduced by one forced outage per year.

This project has demonstrated that Unit 9

with the new DCS is capable of regulation at 3% per minute or better over a 50% load

range. Prior to the retrofit, Unit 9 was limited

to 1% per minute.

Improved steam temperature controls could

allow the unit to return to steam temperatures

of 1025 °F from 1000° F, while providing

greater protection from excursions and

reduced boiler and turbine damage. There are current negotiations with the plant operations

staff to raise these steam temperature

setpoints.

The unit carbon loss (LOI) was reduced from

6% down to 3% This is a measure of the

improvement in the combustion process and

the addition of primary air controls on the

pulverizers.

Startup time for Unit 9 has been reduced by at least 2 hours due to improved ignitors and lowload temperature controls.

Velocity induced wear on fuel system

components from pulverizer to burner nozzle

was reduced by 35% because of reduced

primary air flow.

The environmental emissions have been

reduced by improving the unit heat rate and

burning approximately 8,000 tons less coal

per year on Unit 9. The life of the Unit 9 has been extended by

replacing the 40 year old field cables and other

plant equipment.

PROJECT BENEFITS

The benefit details are shown in the Table 1, and

indicate the planned vs. actual benefits. Benefits

on a $/Year basis are shown. The benefits listed are based on an 80% capacity factor and a 15%

discount rate. Some of the actual cost numbers are derived from financial figures deemed confidential

by the TVA and cannot be disclosed.

LESSONSLEARNED

Listed below are the major lessons learned which

came out of this project:

1. The Project Team

This team was responsible for budget, schedule,

and overall coordination of project activities.

This project was managed much differently than

most TVA projects. A Project Team was

established and reported to the Kingston Plant

Manager. The project was managed with a site

perspective instead of the usual central office

Design Engineering approach. The Project team

selected was directly involved in preparation,

review, award and management of equipment and

construction fixed price contracts. Most members

had a strong instrument or controls background.

The Project Team approach was very successful in

controlling the project and resolving problems as they arose. The project was completed utilizing

fixed price contracts and completed on schedule

with almost no scope changes. A design package

has been completed to be used for future DCS

retrofits. This will reduce the cost considerably for

design, construction, and implementation of

similar projects in the future. The continuity of

responsibilities achieved by a single party being

responsible for design, equipment supply,

construction and startup of the unit was a very

valuable asset.

2. Plant Ownership

This project has clearly demonstrated the value of

plant involvement in every step of the project

from conception and justification to design,

397
construction, startup and benefits documentation.

The level of involvement at Kingston was from

the plant manager through the entire staff

including Trades and Labor personnel who assisted

in the checkout and startup.

3. Operations and Graphics Design

Plant operators designed the pictorial graphics

that were used on Unit 9 and the Simulator. The

use of existing operations staff to build the Data

Acquisition-type graphics fostered considerable

ownership of the project from the operations

personnel at the site. Operators were selected on

a voluntary basis for the initial start-up and

subsequent operation of the new system

Operators were encouraged to comment on

graphics being developed and suggestions were

implemented when appropriate. This gave

operators ownership and satisfaction in being part

of the "design."

4. Pulverizer Primary Air Flow Measurement

And Control

Install primary air flow measuring and control

equipment on all CE pulverizers. The cost

(approximately $ 1 2k/pulverizer on this project)

and specifications for each installation are site

specific and will require a study to determine the

technical requirements. The Unit 9 project has

demonstrated that primary air control is a major

key in the boiler optimization process.

5. Furnace 02 Balance

It was decided to try to control the 02 leaving

each furnace and the windbox-to-furnace

differential pressure using only the secondary air

dampers. This strategy has worked well

throughout the load range with no apparent

disadvantages. It is a recommendation of this

project that any ABB CE Twin-Furnace unit with

automated secondary air dampers employ this

strategy for a more steady control of 02 , better 02 balance between furnaces, and good windbox-tofurnace differential pressure control.

6. Boiler Safety/Carbon Monoxide

Monitoring

Install boiler carbon monoxide (CO) monitors on

all boilers that must optimize for NOx emissions.

CO is a better indicator of incomplete combustion

than excess 02 when operating at very low 02 levels. The unit must operate in a region that has

no margin for error.

7. Use of experimental design and model to expedite performance and NOx optimization

testing

Statistical experimental design techniques were

used to select specific test points for NOx minimization and plant optimization testing.

8. Fuel System Improvements

There were several lessons learned dealing with

pulverizer optimization. Coal pipe rifflers play a very important role in providing equal fuel

distribution to all coal pipes. Rifflers should be

checked for primary and secondary alignment,

excessive wear, and size variations which can cause flow to bypass the rifflers. All of these items

affect fuel balance and unit optimization for

emissions and efficiency control.

Tests and discussions with ABB CE experts have

confirmed that air in-leakage on Raymond bowl

mills is approximately 20 to 25%. This is normal

on all negative pressure pulverizers and should be

accounted for in the fuel/air optimization process.

During the process of optimizing pulverizer

performance to reduce LOI and improve heat rate and NOx emissions, it was pointed out that ABB

CE had recommended extending the pulverizer

classifier deflector ring to the bottom of the

classifier openings to improve 50 mesh coal

grinding. Controlled test on Unit 9 indicated that

both 200 and 50 mesh coal grinding was improved,

especially when the primary air was controlled near the correct fuel air ratio of 1.8 pounds of air to 1.0 pound of coal.

9. Improved Performance Monitoring

Package

It is recommended to install an on-line

performance monitor in conjunction with the DCS

retrofit. On this project, EPRI's Performance

Monitoring Workstation (PMW) was used and has

proven to be an effective tool for monitoring

plant performance. The monitoring software

should be configurable by plant personnel to allow

398
additions and modifications without major

expense.

CONCLUSION

10. Simulator - Training

The use of the simulator provided an excellent

tool in the training of the operators for Unit 9. The training familiarized the operators with the

new CRT man-machine interface, gave the

operators further opportunity to customize the

graphics, and identified some problems prior to

startup and enabled faster resolution of problems

during startup.

1 1 . Simulator - Engineering Uses

The simulator provided on this project is a valuable engineering tool in addition to its usefulness as an operator training system. There

are several benefits an engineering simulator can

provide to a retrofit project such as this one.

First, it can be used to verify proper operation of

the control system logic prior to the start up of

the new control system. Second, it can be used to

test proposed modifications to the control system

whether they are simple logic revisions or completely new control algorithms. Third, it can

be used to evaluate plant performance and

proposed modifications to the plant mechanical

systems.

12. Marketable Ash Product

Due to improved combustion control, the Unit 9

flyash now has low enough unburned carbon to be

a salable product.

13. Plant Wide Historian

Modern digital control and data acquisition

systems like the DCS installed on Unit 9 are capable of collecting large amounts of plant

operating data. This operating data is very

valuable in analyzing plant performance and

operating problems. It is recommended that all DCS retrofits include a comprehensive plant

archive system which can store data from not

only the DCS but also from any other plant

system which collects data.

The benefit justification for a typical DCS retrofit

has been lacking. EPRI and TVA initiated a

project to quantify the benefits of installing a new

distributed control system on a 40 year old coal

fired plant. The retrofit has been completed and

project benefits documentation is continuing. The

primary benefits to date are heat rate improvement, NOx emission reduction, and

dispatch response improvement. Evaluation of

long term benefits is continuing and will be

documented in the future.

399
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Evaluation measures for the collective intelligence of

CLOSED SOCIAL STRUCTURES.

SZUBA Tadeusz

Department of Mathematics and Computer Science, Science College, Kuwait University,

P.O. Box 5969 Kuwait, 13060 SAFAT. E-mail: szuba@mcs.sci.kuniv.edu.kw

Abstract

Different live beings are co-operating (ants, wolves, humans, etc.)

inside closed social structures, which express collective intelligence

to solve their problems. Individual beings, express intelligence for

their own purposes, as well as for their groups, even if some beings

temporarily behave illogically or even against their social structure. Such social structures solve different problems in parallel, chaotic ways. Another observed phenomenon is that some problems are

partially solved unconsciously in advance; thus when the problem

arises, the solution is almost waiting to be applied. The phenomenon

of collective intelligence, also known as swarm intelligence, can be

considered a part of semiotics because the essence of intelligent co- operation is either direct exchange of information or observation and

evaluation of the activity signs of other beings. This paper will try to define formal measures for collective intelligence based on the inferring ability of closed social structures. A social structure will be

mapped into the Random PROLOG Processor (RPP), and on this

basis, the efficiency of the N-step inference will be evaluated as the IQ for the social structure (IQS). The proposed concept of 1QS can be

developed in a formal way, as well as for practical evaluation of the given grounded structure. On a simulation base we will demonstrate

how some properties of social structures affect the value of IQS.

1. Introduction.

Let's assume that there is a given computational_space (CS)

filled with objects (agents). They take fixed positions, or per- form arbitrary movement. Some agents (interpreted as live

beings, computers, etc.) can express inferring ability; other

which are not able to do this will be interpreted as messengers

or messages. It will be demonstrated in this paper (see also [9],

[10]) that one common, formal description can be used for all

types of agents, based on the concept of the informationjnolecule (IM) and the membrane, defined for the first time for the Chemical Abstract Machine by Berry, et al. [2]. The term IM is claimed here to be more general than the term

agent because the concept of IMs of different levels, can cover

the whole spectrum of agents. A single message can be considered as an agent without a membrane and inferring ability.

To create the structure/batch of messages, it is sufficient to enclose such agents inside the membrane. The concept of the

membrane also allows us to define the independent internal

structure of an IM, other than the obligatory structure of an

exterior. The individual inferring agent can be considered as the membrane enclosing an inferring system of any nature,

consisting of IMs of e.g. facts, rules, and goals (similar to the

structure of the Expert System). This formal approach can be

continued up through the levels of social structures such as the

village, city, etc. The top level CS, filled with agents, can even

be considered a meta-IM. In general, a given IM is characterized by its inferring ability, the properties of it membrane - which define Input/Output characteristics, and its mobility.

Zero-mobility means that it takes a fixed position in the CS;

non-zero mobility must refer to the characteristic of IM

movements (e.g. chaotic movement, displacements along the

structure of streets, along data-pathways etc.). The lowest level of IM is proposed to have the form of logical, PROLOG

clauses of facts, rules, and goals. The lowest level of the infer- ence process is proposed to be the act of rendezvous of IMs

followed by a PROLOG-like inference. Higher order IMs are

suitable to model, e.g. live beings by defining the proper

membrane incorporating any internal inferring system used

for modeling behavior of, e.g. ants. Higher level social struc- tures can be defined as CS with spatial structure where any

displacements of IMs of different complexity take place. The

proposed concept of CS filled with IMs is able to model social systems of quasi-randomly moving insects e.g. ants, which

communicate through the use of pheromones. We can define

necessary (static or dynamic) spatial fields of IMs, carrying

unit clauses (atoms), corresponding to the information carried

by chemical molecules of pheromones. The insects themselves

will be higher order IMs. Also structures of biological cells in any organism/body which make contact through hormones,

can be modeled on the concept of structured IMs and membranes.

An Intelligence Quotient (IQ) based on pattern recognition

and problem solving tests can be defined for different beings,

including humans. Tests can have different parameters and

natures, that can verify certain components of intelligence. For

tests based on pattern recognition and problem solving ability

equivalent logic inferring systems can be written, able to solve a given test and to give the number of necessary inference

steps [6], [8]. As the IQ measure for closed social structures, we propose to use the N-step inference. The concept is that a given social structure will be mapped into the RPP, which will be described in the second part. In the RPP we can model or formally evaluate N-step inference process, which will provide

us an IQS measure. It is important that the PROLOG is used

as it is based on mathematical logic of 1 -order predicate calculus. The different activities and behaviors of a social system can be described through formalism of facts, rules, and goals

as an inferring system, without regard to nature of the given

401
behavior. It can be the "informal dance of the honey bee", or the output of pheromones, or a network message.

The third part of the paper will discuss N-step inference as a

Social IQ test. In the fourth part examples of mapping from

social structure to the RPP will be given, with simulations and

evaluation of IQS for some specific social structures. A simple

case will be considered where a being is approximated by a

single clause of a fact, rule, or goal. This way the effect of IQS

on certain configurations and statistical factors of closed social structures will be verified.

2. Virtual Random PROLOG Processor.

2.1. RPP Architecture.

The Virtual Processor for the RPP is defined as the CS using

the notation of Multisets [1] and cham [2]. The 0-level CS" is defined as a single IM of one PROLOG

clause c, of a fact or rule or goal. It can only undergo internal

transition. For any CS, we can define the membrane [2] denoted by I . I which encloses inherent facts, rules, and goals.

' 'p, CS° has no membrane. It is obvious that CS, ={c1 ,..r„}=jc1 ,..r^}

For the given kind of membrane its type p, defines which IMs

can pass through it. Such an act is considered as Input/Output.

If the CS also contains other CSJ it is then considered a higher

order one, depending on the level of internal CSJ

. Such internal CSj will be also labeled with v

; e.g. CS 2 = |cIv..,CS! ,...,cB |} iff cs{ = jv->M}

where b, i = \...m and c

j j = \...n are clauses

Every c, internal CS will be labeled with v

y to denote characteristics of its individual displacements. The general practice

will be that higher level CSs will take fixed positions, i.e. will

create structures, and lower level CSs will perform displace- ments. For a given CS there is a defined function pos (position) of any nature: pos: Ot -» (position descriptio n) U undefined

where Ot e CS

The following examples ofpos can be given:

pos(o,,t) = (x,y,z)

where x, y, z are fixed Cartesian co-ordinates or position at a given moment t; pos(0„M)=(Ax ,Ay ,A: ) where Ax, Ay, Az are components of the vector in 3-D space

describing the displacement of the element in the given time

period At ; pos{o„t or At)= p.(x,y,z)

where u is any fuzzy function over Cartesian space, defining

the position of a given clause or the internal CS. Obviously

there are also other possible definitions ofpos.

If there are any two internal CS objects 0„ Oj in the given CS,

then there is a defined distance function

and rendezvous distance d e 9?. We say that during the computational process, at any time / or time period At two objects

O,, Oj come to rendezvous iff

r[pos{o),po{o^<d.

The rendezvous act ® will be denoted by the relation

1 e.g. Oj ® Oj which is reflexive and symmetric, but not transitive.

The computational process for the given CS is defined as the

sequence of frames F labeled by / or At , interpreted as the

time (given in standard time units or simulation cycles), with a well-defined start and end e.g. Flfj ,...,F, . For every frame its

multiset Ff = (|c,,...,cm |) is explicitly given, with all related

specifications: pos(.), membrane types p, and movement

specifications v. The simplest case or Virtual Processor for the RPP is the 3-D

space with randomly travelling clauses of facts, rules, and

goals. Such a simple processor is initialized to start the computational process, in such a way that the set of clauses, facts,

rules, and goals (defined by the programmer) is injected into

this CS. After some time, if the proper form of goal clause is reached e.g. c, = answer(...). then v of this clause is automatically changed to provide migration to the necessary destination, e.g. to bottom of the cube. Later on, such IMs can pass through the CS membrane to the outside. In this way, the ap- pearance of the solution of the problem, anywhere in CS is observable. More advanced examples of the Virtual Processor

for the RPP are e.g. a single main CS2 with a set of internal

CS' which take fixed positions inside CS2, and a number of

CS° who are either local for a given GS,

1 (because the membrane is not transparent for them), or global for any subset of

CS) e CS2. When modeling the inference power of closed social structures, interpretations in the structure will be given for all CSTM i.e. "this CS is a message"; "this is a single being";

"this is a village, a city", etc. At the end of this section, the

importance of properly defining v for every CS'j should be

emphasized. As has been mentioned, the higher level CS'j

1 For another definition of rendezvous as the ^.-operator, see Fontana, et al [3].

402
will take a fixed position to model substructures like villages

or cities. If we model a single being (e.g. human) as CSj

then Vj will reflect displacement of the being. Characteristics

of the given v can be purely Brownian or can be quasirandom, e.g. in lattice, but from the computational point of

view, it is profitable to subject it to the present form of CS'j

With the proper characteristics of Vj , the following can be

provided:

• migration of the goal clause, when it reaches the final form

answerf...). toward the Output location. This can be a membrane of the main CS or even a specific, local CS;

• temporarily, the density of some IMs can be increased in the given area of a main CS in such a way that after the

given low-level CS'j reaches the necessary form, it migrates to specific area(s). This will significantly increase

the speed of inference.

2.2. Language of Random PROLOG.

The RPP language is elementary, but elements from attribute

grammars are necessary, as well as the redefinition of rule and

goal clause. The rule and goal clause in the RPP is an unor- dered set 5( ) of unit clauses, contrary to the standard

PROLOG, where it is the ordered list of unit clauses. Such a

set can even be considered as a local, invariable CS of rule or

fact, containing unit clauses. This approach is compatible with

the general philosophy of the RPP, and introduces additional

nondeterminism of inferences on the level of unification. In the RPP, every fact, rule, and goal is associated with two in- herited attributes: position pos and probability P of occurrence

at the given state of computations. During the simulations, the

value of certain attributes is very attractive, e.g. the probability

value that the given inference will be successfully done. Our

experiments demonstrate that in practice it is difficult or even

impossible to calculate P for more complicated cases. Only

general conclusions can be reached in a formal way. For some

simulations it will be profitable to introduce one more attribute: configuration, to define the shape and to order in any way

(linearly or even spatially) the unit clauses in the £( ). This

will provide an easy instantiation of the RPP clause to the

linearly ordered clause of standard PROLOG.

The general pattern of inference in Random PROLOG generalized for any CS has the form:

CS'j ® CSf , ; rendezvous exists

U( CS'j , CS* ), ; check unification

C(one or more CSTM of conclusion) ; check if satisfiable

" h K( CS'j or CSt )

; retract parent IM if necessary.

In general, successful rendezvous can result in the birth of one

or more child IMs. All of them must then fulfil a C( ) condition; otherwise they are aborted. Because our system is based on inferring in logic, the symbol of reaction -> used in cham

semantics is replaced with |- (inference)

Our proposed implementation of the RPP is tuned to evaluate

the inference power of closed social structures. It was necessary to make some simplifying assumptions. Rendezvous and

direct inference between two CS'j if i>\ will be left for

further research. Thus this paper deals with a single CS' as the

main CS only. The example of multiple lower level subspaces

CS' and clauses CS° existing, being displaced, and inferring in a given higher level CS2 makes it possible to model multiple

beings H, performing internal inferences (in their brains),

independently to higher level, co-operative inferences inside

CS2 and exchange of messages of type CS°.

It is also important to assume that the results (products) of

inference after this are not allowed to infer between themselves. Products of inference must immediately disperse; however, later on, inferences are allowed - if they rendezvous.

Now, let's discuss the example type of inferences between

clauses, when the rendezvous takes place.

Inference: fact with rule

a(l) . ® answer(Y) :- a(X),

(fact) (rule) greater (X, 0),

sum(X, 5, Y)

retract ( a (X) . )

assert

message ( "molecule a(X). killed").). |- answer ( 6 )

. (logical result)

Therefore, after the rendezvous the following processing takes

place:

step 1: matching;

unification of clauses a ( 1 ) and a (X) => {X71

}

step 2: evaluation

logical evaluation of greater (1, 0) => True numerical calculation of sum (1, 5, Y) => True

step 3: retract and assert control actions:

retract one parent; fire the message molecule into the RPP;

step 4: child molecule is produced

logical expression (parent rule) reduces to unit clause i.e.

fact answer (6) . (because there are no evaluations into

False and all built-in predicates are executed successfully).

An IM answer (6) . can be considered a legal child. The

message molecule is the "background child".

The syntax of a PROLOG dialect used for RPP resembles a simple PROLOG. Nevertheless, a quite different execution

model yields new possibilities of inference diagrams, as well

as creating new demands for built-in clauses, especially for

control clauses. In the standard PROLOG execution model

(e.g. WAM) we are restricted to backward inference, starting

403
from a goal [4], [5], [7], [11]. The nature of the RPP is ran- dom or quasi-random, with parallel rendezvous of IMs carry- ing clauses, so it is obvious that it is possible to implement more inferring diagrams between facts, rules, and goals. We

can have backward, forward, and aggregated inferences (i.e. rule with rule) at the same time.

Remarks:

• simulation experiments for the N-step inference have demonstrated the power of a rule-rule inference diagram. Rules

infer together building "aggregates" which are more powerful rules (observed also in GAMMA [1]). As a result,

suddenly the final solution can be generated on the basis of

e.g. a starting fact and such an aggregated rule;

• in the RPP when a clause is produced in the form an- swer (...), parameter Vj is changed in such a way that

this IM moves toward assumed Output of the RPP;

• there is no restriction on how many copies of a given fact or rule or goal we can have in the RPP. This is a very useful tool to speed up some inferences.

3. N-STEP INFERENCE FOR IQS MEASURE.

The basic question is to find proper IQ tests for closed systems

HS of beings H. Different beings express intelligence through

different actions: e.g. ability to find a path in a maze. It can be

expressed as inferences, in a similar way as we simulate intel- ligence of Human through structure of Expert Systems. The

number of inferences per given period of time as the IQS test

is not sufficient. It is easy to find examples of situations when

the frequency of inferences is high, but the desired final conclusion is not reached at all (e.g. infinite loops). The benchmark which is proposed in this paper is the N-step inference

(NSI). It can be defined as follows:

Definition: N-step inference (NSI)

There is a given 1 -level CS CS1 = |c,,...cn | such that the

following are defined

• D^pos^O,}, po^Oj jj —> 9? and rendezvous distance

d;

• v j = \...n i.e. characteristics of random displacements;

• in CS1 = (c,,..,.cn ] there exists a subset of clauses (one

fact, some rules, one goal) of the form

{a0 , ax

: -a0 , a2 :-<*,, ...,a„ : -an_x }. The number of

copies of selected Cj is one, to make the benchmark more

rigorous.

• The IQS is measured by the probability P that after m

frames F, the conclusion a„ will be reached, from starting

fact a0 . This is denoted IQS = Pnlstep

""

. If we use experimental evaluation, then the average number of frames m

is given2

, after which a„ is reached.

Justification for this benchmark is as follows.

1 . N-step inference can be very broadly interpreted as:

• any problem-solving process in HS or inside a single H,

where N inferences (logical or computational steps) are necessary to get a result;

• any production process, where N-technologies/elements

have to be found in HS and unified into one final technology or production etc.

2. Simulating N-step inference in the RPP, we can model the

situation in a very natural way, where the resources for in- ference (represented by starting fact, rules, goal) are dissi- pated, moving, (or locally concentrated) around the CS.

This reflects well dissipated, moving, or concentrated re- sources in the village, city, or nation;

3. With this benchmark very easy cases can be simulated

where some elements of the inference chain (missing facts,

rules) are not available at the moment. This means that the

chain of inference is temporarily broken, but after a certain

time period, another inference process (e.g. which is run- ning in the background or parallel) will produce the missing component. Such situations are well known in Human

Systems, e.g. when a given research or technological dis- covery is blocked until missing e.g. theorems or subtechnology is discovered/produced/found.

4. HS of Humans infer in all directions i.e. forward (e.g.

improvements of existing technology), backward (e.g.

searching how to manufacture given product going back

from the known formula) and also through generalization,

e.g. two or more technologies can be combined into one more general and powerful technology or algorithm. Nstep inference simulated in the RPP reflects all these cases very well.

4. Evaluating the inference power of

closed social structures.

Now let's investigate with the help of the proposed IQS

benchmark some very simple problems referred to within the

HS. Phenomenon 1: City

Suppose that a CS is given, and IQS is a 10-step inference.

Let's analyze how the speed of NSI is affected, if the city is defined in the CS as any privileged area. It is difficult to define what the city really is even for humans; thus the simple

intuitive concept is applied for these experiments, where the

HS consists of a highly populated area (city) surrounded by a lowly populated region. For our experiment we define city as

2 In computer simulations, every frame F corresponds to one

cycle of recalculation of situation in CS.

404
the local CS c CS with a fixed position at (0,0,0), and

the radius R = 0.2 while the whole CS is the cube lxlxl.

The membrane for CS' is defined in such a way that IMs after entering the (city) CS' must stay there for a period of a fixed

number of cycles I (the membrane will reflect back into the

city all molecules staying there fewer than presumed number

of cycles), and after this period the IM is allowed to depart

through the membrane to the outside. In the city, the properties of random walking should be different; thus, the variance

of Gaussian distribution of speed is set to v = R 1 2 (half of

city radius R). The city will speed up the NS1 in a surprising

way, what is demonstrated in Table 1. The conclusion from

the simulations confirms what looks trivial and obvious to us:

that the existence of the city is profitable outside of any dis- cussion, at least from the speed of inference point of view.

Now with the RPP and NSI we have tools to analyze this phenomenon, and immediately we can raise the following analytical problems:

• the optimal size of the city as the function of population

size, d, location of the city in CS, parameters of movement

of IMs, etc.;

• the better option for HS: a single city or a structure of cities

- which type of cities is optimal?;

• how far the city will reduce the v (which can be recalculated into energy savings in structures of beings) if the city

is introduced, assuming the same NSI speed as before;

• etc..

Rendezvous distance d = 0.025 ; Size of CS: 1 x 1 x 1

size of CS' : sphere at (0,0,0) R = 0.2 ; Brownian movements: Gaussian distribution ! with variance v=0.124, u=0;

NSI=10-step inference;

CS without City with City

(50 cycles

inside)

Conclusion reached after cycles 17643 1436

Final number of IMs in CS 69 74

Table 1 Influence of City to speed of NSI

Phenomenon 2: Ability to travel/communicate

The average global speed of molecules (vglohal j can be easily

interpreted as the average ability to travel and to communicate. If we want to simulate the ability to communicate (exchange information), it is necessary to introduce a special type

ofIM M, where M * H interpreted as the messages H -> it . By

definition M has very high (compared to being) ability to

travel i.e. (v M)» (vH ). As a result, the (vgto6a/ )will

increase in the CS simulating given HS to a high level. In the

HS systems with restricted communication abilities, the

(v

g/ofto/) w'" t>e mucn lower because the (v H } component

will prevail. Let's investigate this problem with the help of a simulation of

NSI = 10-steps in the simple CS (without the city). The exis- tence of the city highly compensates for the lack of ability for distance travelling or remote exchange of information, because

"everything is nearby".

The general conclusion that higher (v) gives higher speed of

NSI (see Table 2.) is not very revealing, but with the RPP

model of computations we can evaluate this conclusion toward

practical applications e.g.: "how introductions of the remote communication system e.g. telephone system, affect speed of inference measured with the

help of NSI in the given HS". Statistical data like "the number

of trips and the average distance per human per year", "the

number of telephone calls and the average distance of the call per person per year" should be easily available;

Rendezvous distance d = 0.025 ; Size of CS: lxlxl;

no City

Brownian movements: Gaussian distribution with u=0;

NSI=10-step inference;

variance

Conclusion reached

after cycles

Final number of IMs in CS

<-> =

0.124

17643

69

0.062

28265

44

(v) =

0.031

45029

97

Table 2 Influence of average speed (v) to speed of NSI.

Phenomenon 3: The problem of Opposition, (ability

to infer in logically inconsistent environments).

One of the phenomenon of Social Structures HS is opposition.

It can be any action of being(s) with individual interest di- rected against the global interest of HS. It can be also unconscious wrong doing of being(s) (caused by the lack of necessary information), or even technical failure/accidents. With

help of mathematical logic we can express such a situations

with an inconsistent inferring system. Simple case of opposition doing can be expressed in such a way that negated conclusions are made in parallel to correct ones e.g. in different

areas of CS. Rules a=>b ; a=>-.b can be used to get contradictory results. Another possibility is that if the global interest of HS is to reach a given goal as soon as possible, through a given chain of inference, some being(s) H will always go back

to reverse/obstruct these inferences. In the Fig. 1 IL loops

represent such a situations. In our simulations, for compensation purposes it has been be assumed that favorable events also

exist in the inference process, marked with J, to model situations where some conclusions have been done "way ahead". It

405
is interesting to demonstrate, that chaotic inferring systems can exist and work well, even with opposition, but under the

condition that stabilizing measures are applied to reduce comj

i] v r \

—>.•<

-,a,

fact

a.

.IL

1L IL

IL

a,

a,

- a*

a,

a,

a,

goal

Fig. 1 . System with infinite loops and inconsistent inferences.

binatorial explosions of inferences. This is also the genera

problem of other inferring systems, when incorrect heuristics are applied. Systems HS with opposition can't exist at all without introducing tough stabilizing measures to control the

number of IMs. The alternative is immediate combinatorial

explosion and "death" of any such inferring system. The simplest proposal to reduce the combinatorial explosion is based on the assumption that every new conclusion will retract an

old one (e.g. parent(s)); which can be freely interpreted in real

life as exchange of generations of beings. The problem of

inferences a=>b; a=>-ib can be stabilized in such a way that when there are rendezvous of IMs like b ®—-ib, the result

will be retraction of both. The following rule can be used:

retract ( X(Y) . ) , retract (-iX(Y) . ) :- molecule (X(Y) .

) , molecule (-.X (Y) . ) .

In Fig. 1 . the main point of interest are infinite loops caused

by certain types of opposition inside HS, and how effective the

proposed stabilizing measures are. Thus the negative infer- ences i.e. a=>-ib are left dangling.

Size of CS: lxlxl; rendezvous distance d -= 0.025 ;

; no City

Brownian movements: Gaussian distribution with u.=0; (v>= 0.124

NSI=10-step inconsistent inference;

Conclusion reached after cycles 25436

Final number of IMs in CS 108

Table 3. Influence of opposition inferences to speed of NSI.

5. Conclusion

This paper presents the concept of Intelligence Quotient IQS

for Social Structure, of any nature. As the theoretical base, the

chaotic, molecular model of computations has been used - which can be considered as implementation of the NonDeterministic Turing Machine. For programming purposes, a dialect of the PROLOG is used, because the logic of predicate

calculus gives the best chance to describe any different behaviors inside social structures which can be considered as infer- ring processes. The simulation system has been built in parallel C for an 8-processor SGI computer, with 3-D graphics to observe chaotic parallel inferring processes. With this tool our

simulations were implemented. The presented research results give clear directions for future research and intended commercial application:

• Different HS can be compared for their IQS values and

ordered, both theoretically and through simulations;

• How certain social, political and technical factors affect the

IQS can be analyzed for a given HS;

• The proposed approach gives a way to define a formal

theory of IQS for HS;

• Further studies are necessary on the methodology of, how

the behavior of some non-Human beings (bees, ants etc.) should be translated into facts, rules, and goals, which subsequently could be used for IQS evaluation.

6. References

[I] Banatre J-P., Le Metayer D.: Programming by multiset

transformations. Communications of the ACM. Jan. 1993.

[2] Berry G., Boudol G.: The chemical abstract machine.

Theoretical Computer Science. 1992. p. 217-248.

[3] Fontana W., Buss L. W.: The arrival of the fittest - toward

a theory of biological organisation. Bull. Math. Biol. 56, 1994

[4] De Kergommeaux J. C, Codognet P.: Parallel logic pro- gramming systems. ACM Computing Surveys. September

1994.

[5] Kogge P. M. : The architectures of symbolic computers.

McGraw Hill. 1991.

[6] Laurie J-L.: Problem solving and Artificial Intelligence.

Prentice Hall 1990.

[7] Newmarch J. D.: Logic programming in PROLOG and

stream parallel languages. Prentice Hall 1990.

[8] Sternberg R. J.: Beyond IQ. Cambridge University Press,

1988.

[9] Szuba T.: Random parallelisation of computations in the

Random PROLOG Processor. Journal of Kuwait University.

Topical Issue No 1. 1996.

[10] Szuba T., Stras A.: On evaluating the inference power of

closed social structures with the help of a Random PROLOG

Processor. PAP'97 "Practical Application of PROLOG". 21-24

April, 1997 London

[II] Takeuchi A.: Parallel logic programming. Wiley & Sons.

1992.

406
The Semiotics of Autonomous Investigations of Natural Systems

Paul S. Prueitt

Highland Technologies Inc. paul@htech.com

Abstract: A view point is presented that

emergence is a fundamental property of open

complex systems and thus that natural language

understanding by humans depends on the

emergence of understanding. Human

understanding is based on the assembly of

components from implicit memories.

Autonomous understanding of targets of

investigation, by computational systems, depend

critically on the extraction of features from the

target and the use of logio-linguistic principles to encode structural characteristics of these

features. It is argued that linguistic principles

reflect general systems properties because the

underlying morphology of concept formation

must conform to a class of general systems

properties. Also, linguistic principles reflect

general systems properties that occur in the

world. New logical principles are required to design and implement machine based

autonomous investigations of natural systems.

Introduction: Neural systems derive implicit

structure and encode structural representation of

this structure into a physical substrates of the

brain (Schacter & Tulving, 1995). Through

adaptation, the components of the substrate

express emergent neural phenomena that have

correspondence between the structural invariants

of the world experienced and internal mental

event that represent this experience to the higher

order processing centers of the brain (Pribram,

1991; Levine et al, 1993; Prueitt, 1997).

The phenomena of emergence goes to

the issue of how knowledge can be extracted

from a data source, because the extraction must

make correlations over time and develop a

flexible mapping between internal

representations and external objects and agents

(Michalski, 1994). The computational system

must have an "understanding" of how objects are composed from a substrate and how they

function over time. This understanding can be

"engineered" into software and hardware;

however, the situational analysis that is to be

derived must have some of the same properties of

openness as do natural systems.

Open systems theory extends

engineering and close loop control theory into a new class of logics similar to quantum logic and

the logics of C. S. Peirce. These new logics

reflect several classes of open systems

properties. The permutation of systems into

each other produces one class of properties,

however, the focus of this paper is on the

features of assembly/disassembly processes.

The logics of situational analysis for

complex natural systems must have formal means to describe how constituents are assembled into operational wholes and how

operational wholes are disassembled into

components. It is only when these properties are

part of the computational paradigm that one is

entitled to talk about autonomous intelligence.

This means that formal tools for

describing assembly, degeneracy and

indeterminacy must be part of the computational

logic (Tzvetkova, 1995). The interface between

a human user and a computational system will

have to use such tools to organize information

and provide a pragmatic axis to situational

analysis (Prueitt, 1997). This means that

theoretical/experimental results from general

systems theory must inform the architectural

issues regarding the design of the human/

computer interface and the issue of machine

understanding of natural language.

A central issue facing general systems

theory is about whether or not a class of

transformations can be characterized using

methods more powerful than numerical models.

In fact, Zabezhailo et al (1995) demonstrates that a predictive theory of biochemistry is realizable

by using special logics that perform iconic

computations. These computations are carried

out using the special inference operators of Quasi

Axiomatic Theory (QAT) (Finn, 1991, 1995).

The paths in "iconic" space are analogous to

trajectories in numerical state spaces; however,

these iconic trajectories are lawfully constrained

by the information in a database containing the

results of specific analysis of biochemical

structural activity relationships. Pospelov (1986;

1995) refers to these trajectories as syntagmatic

chains.

407
As another example, the relationship

between canalization in simplicial complexes

(Johnson, 1996) and structural adacity (Burch,

1989) in artificial life systems provide a means

for the simulation of some of the mechanisms

that are enfolding the individual experience of

computational agents in a complex artificial ecosystem. However, much more needs to be

done with artificial life systems before they will

provide adequate models of the properties of

natural open systems.

Natural and Artificial Systems: In (Prueitt,

1996a) the author postulated a fundamental

difference between a natural system and a computational system. It is postulated that the

difference is so great as to identify an

oppositional scale with "natural system" at one end and "computational system" at the other. As

in all oppositional scales the midpoint is most

interesting because it is at this point that the

classification of a system as computational or

natural breaks down completely (Pospelov,

1994). Figure 1 identifies this midpoint as a

perceptual system. Language systems and iconic

systems are born from complementarity, with

iconic systems more computational like and

language systems more similar to nature.

Language System

Iconic System Figure 1: A semantic oppositional scale between natural systems and computational systems

Semiotic knowledge bases are indexed

to numerical computations, as are computer

implementations of structural adacity and

canalization. Engineering is in total control,

except to the extent that some critical issues

regarding how things are composed might be left

to the decision of a natural system in interaction

with the computer. But seamless human/

computer interaction supporting situational

analysis has been very difficult to achieve.

How then do we actually get out of the

domination of computational processes in the

development of situational models. The answer may be in the definition of situationally specific

"intermediate" languages as an aid to translation

between the computer and the natural system.

These transitional tools will map linguistic

descriptions of situations to formal systems and

computational inference engines.

A semantic oppositional scale between

natural systems and computational systems

suggest that human perception uses computational like iconic representations (mental

images) as well as language to describe the

world. For example, we observe the cognitive

act of counting as a singular process only

because this act is already deeply embedded into

mature neural processes. Moreover, the

cognitive act of counting is but one manifestation

of the mechanisms of mental imaging. These

mechanisms include tools for measurement of

new observables by living systems. In a generic

sense, these mechanisms function as part of a process cycle expressed as action followed by

perception.

Ecological processes: Action perception cycles

are emergent from the physical properties of

subsystems and are driven by a class of periodic

forcing functions. The scholarly research in

ecological psychology and ecological physics

views periodic forcing is an essential part of the

temporal stratification of biological organization

into levels (see Prueitt, 1997 for review). In this view, any one level of organization contains

objects that are emergent constructions from a

relatively stable substrate of basic elements.

Figure 2: Natural systems stratify

The relationship that must always exist

between a substrate and a natural system is the

critical issue that must be resolved in any

situational analysis of natural systems. In Figure

2 each level, Lj , has the capability of forming a

substrate from which new organizational wholes

may emerge. Each of these levels, and their

interaction, can be partially simulated by a thermodynamical model.

Natural systems are "open" systems

with varying degrees of openness. For example,

enzymes produce micro environments where

constraints are placed on the "meaning" of

408
assembled biochemical agents, and in the

hippocampus micro environments fuse the

associational traces of implicit memory into

compartmental invariances that are "judged" by

the processes of other limbic systems and of

cortical regions. These micro environments are

agile semi-closed flexible and capable of

responding to novelty and nonstationarity in the

environment.

The stratified thermodynamical model

of open systems, in Figure 3, have micro

environments that emerge through some coherent

aggregation of compatible processes. The model

can be used under the assumption that the

average life time of processes at a certain level is an order of many magnitudes different from the

average life time of the processes at the next

level. For example, atoms form one level and

chemicals form a different level.

H|(x,x) - K(x) + P(x) + D(x,x) + E(x,x)

Figure 3: Stratified thermodynamical model of open

systems, where one of the levels has collapsed.

The collapse of one of the micro

environments leads to the diffusion of material

into an environment that supports the reassemble

of this material, and other similar material, into

new micro environments. As these new

environments arise, the structure and function

reflect the characteristics of the material as well

as the state of the environment.

Application to Machine Intelligence: Our

approach to machine translation and knowledge

representation assumes the existence of a table

(database) where the system states, i.e. those

states that a compartment can assume, are all specified and related to a database of subfeatures.

We have a system that is specified in a formal

fashion and which is computable. In this case, a theory of the world is provided in the form of

computer program, with data, as a "computational ontology".

Within the compartmental boundary of

this program, an underlying ontology, as

expressed in a semantic net or table, can assume

different system states and thus captures how the sense of the terms may drift. The rules that

govern an ontology allow a modification of the sense of the terms. This gives us hope that issues

of interlingua and pragmatic type can be

addressed within individual compartments

(Citkina, 1996). However, the procedures for the

formation and dissolution of these programs must

allow for the limitations that formal systems have

in general and that the specific program has in

particular. How is this accomplished?

Machine intelligence can also have a layered architecture where data constructions in one layer are combined to produce flexible

concepts using partially defined relationships.

An inductive analysis of the situation is then

possible, where a fusion of data occurs based on

the accommodation of characterizations of the

novelty of the situation with characterizations of

the background knowledge. This fusion must

have the nature of learning (Michalski, 1994).

Learning involves a reorganization of an

underlying constructive field that has certain

general properties (Pribram, 1991). For

example, the system states of advanced

computational ontologies may be evaluated with

respect to oppositional scales (Pospelov, 1994).

good

up

/

/

/

/

out /

/

/

/

down

bad

Figure 4: Oppositional scales provide metrics for the

interpretation of phenomena.

Oppositional scales are specified, as expected, within a semantic space that reflect

pairs of evaluators, such as good and bad, and

qualitative properties of the system states (Figure

4). The formation of the compartment for

modeling a specific situation might deal directly

with the observation of data and the extraction,

from this data, of a minimal set of oppositional

scales. The use of these oppositional scales must

contain a logical means for restructuring the

409
semantic space by using a group transformation on the space's basis set. Transformation rules are augmented by

quasi axiomatic theory as an "open" algebraic

transformation to allow the introduction of new

observables and the formalization of second

order cybernetic transformations of semantic

spaces. The properties of these semantic spaces

are representable in the form of a database plus a

specific situational language and logic.

Various approaches have been made

towards a formal description of second order

cybernetics, including; quasi axiomatic theory

(Finn, 1991), constructive induction (Michalski

& Ram, 1995), and connectionist architectures

for resolving explanatory coherence (Thagard,

1988). However, none of these formalisms have

had the success enjoyed by simple biological

systems. Complex natural systems are open

systems that (1) are embedded in a larger space

(2) are composed through an assembly process,

(3) have behavior properties with internal and

external work cycles, (4) can be described as variably stratified (Figure 5).

scale 3

image

scale 2

disassembly

scale 1

Figure 5: The Target of Investigation is observed a number

of times

Because of these four properties, the Target of

Investigation must be observed a number of

times

T = { Oj , 02 , . . . , On }

• each "observation", O, of the target has a "bag" of properties P = {pi , p2 , ... , ps }.

The cardinality of the bag of properties is

finite (but open).

• each "observation", O, is composed from a

"bag" of basic elements A = {ai , a2 , ... , a^ The cardinality of the bag of elements is

finite (but open).

• logical hypothesis (J.S. Mill) can be asked

1) does an observation have (not have)

property p

2) for each basic element, a; , is a; cause

of (or not a cause of) the property p

Of course, the descriptions of properties and the

descriptions of basic elements of the Target of

Investigation must be possible.

The quality of any automated reasoning

system is a function of its power to reveal the

basic signature of a situation under investigation

(see Ritz and Huber, 1996). General systems

properties, such as oppositional scales, are required to extract and reveal this signature. A

system that creates and resolves paradoxes will

produce complementarity described by the

oppositional scales mentioned in Pospelov

(1994). Multiple viewpoints are then

accommodated through the emergence of a new

system for understanding both ontologies and

their natural inter-relationships; and a new player

in the situation, the accommodation itself.

Block Diagram for Situational Analysis: The

block diagram in Figure 6 is open to architectural

instanciations of computational systems that duplicate the structural mechanisms that experimental neuropsychology suggest are used

by biological systems.

Interpretation Space

Figure 6: Block diagram for Situational Analysis

First, a data source is attended to by the

system using measurements about properties and

features. These properties and features are represented, approximated, as elements of a set of primary components. For example, the

Fourier transform produces a representation of

the spectral domain as the sum of weighted

principle components. The Gabor representation

may play a similar role in the human cortex (see

Prueitt, 1997 for literature review). The theme

vector transformation of a document's content

produces a similar representation (Rijsbergen,

1979; Prueitt, 1996b). The type space is then

projected into a system for visualization. In the case of human perception, this projection is a

410
reentrant bi-projection between the lateral

geniculate nucleus and the layered visual cortex. Very few software systems have

visualization of theme (feature) space as well as an integrated representation of knowledge in the

form of a concept database. Concept databases

exist in a few cases (Abecker, et al, 1997), but

are primarily restricted to mechanical systems or

industrial plants. Software packages such as

Spires, developed by Pacific Northwest National

Laboratories, makes projections into feature

spaces based on cluster analysis. New

computational projection schemes are being

based on situational semantics. The object of

visualization might be related not only to a themespace but also a concept space.

The scientific challenge is to see both

computational visualization and human

perception within the same paradigm. This may

not be so difficult. A large amount of

experimental research exists and some of this has

been integrated into explanatory frameworks.

The study of these frameworks suggests that the

human brain achieves the formation of concepts

through a distributed disassembly and reassembly

of representational features (Figure. 7). This

framework can be seen to be illustrative of a general systems property regarding the

emergence of operational wholes within

ecosystems.

Figure 7: The niches in ecosystem share in the common use of a finite class of natural type.

It is also suggested that the human in

vitro concept space is a virtual space in the sense

that the space does not actually ever exist in total

in any specific circumstance. Parts of this virtual

space come into being while other parts are blocked by various types of competitive

cooperative network dynamics. Of course, this simple architecture disguises the complexity of

how the brain uses both its neural architecture

and its chemical composition.

A projection from a complete

enumeration of a knowledge engineering type

concept space can be made onto a concept

subspace. In Figure 4 this is called an

interpretation space. This subspace may be

mirrored by activation of components of a

situational model supporting automated

reasoning. The mirrors can be maintained by a

neural network associative memory as demonstrated in (Dubchak & Muchnik, 249).

The mirrors can be two way, and as a consequence a separate mapping back to a concept subspace may be made after an inference

engine has changed the state space of the

situational model. This notion of projections and

mirrors between representational spaces is a

reasonable first model for the production of

computer based situational models. However,

there are a number of scientific issues that are not

yet resolved.

The structural form of a computer based

concept space has not been worked out. Simple

themespaces have been defined, but a new class

of objects are needed in themespaces. These

objects will create topological distortions of the

otherwise flat Euclidean space, and instanciate a theory of semantic operators defined in coincidence with the inference engines.

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412
SOFT MODELING

Soft Modeling for Intelligent and Complex Systems

Paul P. Wang

Department of Electrical & Computer Engineering

Duke University

Box 90291

Durham, NC 27708-0291

ABSTRACT

This paper proposes a three-level hierarchical mathematical

model for intelligent and complex systems. Motivation,

background, rationale and interpretations are given. Illustrated

in a block diagram are different visions from different schools

of thought. The concept of "soft-modeling" represents a dramatic departure from conventional mathematical modeling

is also presented. The characteristics, approach, types of

mathematics used, and the interpretations that will eventually

lead to engineering realization and commercialization are also

presented.

KEYWORDS: soft modeling, intelligent systems, hybrid co ntrol,

intelligent control, computational intelligence, fuzzy logic, first order

predicate calculus, fizzy constraint network, cognitive science, pattern

recognition, adaptive intelligence, control of complex systems,

computing with words, soft optimization, soft computing.

1. INTRODUCTION

In recent years, we have observed the rise of the concept of

"soft computing" both in recognition of importance and in the

increase in number of technical papers published in open

literature [1,2,3,4,5,6,7]. No doubt, soft computing as Lotfi

A. Zadeh conceived has been and will continue to influence

the intelligent engineering. Because its foundation is biologically inspired, soft computing can solve difficult

problems, especially nonlinear problems. At the same time,

Lotfi A. Zadeh and many other leading researchers in the field

agree that the most fruitful areas of application will concern "complex systems" and "intelligent systems." The definition

of "intelligent" is very complicated and we will not be able to draw any sensible conclusions for a very long time. On a more optimistic note, the desirable features constituent of

intelligent, such as adaptation, reasoning, generalization,

similarity, focusing attention, pattern recognition,

introspection, combinational search, etc., are useful and

important for making better products by improving quality,

reliability, and performance of industrial products for human

beings. All these desirable features can happen by lowering

the cost of production and saving energy, materially and

humanly.

As far as complexity is concerned, the impact will be at least equally, if not more profound. The complex systems, both

static and dynamic, are in front of us and surround us everywhere. Historically, the understanding of these systems

is limited because they are usually not mathematically

traceable. The types of mathematics referred to are those

recognized by earlier researchers or with already established

credibility in the sense of rigorous scientific methodologies

and traditions.

The mathematical system theory begins with mathematical

modeling of pragmatic and realistic systems, physical or manmade. There is very little one can do if a mathematical

model cannot be established. In other words, all the analysis

and engineering design that follow it cannot be processed.

The mathematical model, in a sense, represents some

mathematical constraints that must be satisfied. This is the

place where the difficulties in analyzing complex systems

arise. In retrospect, all mathematical approaches have

traditionally used in systems analysis belong to what one may

call " = " or "equal culture." In other words, the constraints are exact. Unfortunately, this constraint condition is not

always where we are ready to tackle complex systems.

The purpose of this paper is to propose a novel approach to

soft modeling. Soft modeling is a generalization of the

concept of mathematical modeling in the traditional sense. Three area of generalization worthy of mentioning:

1. The generalization in mathematical constraints.

2. The generalization of the type of mathematics being

used.

3. The generalization of the types of physical or manmade

systems to be treated (i.e., the mixture of the physical,

engineering, and social economic systems).

2. THREE-LEVEL SYSTEM

ARCHITECTURE FOR INTELLIGENT

AND COMPLEX SYSTEMS

To ease the discussion of three-level system architecture,

Figure 1 illustrates this system in terms of three separate

blocks. Furthermore, to cover more ground, different schools

of thought that currently exist are also listed. (Please bear in

mind that the investigation of systems of this type can quickly

415
Top Level

Middle Level

Bottom Level

Soft Modeling

Soft Computing

Conventional

Controls

(i) Taxonomic Vision (ii) Cognitive Science Vision (iii) Soft Computing Vision

Social-Political-Economy Operations Research

Machine Intelligence

Computer Science

Intelligence

Interdiscipline

Classical & Modern Control

Control

Engineering

(iv) Hard Computing Vision (v) Scientific Discipline Classification

Figure 1: Three-level hierarchical models for different schools of thought.

be extremely complicated while the features of intelligence and

learning are to be incorporated.)

For the proper perspective on the kinds of problems being

addressed, A. C. Antoulas of Rice University [8] says". . .

Scientific activities can be divided today into two broad

categories. The first category includes by in large the natural

sciences. . . Its objective is to investigate fundamental

properties of matter, and big bang, black holes . . . The

second category is concerned with phenomena and structures which display high complexity. These can be found in nature,

biological phenomena and the structure of molecules, like

DNA, are two examples. But for the most part they are

artificial, generated by disciplines such as engineering,

computer science, cybernetics, ecology, operations research,

economics, etc."

In other words, the complex systems described in this paper

will deal exclusively with the examples in category 2. Although we may be deeply involved with the study of brain

phenomena in order to get biologically inspired spirit out of it, we are neither addressing DNA, or crystal structures. Antoulas [8] went on to say, "... The main distinction

between these two categories is their system component: the

former has a small system component while the latter has a

large system component.

Before we enter the detailed description of all three levels of

the proposed hierarchical structure, all three levels will be

briefly described in three practical complex systems: (1) a

large hotel complex, (2) an automatic manufacturing plant,

and (3) the command of a battlefield.

416
In a nutshell, a three-level hierarchical model consists of three

levels: (1) the mission statement is the top level or constraint

imposed by the society of meaningful human endeavor. The

soft modeling as proposed in this paper is intended for

modeling this level. (2) The existing technology is the

bottom level. And (3) the middle level, on the other hand,

is called cutting edge research and development.

These three levels are:

1. Top-Level Subsystem — The goal of achieving some

global optimization for a large complex hotel (example 1) is

to optimize yield management with a set of constraints. The

set of constraints include law, public policy, economic

condition, number of available workers, several reservation

priorities, geographical location of hotel complex, seasonal

variations, special events and cultural activities, etc. In order

to establish a mathematical model successful, a new modeling

methodology (soft modeling) is needed to make use of

different mathematical tools.

Example 2, similarly, has a set of constraints. These are very

realistic constraints that the complex system must satisfy:

purchasing orders, availability of raw materials, defective

parts replacement, number of available workforce,

international trade, inventory, public policy, up-dating of legal

codes, environmental regulations, up-grading of the production

lines, etc. And, finally, soft modeling is also needed for the

battle field command of Example 3. Availability of

communication networking, food and material supplies,

injured soldiers, field hospital, transportation, ammunition and

weapons supplies, intelligent information fusion, etc. are just

a subset of constraints which must be handled.

Yes, these are constraints that come in different sizes, forms,

units, measurements, emphasis, criteria, values, inherited

culture, etc., etc. That is precisely the motivation for the

novel concept of soft modeling.

2. Middle Level Subsystem — This subsystem is the

most important and exciting components of the complex

system. The recognition of its importance has been firmly

established by a number of leading researchers. However,

this is not the main theme of this paper, because we are discussing the issue of the top-level subsystem. For the sake

of completeness and an overall picture of how to handle

complex systems issues, J. S. Albus of NIST summarizes

"enabling technology" in his paper [9]. "The latter half of the

20th century has seen a number of fundamental breakthroughs

that have radically altered the landscape of technological

possibilities:

a. The power and speed (per unit cost) of electronic

computing has risen exponentially by more than a factor of ten per decade for over four decades. . .

b. The store of knowledge about how the biological

brain works has also increased many fold over the last half

century, . .

c. Solid theoretical and mathematical foundations

have been established and progress is rapid in the scientific

study of language and speech understanding, image

understanding and perception, knowledge representation,

simulation, reasoning and decision making, planning and

control.

d. Engineering approaches have begun to emerge

for designing, constructing, testing, and exploiting intelligent

systems for practical applications in commerce and industry." In large measure, one may say that the soft modeling concept

as proposed in this paper was motivated by item d quoted

above. Tremendous research and development opportunities

exist in the course of the realization of the item d. It is fair to say that a satisfactory answer for the middle-level

subsystem's problems might take a long time to obtain.

3. Bottom-Level Subsystem — There is very little that

needs to be said about this third level subsystem. It would not

be far off to say this subsystem is already here. During and

after World War II, researchers and engineers have brought

us to the present level of maturity. However, it is not to be

said that we do not have new problems. In fact, there is a whole research community of hybrid systems conducting

pioneering work in this area. The 5th Hybrid Systems

Workshop, headed by Panos Antsalkis, will take place at Notre Dame [10]. Hybrid systems research is very solid and

down to earth. As we look to the future of intelligent systems

research, it is worth considering an even deeper system

structure. Referring to Figure 2, one can look at hybrid

system design as a special case of the proposed three-level

model in at least two aspects: the automation is just a special case of a much more general mathematics linguistic model and

without considering the lop-level subsystem, then the problem

of both intelligent and complex systems has not been fully

addressed, in our opinion.

The research activities for the middle level subsystem are very

active at present and will continue to be very active for a long

time to come. Again, the main concern of this paper is soft

modeling of intelligent and complex systems.

Automaton

I t

Conventional

Control

Hybrid

Control

Figure 2: Hybrid control systems.

In Figure 1, five hierarchical block diagrams represent five

417
different visions depending on different schools of thought.

The semiotic view by Alex Meystel and James Albus is not

illustrated here because it is difficult to present it in this

structure. Please refer to Meystel's original works for proper

reference [9].

One thing is certain, with FCN as the top subsystem and

approximate reasoning in the middle, a much better

performance of a complex system can be realized as shown in

Figure 3.

Fuzzy Constraint

Network (FCN)

I

Approximate

Reasoning

$

Control Systems

Figure 3: A fuzzy-based realization of soft-computing model.

3. SOFT MODELING

With all the above background, we now embark on the task of

explaining the concept of "soft-modeling." By no means does one pretend to borrow fancy words in order to gain attention.

Rather, it is an outgrowth of necessity. In Section II. 1, we have introduced three realistic examples of

a top-level subsystem. Traditionally, for this type of problem,

the modeling has been done by operations researchers. Their

approaches are not unique. One standard approach is using

linear programming. Another approach introduced by Lotfi

A. Zadel [5,6] is a fuzzified version of First Order Predicate

Calculus (FOPC) method. The novelty aspect as described in

this paper is the interface between the top level and the middle

level subsystems. In a later section, we shall also show a

linear programming approach that is a special case of the

fuzzy FOPC formula.

To appreciate the need of soft-modeling, we must go back to study the evolution of convention control. It is well

recognized that the first mathematical model to describe plant

behavior for control purposes is attributed to J. C. Maxwell,

of Maxwell's equation fame, who, in 1868, used

differentiation equations to explain instability problems

encountered with James Watt's flyball governor [11]. Control

theory has made significant strides since 1868. During the

1930s, World War II, and the 1940s, the use of frequency

domain methods and Laplace transforms were the dominant

methods for analyzing and designing control systems.

What does the above statement tell us? That we can solve

only problems that are linear and time invariant? In fact, only

'

linear time invariant systems can be solved because both

Fourier and Laplace transforms are linear transformations,

j Conventional control systems have always been designed using

mathematical models of physical systems. A valid ! mathematical model is a prerequisite for control system

designs. Yet, with this very restricted and often unreasonable ! approximation (linearization), it is obvious that we have left

j many problems unsolved. In fact, in conventional control

approaches, a mathematical model that captures the dynamic

behavior of interest must be simple enough to be analyzed

with the available mathematical techniques and accurate I enough to describe the important aspects of the relevant

dynamic behavior [11]. For nearly half a century, engineering

students were trained for the most part via so-called small

signal theory. This kind of approximation only delivers the

behavior of a plant in the neighborhood of an operating point. ' This is true for all electronic, vacuum tube, transistors, VLSI j products as well as electrical, mechanical, optical, hydraulic,

and thermo systems and any combination thereof. So what is the point? The point is that serious restrictions are artificially

imposed in order to use frequency domain analysis and

Laplace transforms. These restrictions basically rule out the

opportunities to solve many important and pressing complex

problems. This observation leads to one of the explanations

for the need of soft-modeling.

The second reason deals with the nature of the systems we

must learn to cope with. Contrary to mathematical modeling

that is almost always based on the Hamiltonian principal and

Lagrangian equations for continuous mechanics, there exist j few guidelines for the three different types of examples as described in Section II. Depending on the designers'

background and disciplines, the outcomes of modeling can be

very different. The fact is that no principle similar to J Hamiltonian and Lagrangian is available for use in solving the

three examples. In other words, new methods of solving these

kinds of examples must be developed. These methods would

be different from ordinary differential or difference equations

and static algebraic equations. For example, binary logic, j fuzzy logic, the concept of relations, the operations of subsets i

all of a sudden become very important. Predicate Calculus

and First Order Logic are very general methods for solving

problems when the theory is applied to many different physical or human societal problems [12]. Fuzzification does not alter much in terms of modeling, but it makes a difference in terms

of problem solving abilities. The dramatic difference in soft modeling is brought about by

the type of mathematics used. For example, we have seen what linear programming methodology can do for operations

researchers. This methodology includes the so called
"inequality" or symbolic "<" that is relation in a mathematical concept. To fully understand soft modeling, one

can think of the solution for a state vector that may not be

unique and one must talk about "solution space" instead ofjust

a unique "solution. " In optimal control theory, the solution is

nearly always unique. In the case of soft modeling, this will

not hold true. This very fact may be justification for the

nomenclature "soft computing" as coined by Lotfi A. Zadeh

[3]. The work "soft" means the solutions will be "solution

space" as a direct consequence of the soft modeling.

Several important observations concerning soft modeling are

in order (refer to Figures 4 and 5):

HI Rnnc Solution Spats i„, IntTniic Solution Space

iGniunJmL* Soft-Modeling I

Figure 4: Solution space.

Shrinking of Solution Space

Figure 5: Learning of soft-modeling.

Observation No. 1 — There are two types of solution

space—finite and infinity.

Observation No. 2 — The quality of soft-modeling depends on the size of solution space, the smaller the better.

Observation No. 3 — An infinitive solution space can be

change to a finite solution space. In principle, this is always

possible for manmade social-economic systems. The real difference is at what cost. Observation No. 4 — It is impossible for a solution space to be reduced to a single point in state space. Should it happen

that the solution space is reduced to a single point under very

special conditions then the system involved can no longer be

call soft modeling.

Observation No. 5 — The learning problem as defined by

soft modeling is eminently related to the shrinking of solution

space.

Observation No. 6 -• The optimization process for soft

modelled systems begins where the final solution space is finished. (Actually one says the soft system is grounded or it

is established.) The optimal solution then can be established

by examining the optimal solution over the solution space.

4. FUZZY CONSTRAINT NETWORK

Fuzzy Constraint Network (FCN) is the fuzzy version of

FOPC and has been recognized as a key methodology in the

top- level subsystem in our hierarchical structure. FCN was

first presented to the intelligent system community by James

Bowen and Robert Lai in Lai's 1 dissertation [13,14]. Didier

Dubois and Henry Prade have also been working on a somewhat different approach for many years [15].

Subsequently, FCN has been investigated further by Paul P. Wang, Dennis Bahler, C. Y. Tyan [16]. The application of

FCN has always been fairly broad and subsequently there is no lack of papers in this field. Potentially, FCN can play a very important role in soft modeling.

As discussed in Section I, the concept of mathematical

modeling must be critically revisited in order to meet the

challenges of solving intelligence and complex problems.

Some thoughts on this very issue are in order. Since the

systems are complex, to find suitable mathematics to produce

quantitative results may not be readily available. As Lotfi A.

Zadeh has demonstrated, fuzzy logic can solve complex issues

that are otherwise impossible [2]. One can view the

mathematical modeling as an attempt to search for some kind

of mathematical language to provide useful information and

consequently some numerical value available and useful. On

the other hand, it is not one's intention to make this over

complicated. Cover and Thomas have discovered Einstein's

saying in a Chinese fortune cookie: "Everything should be

made as simple as possible, but no simpler." [17] Upon

further examination of the three examples, one discovers the

fuzzy FOPC has indeed exhibited remarkable express power

in modeling the reality of a complex system. This kind of

model can also be made quite robust and should be

constructed in an adaptive manner. This is precisely what the

FCN methodology is good form.

In conventional control theory, the design of a physical system

often consists of four steps [18]:

1 . Modeling

2. Setting up mathematical descriptions

Ph.D. dissertation at Computer Science, North

Carolina State University

419
3. Analyses

4. Design

The physical system, theoretically speaking, is an object

existing in the real world, its precise characteristics are often

unknown to us. The difficulties will increase many fold when

the systems are complex. Our final objective, of course, is to accomplish items 1 through 3 successfully and eventually

develop a good design. With this perspective in mind, the

research needed for this proposed system hierarchical structure

is only the beginning. Indeed, we have a long way to go.

5. CONCLUDING REMARKS

As early at 1958, researchers [19] recognized a logic circuit can be incorporated in a conventional control system for one

of two general purposes: for adjusting the control system

parameters or for overriding the conventional control system.

It took many years for hybrid control systems to become a serious research topic [10]. The thesis of this paper actually

is quite straightforward. Since fuzzy logic is much more

general than bivalent logic and its ability to handle imprecision

and incomplete situations have been demonstrated many times

already, the proposed three-level architecture ought to be the

general problem solver by adopting FCN [16].

Three-level architecture is analogous to that of a three-layer

neural network as a generic term. Theoretically speaking,

because the architecture of a large complex system can assume many variations in form and structure, many possible

combinations of the basic building blocks are possible.

Depending on the nature of the real-world problems, the

number of possible combinations and variations can indeed be

huge. What we have presented in this paper is just the very

basic structure of a generic subsystem.

System theory is a discipline which aims at providing a common abstract basis and unified conceptual framework for

studying the behavior of various types of forms of systems

[19]. The foundation issues covering fundamental concepts

such as system, state, stability, controllability, observability,

determinateness, equivalence, etc. are not going to be easy for

the intelligent systems of this type. It is highly possible that

new concepts will be developed as we move along. On the

other hand, we are fortunate to have a collection of various

methods, techniques, and algorithms designated as soft

computing for studying the behavior and design of complex

systems.

The study of intelligence, learning, and training has not been

mentioned in this paper because our focus has been on the

concept of soft modeling for complex systems. Many

problems remain to be investigated.

REFERENCES

[I] Wang, Paul P. Fuzzy Subsets and Logic: An Effective

Tool for Machine-Intelligence Control System, Proceedings of

the 1996 International Multidisciplinary Conference,

Intelligence System: A Semiotic Perspective, V. II, Applied

Semiotics, 1996, pp. 293-297.

[2] Zadeh, Lotfi A. "Outline of a New Approach to the

Analysis of Complex Systems and Decision Processes, " IEEE

Transactions on Systems, Man, and Cybernetics, pp. 28-44,

1973.

[3] Zadeh, Lotfi A. "Fuzzy Logic = Computing with

Words," IEEE Transactions on Fuzzy Systems, 4(2), pp. 104-

111, 1996..

[4] Wang, Paul P. and C. Y. Tyan "Fuzzy Dynamic

System and Fuzzy Linguistic Controller Classification,"

Automatica, 30, pp. 1769-1774, 1994.

[5] Zadeh, Lotfi A. "Knowledge Representation in Fuzzy

Logic," IEEE Transactions on Knowledge and Data

Engineering, 1(1), pp. 89-100, 1989.

[6] Zadeh, Lotfi A. PRUF - A Meaning Representation

Language for Natural Languages, Memo No. UCB/ERL

M77/61, University of California, Berkeley, CA, 1977.

[7] Buckley, J. J. A Fuzzy Expert System, Fuzzy Sets and

Systems 20, North Holland, 1986, pp. 1-16.

[8] Antoulas, Anthanasios C. (ed.) Mathematical System

Theory — The Influence of R. E. Kalman, Springer Verlag,

ISBN 0-387-52994-2, 1991.

[9] Albus, James, and A. Meystel. Intelligent Systems —

A Semiotic Perspective. A conference newsletter for

Multidisciplinary Professional in the Area of Intelligence,

Large and Complex Systems, Knowledge Engineering, and

Others., No. 1, 1996.

[10] IEEE Control Society 1997. E-Letter on Systems,

Control and Signal Processing, No. 106.

[II] Antsaklis, Panos J., M. Lemmon, and J. A. Stiver.

Chapter 2, Learning to be Autonomous — Intelligent

Supervisory Control in Intelligent Control Systems. IEEE

Press, IEEE Neural Networks Council, 1989, pp. 27-62.

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[12] Nilsson, Nils J. "Logic and Artificial Intelligence,"

Artificial Intelligence, 47, pp. 31-56, 1991.

[13] Bowen, R. Lai, and D. Bahler. "Lexical Imprecision

in Fuzzy Constraint Networks," Proceedings of 15th

International Joint Conference on Artificial Intelligence, San

Jose, CA, 1992, pp. 616-621

[14] Bowen, J., R. Lai, and D. Bahler. "Fuzzy Semantics

and Fuzzy Constraint Networks, " Proceedings of First IEEE

International Conference on Fuzzy Systems, San Diego, CA,

1992, pp. 1009-1016.

[15] Dubois, D., H. Fargier, and H. Prade. Flexible

Constraint Satisfaction with Application to Scheduling

Problems. Report IIT/93-30-R. Institute de Recherche en

Informatique de Toulouse, France, 1993.

[16] Tyan, C. Y., Paul P. Wang, D. R. Bahler, and S. P. Rangaswamy. "A New Methodology of Fuzzy ConstraintBased Controller Design Via Constraint-Networking

Processing," IEEE Transaction on Fuzzy Systems, 4(2), pp.

166-178, 1996.

[17] Cover, Thomas M., and Joy A. Thomas. Elements of

Information Theory, Wiley Series in Telecommunications,

John Wiley & Sons, Inc., New York, 1991.

[18] Chen, C. T. Introduction to Linear System Theory,

Holt, Rinehard, and Winston, New York, 1970.

[19] Zadeh, Lotfi A., and E. Polak. System Theory, Inter- University Electronic Series, 8, McGraw Hill, New York,

1969.

421
Computational Embodiment: Biological Considerations

Kirstie L. Bellman

Information Technology Office, Defense Advanced Research Projects Agency

3701 N. Fairfax Dr., Arlington, Virginia 22203-1714

Phone: (703) 696-2219, FAX: (703) 696-0564, E-mail: kbellman@arpa.mil

Christopher Landauer

National Systems Group, The Aerospace Corporation

The Hallmark Building, Suite 187, 13873 Park Center Rd., Herndon, Virginia 20171

Phone: (703) 318-1666, FAX: (703) 318-5409, E-mail: cal@aero.org

Abstract

Computational Embodiment is the computer implementation of principles that we believe will lead to more au- tonomous and self-generating behaviors that will allow

software systems to exist in and interact with complex

environments. We restrict our attention here to symbolic

environments (MUDs), as an initial step towards understanding and constructing "interaction spaces" in which

humans and computer programs can interact on an equal

footing.

Our approach to constructing autonomous software sys- tems is based on theoretical work on the structures that

underly language and movement in biological systems and

on the structure of constructed complex systems mediated

or integrated by software.

This paper describes some of the important lessons to be

learned from biological systems, and points towards some

of the principles of construction of autonomous systems.

1 Introduction

In this paper and its companion [17], we describe an approach to constructing autonomous agents that is based on theoretical work on the organization of structures that

underly language and movement and on the structure of

constructed complex systems mediated or integrated by

software. We are not only interested in control of such sys- tems "to keep the system within a desired space" (which to us includes planned or computed reactions to unplanned

events or behaviors), but also in instrumentation to find

out what is going on inside and outside the system, in

on-line management of system resources for efficiency, in

negotiation among system resources, and in system architectures that will help us design, build, use, maintain, and

analyze such systems.

We are constructing autonomous software agents in symbolic environments called Multi-User Domains (MUDs)

[20] [21] [9], using a style of "computational embodiment",

which is part of our research program on interaction spaces

[13].

In our view, a system is "autonomous" if it can be said to have "purposeful behavior", e.g., act independently based on internally generated intentions [5]. There are really

only two classes of (difficult) requirements for effective

autonomy: robustness and timeliness. Robustness means

graceful degradation in increasingly hostile environments,

as well as an ability to exploit unexpected aspects in the

environment to one's own advantage, which to us implies a requirement for adaptability. Timeliness means that sit- uations are recognized "well enough" and "soon enough",

and that "good enough" actions are taken "soon enough".

There is not necessarily any optimization here.

In this paper, we describe some fundamental theory

of computational embodiment, primarily theory derived

from biological systems (Section 2). In the companion paper [17], we show how our notion of wrappings as dynamic

infrastructure supports the theory, and describe how the

architecture we use is being implemented.

An earlier version of this paper appeared in [10], and a summary in [4].

2 Biological Characteristics

It is instructive to compare computational systems with

biological systems, since those are the only ones we know

that have any interesting complexity and variety of behavior [5]. From the very smallest and simplest organ422
isms, biological systems have generative processes that

provide varying numbers of appropriately constrained ac- tions that retain sufficient flexibility for robust behavior.

These "controlled sources of variation" require both variation (spaces within which choices are constrained) and

control (of the choices), and remain one of the most difficult areas in theoretical biology. We note also that the use

of language for communication among biological entities can be viewed as an extension of movement processes [3], both being essentially defined by layers of symbol systems.

In biological systems, generative processes make use of

many different types of mechanisms at different levels of

the system; everything from mechanisms that take advantage of side-effects and even inevitable errors (e.g., the

inability to replicate DNA perfectly becomes eventually a critical source of genetic variation, leading to different phenotypes that can be acted upon by natural selection) to mechanisms that allow partial or graded behavioral responses (e.g., diffusion of neurotransmitters across synapses, different conduction rates in bundles of neurons,

and modulation of chemical channels across cell membranes) to mechanisms that allow rich cognitive control over behavioral choices (and for us, at least, conscious

manipulation of symbol systems). Generative processes in

biological systems have dynamic behavior that can be used

both for organizing behavior and creating information.

In contrast, computational systems are relatively trivial,

since the absence of generative processes means that the

system developers must provide these controlled sources

of variation explicitly, generally using knowledge bases

and computational resources [18]. This need to build all the parts and all the selection mechanisms severely limits our ability to construct large systems with many types of

adaptive and coordinative behavior. One of our philosophical principles for system architecture is the analogue of

the "controlled sources of variation" mentioned above: ev- ery flexibility we want in a constructed system must have a corresponding coordinative mechanism that manages the

flexibility. We use the notion of layers of symbol systems

to interpret action and behavior as extensions of computation [3], gaining some conceptual simplicity thereby, and

though most of the hard questions still have no good answers, we have made some progress in defining essential

features of complex computing systems [10] [12] [13] [14]

[2] [15] [16].

Our purpose is to improve the capabilities of computerbased agents, so that they can work with humans to perform increasingly difficult cognitive tasks, such as finding

relevant information, filtering and refining the presentation of information for our purposes, and organizing and

executing the sequence of command steps for such machines as factory product lines or autonomous land vehicles. We believe that the growing field of agents research

could make more use of the hard-won lessons from biological research and robotics about what it means to carry out

intelligent functioning within ANY world (be it abstract

or physical).

These four lessons include:

1. Developing "ecological niches" or portable contexts

for computational agents;

2. Creating artificial "embodiment" for abstract agents;

3. Creating entities with "social" behaviors; and

4. Developing capabilities for growth and adaptivity of

behaviors.

Before we expand on each of these points below, we want

to emphasize here that each of these directions is being

considered in current agent research [19], but often only

indirectly or implicitly. We suggest that by placing the

agents within an explicit context (with its own processes

for being examined and modified), by giving agents a definite "shape" and body within this context, and by giving

agents a means of socially responding to other agents in explicit and observable ways, we can strengthen the agents'

performances by creating new and stronger information

with which to evaluate our ideas of intelligent functionality by agents. We believe that ecological niches, embodiment, and social intelligence are all good starts to building agents with a much richer repertoire of mechanisms

for adaptation and growth.

The grounding of agent behaviors within an observable

context lets us build active, generative processes that can monitor their own behavior, change it, catalog it, and learn

from it. But in order to capitalize on the creation of such

processes, the agent needs (1) architectures that allow it to pull in new types of processing resources, and (2) self- reflective capabilities. In a companion paper [17], we describe our wrapping approach to dynamic infrastructure,

which provides the flexibility and infrastructure that supports these two goals.

2.1 Ecological Niches for Agents

In nature, the capabilities and characteristics of any given

animal are strongly related to the environment within

which it lives. The context within which the animal must

perform includes the physical world, the other species that

exist within that area, the history of its own species within

that environment, and its immediate social interactions

with others of its own kind. Biologists continue to struggle with understanding the kinds of powerful principles

that lead to the extraordinary amount of specialization

and variety that has resulted.

423
We need to take a lesson from biology here: there are no

such things as "general purpose fish". They are all rec- ognizably fish, and hence there are many general aspects

that we can use in creating architectures and standard processes for "fishness". However, fish are specialized by liv- ing in saltwater or fresh; living near the top sunlit waters

or being bottom dwellers; by surviving near fierce predators or by having few competitors; by living in schools

or developing other protective mechanisms; and so forth.

Eventually, we want to enumerate the corresponding "ecologically" important distinctions for "agents", e.g., do they

live on the Internet or in a digital library; do they have to

fight for our attention or do they have dedicated lines or other access to us; do they work as part of a temporary

alliance of known (or harder, unknown) resources, or are they a simple logic or filter component in a larger process;

and so forth.

The research advantages of building explicit contexts for our agents are clear. Instead of trying to align our

"agents" and their behaviors to a hidden or implicit context, we can start to represent and manipulate "niches" explicitly, study the mechanisms by which our agents relate

to that kind of context, study the behaviors of our agents

within the explicit contexts, and begin to build principles

of how we distribute information and processing capabilities between the agent and its operating environment.

Multi-User Domains (MUDs) are an interesting new kind

of groupware that incorporates people into the program.

MUDs have become enormously popular as games and as educational support tools over the last few years because

they get the human interactions right in some fundamental sense, and because they engage our sense of "place".

MUD clients and servers are easy to obtain and run (most

servers and clients are free), but they usually only provide

text worlds; there is little interaction with existing tools

that are outside the MUD; though some have construction languages that allow complex programming, it is the

usual kind of programming; and it is not very easy to access large volumes of information. We have been exploring

the use of MUDs as an ecological niche for agents [13].

2.2 Embodiment

The next hard-won lesson from biology and robotics is that

intelligent functionality needs a body, e.g., it needs a shape

that defines and limits its capabilities and scope. In animals, bodies reflect both the short-term and long-term history of a species' adaptation to its ecological niche. In animals, bodies reflect the physical constraints of the environments, the historical and immediate interactions, choices,

and methods of dealing with the environment (which includes others). The embodiment is the grounding of the

agent and its means of relating to its environment.

Three other critical issues emerge from considering bodies.

The first is that an embodied agent reminds us that an

agent always exists within its world and that it is always

doing something within that world. Even "idling" is a behavior, the result of which can be quite unpleasant for prey

in the real world, or simply annoying to a user waiting for

performance. Therefore, we must account for the causal

connection to and from the environment, that is, the ef- fects of events in the environment on the agent, and the

effects of agent activities on external objects. The agent can learn of these effects or cause others only through

the specific interface between the agent and the environment. That interface must make actions available, so that

the use of tools and other activities has the proper effect. There must be appropriate sensors to collect information

for the agent from the environment, sufficient effectors, so the agent can change its relationship with the environment, including motion, so it can announce information j to environment, make changes in the environment via the

use of tools, and there should be probes, which are tasked

sensory activities governed by a focus of perception.

Our computational version of the language and movement

theory [3] is that there are layers of symbol systems that

separately normalize external signals into interesting information spaces, so that the useful processing can take

place in those spaces (this separation is the analogue of

the behavior of different senses).

The second is that the body is a barrier; we cannot reach

j into the embodied system and turn switches when we want

something to happen [2]. Commands are only suggestions, I since we cannot force any particular kind of behavior on

the system. We can provide compelling reasons, and try to arrange that we have programmed the system to respond

appropriately, but we can't enforce it. This is one of the

j main differences we see between computer programs that

we want to call agents and ordinary computer programs.

The third is that embodiment is an explicit representation

of the "Integration Concept" for the "whole" animal. This

integration concept provides a unity to the whole system, j It is what turns a bag of parts into a coherently operating

individual entity. A body has many parts, but works as j one entity, integrated across disparate resources (unless it

is sick or dysfunctional).

In our opinion, some of the most important aspects of

autonomous systems revolve around this notion of "embodiment" , that is, the connection of the computation to an entity in the physical world. Embodiment in this sense has several essential properties:

• a sense of environment: the environment has prop424
erties and contains tools, objects, and other agents,

and makes certain actions available

• a sense of presence: there is a causal connection

to and from the environment, so that the use of tools

and other activities have a direct impact on it

• a sense of time: it is important for the agent to

remember the history of what has gone before, to rec- ognize certain kinds of event patterns, and to make

predictions

• a sense of place: what happens and what exists take

place in some locality, which has a notion of geography, connectivity or connection, distance, and space

• a sense of will: autonomous means self-governing, so an autonomous system must generate its own goals,

and exhibit a sense of purpose and intention

• a sense of self: an autonomous system needs to have

a notion of its own resources, abilities, and internal

state

• a sense of perspective: in order to make effective

choices and recognize opportunities and threats, an autonomous system needs a viewpoint of itself in its environment

These qualities are analogous to the well-known "where,

when, what, who" of descriptive reporting, the "why" of

interpretation, and the "me, here" of local viewpoints. We

have organized them in this way to show the analogies.

Current research work on MUDs includes ways of embodying intelligent agents and studying them in a context where humans and agents can interact. A number of

researchers under the DARPA CAETI (Computer-Aided

Education and Training Initiative) program [1] have been

embodying evaluation agents, intelligent tutors, librarians,

receptionists, and guide agents as part of research in the

use of MUDs and agents in education.

2.3 Social Intelligence

Part of the context for any animal is the presence of other

individuals, both competing species and members of its own species. If we imagine the jungle of the Internet, we

can well envision the situation in which one's own agents

will have to deal not only with well-behaved conspecific

agents, but all sorts of tools with different degrees of intelligence and behavior. They may even have to deal with

malicious software or rogue agents.

Furthermore, even if we have agents that deal only with

carefully selected others, we need to develop much better

ideas of what it means to communicate and behave cooperatively among agents. Many social scientists and now

a few computer scientists [6] [8] have been pointing out

for some time that cooperative behaviors - shared goals,

work, understandings, communications - do not occur inside a participant alone. In addition to the interpretations

of the acts or symbols within each participant alone, there

is also an act of negotiation and agreement among participants as to the meaning of acts (including speech acts).

These mutually-defined meanings are necessary in order

for the group to interact even on the simplest levels, e.g., to determine what constitutes the desired results of even

individually determined actions, or what constitutes that an action has been "done" in order for another agent to

proceed. Clearly these "meanings" can be built in (and

in fact usually are in most agent interactions, in the form

of stopping rules or predefined preconditions for further

activity), but eventually we want to have agents that are "smart" enough to act more autonomously and adaptively.

A key aspect of being able to negotiate among agents turns

out to be the ability to share a common context and to observe the other behaviors within that context. The notion

of niche allows us to create places within which an agent's

behaviors are visible and interpretable both by itself and

by others. In an immediate practical sense, this increases

the "bandwidth" of information that others can process

about the agent; instead of just relying on messages and

self- report, other agents can observe and infer usable information from the agent's behavior. Eventually, we want to use such behavioristic information to form the basis for a

shareable semantics - a real semantics, grounded in shared

experience within this niche - for human-agent communication.

2.4 Growth, Adaptation, and Development

Lastly, Adaptation, like all other sets of mechanisms, will

be itself specialized to different worlds. We consider adaptation to have two somewhat different aspects: one is the

construction and selection of variation spaces within which

the adaptations may occur, and the other is the selection

of actions within those spaces. Biological systems seem

to be able to generate both of these kinds of process as needed, at least to a limited extent. In order that the

system can respond to a wide dynamic range of possible

environmental conditions, a very broad range of potential

behaviors must be available to the system. We call these

collectively the "variation space" for the problem at hand,

and regard the problem of constructing the appropriate

variation spaces as the fundamental part of adaptation.

Making choices once the choices are presented is not as hard.

425
There must be processes that construct variation spaces

within which adaptation can take place, and decision processes that can make adaptive choices within those spaces.

We want algorithms for generating appropriate variation

spaces and decision processes. We want change processes

to make evolutionary behavior automatic. We want some

changes to be directed by history, some by environment,

and some by intention.

We claim that the purpose of adaptation in systems is to allow them to be effective in uncertain dynamic environments, that this purpose argues for complex heterogeneous

systems, and that regardless of the algorithms used for

adaptation, the rest of the organization must have certain

properties for adaptation to work. Adaptation requires

flexibility; every flexibility must have a corresponding co- ordination mechanism, and every such pairing can use dif- ferent methods for adaptation. In fact, every such pairing

must use different methods for adaptation, at least superficially, since their context and scope are different. This

argument leads directly to the requirement for multiplicity

in ALL aspects of the system, including the basic adaptation algorithms.

Adaptation of external interaction behavior (input collection, motion, and communication), using internal representations of that behavior and its effects, is important

for real-world embedding, because it lets the system adjust the dynamic range of its sensors to the current en- vironmental characteristics. Adaptation of internal representations (notations, interpreters, and other processes) is the same process, applied to the internal processing in the

system.

2.5 The Use of Symbols

Biological entities use symbols (mainly chemical) and their

interpretations (mainly through chemical processes) to represent and transmit knowledge of their interior and exterior context [3]. Over time, they somehow also make

interpretations and distinctions at increasing depths of detail, and use previous distinctions to define contexts that

allow them to focus more and more precisely. Eventually,

new symbols arise in context via their use in interactions.

Their meaning is usually inferred, not explicitly transmitted. The general success of this process must mean that

the assumed shared experience that underlies interaction

is sufficient. With computers it will be different; there

is no reason to believe that they will ever have the same

shared experience, so we must examine very carefully how

we can provide the appropriate replacement for the context and knowledge structures supplied by that experience

[15].

In particular, there is a fundamental difference in the way

symbols are grounded. Biological systems have symbols

grounded in the "real world" . Computational systems generally have their symbols grounded in a small discrete sys- tem. We want to construct complex heterogeneous computing systems that have increasingly interesting and ro- bust complexities of behavior, and we believe that this goal

requires an advance in computational practice: changing

the ways in which symbols are represented and used in

computers. We must therefore define computationally vi- able theories of symbols and representation, that is, ways

for programs to work more effectively with the meanings

that underlie the labels used in them, given the relatively

primitive operations on those labels currently available to computing systems. We believe that these theories cannot

be restricted to structures built from indivisible units, and

that we therefore need some new developments in Mathematics to treat this new kind of semiotic foundation for

systems [11] [16].

3 Prospects

Autonomous systems must be complex systems, with an

ever-increasing repertoire of possible behaviors and processes for selecting them, fallback choices to account for

incorrect situation estimation, and quick partial solutions

to reduce decision time. All activity is situated, strongly

dependent on context, and there need to be different decision processes in different situations. This flexibility re- quires an architecture in which many parts of the system

are infrastructure, organizing other parts of the system to identify and address problems, and monitoring their behavior [7]. The ability to reflect on one's own behavior

(and modify it) is one of the main keys to effective autonomy.

We believe that with proper attention to niches, embodiment, social behaviors, and architectures supporting adaptive and reflective behaviors, we can build agents that are more useful partners in an increasingly complex information environment.

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/CAETI" (availability last checked 18 January

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427
The Neurodynamics of Intentionality in Animal

Brains Provides the Basis of Intelligent Behavior

Walter J Freeman

Department of Molecular and Cell Biology

University of California

Berkeley CA 94720-3200

http://sulcus.berkeley.edu wfreeman®socrates.berkeley.edu

Abstract

Intelligent behavior is characterized by

flexible and creative pursuit of

endogenously defined goals. It has

emerged in humans through the stages of

evolution that are manifested in the brains

and behaviors of the vertebrate series.

Intentionality is a key concept by which

to link brain dynamics to goal-directed

behavior. The archetypal form of

intentional behavior is an act of

observation into time and space, by

which information is sought for the

guidance of future action.

The neurodynamics of

intentionality in the process of

observation

The first step in pursuit of an

understanding of intentionality is to ask,

what happens in brains during an act of

observation? This is not a passive receipt

of information from the world. It is a purposive action by which an observer

directs the sense organs toward a selected

aspect of the world and interprets the

resulting barrage of sensory stimuli. The

concept of intentionality has been used to

describe this process in different

contexts, since its first use by Aquinas

700 years ago. The three salient

characteristics of intentionality as it is

treated here are (a) intent or directedness

toward some future state or goal, (b)

wholeness, and (c) unity (Freeman

1995). These three aspects correspond to

use of the term in psychology with the

meaning of purpose, in medicine with the

meaning of mode of healing and

integration of the body, and in analytic

philosophy with the meaning of the way

in which beliefs and thoughts are

connected with ("about") objects and

events in the world.

Intent comprises the endogenous

initiation, construction, and direction of

behavior into the world. It emerges from

brains. Humans and animals select their

own goals, plan their own tactics, and

choose when to begin, modify, and stop

sequences of action, and humans at least are subjectively aware of themselves

acting. Unity appears in the combining

of input from all sensory modalities into

Gestalten, in the coordination of all parts

of the body, both musculoskeletal and

autonomic, into adaptive, flexible, yet

focused movements. Subjectively, unity

appears in the awareness of self.

Wholeness is revealed by the orderly

changes in the self and its behavior that

constitute the development and maturation

of the self, within the constraints of its

genes and its material, social and cultural

environments. Subjectively, wholeness

is revealed in the remembrance of self

through a lifetime of change.

The limbic system is the organ of

intentional behavior

Brain scientists have known for over a century that the necessary and sufficient

part of the vertebrate brain to sustain

minimal intentional behavior is the ventral

forebrain, including those components

that comprise the external shell of the

phylogenetically oldest part of the

forebrain, the paleocortex, and the deeper

lying nuclei with which the cortex is

connected. These components suffice to

support remarkably adept patterns of

intentional behavior, in dogs after all the

newer parts of the forebrain have been

surgically removed (Goltz 1892), and in

428
Dynamics of Intentionality Walter J Freeman

rats with neocortex chemically inactivated

by spreading depression (Bures et al.

1974). Intentional behavior is severely

altered or absent after major damage to

the basal forebrain, as manifested most

clearly in Alzheimer's disease.

Phylogenetic evidence comes from

observing intentional behavior in

salamanders, which have the simplest of

the existing vertebrate forebrains (Herrick

1948; Roth 1987). The three parts are sensory (which, as in small mammals, is

predominantly olfactory), motor, and

associational. The latter part contains the

primordial hippocampus with its

associated septoamygdaloid and striatal

nuclei, which are identified in higher

vertebrates as the locus of the functions

of spatial orientation (the "cognitive

map") and temporal integration in

learning (the organization of long and

short term memory). These processes are

essential, inasmuch as intentional action

takes place into the world, and even the

simplest action, such as searching for

food or evading predators, requires an

animal to know where it is with respect to

its world, where its prey or refuge is, and

what its spatial and temporal progress is

during sequences of attack or escape

.

Neurodynamics of intentionality

The crucial question for neuroscientists

is, how are the patterns of neural activity

that sustain intentional behavior created in

brains? The answer is provided by

studies of electrical activity of the primary

sensory cortices of animals that trained to

respond to conditioned stimuli (Freeman

1975, 1992, 1995; Barrie et al. 1996;

Kay et al. 1996). Cortical neurons are

selectively activated by sensory receptors

to generate microscopic activity. By

interactions among the cortical neurons a

population forms that "binds" their

activity into a macroscopic pattern (Haken

1983; Gray 1994; Hardcastle 1994;

Singer and Gray 1995). The brain

activity patterns that are seen in

electroencephalograms (EEGs) reveal the

macroscopic brain states that are triggered or induced by the arrival of stimuli.

These brain states are not representations

of stimuli, nor are they the simple effects

caused by stimuli. Each learned stimulus

serves to elicit the construction of a

pattern that is shaped by the synaptic

modifications among cortical neurons

from prior learning, and also by the brain

stem nuclei that bathe the forebrain in

neuromodulator chemicals. It is a

dynamic action pattern that creates and

carries the meanings of stimuli for the

animal. It reflects the individual history,

present context, and expectancy,

corresponding to the unity and the

wholeness of the intentionality. The

patterns created in each cortex are unique

to each animal. All sensory cortices

transmit their signals into the limbic

system, where they are integrated with

each other over time, and the resultant

integrated meaning is transmitted back to

the cortices in the processes of selective

attending, expectancy, and the prediction

of future inputs.

The same kinds of EEG activity as those

found in the sensory and motor cortices are found in various parts of the limbic

system. This discovery indicates that the

limbic system also has the capacity to

create its own spatiotemporal patterns of

neural activity. They are related to past

experience and convergent multisensory

input, but they are self-organized. The

limbic system provides a neural matrix of

interconnections, that serves to generate

continually the neural activity that forms

goals and directs behavior toward them.

EEG evidence shows that the process

occurs in discontinuous steps, like frames

in a motion picture. Each step follows a

dynamic state transition, in which a

complex assembly of neuron populations

jumps suddenly from one spatiotemporal

pattern to the next, as the behavior

evolves. Being intrinsically unstable, the

limbic system continually transits across

states that emerge, spread into other parts

of the brain, and then dissolve to give rise

to new ones. Its output controls the brain

stem nuclei that serve to regulate its

excitability levels, implying that it regulates its own neurohumoral context,

enabling it to respond with equal facility

429
Dynamics of Intentionality Walter J Freeman

to changes that call for arousal and

adaptation or rest and recreation, both in

the body and the environment. It is the

neurodynamics of the limbic system,

assisted by other parts of the forebrain

such as the frontal lobes, that initiates the

novel and creative behavior seen in search

by trial and error.

The limbic activity patterns of directed

arousal and search are sent into the motor

systems of the brain stem and spinal

cord. Simultaneously, patterns are transmitted to the primary sensory

cortices, preparing them for the

consequences of motor actions. This

process has been called "reafference"

(von Hoist and Mittelstaedt 1950;

Freeman 1995), "corollary discharge"

(Sperry 1950), "focused arousal" (Sheer

1989), and "preafference" (Kay et al.

1996). It sensitizes sensory systems to

anticipated stimuli prior to their expected

times of arrival Sensory cortical

constructs consist of brief staccato

messages to the limbic system, which

convey what is sought and the result of

the search. After multisensory

convergence, the spatiotemporal activity

pattern in the limbic system is up-dated

through temporal integration in the

hippocampus. Between sensory

messages there are return up-dates from

the limbic system to the sensory cortices,

whereby each cortex receives input that

has been integrated with the output of the

others, reflecting the unity of

intentionality. Everything that a human

or an animal knows comes from this

iterative circular process of action,

reafference, perception, and up-date. It is

done by successive frames that involve

repeated state transitions and selforganized constructs in the sensory and

limbic cortices. This neurodynamic

system is defined here as the "limbic self

1

in the brain of an individual, where

intentional behavior is created, with help

from other parts of the forebrain.

An act of observation comprises Aquinas'

intentional action of "stretching forth" and

learning from the consequences, and the

existential "action-perception cycle" of

Merleau-Ponty (1942). It corresponds to

Piaget's (1930) cycle of "action,

assimilation, and adaptation" in the

sensorimotor stage of childhood

development. His postulated sequences

of equilibrium, disequilibrium, and re- equilibration conform to state transitions

in brain dynamics, which initiate and

sustain action, construct dynamic patterns

in the sensory cortices, and up-date the

limbic patterns by modifying synapses in

the learning that follows the sensory

consequences of intended actions. For

Piaget, cause and effect are chains of

events that have the appearance of linkage

corresponding to the unfolding

experience of that exploration, by which a

child is trying to make sense of its world

by manipulating objects in it. The origin

of causal inference is buried deeply in the

pre-linguistic exploratory experience of

each of us. It is not easily accessed by

cognitive analysis or introspection.

We are all aware of our acts of

observation. It is partly by expectation of

what we are looking for through

reafference, partly by perceiving the

changes that our actions make in the

dispositions of our bodies through

proprioception, and partly by our

selection of stimuli from the environment

through exteroception. We perceive our

intentional acts as the "causes" of changes

in our perceptions, and the subsequent

changes in our bodies as "effects"

(Freeman 1995). If this hypothesis of

limbic dynamics is correct, then

everything that we know we have learned

through the action-perception cycle, and

the iterative state changes by which it is

produced in brains.

Characteristics of brain states

The "state" of the brain is a description of

what it is doing in some specified time

period. A state transition occurs when

the brain changes and does something

else. For example, locomotion is a state,

within which walking is a rhythmic

pattern of activity that involves large parts

of the brain, spinal cord, muscles and

bones. The entire neuromuscular system

430
Dynamics of Intentionality Walter J Freeman

changes almost instantly with the

transition to a pattern of jogging or running. Similarly, a sleeping state can

be taken as a whole, or divided into a

sequence of slow wave and REM stages.

Transit to a waking state can occur in a

fraction of a second, whereby the entire

brain and body shift gears, so to speak.

The state of a neuron can be described as

active and firing or as silent, with sudden

changes in the firing manifesting state

transitions. Populations of neurons also

have a range of states, such as slow

wave, fast activity, seizure, or silence.

The science of dynamics is designed to

study states and their transitions.

The most critical question to ask about a

state is its degree of stability or resistance

to change. Evaluation is done by

perturbing an object or a system

(Freeman 1975). For example, an object

like an egg on a flat surface is unstable,

but a coffee mug is stable. A person

standing on a moving bus and holding on

to a railing is stable, but someone

walking in the aisle is not. If a person

regains his chosen posture after each

perturbation, no matter in which direction

the displacement occurred, that state is

regarded as stable, and it is said to be

governed by an attractor. This is a metaphor to say that the system goes ("is

attracted") to the state through an interim

state of transiency. The range of

displacement from which recovery can

occur defines the basin of attraction, in

analogy to a ball rolling to the bottom of a bowl. If the perturbation is so strong that

it causes concussion or a broken leg, and

the person cannot stand up again, then the

system has been placed outside the basin

of attraction, and a new state supervenes

with its own attractor and basin.

Stability is always relative to the time

duration of observation and the criteria

for what is chosen to be observed. In the

perspective of a lifetime, brains appear to

be highly stable, in their numbers of

neurons, their architectures and major

patterns of connection, and in the patterns

of behavior they produce, including the

character and identity of the individual

that can be recognized and followed for

many years. Brains undergo repeated

transitions from waking to sleeping and

back again, coming up refreshed with a

good night or irritable with insomnia, but

still, giving the same persons as the night

before. Personal identity is usually quite

stable. But in the perspective of the short

term, brains are highly unstable.

Thoughts go fleeting through awareness,

and the face and body twitch with the

passing of emotions. Glimpses of their

internal states of neural activity reveal

patterns that are more like hurricanes than

the orderly march of symbols in a

computer. Brain states and the states of

populations of neurons that interact to

give brain function, are highly irregular in

spatial form and time course. They

emerge, persist for a small fraction of a

second, men disappear and are replaced

by other states.

In using dynamics we approach the

problem by defining three kinds of stable

state, each with its type of attractor. The

simplest is the point attractor. The

system is at rest unless perturbed, and it returns to rest when allowed to do so. As

it relaxes to rest, it has the history of what

happened, but that history is lost after

convergence to rest. Examples of point

attractors are silent neurons or neural

populations that have been isolated from

the brain, and also the brain that is

depressed into inactivity by injury or a

strong anesthetic, to the point where the

EEG has gone flat. A special case of a point attractor is noise. This state is

observed in populations of neurons in the

brain of a subject at rest, with no

evidence of overt behavior. The neurons

fire continually but not in concert with

each other. Their pulses occur in long

trains at irregular times. Knowledge

about the prior pulse trains from each

neuron and those of its neighbors up to

the present fails to support the prediction

of when the next pulse will occur. The

state of noise has continual activity with

no history of how it started, and it gives

only the expectation that its amplitude and

other statistical properties will persist

unchanged.

431
Dynamics of Intentionality Walter J Freeman

A system that gives periodic behavior is

said to have a limit cycle attractor. The

classic example is the clock. When it is

viewed in terms of its ceaseless motion, it is regarded as unstable until it winds

down, runs out of power, and goes to a point attractor. If it resumes its regular

beat after it is re-set or otherwise

perturbed, it is stable as long as its power

lasts. Its history is limited to one cycle,

after which there is no retention of its

transient approach in its basin to its

attractor. Neurons and populations rarely

fire periodically, and when they appear to

do so, close inspection shows that the

activities are in fact irregular and

unpredictable in detail, and when periodic

activity does occur, it is either intentional,

as in rhythmic drumming, or

pathological, as in nystagmus and

Parkinsonian tremor.

The third type of attractor gives aperiodic

oscillation of the kind that is observed in

recordings of EEGs. There is no one or small number of frequencies at which the

system oscillates. The system behavior is

therefore unpredictable, because

performance can only be projected far

into the future for periodic behavior.

This type was first called "strange"; it is

now widely known as "chaotic". The

existence of this type of oscillation was

known to Poincare" a century ago, but

systematic study was possible only

recently after the full development of

digital computers. The best known

simple systems with chaotic attractors

have a small number of components and a few degrees of freedom, as for example,

the double-hinged pendulum, and the

dripping faucet. Large and complex

systems such as neurons and neural

populations are thought to be capable of

chaotic behavior, but proof is not yet

possible at the present level of

developments in mathematics.

The discovery of chaos has profound

implications for the study of brain

function (Skarda and Freeman 1987). A

chaotic system has the capacity to create

novel and unexpected patterns of activity.

It can jump instantly from one mode of

behavior to another, which manifests the

facts that it has a collection of attractors,

each with its basin, and that it can move

from one to another in an itinerant

trajectory (Tsuda 1996). It retains in its

pathway across its basins its history,

which fades into its past, just as its

predictability into its future decreases.

Transitions between chaotic states

constitute the dynamics we need to

understand how brains do what they do.

The cortical state transition is

the elemental step of

intentionality

Systems such as neurons and brains that

have multiple chaotic attractors also have

point and limit attractors. A system that

is in the basin of one of its chaotic

attractors is legendary for the sensitivity

to what are called the "initial conditions".

This refers to the way in which a simple

system is placed into the basin of one of

its attractors. If the basin is that of a

point or a limit cycle attractor, the system

proceeds predictably to the same end

state. If the basin leads to a chaotic

attractor, the system goes into ceaseless

fluctuation, as long as its energy lasts. If

the starting point is identical on repeated

trials, which can only be assured by

simulation of the dynamics on a digital

computer, the same aperiodic behavior

appears. This is why chaos is sometimes

called "deterministic". If the starting

point is changed by an arbitrarily small

amount, although the system is still in the

same basin, the trajectory is not identical.

If the difference in starting conditions is

too small to be originally detected, it can

be inferred from the unfolding behavior

of the system, as the difference in

trajectories becomes apparent. This

observation shows that a chaotic system

has the capacity to create information in

the course of continually constructing its

own trajectory into the future.

In each sensory cortex there are multiple

basins corresponding to previously

learned classes of stimuli, as well as to

the unstimulated state. This chaotic

432
Dynamics of Intentionality Walter J Freeman

prestimulus state of expectancy

establishes the sensitivity of the cortex, so that the very small number of sensory

action potentials evoked by an expected

stimulus can carry the cortical trajectory

into the basin of an appropriate attractor.

The stimulus is selected by the limbic

brain through orientation of the sensory

receptors by sniffing, looking, and

listening. The basins of attraction are shaped by limbic input to sensitize the

reception of a desired class of stimuli.

The web of synaptic connections that was

modified by prior learning contributes to

the formation of basins and to the

attractors. This is an act of observation.

Acknowledgement

This work was supported by a grant from

the National Institute of Mental Health,

and from the Office of Naval Research

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433
Hypermedia Integration of Information Resources for Plant Operations

Lefteri H. Tsoukalas and Robert E. Uhrig

*Purdue University

West Lafayette, Indiana 47907-1290

University of Tennessee, Knoxville, TN 37996-2300 and

Oak Ridge National Laboratory, Oak Ridge, TN 37831-6005

ABSTRACT

Computer hypermedia technologies offer significant

possibilities for integrating data, information and

multifaceted knowledge resources abounding in existing

and next generation plant operations. A hypermedia

system may be viewed as a set of nodes and links

allowing non-linear access to plant information residing

in computers regardless of format. The process of

accessing information in hypermedia systems is known

as navigation. After reviewing the state of the art we

present quantitative criteria for the development of

hypermedia databases and a fuzzy graph-based

methodology for navigating the large information spaces

involved in nuclear plant operations. In the developed

methodology membership functions embodying context- dependent criteria provide application-specific tools for

navigation. The methodology is illustrated through

numerical examples and a HyperCard-based prototypical

system for monitoring special material in a next

generation plant.

KEYWORDS: hypermedia databases, fuzzy graphs,

navigation systems, information systems

1. INTRODUCTION

Among the various aspects of plant operations,

the maintenance and upgrade of stored records and

information resources is probably the least urgent on a

daily basis, yet one of the most important contributors to

life long performance and efficiency. Indeed the

outcome of records and other information resources maintenance and utilization has far reaching implications

for the efficiency of operations, the integrity of safety

systems, the effectiveness of training and the overall

performance of plant technical, operations and

managerial personnel. Hypermedia and the related field

of virtual environments, once thought of as science

fiction-like technologies, are opening new ways for

improving a variety of tasks including, but not limited to, enhancement of training, outage planning, and

component inspections in hard to reach areas.

1,2 In essence, hypermedia allows for a more flexible encoding

and utilization of plant records and human expertise

through the integration of textual, visual and audible

data, with a variety of plant information and knowledge

resources residing in networked computers.

It is technically feasible and possibly

advantageous that records such as design drawings,

scientific and engineering calculations, safety analysis

reports, technical specifications, purchasing and

accounting data, and audit reports, although stored in different formats and platforms, can be integrated and

transparently available to users having a diversity of

backgrounds and plant functions. For example, through

a plant hypermedia system, a safety system may be

viewed not only as a physical object, but a programmable

computer object possessing a number of distinct, yet

equally valid representations, e.g., relations with

neighboring objects (pipes, valves etc.), technical

specifications, manufacturing data, photos, maintenance

records, location video, or acoustic data signatures.

The driving force for hypermedia integration comes from the rapid ongoing advances in distributed

(networked) computer systems transparently sharing

memory and software resources. Computer storage in the order of Gigabyte (10

9 bytes) and network

communication speeds in the order of Mbauds (10

6

bits/sec) are at present readily available; the world wide

web and hypermedia browsers such as Mosaic, Netscape

and Internet Explorer are familiar tools in the vast global

networks of computers opening new commercial

activities around the globe. Hence, it is now apparent

that distributed hypermedia databases will be of great

benefit in, amongst others, tracking the entire history of

plant components, enhancing training, improving

planning and the overall conduct of plant operations.

In hypermedia information is organized as networks of nodes connected by links. A node is the

smallest unit of meaningful information to which a hypermedia link is made. For example, a piece of text, a photograph, a computer screen, a 2-minute video

segment, and a maintenance record of an emergency

diesel generator, can all be thought of as nodes. Nodes

may contain text, graphics, audio, video and software for

operating on numerical and/or symbolic data. A link is a connection between information stored in two different

nodes. A group of links that have related functions is referred to as a link family, and most hypermedia systems

feature link buttons (link icons) which can be arbitrarily

embedded within the content material.

Yet, while it is feasible to store in hypermedia

databases, a multitude of design, maintenance and

434
operations data, as well as plant information and

knowledge to an unprecedented extent, user

disorientation and possibly confusion become the

limiting factors in their efficient utilization. Increasing

the number of connections, or links, increases the

possibility that a user will get lost in irrelevant

information; a situation proverbially known as the "lost

in hyperspace problem." User disorientation may be

particularly severe for large scale applications such as those involved in nuclear plants and given the critical nature or many plant operations, it may actually be a

prohibitive bottleneck as far as the field deployment of

the technology is concerned.

2. REVIEW OF HYPERMEDIA

Hypermedia allows for easy and intuitive access

to documents and programs by linking dispersed yet

interrelated information throughout a document, a program or a series of documents and programs.

Conventional information structures use a hierarchical or sequential logic, i.e., there is a single linear sequence

defining the order in which text is to be accessed. The

typical design report of a plant provides an example of a

hierarchical structure. The report has several chapters;

each chapter is broken to several numbered sections;

each section has one or more numbered subsections; each

subsection may have several numbered sub-subsections

and so on. Figure 1 illustrates the way information is structured in Chapter 10 Materials Handling System of a

Plant Design Report. To access and understand 10,3

Plant Product, we have to proceed from 70.2

Processing, and to understand the description of the

70.2.2 Waste Safety Evaluation, one has to proceed from

70.2.7 Waste Product Descriptions through 10.2.1.1,

10.2.1.2 and 10.2.1.3, solid, liquid, and gaseous wastes

respectively. There are two special articles (shown

within the circular nodes) in the information structure of

figure 1: the Table of Contents (TOQ and the References

(REFS). TOC may be considered an index node (a node

pointing to other nodes), while REFS may be a reference

node (a node pointed to by several other nodes).

Contrary to the hierarchical structure of

conventional information structures, hypermedia

information is structured in a non-sequential or associational manner. An associational information

structure allows a user to go from a node to any other

node directly or through intermediate nodes without

having to observe the linear sequence implicit in figure 1. Hypermedia presents several options to the user who

determines which one of them to follow largely based on

specific informational needs. This nonsequential

organization enables one to store and retrieve

information in a more flexible manner. Research and development in the field of

hypermedia have made considerable progress in the past

decade, steadily moving towards more complex

applications including, but not limited to, pedagogical

projects in numerous fields,

6-7,8' 9 managing and

presenting documentation, 10,11 learning and classroom

applications, ' information retrieval and indexing,

industrial applications,

1 ' 16 electronic journal publishing,

17

and mass media applications.

1819,2 21 ' 22' 23 in several

successful projects, hypermedia systems integrating an

impressive corpus of material related to academic fields

of studies and encyclopedic knowledge have been

developed. Results from a number of evaluations in different learning environments have demonstrated that

hypermedia posses an important edge for accelerating

learning and for supporting new types of learning and

teaching (see ref. 6). In Germany, hypermedia systems supporting

training are currently in the process of being integrated

into existing training systems at several Power Stations.

Since 1994, various hypermedia systems have been

developed and applied to Computer Based Training

(CBT) for plant personnel in subjects such as, thermodynamics, electrical engineering, and operations

in specific plants. For example, a hypermedia learning

program about water hammers in pipes integrating text, video, animation, graphics and sound has been developed

and reported in ref. 1. The system very clearly

demonstrates to users how a high wave blocks the cross- section of a pipe and the resulting liquid plug is accelerated by the flow of steam. Video sequences

provide laboratory visualization of the phenomenon

occurring in a glass pipe and photographs of pipes

damaged by plug acceleration make direct connection

with actual work situations and point to the significance

of the problem in malfunctions that have actually

occurred in several plant environments. The authors of

the system have included a large body of fundamental

scientific knowledge and technical expertise within the

system including possible ways of preventing damage,

user access to system diagrams and operating manuals.

Hypermedia systems feature flexible

information structures and offer great browsing freedom

for the users. Yet, the advantages of flexibility and

freedom come with a potential cost: user disorientation

and confusion or what is popularly referred to as the

problem of being "lost in hyperspace." Previous

attempts to address this problem have concentrated on

improving the user interface through multiple windows,

maps, and tours or path mechanisms. Unfortunately,

multiple windows help only in a limited localized way,

and maps are hard to design and maintain in nuclear

power plant applications when hundreds or thousands of

nodes may be involved.

Another attempt to address the user

disorientation issue is textual analysis, where the

designers of the hypermedia system statistically analyze

word and concept frequencies in order to index nodes by

significant terms, facilitating retrieval and navigation

among relevant documents.

24 Textual analysis provides

only partial solution to the disorientation problem,

435
however, for it is important for readers to individually

grasp the information structure by utilizing their own

criteria and respond to unique application needs. Given

the diversity of user backgrounds and application

requirements, one possible way to achieve this appears to be through fuzzy modeling.

Information-based measures may be used to categorize the links of a hypermedia system in a number

of different ways.

25 One scheme of classification (see

ref. 3) divides all links into: relative position links, hard

links and return links. Relative position links connect

two nodes a pre-defined distance apart. Examples of

such links are the "Go Next" or "Go Previous"

commands allowing a user to go forward/backward

through one node at the time. Hard links, on the other

hand, are connections made from a node to another

specific node, such as for example linking from any node

to a common map or a home page. Hard links are used

in conjunction with conditional structures (e.g.,

IF/THEN/ELSE) to control branching and to control the

display of hidden fields containing information. Finally, return links connect users to a destination node and then

take them back to where the link began, in a way forcing

them to return to the point of departure. Return links are useful for permitting user access to reference nodes and

imposing designer-controlled constraints on where users may go in the information space.

For the purpose of analyzing a hypermedia

structure and facilitating its design through information

measures, it is useful to distinguish between hierarchical

(organizational) and associational (referential) links. The former are used to create a hierarchy while the latter are used to cross-reference information.

3. HYPERMEDIA NAVIGATION USING FUZZY

GRAPHS

In this section we develop a navigational

methodology for hypermedia on the basis of the

generalized theories for information retrieval

26 27 and the

theory of fuzzy graphs.

28 Fuzzy graphs have been used

in connection with fault diagnosis in nuclear

90 applications. In earlier work fuzzy graphs have also

been used in connection with hypermedia integration and

navigation algorithms.

30 A fuzzy graph is defined as follows. Let E\

and Ej be two sets and let XE E-\ and y E &i The

Cartesian product of the two sets is the set of ordered

pairs Ei X E2 A fuzzy graph is defined as the fuzzy

subset G such that

V(x,y)e E) xE2

: He{x >y)^ M

where, JUq (x, y) is a membership function, and M is

the membership set on E\ X E2. The membership

function JJq [X, y

j is a mechanism for grading each

element of the relation represented by the graph.

Afuzzy graph is a graph where the links are not

Boolean, i.e., either 0 or 1, but graded by a membership

function which takes values in the interval [ 0, 1]. A

hypermedia system may be viewed as a fuzzy graph

where different nodes are connected with each other

through some graded link reflecting application-specific or in general user-specified criteria. Thus the navigation

problem in the information hyperspace is translated to a problem of traversing a graph in accordance with some

directional aids quantified through fuzzy membership

functions.

4. A HYPERMEDIA PROTOTYPE FOR THE

MHTGR-NPR

The Special Material Accounting System

(SMAS) is a hypermedia prototype designed to provide

comprehensive monitoring and surveillance of the tritium

produced in the Modular High Temperature Gas Cooled

New Production Reactor (MHTGR-NPR). The objective

of the system is to facilitate meeting required tritium

accountability criteria to within 10 gm of total inventory.

These criteria are established in Plant Design

Requirements Documents along with the overall

performance, functional, interface, operational, safety,

maintenance, inspection and decommissioning

requirements for the plant. An advantage of a hypermedia system in this context is that the multitude of

data and information involved in monitoring the

production of special material over long periods of time, can be integrated with textual, visual and audible data in a manner that facilitates the desired accountability.

SMAS was developed in the HyperCard environment

which includes the object-oriented programming

language called HyperTalk. It consists of three major

subsystems referred to as Target Fabrication, MHTGRNPR Production, and Target Processing. These

subsystems correspond to the three major phases in the

history of the production process, i.e., the fabrication

phase, the production phase (target inside the reactor),

and the processing phase. Once a reliable, tested and

validated version of the system has been developed, it could possibly be integrated with the Production

Assurance Protection System of the Plant.

Figure 2 illustrates the overall architecture of

the Special Material Accounting System. SMAS is designed to have access to historical as well as current

data, and plant information and knowledge as well as access to external networks. In SMAS, the root node is an entrance stack of cards linked to all other stacks.

Buttons that link to a data acquisition program are indicated by the button "Data". Buttons that link to local

historical data are indicated by "Information" and buttons

that include textual or pictorial data are indicated by the

button "Knowledge." A sequence of jumps to a screen

436
containing pictorial information about the target elements

is achieved by pressing the appropriate buttons. The

hypermedia information measures outlined in sections 2

and 3 were used for the development of the system, and

the fuzzy graph based methodology of section 4 provides

the navigational support.

HyperCard is based on the card computational

metaphor where nodes can be either a card, or a

collection of cards is called a stack. Buttons are constructed on the screen (through a HyperTalk

program) and can be activated when a user clicks on

them. Through HyperTalk however, other events can

trigger button actions; for example, when the cursor

enters the button region or when a specified time has

elapsed. A major advantage of HyperCard is that links

do not need to be hard-wired. Through HyperTalk

anything that can be computed can be used as the

destination for a link. This is an advantageous feature

for the purpose of integration. Goto statements achieve

hypermedia jumps or links. Commands such as show

and hide can simulate pop-up windows.

6. SUMMARY

Hypermedia is a technology that takes

advantage of the phenomenal availability of computer

storage and networking capabilities. It allows for the

development of large information spaces, a possibility of

considerable merit for nuclear plant operations. While it

is feasible to store maintenance and operations data,

information and knowledge to an unprecedented extent,

hypermedia utilization is limited by factors such as user

disorientation during access of the large information

spaces involved. To overcome this problem we have

presented a set of information measures primarily

applicable during the design of such systems and a fuzzy

graph methodology pertinent during the use of the

system, i.e., for navigation. The development of

hypermedia systems where information can be retrieved

and utilized to satisfy a variety of needs, requires that a

user can navigate through enormous hyperspaces assisted

by tools that offer context-specific direction. In this paper we outlined a directional tool that allows a user to link to the associated nodes in accordance with

application-specific criteria embodied in membership

functions. Further research is needed to experimentally

test and verify the merit of such approaches in actual

environments. An example of a hypermedia-based

prototype for special-material monitoring was presented.

It is likely that navigational tools will be indispensable

for upscaling development and large-size

implementations where the possibilities opening through

hypermedia for improved operations in nuclear plants

will be tested and realized.

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10.2.2 Safety Evaluations

10.2.1 Waste Product

Descriptions

i

Figure 1. A schematic illustration of the hierarchical information structure of Chapter 10.

438
f

Plant Databases

Local Information

(e.g., historical data,

trends, setpoints)

User

(Operator,

Trainee, Technician, Engineer,

Manager)

Nuclear Plant

Measurements

(On-line Data from Plant Data Acquisition System)

«

Stored Knowledge

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GAMES AND REFLEXION

GAME PROBLEM ON SOFT LANDING

FOR MOVING OBJECTS

Arkadii A.Chikrii

Cybernetics Institute, 40 Glushkov Ave.,

Kiev, 252187, Ukraine

Fax : (044)266-1558

e-mail: chik@dl65.icyb.kiev.ua

Abstract

The game problem on pursuit of a controlled object, moving in the horizontal plane, by another one, moving in the

space, is treated here. In this connection the horizontal

plane may be considered as a state constraint for the pursuer. The goal of the pursuer is to bring together geometric coordinates and velocities of the players (soft landing)

at some finite instant of time. We advance the method

of pursuit for solution of this problem which consists of

three stages. On the first one the pursuit is performed

only by geometric coordinates. The first step ends at so

called critical instant of time which is the last one beginning from which the pursuer can avoid meeting with

the horizontal plane at nonzero angle. The phase states

of the pursuer and the evader at the critical instant are then fixed and on the second stage we solve the problem

of optimal control on the transition of the pursuer into

the evader's position at the critical time with velocity ex- ceeding in magnitude and coinciding in direction with the

velocity of the evader. It goes without saying that during

the transition time the evader leaves his initial position.

That is why on the third stage the pursuit in tracks on the

horizontal plane is performed right up to the soft landing

with the further holding a trajectory in the conditions of

coincidence of geometric coordinates and velocities of the

players.

Keywords : soft landing, differential game, set-valued

mapping, dynamic system, pursuit in tracks, quasistrategy, optimal control.

1 Introduction

In the theory of differential games there is a number of

constructive methods making it possible to solve rather

wide classes of problems under various information conditions. Most employed as strategies are strobostrophic

[4,11], positional [5,19], and quasistrategies [6,14,17]. For

successful termination of the game from the pursuer's

point of view certain advantage of the pursuer in control resources is needed. Most typical and frequently employed

kind of advantage is Pontryagin's Condition and its vari- ous modifications [4,6,11,14,16,17,18].

The specific feature of the pursuit problem on soft landing suggested by J.Albus and A.Meystel [1] as "The Eagle

Snatch" problem is that for this problem not only Pontryagin's Condition but also all its typical modifications

[6,14] fail. The sole exception is the analogue of Pontryagin's Condition dealing with the prolongation of pursuit

time and the allowance for a memory [18]. But even in

this case the constructing of efficient pursuit procedure on

the base of one of the above mentioned methods is rather

difficult problem.

The approach advanced in this paper appears as a combined one that corresponds to the ideology of the Artificial

Intelligence [2,3]. The process of soft landing is partitioned

into three stages. Such procedure seems to be natural and

clear from the physical point of view. It goes without saying that one can not speak about optimality of the time of

pursuit though the behavior of the pursuer on each stage

is guided by the considerations of optimality.

443
Nontheless, the conditions on parameters of the conflict

controlled process are derived ensuring the finiteness of the

time of pursuit for any initial position. Also the controls

of the pursuer ensuring the pursuer's goal are given in

explicit form.

2 Problem Statement

A motion of the pursuer in three-dimensional space is subject to the equation

x + ax — pu, \\u\\ < 1, (2-1)

where x = {x\,X2,x3 ) are geometric coordinates of the

object, namely x\, x 2 denote coordinates in the horizontal plane and x3 is a height. Vectors x and x are a velocity

and an acceleration respectively, integer a > 0 is a coeffi- cient of friction, p > 0 is a force coefficient, u is a control

parameter taking its values in the unit sphere, centered

at the origin of space R

3

, besides function u(t), t > 0, is assumed to be Lebesque measurable [20,24].

A motion of the evader evolves in the plane in the fol- lowing way

y + /3y = <rv, IHI < 1, (2.2)

where y = (y\, 2/2), y and y are a velocity and an acceleration, 0 > 0 is a friction coefficient, a > 0 is a evader's

control parameter taking its values in the planar sphere

centered at zero and being a time measurable function. In order to treat y as a vector in R

3 we shall sometimes write

V = (yi,y2,0) or y = (y,0).

We shall analyse the game (2.1), (2.2) standing on the

pursuer's side. He should perform the soft meeting with

the evader at some finite instant of time, that is, at this

instant the inequalities should hold

\\x - y\\ < £1, Wx-tiW < e 2 (2.3)

The hyperplane {y3 = 0} stands for the state constraint

for the pursuer. The pursuer is allowed to move in this

hyperplane not interesting it. If this is not the case a tra- jectory can be shifted by some 8 > 0 above the horizontal

plane and further considerations would be valid for this case too. Without loss of generality we can assume that x3 —

£3(0) > 0, that is, at the initial instant of time the pursuer

finds itself in the upper halfspace.

In the sequel, for simplicity's sake we shall assume that

E\ — £2 = 0, that is the precision soft landing will be

treated. The passage from solution of this problem to the

problem (2.3) is trivial, and what is more, the solution of

problem (2.3) immediately follows from the solution of the

problem on the precision soft landing.

For convenience of further investigation of the problem

(2. 1 )-(2.3) we reduce the second order systems (2.1), (2.2)

to the system of first order with help of the variables'

substitution

zi - x, z2 - x, z3 = y, 24 = y.

Differentiating in t the above equations with account of

(2.1), (2.2) we come to the equivalent system

z\ = z2

z2 = -az2 + pu

h = Z4 (2.4)

Z4 = —(3Z4 + (TV

From the formal point of view the linear system (2.4)

is a system of 12-th order but in fact only of 10-th, since

vectors Z\, z-z, Z3, Z4 are three-dimensional and the two

last have zeroth third components.

The problem facing the pursuer is to bring a trajectory of system (2.4) from given initial state to the fourdimensional subspace

M0: zi = z3 , z2 = 24 (2.5)

lying in the direct product of four planes for any admissible counteractions of the evader.

The condition on the availability of information to the

pursuer in the course of the game will be further specified

during the solution of the problem at hand.

Denote the phase states of the players as follows

x = (x,x) = (21,22), V = (y,y) = (23,24)

3 Rough Method of Solution

The game problem (2.4), (2.5) is the linear differential

game. The matrix of system (2.4) has the form

A =

(

o3 E3 o3 0 3 \

o3 -aE3 o3 o3 o 2 o 2 o 2 E2

0i 0i 0i 04

o 2 o 2 o 2

V

Oi 0i 0i

The fundamental matrix is

/ E3

l ~ e ~ at E3 a

J o3 o3 \

o3 e~

at E3 o3 o3

0 2 o 2 E2 (3 ^2

0i 0i 0i 0i o 2 o 2 0 2

\

0i 0,i 0i Qi /

Here Ei, 02

- are respectively unit and zero matrices of or- ders i = 1,2,3. We now verify Pontryagin's Condition [4].

444
In so doing the fact should be taken into account that the

orthogonal complement to the subspace Mo is the eightdimensional space L consisting of vectors of the form

(Pi, Qi,P2,q2, ~PuQ3, -P2,?4),

where pi , p2 are arbitrary two-dimensional and qi, i — 1,4,

arbitrary one-dimensional vectors. It is just the subspace

L on which the players' control resources are compared.

Thus, Pontryagin's Condition [4,6,16] for the problem

(2.4), (2.5) is

"

U(t) - V[t) + 0 V* > 0, (3-1)

where

U(t)

1 -e-at

a

pu,e at pu

) MMI<l}.

V(t) =

l_ e

-/9< — av, e 0t av )

: v = (v, 0), < 1

and — is the operation of geometric subtraction or Minkowski' difference [4,6]

X -Y = {z:z + Y CX} = DyeY (X - y)

Note that U(t) and V(t) are convex- valued, compactvalued mappings acting from [0, oo) to 2 R . The relationship (3.1) at fixed t implies that a sixdimensional vector d = (rfi, d2 ), di E -ft3

, exists such that

for any v, \\v\\ < 1, the equations for u, \\u\\ < 1,

-0t-av + di —

1 at

P a

e0t

<jv + d2 = eat

-pu (3.2)

pu

are solvable. This occurs, in particular, at v = 0. Therefore

1 - e~

at d\ = pu0} d2 = e at pu0 , a

where Uo, \\uo\ \ < 1, is the solution to system (3.2) corre- sponding to v = 0. In other words, the system of equations

for u, \\u\\ < 1,

l-e-0* _ l-e-at

, av = p(u — uo)

e Pt av = e

a

-at p(u - u0 )

has solution for any v, \\v\\ < 1. Consequently the equations

1 ,-pt1 - e

-at -av - P a

-pu, (3.3)

'av = e~

az pu, u G Rr, \\u\\ < 2,

have solution u for any v, \\v\\ < 1. Evidently u = Xv,

where A is a certain integer which is positive for v ^ 0. Let us fix some v ^ 0. Then from the second equation of

(3.3) we have

P

Substituting obtained expression for A into the first equation of (3.3) we have

a + (0 - a)e~pt - pe~^~ a)t = 0 (3.4)

When a / (3 the left side of the relationship (3.4) may

vanish only at finite number of points (has no more than

two real roots). These are just the points at which Pontryagin's Condition holds when p < a. If p > a this

condition fails and the method does not work because the

avoidance of meeting is then possible even in the geometric

coordinates [4,25].

Thus, for the problem (2.4), (2.5) Pontryagin's Condition fails. Nevertheless the problem (2.4), (2.5) is in principle solvable in a finite time under certain conditions. Below these

conditions will be given. For this purpose we shall use the

following technique.

Set Ax = zi - z3 , A2 = z2 - z4 . Then from (2.4), (2.5)

we have

Ai = A2 , A2 = -az2 + (3z4 + pu — av

We add to and subtract from the right side of second equation the value 7A2, where 7 > 0 is some integer. Then

Ai = A2 , A2 = -tA2 - (a - j)z2 + (/? - j)z4 + pu - av

(3.5)

From formula Cauchy for the equations (2.4) there follows

that integers ^(.z2

) and t^(z^) exist such that for t >

{a-j)z2 (t)\\ < -\a-y\ +e,

a

and for t > t 2

e (zl)

ll(/?-T>4(0ll<^l/?-7l + £ 1

where e > 0 is an arbitrarily chosen small number.

Note that we may set

(3.6)

(3.7)

and

ln[(|>2

0 ||+i)|a- 7 |]-lne

a

ln[(lk°ll + f)l/?-7|]-ln £

0

So far as the term —(a — y)z2 + (/? — 7)24 has bounded

value beginning from some instant of time, in order to

445
supress its influence with the help of parameter u, we take

into consideration the function

/(7) = -|«-7l + £l/*-7l

a p

(3.8)

Let us find its minimum. One can easily see that it is furnished by 7 equal to either a or /?, and therefore

min/(7) = min{^, ^}- \a-/3\

In order that the pursuer has advantage in the right side

of the equation (3.5) it is necessary that

p-mm{-,?-}\a- /3\ > a

a p

So far it is assumed that ^ > | [4] even for the coincidence

of geometric coordinates the above inequality is equivalent

to the following one

P-j\<*-P\> (T

>

which in the turn is equivalent to the inequalities

p > a and — > — , when a > /?, a p

a

p > (2 — -r)c, when a < /?. r Then for t > max{^(z2), ^1{ za)} the equations (3.5) may

be changed for the equations

Ai = A2 , A2 = -c*A2 + pu-r), (3.9)

where vector rj satisfies the equation

\\ri\\<<T(l + ±\ a -f3\ + e),

in addition p > <r(l + A|a — /3\ 4- e).

It is known [5] that the game problem (3.9) as the problem for the same type objects with the goal Ai = 0,

A2 = 0 is equivalent to the problem of control of the

system

Ai = A2 , A2 = -c*A2 + C, (3-10)

where < p — &(1 + \\a — /?|), with the goal of its bringing to the origin.

It will be shown below that the problem (3.10) has a

solution in a finite time. Thus, if

P>(r(l + L\a-I3\), (3.11)

then the game problem (2.4), (2.5) has a solution in a

finite time. But this time may be rather great since the

estimates of the kind (3.6), (3.7) should hold.

Below we advance another method of solution of the

problem (2.4), (2.5) in lesser time, though this time, generally speaking, is not optimal. The process of the problem

solution will consist of three stages with further holding a trajectory in the set (2.5). The first stage refers to the

game problems of pursuit in geometric coordinates, the

second one is a problem of control for a system of the

type (3.10) on transition from one point to another, and

the third stage is a pursuit in tracks with exceeding velocity. At the first and the second stages one should handle

carefully the state constraint of the pursuer.

4 The Problem of Pursuit

Let system (2.4) at t = 0 be in the position

z° = (zlzlzlz°) (4.1)

We shall treat the problem of pursuit for this system with

the terminal set M* : z\ = z3 . (4.2)

The solution to this system is known and can be obtained either in the class of strobostrophic strategies [4,16] on the base of Pontryagin's First Direct Method or with

the help of Extremal Targetting Rule of Krasovskii [5] in

the class of positional strategies, or in the class of quasistrategies on the base of the Method of Inverse Minkowski

Functionals (Resolving Functions) [6,14]. The guaranteed

time of pursuit is the same for all these methods and appears as optimal. We now dwell upon the last of the

above mentioned methods [6]. Pontryagin's function for

the problem (2.4), (2.5) has the form

TIT/ x 1 - e~

at „ * 1 W(t) = PS3 - -

a

l-e~at l-e'P*

p a

-pt-vS-2 =

a

0

S3 = L0(t)S3

where Si is a unit sphere in space R{, and Pontryagin's

Condition holds if u>(t) > 0. This is true when [4]

p a P><T, ~ >

a p

(4.3)

what is more, if at least one of the inequalities is strict

then u(t) > 0. Denote

1 — p~ at 1 — p~P% at, z°) = z\- z\ +

x-^z\ -l—^—zi

a p

Then the time of the pursuit termination is

T = T(z°) = mm{t>0:\\l;(t > z

o )\\= I u(r)dr} (4.4)

Jo

446
When k — £ - § > 0 the equation in the relationship (4.4)

has a positive root for any z° since at t = 0 the left side

is greater then the right one and as t —> +oo the former

remains bounded while the latter grows linearly with the

coefficient k. In order to find the control, ensuring the capture, we

shall introduce the resolving function of the problem (2.4),

(4.2) according to the technique developed in [6,14]. Set

l-e-X*-')

a(t,T,z°,v) =

+

l_ c -/»(*-r) 1 —<7 P

0\||2 +\m,n\\

,-P(t-r)

1 _ e -f(l-r)

P

a

<T2\\V\\ 2

1/2 -2

Then, if £(T, z°) ^ 0, then on the active segment of pursuit

[(M*), where t+ is an instant such that the test function

[6]

h(U) = l- I

' a(T,T,zQ ,i(r))dr

Jo

vanishes, we choose the pursuer's control in the form

u(t)

,-a(T-r)

a

1 M_ c -/»(T-r)

P

<tv{t)- (4.5)

-a(T,T,z°,i(T))aT,z°)

On the passive segment [t+ , T] we set

u(t) = l_ e -«(T-r)

"J ~P

a

-l

1 _ e -/?(T-T)

cr{;(r) (4.6)

If, otherwise, £(T, z°) = 0 then the control of the pursuer

for r € [0,T] is chosen in the form (4.6). It corresponds

to the control by Pontryagin's First Direct Method [6,16].

This control ensures the bringing of a trajectory of the

process (2.4) to the set (4.2) at time T or, in other words,

this control guarantees the capture of the evader by the

pursuer at time T beginning with the initial state z°

.

We assume that the game evolves under perfect information, that is, in the course of the game an information on current states of the players is available to both players.

Note the following circumstance. At the time of the

evader's capture the velocity of the pursuer X2(t) may form

obtuse angle with the normal to the horizontal plane. This

fact would point to the further intersection of the horizontal plane by the pursuer, that is, to the violation of the

state constraints. This is the reason why the process of

pursuit is ceased at certain instant of time r* , r* < T.

Below we describe how this instant is chosen. Denote

by D(x(T*),t) the attainable set in geometric coordinates

of the system (2.1) at time t from the point x(r*). Then

1 - e~

at D(x(r»),<) = x(r+ ) + x(r.

a Jr. a

-pdrS3

The integral of this set-valued mapping is defined in a standard way [20] as a union of the integrals of measurable

selections of the mapping. In our case the integral of the

sphere of variable radius is the new sphere of the radius

equal to the integral of the initial sphere radius [6,14]. Set

n = max {D(x(r),t) n {x3 > 0} / 0 V< > r},

re[0,T]

where {x^ > 0} is the upper halfspace (above the horizontal plane).

If a motion of the pursuer is to evolve at distance 6 >

0 above the horizontal plane then for the evaluation of

instant r, the halfspace {£3 > 0} should be changed for

the halfspace {#3 > 6}.

Evidently, r* is just the last instant of time when the

pursuer may avoid unwanted meeting with the horizontal

plane. He is allowed only to touch it, not intersecting.

Thus the process of pursuit will be performed only on

the interval [0, r*].

5 The Problem on System Transition from One Point to Another

Let us fix the instant r* and the corresponding states of

the players x(r+ ) and y(r*). We shall analyse the problem

of optimal control of system (2.1) on the fastest transition

from the state x(r*) into the state y(r»), y(r*)(l + e),

0 < e < 1. Thus, the problem is to achieve in the shortest

time the concurrent coincidence of the players' geometric

coordinates and velocities' directions under the advantage

of the pursuer in the velocity's magnitude. It goes without

saying that in so doing the state constraints should not be

violated.

The integer e accounts for the magnitude of wanted advantage of the pursuer over the evader in velocity at point

y(r*). By virtue of Cauchy formula the attainable set of

the system (2.1) in six-dimensional space has the form

D(x0) <) = $(<)xo + $(r)

0

pu

1 l-e

u|| < ljrfr,

(5.1)

a where <!>(<) at J ® ^3 (® i s Kronecker symi I e bol) is a fundamental matrix of the homogeneous system,

and xq = (z^z®) is the initial phase state. This set

447
is convex and closed. Therefore the fact that the point r(^*) = 9 + t*, r(t*) = 1, x* = = (y(T# ),i/(r*)(l + e)) lies in the set (5.1) can be expressed in terms of support functions in the fol- where <* = ^ e

* Then, beginning from the instant 9

lowing way: at each instant of time 9 + t, t > 0, the pursuer will use the information on x(9 + t), y(r(t)), and v(r(t)) striving

( *\ . / *\ < ( — e ~ at °\ _l ft; o\ *° P erf°rm the soft meeting with the evader by moving

[Pi,*i) + [P2,z2 ) S + - z2 J

+ \p.2) hig trackg> that ^ by holding the relationship

i -at o\ f* fl-e~ aT _ aT \ s(0 + f) = y(r(f)), <> 0. + (p2 ,eat 22

° + / p max Pl + eaT

p2 , u dr V ; yK K Jh ~

Jo IMI<i \ <* /

From the wanted relationship (6.3) there follow the relafor allp=(p1)P2 )Gie6

, ||p|| = l- tionsMps

Above the integral and the maxima are interchanged on . . . . _ , . . . the basis of Lyapunov's theorem on vector measures [20].

Thus, the issue on the possibility and the duration of ^

+ t) = jj(T(t))f(t) + §(r(t))i(t) (6.5)

the transition of the system (2.1) from point xq to point

x* reduces to the issue on the existence of a positive root These relationships are equivalent to the inclusion

of the following equation for t

(6.3)

mm

IIpII = i L , z\ - zl + ^—f^'S) + (P2,e~

at z°2 - ,*) +

/JO

(x(e + t),y(T(t))) eMr( t)-i, t>o,

+ / p

where

( 5 - 3 ) M£ = {x = y, x = jj(I + e)}.

' ^

_i_ — OCT J A a ~ From system (2.1), taking account of the relationships

(6-4), (6.5), and (2.2), we deduce the explicit form for

Such root exists. Denote the least of them by p. To ^ , , i J the pursuer s control

it corresponds vector p* = (p*,p2 ) which furnishes maximum in (5. 3). a .. \. In accordance with the Maximum Principle of Pontrya- u ( d + *) = ~ ^)£( r(0) + -y( T(t))f{t)+ (6.6)

gin the program control of the pursuer satisfies the relationship a a

(p(t),u(t))= max (?(<),«), t e[0,e], (5.4)

+ f(t)v(r(t)), t£[0,t*}.

P P

w

system

From the equations (6.1), (6.2) with account of (6.3), (6.4)

i ~ tc\ \ a n\ • ij f , , we obtain the equations

here u = (0,'u), and p(t) is a solution oi the conjugate M

x(^ + r) = y(r(r)) (6.7)

PW= (-1 a )®E3p{t), p(e)=p*. x(9 + t*) = y(r(t*)).

Thus, the soft landing is performed.

6 Pursuit in Tracks

Thus, right to the time 6 the following relationships are

'J The Problem Oil Holding of a

true

x (9) = y(n), x{9) = £(r*)(l + e), n < 9. Trajectory

Performing a soft landing sometimes it is necessary that

Set the equalities in geometric coordinates and velocities hold

2 during some period of time.

r{t) = t* + (1 + e)t 1 2

, t > 0. (6.1) We shall follow the line of reasoning of the previous sec- r*) tion and choose the control of the pursuer from the condiOne can easily verify that tion of the coincidence of current velocities analogously to

(6.6). Then we shall obtain the control which will ensure

r(0) = r#, f(0) = 1 +e, (6-2) the holding of a trajectory in set Mo for t > 9 + t* . The

constraints on the process parameters imposed in Section

r(<) < 9 + t, 0 < t < t* , 3 make such choice possible.

448
8 Conclusion

Thus, the sufficient conditions for solvability of the game

problem on soft landing (2.1), (2.2), (2.5) in a finite time

beginning with any initial state are derived. The process

of pursuit is partitioned into three stages. On the first stage the pursuit in geometric coordinates is performed

on the active and passive segments and the control is cho- sen in accordance with formulas (4.5), (4.6). In the case

of availability of information only on a current position

the same goal may be attained by the methods contained

in [5,19,25]. On the second stage the typical problem on

transition from one point to another is solved. The control

is chosen from the relationship (5.4). This process may be

realized on the base of Pontryagin's Maximum Principle.

Finally, the last stage is a pursuit in tracks. The control ensuring the soft landing is given by expression (6.6).

What is more, the proximity of geometric coordinates and

velocities may be maintained during as great as possible

period of time.

References

[1] /. Albus, A. Meystel, The Eagle Snatch, Intelligent

Systems: A Semiotic Perspective, Proceedings of

the 1996 International Multidisciplinary Conference,

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[3] A. Meystel, Intelligent Systems: A Semiotic Perspective, Proceedings of the 1996 International Multidisciplinary Conference, NIST, Gaithersburg, 1996,

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of Several Dynamic Processes, Izdat. Gos. Univ.,

Moscow, 1990, 198p. (Russian).

181 D.Zonnevend, On One Method of Pursuit, Dokl.

Akad. Nauk SSSR, vol.204, No6, 1972, pp. 1296-1299

(Russian).

191 A. A. Chikrii, Differential Games with Many Pursuers, Matematical Control Theory, Banach Center

Publ., PWN, Warsaw, Vol. 14, 1985, p. 81-107.

201 A.D. Joffe, V.M. Tichomirov, Theory of Extremal

Problems, North Holland, Amsterdam, 1979, 479p.

211 J. -P. Aubin, I. Ekeland, Applied Nonlinear Analysis,

John Wiley, New. York, 1984, 512p.

221 J- Warga, Optimal Control of Differential and Functional Equations, Nauka, Moscow, 1977, 623p. (Russian).

231 T. Rockafellar, Convex Analysis, Princeton Univ.

Press, New York, 1970, 472p.

241 A.N.Kolmogorov, S.V.Fomin, Elements of Functions

Theory and Functional Analysis, Nauka, Moscow,

1981, 544p. (Russian).

251 A. A. Chikrii, Methods for Investigation of ApproachAvoidance Game Problems, Doct. Thesis, Math.,

Kiev, 1979, 282p. (Russian).

449
Game Problems of Control with Delay of Information

Greta Ts. Chikrii

Cybernetics Institute, 40 Glushkov Ave.,

Kiev, 252187, Ukraine

Abstract

An approach to treat linear differential games

with information time lag appearing as a function of

time is presented here. This approach consists in

reduction of linear differential game with

information time lag to equivalent one with perfect

information. It makes possible using all methods and

approaches developed for perfect information

differential games to solve linear differential games

with variable information time lag.

To apply the method connected with time of the

"first absorption" to the reduced game it was

extended to nonstationary case. Sufficient conditions on the game parameters are derived to construct the

control bringing a trajectory of the game with

information time lag to the terminal set in the "first

absorption" time.

Keywords: time lag, terminal set, time of "first

absorption", pursuer, evader.

1. Introduction

R. Isaacs in his monograph [1], dedicated to the

theory of differential games, imphasized an

importance of problem statements in which one of

the players has a time lag on the availability of the

opposer's state vector. In fact, such models most

accurately describe physical dynamic situations of

conflict. There exists a number of methods for

solution of differential games of pursuit [2-4] but all of them work under the assumption that the pursuer

has perfect information about a current position of

his adversary. However, in practice such information

may be available only with some delay in time,

needed for example for processing the incoming

data.

M. Giletti was first, who provided a rigorous

formulation of a broad class of two-person zero-sum

differential games with imperfect information in the

form of a constant time lag [5,6]. He extended so- called Hamilton-Jacobi theory of optimal control and

main equation analysis, developed by Isaacs, to the case of payoff separable with respect to opposer's

control parameter. In the case of separated motions

of the players the differential game of pursuit with

constant information time lag immediately reduces

to the perfect information differential game [7].

In [8-10] the author suggested an approach to

treat general linear differential games with constant

time lag, later extended to the case of variable time

lag [11-131, which made possible using all methods

developed for perfect information games [2-4]. In

this paper we adress the linear differential games

with information time lag which appears as a

function of time. Herein we outline an approach for

studing this class of differential games consisting in

reduction of the game to equivalent one with perfect

information and further extension of the known

method [4] to nonstationary case.

2. Equivalent Game

Let the motion of conflict-controlled system be

snbject to tile linear differential equation

z = Az + u + v, (1)

where z e fl", A is a matrix, ue U, v e V, U c R",

Vc/T. The terminal set,

M, M c fC, (2)

is given. Two players (the pursuer and the evader)

choose controls u and v in competition. The goal of

the pursuer is in the shortest time to drive a

trajectory of the system to the terminal set M by

means of his control choice. The goal of the evader

is the opposite.

As admissible controls of the players serve measurable functions with values in U and V

respectively. Denote the sets of admissible controls

by Qt

, and Qv

. We shall analyze the development of game from

the pursuer's point of view. The crux of the problem
facing the pursuer is the time lag on the availability

of a current state vector. This time lag appears as a

function of time x(t), defined on a half-closed

interval [0, +°°), where x(0) =t o,t ()>0. x(t) is assumed to be nonnegative smooth function with

reasonable restriction on its growth rate: T(t) < 1. The last condition provides current information

about the system development to be continuously

updated. On the initial time interval [-x 0,0) the

pursuer applies an arbitrary admissible control. At

instant t = 0 he comes to know the initial state of the

system, and besides he remembers own control on [-

t

0

, 0), denoted by u" (

•). The pair (z°, u (•)) stands

for the initial position of the game. By position of the

game at instant t is meant a pair (z(t -rfr)), «'(•))>

where «'(•) is realization of the pursuer's control on

the half-closed interval [t - r(t),t). Let Z(t) be a set of

all points attainable at instant t from the point z(tr(0) through «'(•) and various admissible controls of

the evader on [t - T(t),t). In view of formula Cauchy

we have

Z(t)=2T(t)+V(T(t) ) , (3)

where

z(t)=e r(t)A z(t-T(t) )+

t (4)

+ \e it ~6)A

u

t (e)d6l t-T(t)

T(t)

V(T(t) )= je0A VdO (5)

o

We shall say that the differential game of pursuit

with infotmation time lag can be terminated at time

instant t, t > 0, if there exists a strategy of the

pursuer, providing the inclusion Z(t) c M for any

control of the evader. This inclusion can be rewritten

with regard to (3)-(5) in the form

z(t) e M(T(t)), (6)

where

M( r(t))=M - V(( r(t)) (7)

Above the operation of geometric subtraction of

sets [2] was used:

X - Y={z:z+ YdX/,X,Ycz ET

451

It is easily verified that on [0,°°) vector z(t

)

satisfies the differential equation

z (t)=A z(t)+u(t)+

+(1- r\t))e^\(t- r(t)) (8)

with the initial condition

0 z(0)=e T ° A z

0 +je-eA u

T

° (6)dd

Reference to (4) shows that the pursuer has

perfect information about current value of z(t).

Let us consider the perfect information differential

game, described, by the differential equation (8) and

the terminal set M( r(t)) (7). Above reasoning led to the following assertion.

Theorem 1. Let set M(z(t)) be nonempty for t e

[0,°°). The linear differential game (1), (2) with

information time lag t(t) can be terminated at time T

from initial position

(Zq, u (•)) if and only if the corresponding perfect

information differential game (8) with terminal set

M{ r(t)) can be terminated at the same, time T. From this theorem it follows that all methods and

approaches, developed for differential games with

perfect information, can be applied to solve linear

differential games with variable information time

lag.

3. Time of "First Absorption"

To apply the method, connected with the "first

absorption" time [3, 4], for solution of the perfect

information differential game (7), (8) we need an

extension of this method to nonstationary case. Below we provide conditions on parameters and

initial position of the linear nonstationary differential

game with perfect information which are sufficient

for bringing a trajectory of the game to some time

dependent terminal set in the "first absorption" time.

These conditions are an extension, of well known

result [4].

Let the motion of a conflict-controlled system be

described by the following equation

z( t )=A ( t ) z+B ( t ) u+C ( t )V (9)

Here z e R" , u e U, v e V, U and V are convex

compacts, U c R

r

, V c R

5

, A(t), B(t), and C(t) are matrices of order n x n, n x r, and nx s, respectively,

with their elements to be time continuous functions.
The goal of the pursuer is, in the shortest time to provide the inclusion z(t) € M(t), where M(t) is nonempty, convex set, closed for all t e [t

0,°°).

It is assumed that the support function of set M(t)

w = sup (y,x)

XEM(t)

in continuous in \j/ on set

Kw = (v:V€jr,Wiw.W< + -}

and convex cone KM(lj is closed at t e [f

0,°°).

Denote the pair (t,z(t)) by position of the game at time instant t. Let the initial position (t

0 z0) be given.

We shall say that this game with perfect information can be terminated in time T(t0 z0) from the initial

position (t

0 z0) if there exists a strategy of the pursuer,

bringing a trajectory of the process to the terminal

set at some time instant t

; , t; < T(t0 z0), that is

Set

z(t,) g M(tJ

W(\j/,t, z,s)=

s = (6* (s,t)\i/,z)+\max(d* (s, 0)W, B(0)u)dO+

J ueU

t s + [min(6* (s,e)\i/,C(e)V)de, (10)

t X(t,z/ s)=inin[W(y/,t/ s,z)+WMIS) (-yr) J, (II)

A(t, s,z)={ y/:\\i/4=l

W(y/,t,z,s)+WM(s) (-y/)=A(t,z,s) } (12)

Here 6(s,t) is a matrizant of homoge-neous

system z= A(t)z, A(t, s, z)c - KMfs)

. If z(t) € M(t)

then from the definition of support function it follows that

X(t,z(t),t)= min [fv, z(t))+V/MW(-\v )]< 0

m=1

Denote by T(r, z) the least root of the equation for

s X(t, s, z) = 0, which is more or equal t. If there is no such root we set T(t, z)=+°°. Evidently T(t,z)= t only for z(f) e M(r). Unlike stationary case, where

by T(z) is meant the time which is left before

absorption of the terminal set by the attainable set, in

nonstationary case T(t, z) is the time instant of this

absorption exactly.

Theorem 2. Let for any position (tlt z,) such that

T(f7,z; ) < +°° the following conditions hold

a) set A(t, z, T(?; ,z; )) consists of a unique vector

y(t, z, T(tt ,Zj)) for all (t, z) from the neighborhood {t

i

,z,);

h)for all points from this neighborhood

max(0*(T(t1,z1 ),t)y(t,z, T{tP

z)), B(t)u)

is furnished, by unique vector u{t,z,T{t, ,z)).

Then the pursuer can terminate the game in time

T(t

ff z0

).

Proof. Let initial position (t

ff z0) be given and T(tg,z

0) < +<». By assumptions of the theorem there exists a neighborhood of the point (^z0), where vector

\\r(t,z,T

0) T= T(^z0), is uniquely defined. Let us denote this neighborhood by Q(^z0

). Since function

W(\|/, t, z, T0) + WM(To) (-y) is continuous in t, z, and

\|/ then function \|/(f, z, T0) is continuous in t, z and

the' control u°(t, z, T0) furnishing maximum to expression

(6*( T0 t)\f{t, z, T0), B(t)u),

is continuous in t, z. We assign the pursuer's control

inside £2( t

0 z0) to be of the form u = =u°(t, z. T0). Consider the equation

z=A(t)z+B(t)u° (t,z,T0 )+C(t)V(t) , z(t0 )=z0

(13)

For any control v(t) of the evader this equation

has a solution which can be extended up to the

boundary of Q( t

0 z0

). Thus, a trajectory of (13) is constructed on some time interval [t

0 We now

prove the following inequality

T(tI/ z

£7ti ; )<T(t0 ,z0

)

To do this it will suffice to show that

A(t,z°(t) ,T(t0 ,z0 ) )>0,

t0 <t<tx.

(14)

(15)

So far as A(t,z,T0) consists of a unique vector

\\f(t,z,T

0) inside Q( t

0 z0) then X(t,z,T0) has continuous

partial derivatives in / and z there. We now evaluate

the time derivative of X(t,T0,z°(f)), taking into

account the pursuer's control choice on [t

0 ,/J.

452
dX(t,z°(t) ,T0

) _ dt

-(A* (t)lff(t,z°(t) ,T0 ) ,6(T0 ,t)z°(t) )-

max(6* (T0 ,t)y/(t,z°(t) , T0

) , B(t)u)-

min(6* (T0 ,t)y/(t,z° (t) ,T0

) ,C(t)V)+

veV

+ (6*(T0 ,t)y/(t,z°(t) ,T0

) ,A(t)z°(t)+

+B(t)u°(t,z°(t) ,T0 )+C (t)V(t) )

Theorem 3. Let the assumptions of Theorem 2 hold

for the game (9), (8). Then the linear differential

game (1), (2) with time lag x(t) can he terminated

from the, initial position (z°,u°( )) in time T/0, z 0)

4. Example

Below one model game [1] complicated by

variable information time lag on the availability of an object state vector is solved to illustrate obtained

result.

Let the motion of object be subject to the system

of equations

It is seen that the above expression is nonnegative on

[f

0 ,fj, that is function X(t,z°(t),

T

0) does not increase

along z°(t),

te [t

ff t,]. So far as X(t0 ,zff T0) >0. Formula (15) is

true. In a similar way, beginning with the position (tr

z°(t,)) we shall construct a solution of (13) on some

interval [t

; ,t

2

] such that

T(t2 ,z°(t2 ) )<T(tllZ

0 (t,) )

It is easy to see that the construction of trajectory can be prolonged until T(t, z°(t)) will vanish. By

virtue of the inequality (14) which holds true in the course of the pursuit it will occur no later than at time T (t

0, z0

). ) Proved.

Substituting into expressions given by formulas

(10)-(12) the parameters of the equivalent game (7),

(8)

TltlA 0(s,t)=e's- c ' A ,B(t)=I,C(t)=(l-T(t) )e

o z°=e r ° A

z

0 +\e-eA u°(e)ad

-To we denote them by W/\|/,r,5, z ), Xfas, z ), A(t,s, z

)

respectively.

Let T^t, z ), be the least root of the equation for s Xfas^j^O

which is more or equal t. We suppose that for all te [0,<») the support

function of set M(x(t)), namely, WMftfw

(v|/), is continuous on set KMW))= (V-'fe R" Www„(\|/) <

+«>} and set KMfW) is closed. Clearly Theorem 2 holds

true when z is substituted for z. We came to the

following result in view of Theorems 1, 2.

zi=z2 ,z 2 =u,Z3=V, (16)

where z .eR

n

, i=l, J/ ||u||<l,||v||<2/ n>2

We consider the game terminated as soon as 1^-23 1|<£ (e-capture in geometric coordinates).

Let (z°, z°, z°, u°( ) ) be the initial position of the

game. Function x(t), x(t) e C

; [0,°°), x(t) < e, x(0) =x0

is given. Here

M=fz;||z1 -z3 |<£; (17)

Then

¥2 =0,¥; e R",i=l,2,3}

and on KM WM CV) = e||\|/J. Performing calculatios

we obtain

W(y/, t,z°)=(y/1 ,z

0

1 +tz°-z03 )+

t\max(Oy/1 ,u)d0+

\min[ (l-T'(O) ) (-y/ lt v)]dd

0 We observe that V=v=-. furnishes maximum

and minimum in the above expression. Therefore

W(ys, t, z°)=(y/lf z°+tz°-z°3 )+

\¥i\\(—-r0 -t+T(t) )

,

4j

453 Kwm ~am
and for \|/ e KM

^W=lkJI(e-T(t)),

X(t,z0 )=min[ (y/lf z°1 +tz°2 -z°)+

t

2 /2-t-T0 +£]

Minimum in above expression is furnished by the

vector

z°+tz°-z?

provided ||z^+t^-zj*a Then A(t, z 0

) consists of a

unique vector

\j/(t,z° WyfJtrZ- 0

) .O-y^t,*0

) ) ,|M|=V2,

and T(0, z 0)=Tl( (z°,u°( )) can be found from the

equation

z2 +tz2 -z3 =t2 /2-t+£-T0 , (18)

where

0 z

o

1 =z

o

1 +To z°2 +jeu o (0)de/

0 z°2 =z°2 + \eu°(d)dd, z°3 =z

In order that the condition a) of Theorem 3(2) be

satisfied it suffices that the inequalityt72-T0 -t + e>0

holds for t > 0. In the turn, the latter holds when 8 >

T0+l/2. In these conditions u =\|//£, z) is uniquely

defined, that is the condition b) of Theorem 3(2) is

satisfied. From Theorems 1, 3 there follows that

when e > t0+1/2 the game (16), (17) can be

terminated from the initial position (z,°, z°, z°, u°( ) ) in time T(z°, u°( )) defined as the first positive root

of the equation (18).

References

[1] Isaacs, R., "Differential Games", Wiley, New

York, 1965.

[3] Krasovskii, N.N., "Game Problems on the

Encounter of Motions", Nauka, M., 1970 (in

Russian).

[4] Pshnitchny, B.N., "Linear Differential Games",

Avtomatika i Telemechanika, No.l, 1968 (in

Russian).

[5] Giletti, M.D., "Results in the Theory of Linear

Differential Games with an Information Time Lag,

Journal of Optimization Theory and Applications,

Vol.5, No.5, 1970.

[6] Giletti, M.D., "New Results in the Theory of

Differential Games with Information Time Lag",

Journal of ptimization Theory and Applications,

Vol.8, No.4, 1971.

[7] Chernousko, F.L., "On Differential Games with

Information Time Lag", Dokl. Acad. Nauk. SSSR,

Vol.188, No.4, M., 1969 (in Russian).

[8] Dzyubenko (Chikrii), G.Ts., Pshenitchny B.N.

"Discrete Differential Games with Information Time

Lag", Kibernetika, No.6, 1972 (in Russian).

[9] Dzyubenko (Chikrii), G.Ts., "Linear Differential

Games with Information Time Lag", Kibernetika,

No.6, 1973 (in Russian).

[10] Dzyubenko (Chikrii), G.Ts., "On Linear

Differential Games of Pursuit with Information Time

Lag", Kibernetika, No.2, 1974 (in Russian).

[HJChikrii, G.Ts., "On Problem of Pursuit with

Variable Information Time Lag on the Availability

of Object State Vector", Dokl. Acad. Nauk Ukrainy,

No. 10, 1979 (in Russian).

[12]Chikrii, G.Ts., Bardadym, T.A., "On One

Problem of Pursuit with Variable Information Time

Lag", Kibernetika, No.6, 1980 (in Russian).

[13] Chikrii, G.Ts., "On One Approach to Solution

of Linear Differential Games with Variable

Information Time Lag", Problems of Control and

Informatics, No.6, 1994, Scripta Technica, Inc. A

Wiley Company (USA).

[2] Pontryagin, L.S., "On Linear Differential

Games", 1, Dokl. Acad. Nauk SSSR, Vol.176, No.6,

1967 (in Russian).

454
REFLEXIVE GAME THEORY

Vladimir A. Lefebvre

School of Social Sciences

University of California, Irvine CA 92697

ABSTRACT

Traditional game theory is a normative science and is not meant for modeling the real behavior of players. This paper describes

a method the goal of which is to predict the choices of players in real situations rather than to compute optimal decisions. It is assumed that each player faces a choice between two strategies: active and passive.

The method is based on structural representation of a subject together

with his images of the self and another. This representation allows us

to compose systems of equations whose solutions are the probabilities

with which the players choose the alternative strategies.

KEYWORDS: reflexive games, decision making, dynamic

systems

1. THE TRADITIONAL APPROACH TO

GAMES

Game Theory allows us to construct models of the ideal

behavior of players seeking to guarantee themselves optimum

outcome. At its birth game theory seemed to be able to serve not only as a basis for rational decision making but also as a tool for

modeling the real behavior of players. This approach looked

promising at first because laboratory experiments showed that in certain cases game theory can predict players' choices. Most

attempts to use game theory for modeling real strategic behavior

with the purpose of its prediction have failed, however, and are now no longer undertaken. The reason for this negative result is

that the real decisions in strategic situations cannot be explained

only by the players' desire to guarantee optimum outcome.

Today we still face the necessity of creating a general game

theory capable of predicting human choice under conditions of

the conflict of interests.

2. AN ALTERNATIVE APPROACH

In real games players make decisions based on images

of themselves and of their partners. These images are reflexive: a subject can "see" himself and others, together with the images

they have. A simple reflexive structure is represented in Fig. 1. Rectangle a, represents a player who performs an action X,;

rectangle a2 is his image of the self and y2 his image of his

partner. Symbol * is the image of their relationship, and

rectangle x3 is the subject's knowledge about his image of

himself. Speaking in psychological language, in this rectangle

there appear the player's conscious plans and intentions.

Figure 1 . The subject's reflexive structure

In 1966 I put forth the hypothesis that an alternative

game theory could be based on schemes similar to that in Fig.l

[1]. At that time it was only an idea. To construct a theory of

"reflexive games" one needs to know the functions which

connect the rectangles in Fig.l. These functions must be

universal in relation to various human activities, that is, they

must reflect the psycho-anthropological fundamentals of human

choice. In my subsequent work [2,3] I argue that these basic

functions are the following:

y def z,=x == 1-y+yx, (1)

def z2=x»y == xy, (2)

def z3=x©y == x+y-xy, (3)

where x,ye[0,l].

The value of each variable is interpreted as a "measure

of positivity." Function z, describes the correlation between a

player's reflexion and his state: the value of z, is the measure of

the player's positivity when the world influences him with the measure x and he "sees" a situation with the measure y. Symbols

• and © correspond to relationships between the players which

can be only of two types: strong (•) or weak (©). The values of

z2 and z3 are the measures of positivity of situations when

players with the measures x and y are involved.

Now we can begin developing the theory of reflexive

games.

455
3. THE REPRESENTATION OF A PLAYER 4. SAMPLE APPLICATION

We assume that every player faces a choice between

two strategies: an active strategy and a passive one. An active

strategy is a positive pole, a passive strategy is a negative pole.

The relationship between players is described by the operation

def x p y == p(x-y)+(l-p)(x®y), (4)

where pe[0,l].

This operation is a generalization of operations (2) and

(3). Now the reflexive structure in Fig.l can be assigned

functional meaning and written as the following expression:

02 P y2 =X, (5)

where a„a2 ,x 3 ,y2 ,pe[0,l ].

It follows from (5) that X,e[0,l]. The value of a, is interpreted as the measure of the external world's pressure

toward an active strategy on the non-conscious level; the value

of a2 is the measure of pressure of which the player is aware. The

value of y2 is interpreted as the measure of an opponent's

readiness to choose an active strategy, from the player's point of

view. The value of p is the player's subjective estimate

concerning the extent of his involvement in a relationship with an opponent. In a situation of conflict the value of p can be

interpreted as the intensity of confrontation. The value of x3 is

the player's plan or intention, and the value of X, is the objective

readiness of the player to use the active strategy. This value can be interpreted as the probability of the player's choosing an

active strategy. Therefore, X, corresponds to the real choice and

x3 to the player's subjective intention.

Further we will consider a player who performs

conscious actions, that is, he uses only such plans x3 for which

the following equation holds:

X3 -X,. (6)

With the condition (6), expression (5) turns into

equation in relation to x:

Let two companies, A and B, be in conflict. A blames

B for failing to fulfill its obligations. Company A can either use an active strategy, that is, to sue the other firm, or a passive one,

refrain from suing. Company B also has two strategies: active,

to file a counter-claim, and passive, to refrain from filing.

Further we will consider the situation from B's point of

view. Let B not want A to file a suit. A consultant hired by B

advises to threaten A with a counter-claim. To do so, B must

publicly dramatize the situation, using the mass media. But these

actions are expensive. B's executives face a dilemma: to accept

the consultant's advice or to refuse it. The theory of reflexive

games can help B. The analysts from company B have to construct a model of their opponent based on equation (7). Let

it be known that A's lawyers are trying to push the executives to

start the law suit, so B's analysts assume

a2>0. (8)

Since there are no signs that A's lawyers can covertly influence

the executive's subconsciousness,

a,-a2

. (9)

The value of p is the degree of dramatization of a conflict. When

p=l, dramatization is maximal; when p=0, it is minimal. The

value of y2 in equation (7) is B's readiness, from A's point of

view, to file a counter-claim. The more B dramatizes the

situation and threatens A with a counter-claim, the greater y2

. To

reflect this in the model, B's analysts must choose the

monotonically increasing function y2=<p(p). The simplest

function of this type is

y2 =p- (10)

In solving equation (7) with limitations (8), (9), and (10), the

analysts find the probability of A's filing a law suit as a function

of p: l-{l-ax

) (1-p+p 2

) (11)

l-(l-a1

) 2 (l-2p+2p 2

)

'

p y2 =x.

Theorem 1. For any a|,a2 ,p,y2 e[0,l] equation (7) has the root x0 e[0,l].

Mathematical analysis shows that function (1 1) at the interval

[0,1] has its minimum at p=l and p=0, that is, either when the

(7) dramatization of a conflict is at its greatest or when it is absent.

This answer solves the dilemma: company B must reject its

consultants' advice and not spend money on dramatizing its

relationship with firm A.

While modeling the player's behavior we used very

little specific information about him or about the situation. This

is possible only because the model is based on the fundamentals

456
of human choice. Equations (I) through (4) contain this information.

5. GAME REPRESENTATION

Let two interacting players have correct images of each

other. Then the following system of equations corresponds to the

game:

f,(a„a2,p,y,x)=x "

f2(b,,b2 ,q,x,y)=y .

(15)

whose parameters and variables may be related functionally.

Using the theory of reflexive games it is also possible

to construct dynamic models of games. To do so one has to use systems of equations of the following type:

X

*2 p y = X

q X

(12)

= y

Theorem 2. For any a^.p.bLbj.qelO.l] the system of equations (12) has

solution Xo,y0 e[0,l].

Consider an example: let a,= 1/3, a2=3/4, b,=l/3,

b2= 1/2, p=l, and q=l. Then the system is

3

x

(J)

=x

(13)

(I) «x

In transforming these equations into a standard form we obtain a system of two non-linear equations:

Fl(yn>Xn)=Xn+ l

F2 ( X n>yn)=yn+ l

(16)

From the mathematical point of view the theory of

reflexive games is connected with non-linear equations and

dynamic systems.

REFERENCES

[1] Lefebvre, V. A. Elements of Logic of Reflexive Games. In: Problemy Inzhenernoi Psikhologii, 1966, No.4, pp. 273-299.

[2] Lefebvre, V. A. Algebra of Conscience, Dordrecht, Holland:

D. Reidel, 1982.

[3] Lefebvre, V. A. Cosmic Subject. Moscow: Russian Academy

of Sciences Institute of Psychology Press, 1997.

6-6x-4y+xy=0

3-2x-3y+xy=0

(14)

This system has two solutions, but only one of them has roots in the interval [0,1]:

x0=0.557, y0=0.772 .

The model helps us to find that, under the conditions reflected

by the system (13), the first player chooses an active strategy

with the probability 0.557, and the second one with the

probability 0.772. Generally, a game corresponds to the system:

457
I

I

I

I

I

I

I

I

1

III
XVII COMPUTATIONALAPPROACHES

IN SEMIOTICS
til
SUPPORTING END-USER PROGRAMMING

WITH EXPLANATORY DISCOURSE

Clarisse Sieckenius de Souza

Departamento de Informatica. PUC-Rio

Rua Marques de Sao Vicente 225, Rio de Janeiro - RJ

email: clarisse@inf.puc-rio.br

ABSTRACT

The need to empower end users with programming capacities in order adapt and extend software applications brings forth the opportunity to examine and explore semiotic aspects in computing.

This paper discusses some of these aspects within a knowledgebased extensible environment where (a) software designers can

explain their rationale to users and (b) differentiated discourse for user-system interaction and designer-user communication fosters a better understanding of the application's model and features.

KEYWORDS Semiotic Engineering, End User

Programming, Knowledge Representation

1. Introduction

A growing need to empower computer users so that they can

customize, extend, and create software has been fuelling

research in such fields as Human-Computer Interaction

(HCI), End-User Programming (EUP), and Artificial

Intelligence (AI). Software Engineering is rapidly revealing

its semiotic nature as programs and systems produce,

interpret, and become themselves documents and messages

which groups of people can directly or indirectly exchange.

In the sequel of previous work about the Semiotic

Engineering of User Interface Languages [5], this paper

broadens the scope of computer language and message

design in order to try and meet the challenges of wider

computer literacy. It adopts a communication-centered

architecture to support the users' learning processes required

for programming and uses differentiated agent-designer

discourse to help users grasp the intended application's

model.

The main point in this work is a finer structuring of

communication in interface dialogues (involving users, systems, and designers), which promotes programmers and

systems designers to the role of writers of material to be

learned, adapted, and used as inspiration by computational

readers. This is our interpretation of the computer literacy

challenge of software industry. We unite HCI and AI under

the cover of Semiotics and discuss some communicative

requirements and alternatives for intelligent extensible

computer applications. We do not, however, discuss the

features of the underlying macro language in which users can

codify extensions to the application.

The reported work is part of an ongoing research project

aiming at the construction of a fully-functional EUP

environment. The global idea is presented in Section 2, and

specific implementation aspects are raised and discussed in Section 3, with an emphasis on representation languages.

Section 4 presents our current conclusions about the

linguistic requirements for a communication centered

architecture to stand and be useful, as well as the benefits we

identify in this proposal.

2. A Communication-Centered

ARCHITECTURE

User Interfaces can be seen as meta-communications

artifacts. They obviously send and receive messages during

interaction with users, but they are themselves an achieved

one-shot message sent from system designer to system user. This idea is central to Semiotic Engineering [5], a theoretically-based approach to designing user interface

languages and codes. However, user interfaces must now

support not only productive user-system interaction, but also

end-user programming. This can be achieved by more or less sophisticated techniques for configuration settings, macro

recordings, or programming in the small [12; 15], as well as by some knowledge-based (KB) programming by

demonstration [4].

For users to realize that they need and can re-configure, re- program, or extend software, they first need to understand its meaning, and then understand how new meanings can be

added to it or replace old meanings. Such laborious processes

of interpretation should be facilitated and supported by

conscious Semiotic Engineering of computational languages.

Thus, users should not only be able to make sense of

designers' intents, but also express and achieve their own

meanings.

Designers always predict and prescribe communication form

and content. Good designers make good predictions and

write good prescriptions. However, users are seldom (if ever)

deliberately made aware of the arbitrary rules and models

461
!

that underlie applications. In reaction to an excessive stress on grammatical rule-learning imposed by the command

language interface style, current user interface guidelines seem to be heading to some elusive minimal rule-learning

ideal. Popular Graphic User Interface (GUI) style guides [3;

11] follow the trend of capitalizing on metaphors and

analogies, and requiring trivial click'n'drag interactive

modes. But, there is as much arbitrariness and language

learning there as there is in any command language interface.

Our communication-centered architecture is one which

exposes the existence of arbitrary learnable computer codes,

and optionally unfolds [7] successive levels of their grammatical and semantic design rules, so that users can

potentially wield such linguistic resources to build new

discourse, by adapting and programming applications. Figure

1 presents the global scenario for reference in the following.

question-answering and the visualization facilities. MS Word

for Windows, for example, includes the other 3 alternatives

and a macro language interpreter of its own.

designer

Typical HCI Scenario Extended HCI/EUP

Scenario

Figure 1: Communication in HCI & EUP

Along with each extensible application, a rich learning

environment must be provided to users. Important

components thereof are multimodal multicode interfaces,

explanation KB-systems, on-line help and documentation

modules, as well as textual and graphic programming

environments. Embedded explanation modules should help

designers adopt a communication perspective as if they were engaged in documentary book-writing or film-making, and

cared to get their message across.

The basic architecture we envisage for truly extensible

computer applications, from an end user's point of view, is presented in Figure 2. At first sight, the adopted architecture

may appear overwhelmingly complex and undesirable from a

cost/benefit perspective. Nevertheless, at a closer look, we

realize that a number of popular office automation packages

already offer users most of the proposed components. On the User Interface side, the only lacking modes are the NL

Kowledge

Representation Language Interpreter

/ Graphic Interface Widgets

/ Direct Manipulation Canvas

Natural Language

Question-Answering

I Text and Diagram Vizualization

Text Editing

Figure 2: A Communication-Centered Architecture

The missing end of existing extensible applications is the

knowledge base one. In the lower left side of Figure 2, we

clearly see an embedded intelligent system (reasoner and

Knowledge Base (KB)). In the upper side, we see a runtime

consistency checker and a Program and Data Base (P&DB).

This latter component is the repository of end users' programmed extensions which are added to the application in separate modular form.

The overall communication management is achieved by means of integrated programming-explaining activities. When a user engages into introducing a new functionality to an existing application, explanations are elicited from him or her in schematic form. Thus, not only are new items

introduced in the P&DB, but also the corresponding

explanatory items are added to the KB. This feature requires

that programming and knowledge representation languages

be co-referential and maintain consistency between each

other.

Co-referentiality between input and output languages has

been previously proposed in the framework of user-centered

systems design [8J. Our leap here is to extend linguistic coreferentiality from the realm of interfaces to that of

applications. Of course, requiring users to explain their

programming to the system is preceded by requiring the

applications' designers and programmers to do the same. The

whole point of communication centered programming is to

tell people what we as programmers have in mind and

increase the chances that we are understood, and that our

product becomes really useable and useful.

3. Human-Computer Interaction,

Knowledge-Representation, and EndUser Programming

We will now illustrate how a communication perspective

impacts design by resorting to features of a demo KB

application we have been working on. It is based on Pattis el

al.'s "Karel, the Robot - A Gentle Introduction to the Art of

Programming" [16], whose aim is to teach novices how to

462
program. We have built a Visual Basic Interface to Karel's

World (see Figure 3, at the end of this paper), and provided

interaction for Karel's minimal operating capacities about

moving, turning left, picking up and putting down beepers, in

a gridded (limited) space where walls can block his passage.

We have also opened the opportunity for extensions by

allowing Karel to learn new things. The simplest of these,

appears in the upper side of the screen on Figure 3 ("Karel's

learned actions") — TURN AROUND. Along Pattis's lines,

TURN AROUND is a possible user-programmed extension

to Karel's ability that results from a sequence of 2

consecutive primitive TURN LEFT commands grouped

together by some macro recording and naming mechanism.

But, unlike what holds for the original proposal, we want

users to be told about (1) the original programmer's arbitrary

decisions, (2) this programmer's personal interpretations and

intentions in endowing Karel with computing capacity, and

(3) getting the notion of how he or she can now, as a user, change the original model and express his or her own

interpretations and intentions in playing with the

programmable robot.

At the User Interface level, the new perspective in design

becomes evident in the layout shown in Figure 3. The World

View window allows users to deploy walls and beepers in Karel's world via direct manipulation of graphic objects.

Since the idea is to program (i.e. to tell, in linguistic mode)

Karel to evolve in this space, direct manipulation is halted

when it comes to commanding the robot to move and change

the world. For this, users have the more traditional options of

menu selection and button pressing.

Two additional windows appear at the interface: one for

Karel's messages and another for the designer's messages.

The former are the result of the robot's being asked

situational questions such as: "How many beepers do you

have?" or "Where have you been?". The latter are produced

as a typical result of "Why" and "Why-not" questions. For

instance, queries about "Why Karel cannot carry more than

10 beepers with him" should not be directed to Karel, but to

his "creator" — the programmer. The answer is expected to be that the number 10 is an arbitrated value a user CAN or CANNOT alter in the original application.

Note that knowledge in this scenario is used BY THE

DESIGNER, not by the agent. Karel IS NOT an intelligent

agent. We could endow Karel with virtually no knowledge

and have it shutdown if he is ordered to move forward and

bumps into a wall. However, in our program, we have

decided to test for disastrous actions before they are performed. It is the programmer, and not Karel, who stops

the agent short of shutting down and uses a KB explanation

system to reflect his decision that Karel is a physical model

which does not traverse walls. In Figure 3, another shutdown

situation caused by a wrong MOVE command is prevented

by the designer and explained in the lower right-hand side of

the screen.

An interesting extension case is that of a user "teaching"

Karel how to GO HOME. Experienced programmers would

do this by implementing complex graph navigation

algorithms, so that the shortest possible path between Karel's current position and his home (coordinate 0,0) is securely

followed. End user programming, however, could introduce some apparently "naive" computational solutions as making

Karel go home by walking back on his steps (note that in Figure 3, users can ask Karel "Where have you been?").

Since (1) he always starts his journey from home, and (2)

any place he can currently be has necessarily been reached

through a valid path, he can always track his way back by

resorting to his "memory" of visited places.

Minimal path algorithms can be as much of an idealization as

indefinitely large memory store space (required for Karel to be able to remember EVERYTHING he has done from the

beginning of a session). For an EUP scenario, the best choice

is that which represents the least cognitive effort for the user

to program. But, an experienced programmer certainly has

reasons to go for the minimal path idealization. Among other

qualities, this approach is more general than the maximal

storage one; it serves a general capacity of going from any one point in space to another, no matter the peculiar relations

they may bear on an agent's experience in the world (e.g.

having been previously visited, having beepers at it, having

walls, being home).

For Karel to be able to GO TO anywhere in his world, there

must be KNOWLEDGE about the way he was designed.

Most KB systems have no problem in endowing the agents

with such reasoning capacity. Tale telling interfaces to such

systems slip easily into 1st person discourse and present

messages that start with "I cannot" or mention "my path".

The implications of such anthropomorphism may lead users

to build numerous misconceptions about how intelligent and

able computer agents can be. For instance, given that an

agent knows he cannot traverse walls, he could be expected

to know why and what would happen if he could (i.e. have

meta-knowledge).

In our Semiotic Engineering approach, the designer is a legitimate voice in discourse. Whatever the agent can or cannot do, it is a consequence of human interpretation and

programming. Therefore, if Karel is endowed with the ability

go from any one point to another, or diagnose he is walled

into (or out of) a subspace, this is the product of a designers

intellectual and technical decision.

The impacts of having users identify the origin of such

decisions and interpretations is similar to that of letting them

know that trying to undo a SAVE action in typical text editing interaction is not wrong. It is perfectly logical to try

to backtrack from SAVE, in the same way one backtracks

from a SELECT_ALL and DELETE sequence of actions.

However, it is the cost of maintaining formatted files in "buffers" within the application that gears arbitrary choices, even if net damage in both situations is rigorously the same

463
from the user's point of view (i.e. backtracking from a

disastrous piece of interaction).

The costs of imparting more knowledge in extensible

application environments may be high. But, we will give an example of how we have designed an explainable KB in Visual Prolog, to be coupled to Karel's Visual Basic

Interface. It should show that the effect of such knowledge is quite considerable compared to current commercially

available products. A span of Prolog programming for our KB is shown below.

1 . count_bagbeepers :

not ( beepers_in_bag (_) ), nl , write ( "Karel

and his world have not been loaded

yet. " ), nl, !

.

2. count_bagbeepers :- beepers_in_bag (X)

,

X=0 , nl , write ( "As of now, I carry no beepers in my bag . " )

, nl , !

.

3. count_bagbeepers :- beepers_in_bag (X)

,

X<>0 , nl , write ( "As of now, I carry ",X,"

beeper ( s ) in my bag . " ), nl , !

.

Messages associated to the count_beepers predicate are answers to questions about how many beepers Karel is carrying with him at a given point. Although they may at

first look like regular simple output messages any program

can print, from a KB perspective they are epistemologically

different. Clauses 2 and 3 are consistent with an agentcentered point of view. Clause 1, however, is quite different

in that an agent that hasn't been "created" (loaded) cannot

possibly inspect his state. In communicative terms, clause 1

is used in the generation of a Designer's Messages, whereas

the other two are used in that of Karel's Messages. The effect

of multiple-person discourse is more clearly noticeable in the

following case. no_move ( east , coord (X, Y) ) :-

4.1. NewX = X+l, fallof f ( coord (NewX, Y) ) , nl

,

write ("This move would make Karel fall

off the limits of his world ."), nl ,!

;

4.2. NewX = X+l, bump(coord(NewX,Y) ), nl

,

write ("This move would make Karel bump

right into a wall . " )

, nl , !

.

The above OR clause (";") states the disjunction of

conditions that are sufficient for a move to be impossible

(codified in the KB by predicate the

no_move (east , coord (X, Y) ) ) . In our design, this clause

is used in messages generated by the designer — not by

Karel. Our intention is to prevent Karel from being

conceived as an intelligent (even if modestly so) agent. The

implicatures in switching discourse from designer to Karel

have been associated above to arbitrary levels of metaknowledge designers would have to endow computer agents

with. The role of a designer is then to dismiss

misconceptions with messages such as the proposed in 4.1 and 4.2. Moreover, the very fact of telling "the truth" about a computer artifact duly places designers in their seat of

software constructors, and weakens the idea that software is

"just like that", hopelessly inexplicable.

At KB design time, a communication perspective leads us to generate code of the sort illustrated by the following Prolog

lines relative to reasoning about move:

5.1. move , nl , write (" I have moved

forward . "

) , nl , ! ; 5.2. not (move) , nl , write ( "Karel has not

moved forward . " )

, nl , !

.

In other words, we codify not only the knowledge about the

conditions that allow Karel to move and know such things as

his new position and what action he has just performed, but

also those conditions that prevent him from doing so. In each

case, discourse is produced by different communicators. For

every negated action, there must by an associated WHY

NOT question users may ask DESIGNERS to understand

what happened. This is made possible if designers introduce

knowledge codified as.

6 . karel (Ori , Loc )

, no_move (Ori , Loc )

, !

.

Combined with the instantiation of the no_move predicate

proposed in 4.1 above, goal 6 generates the explanation

illustrated in Figure 3. Thus, a discipline in generating

explanatory discourse for every piece of extensible code in a given application is required from designer. This discipline can be facilitated by a programming environment that elicits knowledge from designers and maintain co-referentiality

between programs and knowledge base. From the Visual

Basic end, the code for MOVING Karel has only minor

additions, as seen in:

7. Public Sub MoveO

Dim newColumn As Integer

Dim newRow As Integer

newColumn = column

newRow = row

'begin prolog

<<KB CHECKING>>

'end prolog

iRow = newRow

iColumn = newColumn

vRobot . SetCoords iColumn, iRow

vRobot . Draw

End Sub

The Prolog program call in the code may include data

exchange or file read/writing instructions. The real change in design is a consistency checking one step before codifying

the new drawings to appear in the GUI depicted in Figure 3. The bonus is the generation of explanations and the transmission of the designer's rationale in building these

parts of the application. We should emphasize that those

parts that are not meant to be extended by the user do not

require the same degree of knowledge elicitation and

explanations.

From a user perspective, the interface overhead is that of

connecting user-generated code to user-generated

explanations about code. Just as EUP languages are not C or Pascal, but some easier subset of these, KB representation

languages are not Prolog. The need for more adequate

programming languages goes hand in hand with the need for

464
more adequate knowledge acquisition languages. This is the

aim of ongoing research in our current project.

4. Conclusion

Computer Semiotics has grown from Interface Design [13],

to Systems Analysis and Design [2], and Multimedia

Applications Design [1; 14]. Previous semiotic accounts of

computing, included mathematical perspectives [e.g. 18], as well as philosophical ones [e.g. 9]. The work of Peirce,

himself, with its original logic underpinnings [17], now

experiences a revival in theoretical computing and

information processing [e.g. 10].

The anticipated need for end user programming has not been

fully explored by Computer Semiotics [6], and requires that software design be made with a view on letting users learn more about applications than is required in most current HCI

scenarios. Heavier cognitive loads involved in programming,

if compared to typical human-computer interaction, magnify

the architectural scope of application environments and

suggest that embedded knowledge-based systems may play a major role in supporting the organization of explanatory

discourse about extensible application modules. In semiotic

terms, reasoning systems allow users to gain one degree of

perspective on a designer's interpretation of a given domain,

its objects and tasks, as well as on his or her encoded

abstractions and arbitration in building a computer model of

the domain and its implementation.

This leads us to adopt a broader semiotic perspective on

Software Engineering, and viewing programs generated in the communicative approach proposed above as effectors of

limited semiosis. Although the term may shock the Peircean

tradition, in Computer Science it gains life and dimension as interface messages are algorithmically interpreted in a procedurally limited chain of signs that turn into other signs

and eventually crystallize into output. Whichever sign is present in this chain was once part of the designer's

interpretant derived from the application's domain.

Knowledge-based components attached to extensible

applications empower the designers' capacity to express

themselves, and the users' capacity to make sense out of

systems. We have shown how embedded KB explanation

systems enlarge the spectrum of interface discourse and

allow for computer agents, programmers and users to express

their why's and why-not's in writing and executing software.

The linguistic overhead is that of designing co-referential

programming and knowledge representation languages that users can access from the application's interface.

Acknowledgements

I would like to thank Simone Barbosa for her valuable help in programming and discussing the main concepts presented in this paper. I also owe much reflection about this theme to Ernest Edmonds and Allen Cypher, and to Frieder Nake who has been

particularly insightful with his discussion of "algorithmic semiosis".

Thanks also go to my graduate students, who always make me learn and grow with their enthusiasm, constant questioning and generous

trust.

References

1. Andersen,P. B.; Holmqvist,B.; and Jensen,P. (Eds.)

Computers as Media. Cambridge. Cambridge University

Press.

2. Andersen,P. B. (1990) A Theory of Computer Semiotics.

Cambridge. Cambridge University Press.

3. Apple Computer, Inc. (1992,) Macintosh Human Interface

Guidelines. Reading,Ma. Addison Wesley.

4. Cypher,A. (\993)Watch what I do: Programming by

Demonstration. Cambridge, Ma. MIT Press.

5. de Souza,C.S. (1993) The Semiotic Engineering of user

interface languages, in International Journal of ManMachine Studies. No.39. pp. 753-773

6. de Souza.C.S. (1996) The Semiotic Engineering of

Concreteness and Abstractness: from User Interface

Languages to End-User Programming Languages, in Andersen, P.; Nadin,M.; Nake,F. (1996) Informatics and

Semiotics. Dagstuhl Seminar Report No. 135, p. 11. SchloB Dagstuhl., Germany.

7. DiGiano, C. and Eisenberg, M. (1995) Self-disclosing

design tools: A gentle introduction to end-user

programming, in Proceedings of DIS '95. Ann Arbor,

Michigan. August 23-25, 1995. ACM Press.

8. Draper.S.W. (1986) Display managers as the basis for user machine communication, in Norman and Draper (Eds.)

User Centered System Design. Hillsdale. Lawrence

Erlbaum and Associates, pp. 339-352

9. Eco.U. (1998) On truth: a fiction, in Eco, Santambrogio

and Violi (Eds.) Meaning and Mental Representations.

Bloomington. Indiana University Press

10. Hammer,E. M. (1995) Logic and Visual Information.

Stanford, Ca. CSLI Publications.

1 1 . Microsoft Corporation (1995) The Windows Interface

Guidelines for Software Design. Redmond. Microsoft

Press.

12. Myers,B. (1992) Languages for Developing User

Interfaces. Boston. Jones and Bartlett.

13. Nadin, M. (1988) Interface Design and Evaluation - Semiotic Implications In Hartson, R. and Hix, D. (eds.),

Advances in Human- Computer Interaction, Volume 2,

45-100

14. Nadin, M. (1995) Negotiating the World of Makebelieve: The Aesthetic Compass, in Real-Time Imaging

1, pp. 173- 190

15. Nardi.B. (1993) A Small Matter of Programming.

Cambridge, Ma. MIT Press

16. Pattis,R.E.; Roberts, J.; and Stehlik.M. (1995) Karel the

Robot: A Gentle Introduction to the Art of

Programming. New York, N.Y. John Wiley and Sons.

465
17. Peirce, Charles Sanders (1931) Collected Papers,

Cambridge, MA: Harvard University Press (excerpted in Buchler, Justus, ed., Philosophical Writings of Peirce,

New York: Dover, 1955)

18. Zemanek,H. (1966) Semiotics and Programming

Languages. Communications of the ACM. Vol.9. No. 3. pp. 139-143.

Karel, the Robot (apud Pattis et al.'1995) Session State Help

EE

"Karel's Primitive Actions*

Ptj^B^gperJ pick Be-aper]

"Karel's Learned Actions"

Turn Around Go Home

Go To ...

10

9

8

7

6

5

A

3

2

10

*

1

1 O

Drag to add:

Walls t Beepers

Drop to remove:

Karel's beepers:

| Reset |

0 1 2 3 4 5 6 7 8 9 10

10

Karel's Messages

Karel, where are you?

How many beepers do you have? |Where have you been?

'm at coordinate (1 0.5), tacing East,

Designer's Messages

What was Karel's world like at the start? Why <world state or Karel's action>? ;Why not <Karel's action>?

This move would make Karel fall off the limits of his world

H i

Figure 3: A snapshot of Karel's Worldscreen.

466
An Approach to Computational Semiotics

Ricardo Gudwin and Fernando Gomide

DCA-FEEC-UNICAMP

Caixa Postal 6101

13.083-970 Campinas - SP - Brasil

e-mails: gudwin@dca.fee.unicamp.br, gomide@dca.fee.unicamp.br

ABSTRACT

The aim of this paper is to introduce the theoretical foundations of

an approach for intelligent systems development. Derived from

semiotics, a classic discipline in human sciences, the theory

developed provides a mathematical framework for the concept of

knowledge and for knowledge processing. As a result, a new

perspective to study and to develop intelligent systems emerges. A

taxonomy of elementary types of knowledge is proposed based on

the classification of types of signs in semiotics, followed by a

another classification of knowledge from the point of view of

application in cognitive systems. In addition, we propose the mathematical definition of objects, objects systems and objects

networks, to model mathematically the different types of knowledge

described. The symbiosis of such key concepts introduces a

computational paradigm to develop and implement intelligent

systems, called here computational semiotics.

KEYWORDS; computational semiotics, theory of objects,

intelligent systems, models of knowledge

1. INTRODUCTION

Human intelligence has always been of interest and curiosity

in the scientific world. In 1991, Albus published an outline

for a theory of intelligence, and simultaneously Brooks [3]

argued that for an intelligent behavior, there should not

necessarily exist representation or inference. Additional

aspects of intelligence, e.g. approximate reasoning (including

fuzzy or incomplete concepts), learning, prediction, and

adaptation are being studied in the fields of computational

intelligence [14] and soft computing [13]. Considerable

research effort on fuzzy set theory, neural networks and

evolutive systems have and still are being pursued. The

contribution of these fields in understanding the nature of

human intelligence has been quite impressive.

Parallel to the developments in computer science and

engineering, in human sciences there was a similar effort to model intelligence and intelligent behavior. Well known

examples include the work of Piaget [2], and the development

of semiotics by Peirce and Morris [12,9,10,11], just to mention a few. Semiotics deals with signs (representations),

objects (phenomena) and interpretants (knowledge), that is, the main issues in cognition and communication. Semiotics

has shown to be an useful tool especially when the basic

ingredients of intelligence and their relationships are of

concern. Despite the challenges in discovering the formal mysteries

behind human intelligence and the intrinsic difficulties in

building machines and computer programs to emulate

intelligent behavior, very few works analyzing intelligence in an integrated and organized manner have been done. Often,

only particular aspects of intelligence are addressed. A

notable exception comes from Albus' 1991 paper. In his

work, Albus provides a systematic study of intelligence, and

gives a description of the different parts composing the global

phenomena. The integration of all parts should lead to intelligent behavior. Albus definitions and theorems are

essentially linguistic due to the lack of a formal system to describe intelligence. In other words, currently there is no

adequate mathematical model to describe intelligence as a

whole. Most existing formalisms are closely tied to particular

aspects, being unsuitable for a global, computational

formalization of intelligent systems. Semiotic Modeling and

Situation Analysis-SSA, developed by Pospelov and his team

in Russia was another important attempt in this direction. A

key feature of the SSA approach is extraction of knowledge

from the descriptive information by its consistent analysis

based upon well established algorithms [7]. From this point of

view, mathematical tools of semiotics are considered to include those used in control science, pattern recognition,

neural networks, artificial intelligence, cybernetics. But

semiotic specific mathematical tools (for combining signs,

symbols and extracting meaning) are still in the process of

development [7]. In [8], the use of semiotics as a tool suitable for the analysis

of intelligent systems was suggested. Concurrently, in [4] the

computational view of semiotics for modeling, development

and implementation of intelligent systems, the computational

semiotics approach, was proposed. Computational semiotics

is build upon a mathematical description of concepts from

classic semiotics. Its formal contents can be regarded as a

contribution towards the development of semiotic specific

mathematical tools. Thus, it is in the very realm of the formal

foundations of intelligent systems. The main purpose of this

paper is to introduce the mathematical aspects which

subsumes computational semiotics.

467
2. ELEMENTARY TYPES OF

KNOWLEDGE

Based on the classification of types of signs in semiotics, we

have derived a hierarchy of elementary types of knowledge,

shown in figure 1

.

Knowledge is divided in three main classes, the rhematic

knowledge, dicent knowledge and argumentative knowledge.

Strictly speaking, rhematic knowledge concerns the semantic

of (linguistic) terms, dicent knowledge combines sequences of

terms with truth values and analyses how rhematic knowledge

relates to a real environment, and argumentative knowledge

embodies the knowledge of how knowledge is transformed

comprising reasoning, inference and learning.

3. APPLIED KNOWLEDGE

Based on its intended use, knowledge can be classified as

designative, apraisive or prescriptive (figure 2), terms coined

by Morris [9,10,11]. This classification is complementary to the elementary types of knowledge. In principle, any

elementary type of knowledge can be used as designative,

apraisive or prescriptive, i.e., this classification is orthogonal

to the elementary classification.

Designative knowledge models the world. For this purpose it uses rhematic, dicent and argumentative knowledge, either

specific or generic. Designative knowledge can also be viewed

as descriptive knowledge. A cognitive system initially has just a few, or eventually no designative knowledge at all. Usually

Knowledge

Designative Apraisive Prescritive

Figure 2 - Classification of Applied Knowledge

designative knowledge emerges from the interaction between

the system and world.

Apraisive knowledge is a type of knowledge used as an

evaluation, a judgment, a criteria to measure the success in

achieving goals. In natural systems, apraisive knowledge is closely related with the essential goals of a being;

reproduction, survival of the individual, survival of the specie,

increasing knowledge about the world, for example.

Depending on the goal it assumes special forms like: desire,

repulse, fear, anger, hate, love, pleasure, pain, confort,

disconfort, etc. Essentially, apraisive knowledge evaluates if a given sensation, object, or occurrence is good or not, as far as goal achievement is concerned.

Prescriptive knowledge is intended to act on the world.

Basically, prescriptive knowledge is used to establish and to implement plans through actuators. However, prescriptive

knowledge will not necessarily end up with an action.

Prescriptive knowledge may also be used to do predictions,

but only one of them is selected to generate an action.

Knowledge

Indexical

Rhematic

/

Symbolic

I

Dicent Argumentative

Iconic

Iconic

Symbolic

Sensorial

4

t Specific

Generic

Occurrences

-J—

Analytic Synthetic

l

Deductive Abductive

Specific Generic

Inductive

Objects

Specific Generic

Figure 1 - Classification of the Elementary Knowledge Types

468
4. A MATHEMATICAL THEORY OF

OBJECTS

This section introduces concepts and definitions as a formal

background for computational semiotics. The focus here is on

the main issues and definitions only. For a more in depth

coverage the reader is referred to [4] or [5,6].

4.1. Variable

Let N be a countable set with a generic element n, and

XcU.A variable x of type X is a function x : N -> X . Note

that a function is also a relation and hence it can be expressed

by a set. Thus, x c N x X.

4.2. Class

A class C is a set whose elements Cj are tuples of the type:

(vi, v2 , ... , v„ , fi, f2 , ... , fm ) , n > 0, m > 0

where v; e V,, and fj are functions

f

i

: Xv^Xv

Here means the cartesian product, Pj c { 1, ... , n} and

Q c{l n}.

4.3. Object

Let C be an non-empty class and c be a variable of type C.

Thus c is an object of class C.

4.4. Object System

A set of objects cs is an object system if the q's are related to each other in the sense that each instance of such objects in a

given instant is a function of the instances of all objects in the

previous time instant:

ck (t+l) = f(c,(t), ... ,cn(t) ).

This is only a concise definition of an object system. The

complete definition is far more involved. The reader is

referred to [4] or [5,6] for details.

4.5. Object Network

An object system is a too generic approach for modeling

elementary knowledge types. An object network is a special

type of object system in which additional restrictions

concerning interactions are included. To distinguish object

network and object system let us assume places and arcs whose roles are similar to those in Petri nets. Objects in

places can only interact with objects in places connected

through arcs. Thus, at each instant, the objects defined should

be at one place. For each place there is a set of places

connected with through of input arcs. These places are called

the input gates of the place. Analogously, each place has a set

of places connected with it by means of output arcs, called

output gates.

4.6. Additional Definitions

Other definitions, important for the particular aspects of some

of the knowledge types, may be found in [4] and [5,6]. They

include the temporal restriction for objects, set variable,

generic objects, fuzzy objects, meta-objects, instances of metaobjects, occurrences of meta-objects in objects, generic objects

and fuzzy objects, generic meta-objects, occurrences of

generic meta-objects in objects, generic objects and fuzzy

objects, fuzzy meta-objects, occurrences of fuzzy meta-objects

in objects, generic objects and fuzzy objects.

5. MODELS OF KNOWLEDGE TYPES

Using the mathematical definitions given above, we are able

to model the elementary types of knowledge and use them to build intelligent systems, mainly concerning the applied

aspects of knowledge, i.e., their property of being designative,

apraisive or prescriptive.

Basically, sensorial and object rhematic iconic knowledges

can be modeled by passive objects, i.e., objects that do not

have functions in its image tuples. Occurrence rhematic

knowledge can be modeled by meta-objects (standard, generic

or fuzzy). Those meta-objects can be reduced, however, to

objects by means of appropriated techniques. Dicent

knowledge can also be modeled by objects. Argumentative

knowledge must be modeled by active objects, i.e., objects that

have working functions in its image tuples. The complete

description of such modeling representations can be found in

[4] or [6]. This leads to a scenario where a whole intelligent system may

be modeled by an object network. The representation by

means of an object network has many advantages. An object

network is more powerful than a Petri net in the sense that it allows modifications in its active parts, what is not possible in

Petri nets. This is important for systems that have learning

and adaptive capabilities, which can not be represented by

Petri nets, including there colored Petri nets. The possibility

of representing an intelligent system by a formal

computational tool allows for a more in depth study of

phenomena involving intelligent behavior. Some properties

that were targeted linguistically in early studies of intelligent

systems (e.g. [1]), may be translated into a mathematical

framework, allowing for a more solid foundation. In this sense, the tools provided by computational semiotics seems to be a very promising set of mechanisms for building a future

theory of intelligence.

469
6. CONCLUSIONS 7. REFERENCES

In this paper we briefly introduced a new approach for the

study of intelligent systems. This approach, called

computational semiotics, uses the concepts brought from

semiotics to propose a hierarchy of elementary types of

knowledge, and based on a mathematical framework, models

such knowledges in a mathematical way. Due to its object

oriented nature, the mathematical model is very suitable for

computational implementation, providing in addition, a mathematical description of intelligent systems.

It is very important to stress, though, that such an approach is

in its very beginning. The presented taxonomy of types of

knowledge, despite significant, is only partial. In his works,

Peirce identifies more than 100 different types of signs,

eventually implying in different types of knowledge. These

are not included in the presented taxonomy. But, the

presented taxonomy provides an elaboration of rather

sophisticated intelligent systems. More than that, it creates an

organization that is not usually found in literature,

concerning the differences among the knowledge used when

building intelligent systems. The formalism presented for

objects in this paper, does not aim to be a general theory for

objects, but simply put foundations for a future grow of such a

theory. Some extensions are actually needed, mainly to consider asynchronous interaction among objects. But, the

formalism, in its current form, is suitable to represent

intelligent systems, what is a very important characteristic.

Despite its representation power, the object networks

developed upon the mathematical concept for objects still have many limitations. For example, analysis tools are still

incipient, when compared with other modeling tools, e.g.,

Petri Nets. Indeed, very few systems have been modeled by

the object network formalism. In addition, there is a lack of a formal representation for the types of knowledge not covered

by our elementary knowledge hierarchy. As new types of

knowledge are included in the hierarchy, new formal

definitions would be demanded. Very few intelligent systems were built so far using the computational formalism. To

consolidate object networks as a valid and general tool for

modeling intelligent systems, it is still necessary to solve a broad class of problems to emphasize its virtues and to precisely identify the extensions needed.

An application example concerning the control of an autonomous vehicle was successfully developed and

implemented using the computational semiotics approach

[4,6].

Acknowledgements: The first author acknowledges CNPq for a

fellowship and to FAPESP. The second author acknowledges CNPq

for grant #300729/86-3.

[I] Albus, J.S. "Outline for a Theory of Intelligence" - IEEE

Transactions on Systems, Man and Cybernetics, vol. 21, n. 3,

May/June 1991.

[2] Boden, M. A. - As Ideias de Piaget - traducao de Alvaro

Cabral - Editora Cultrix - Editora da Universidade de Sao

Paulo - Sao Paulo, 1983 (in Portuguese).

[3] Brooks, R.A.- "Intelligence Without Reason" in

Proceedings of the Twelfth International Conference on

Artificial Intelligence, Vol. 1 (1991) 569-595.

[4] Gudwin, R.R. - Contribuigoes ao Estudo Matemdtico de

Sistemas Inteligentes - Phd Thesis - DCA-FEEC-UNICAMP,

Maio 1996 (in Portuguese)

[5] Gudwin, R.R.; Gomide, F.A.C. - "Computational

Semiotics : An Approach for the Study of Intelligent Systems

- Part I : Foundations" - Technical Report RT-DCA 09 - DCA-FEEC-UNICAMP, 1997.

[6] Gudwin, R.R.; Gomide, F.A.C. - "Computational

Semiotics : An Approach for the Study of Intelligent Systems

- Part II : Theory and Application" - Technical Report RTDCA 09 - DCA-FEEC-UNICAMP, 1997.

[7] Meystel, A.M; Albus, J. - "Intelligent Systems : A

Semiotic Perspective" - Report NIST, Intelligent Systems

Division, Bldb. 220 Room B124, Gaithersburg, MD 20899,

USA, 1996.

[8] Meystel, A.M. - "Intelligent System as an Object of

Semiotic Research" - 1996 Biennial Conference of the North

American Fuzzy Information Processing Society - NAFTPS - New Frontiers in Fuzzy Logic and Soft Computing -

Berkeley, California, USA, June 1996.

[9] Morris, C.W. - Signs, Language and Behavior - New

York : Prentice Hall, 1947

[10] Morris, C. W. - Significant and Significance - New York

- Prentice Hall, 1964.

[II] Morris, C. W. "Foundation for a Theory of Signs" - in

Writings on the General Theory of Signs - The Hague : Mouton, 1971

[12] Peirce C.S. - Collected Papers of Charles Sanders

Peirce - vol I - Principles of Philosophy; vol U - Elements of

Logic; vol III - Exact Logic; vol TV - The Simplest

Mathematics; vol V - Pragmatism and Pragmaticism; vol. VI

- Scientific Metaphysics - edited by Charles Hartshorne and

Paul Weiss - Belknap Press of Harvard University Press - Cambridge, Massachussets, 2

nd printing, 1960.

[13] Zadeh L. - "Soft Computing and Fuzzy Logic", IEEE

Software, vol 11, n. 6, pp. 48-56, 1994.

[14] Zurada, J.; Marks n, R.J.; Robinson, C.J.- Computational Intelligence - Imitating Life - IEEE Press,

USA, 1994.

470
Sequential Algorithm for the Semantic Representation

of Actions in Terms of Moving Parts

Hiroyuki Nishina

Saitama University

255 Shimo-Okubo, Urawa, Saitama 338, JAPAN

ABSTRACT

This paper reports on a new model giving a sequential semantic

representation of an action verb. We show that the algorithm for static

categorization which utilizes Ideational information to represent the

defining characteristics of individuals can also play a central role in the dynamic categorization. Static categorization involved in the

definition of stative predicates is stipulated in terms of Category

Function. Orientation Function, taking as one of its arguments the

defining characteristics of the denotation of each category, is defined to capture the correspondence relation between the bodies of the same

individual at two different time-points. With the former two functions and the function derived from the latter, it is possible to construct an

algorithm to trace the movements of the place-points of individuals'

bases. This enables us to distinguish the parts which have more or less moved from those occupying the same space. Our point is that capturing sequentially the moving parts (of an individual) relevant for an action it performs is, in principle, necessary and probably sufficient

to represent and interpret the cognitive meaning of action sentences. The moving parts playing central roles in order during each action are

defined in terms of the features similar to those utilized in phonology.

After the notion "interval" is introduced to decompose the structure of

action sequentially, Action Function, the total algorithm for specifying

the moving parts involved in each step of an action, is defined and

discussed. The category function is built into this algorithm together

with the interval length function. Action Function is a device for "monitoring" and mark the parts of an action as it proceeds. Action

formula, another algorithm for action without recourse to intervals, is

also defined and investigated. Finally, some residual problems involved

in this framework are pointed out and discussed. KEYWORDS: orientation, categorization, defining features,

intervals, action Junction, action formula

1. HISTORICAL BACKGROUND

In the semantic studies sofarundertaken, efforts have been made to construct the adequate interpreting device based on the semantic

relations bom by the main verb toits arguments. For this purpose,

several universal primitives have been sought to represent and

explain the overall structure of propositional meaning. LakofPs

causati ve analysis showed the maimer to factor verb meaning into

primitives and represent it with lexical decomposition [7], and

Jackendoff proposes the lexical structure in which propositional

meaning is translated in terms of thematic relations [5] , originally

proposed in Gruber [4]. With these, it has become possible to represent explicidy the semantic organization of the overall

state/event structure denoted by die relevant verb ofeach sentence. Thematicrelations wereneatlyaccommodatedinto the government

and binding framework proposed in Chomsky as theta roles [2]. In

the causative analysis, the causer is made distinct from the caused

event, and in the thematic-relational analysis, verb meaning is categorized in terms of moving object, the way of motion, the moving manner, etc. In neither case, however, semantic

"factorization"issequential, thus neither analysiscan represent the temporal change in die motion of the agent of an action in a stepby-step manner. MontagueGrammarwas successful in representing the meaning of

syntacticconstituentsinpurelydenotationalterms.wliichprocedure was achieved in a compositional manner by using type theory [8]. His model theory consists of an ontology, a set of entities, and a

denotation assignmentfuncti on, thelatterofwhichassignsaunique

denotation to each constant in the object language. In this model,

grammatical categories belong to functional types, thus the denotation of transitive verbs of <e,<e,t» being represented as

({1,0}

A)A - This extensional analysis, however, cannot reach the

internal structure ofverbs.unlesssomedecompositional approachis

invoked. It did not dare to decompose verb meaning dynamically,

solely translating it as a semantic primitive.

In this paper, I will introduce a new semantic model in which

denotationassignmentcanbeperformedsequentiallyindiecasesof

action verbs in order to represent each step of their processes. I will show diat by postulating that each individual is a sequence of sets of

place points occupied by it at time-points, a more articulate

structure can be given to die model.

2. CATEGORIZATION AND PARTS

One of the human cognitive abilities is categorization of tilings

fromUieirappearances. This is possible because humans can sort out some individuals as a specific kind from odiers by checking all

the bits of its apparent definition. Humans can also further

distinguish die individuals of die same category, not oidy humans

but odier higher animals, still lower organisms, even minerals. On

die odier hand, diey can identify die same individual, though it is

471
seen from different physical points of view. Thus, humans can

readily identify the upright and upside-down figures of the same

individual. The point is that despite such various differences,

individual or orientational, humans can do readily determine

membership. This indicates that criteriafor categorization should not be too narrow nor broad to include into the same kind.

Whenrecallinga thing ofa certaincategory tomind,wecanreadily

imagine the parts which contribute naturally to the definition ofits

kind. Thus, in the case of "horse", it has such and such a head, a

tail, legs, etc. In that of "human being", he/she has such and such

hands in addition to his/her head and legs. It would, however, be a

bit unrealistic to think of a desk or a table without legs totally.

Weassumethatwhenconfronted withanindividual whosecategory

is to be determined, humans match i t with the stored "prototypical

sets offigures (including their parts) shared among the members of

the relevantcategories. Eachcategory can be successfully assi gned

to an individual only when the tatter's figure can be exhaustively (or

sufficiently in most in exceptional cases) decomposed into the

primitive parts which are to be matched to those of the former's

prototype. Those building parts of the target indi vidual , in turn, can be reconstructed into the meaningful whole belonging to the

former.

3. CATEGORIZATION OF ACTIONS

Motions are spatiotemporal objects. Human beings can recognize

several , not all , ofpossible motions andverbalize Uiem as actions if

they fulfill the definitions of the action verbs of their own

languages. This does notmean that the possible "actions" excluded

from verbal actions cannot belinguistically expressed. They canbe

expressed by building words into phrases. In a purely physical

point of view, actions are spatiotemporal continuums. Each action

involves a continuous change ofappearance exhibited by its agent

It would, however, be incorrect to say that humans can only

recognize such objects as actions if they continue to observe them,

hi real perception, itis very often sufficient to recognize an acdon

merely by glimpsing at the appearance of its agent. This is

sufficiently possible despite the fact that all of the tokens of an

action are distinct in not only time and location of occurrence but

also duration, size, proportion etc. This is a piece of evidence that humans are capable ofcategorizingvarious tokens ofamotionunder one category of action in a manner that does not burden them with so much load for recognition.

4. POSTURES OF MOVING OBJECTS

To understand what an individual is doing and to express (a

part/parts of) its movement in terms of an action sentence of a

natural language, we need to capture not only the position but the

posture of the moving individual at each time during its action.

Seen as a moving physical object, however, an individual

performing an action is undergoing a sequence of changes in the

position of its volume. To decide which category of acdon the

relevant movement belongs to, wehave to deliberately distinguish

the changes in its posture from the concomitant transition of its whole volume.

If we focussed solely upon the course of its movement, we could

easily detect its trace as a path with some thickness occupied by the whole volume of the moving individual. But this is not enough.

To accumulate sufficient information for categorization ofaction, we need to keep calculating the posture at each step of a mover in terms of the parts involved in the relevant action during it There are two possible approaches at present available to realize

this. The first one is to specify totally sequentially the sets ofparts

involved in the relevant action at each timepoint in terms ofa placepoint set. The second one is to show the inclusion relations of

subactions which are sequentially described in terms of the parts

involved in the total action.

5. PARTS IN TERMS OF FEATURES

It is useful toconsiderhow speech soundsare recognized byhumans

and described by linguists. In each particular language, despite die

mdividualdifierencemthestrength,length,pitches,quality,etc.of

the "same" phone produced by speakers, they share some average

/referential sound of psychological reality widun dieir speech

community. Tocapture Uiis.in phonology, each family ofphones

that are approximately equal in articulatory point is selected from

die inventory ofall die phones producible by humans and is given a phonedc value, whichis givenalabel of "phoneme". Furthermore,

ingeneradvephonology.eachphonecorrespondingtoonephoneme

isdefinedasabundleofdisdncdvefeatures.whichspecifyamanner

of ardculadon mainly based upon an articulatory point [3]. This is applicable to the definidon of semandc representation of

acdon verbs, since die latter is definable in terms of "parts involved

ini ts "consd tuent " movements". The difference between diese two

cases is that the latter involves "acdon", the spatiotemporal object

extending over dme in such a procedural manner that requires a

sequential definidon of parts involved in the relevant acdon.

Aldiough the disdncd ve features for one sound mainly involve no

factors related to dme sequence since it is defined in terms of a simultaneous complex of articulatory parts, they provide us a promising hint toward die dynamic representadon of acdon verbs. We thus assume diat each action consists of a sequence of

subacdons (or sets of subacdons) definable in terms of parts

involved in diem.

6. SPATIOTEMPORAL INDIVIDUALS

472
By extending the index introduced in Montague and extended in Barwise and Perry, which consists of a possible world and an

interval of time [1], we propose a model where the spatiotemporal

structure of an action is described in terms ofa sequential set of the

features denoting the parts involved in that action. To enable this,

the location of each individual is established based on placepointtimepoint pairs. Thus, each individual's location is represented as

the set of placepoints occupied by it at each timepoint: Base

Fti/icfio/j.takingindividual andtimepointasarguments, returns the volume occupied by the former at the latter.

7. BASE FUNCTION

In order to specify (sets of) placepoints on individuals, it is necessary to be able to calculate their location at each timepoint

Let each world at a timepoint be full of placepoints, with the same

world continuing toexist along an axis of timepoin ts. At each time

ofits existence, eachindividual occupies a setofplacepoints, which

will henceforth call its "base". To locate individuals' bases at each

time, we define Base Function as:

/?(*, y)=z, where x SIND>y ET, z <ZV.

Witliindividual and timepoint as its arguments, jB returns the set of

placepoints (i.e. base) occupied by the former at the latter.

8. ORIENTATION FUNCTION

Weshowedtliataspecificoccurrenceofactioncanberepresentedby means of Orientation Function [9]. Taking a category, a set of

placepoints and a placepoint as arguments, this returns as value a

content point, whose ordinal numberindicates the orderin which to count the input placepoint of the base:

co(x, y, z)=w,

wherexECAT, y

€2*"- <f>, z €P, w €CU{e }.

The resulting order is the criterion for orientation by which the

relevant individual is cognized by die observer as falling under the input category. It was shown that an instance of walking can be

described in terms ofa set of sequences of placepoints occupied by

the content points of its agent individual.

9. THEORETICAL BACKGROUND

Accommodating die notion of "feature", introduced in Jacobson, Fant andHalle [6] andChomskyand Halle, weproposed elsewhere

diat stati ve categories bedefinedby sets offeatures and diat relevant

(partsof)individualsbelocatedby CategoryFunction . This, taking a subset of placepoints and a feature, returns the placepoint set denoted by diat feature:

y >Z, where x G2P-{4>yy GDj, z&r orz=4>.

This function enabled us to set up Fulfillment Condition, which

specifies anindividual'smembershipinthe set denotedbya category

in the following way: if and only if the union of the subsets of the base ofanindividual whichcorrespond toall ofthedefiningfeatures

of a static category is included into that base at a time point, the

individual belongs to the relevant category at that time. Taking the category BIRD as an example, its prototype has a beak, wings,

stick-like legs, etc. The fulfillment condition for BIRD is:

j

BlRD(inda) at tb & \Jbird(j3(inda,tb), a\) £ j8(inda,tb),

i=l

where Dbirj=^d\.beak, d^.wing, d^.stick-like leg, ...},

saying that at timepoint b, individual a belongs to die category

"bird" if and only if all of the defining features of dus category,

among which are "beak", "wing", "stick-leg", never fails to find

their location on the base of a at b. To be able to idendfy the posture of a moving individual , we need some standard with which to measure the moving parts. For this we invoke the reverse partial function of Orientation Function,

capturing thepoint-to-pointcorrespondencebetweendie basesofan

individual at two different timepoints.

10. PROBLEMS

The first problem addressed here is how to represent the continuous

change in the shape of the moving agent as i t performs an action. It was shown by us that this is done by decomposing each action into

subactions definable in terms of the parts of its agent [10].

The second problem is how to identify various tokens ofone action

as belonging to the same category. Twocandidates for tlii s task are

possible: to define each action as a sequence of sets of features,

which specifies die parts in motion in order and as a complex of

subacdons by specifying a moving part individually. For the first

algori dun, some device lias to be created to focus on the order of the

parts involved in a whole motion, neglecting the real time lengths

between the initial and terminal endpoints of the subacdons

involved in instances of the same type of action. To enable diis.

Interval Length Function is invoked to"neutralize" the individual

difference in the relative lengths of the intervals which switch the

parts in motion. Nointerval function nor i ts equivalent needed for

die secondalgoritlim, where theorderofsubactionsinvolvedineach

action is sufficient for dieir sequential specification. Furthermore it

is necessary to compare the two devices and set up a relation

between these. We will discuss this problem and give it a tentative answer elsewhere.

473
11. INTERVAL LENGTH FUNCTION

Wemust now see an al gori thm which, at each interval on the whole

time axis along which an action takes place, specifies a set of

defining features and locates their denotation on the placepoint set occupied by its agent, i.e. its base. It is important to note, here,

that the 'timing' of changing intervals is not specified, in view of

the fact that agents of the same action usually differ in the lengths

ofcompatible intervals. Thisremindsus the description of speech

sounds in terms of phonemes, which we have seen before. Let us assume that Interval Length Function fmiv\(x)=y takes the integerx

of the or-th interval involved in an action and returns its length y in tenns of the number of the unit intervals constituting that

interval:

X-th interval

1 2 3 4 ...

I I 1 1 1 1 1 1 I 1 1 I I I 1 I 1 • ' '

'i h hUHhh H Mio'n'n'is'u'isWn ... 2 3 6 4 ....

Length y of interval x: where/i„ft,Kl)=2, /i,„v/(2)=3, /i/,/vK3)=6, /mw(4)=4

If werepresent each interval involved in an action as anordered pair

of its endpoints, the endpoints of /-th interval <t

q

,tt> of the whole

interval of an action starting at /j are calculated by using Interval

Function as follows:

<t

q Jf>u such as:

«=1: «Fj,r=fintvl(\)+j>,

u-l u u^2: <q= Z/i,,/v/(k)+j. r= Tfin ^k)+j >.

The calculation of the endpoints of each interval is based upon the

fact diat the number of die right endpoint is equal to that of the

initial point plus Uiat of the left endpoint.

In this sense, Interval Length Function plays an essential role in grouping various tokens of the same action together into one type

of action, which has die invariant denotation of an action verb. By

all owing eachinterval to range freely, this function helps tocapture an observable fact tiiat die lengUis of the durations ofdie subactions

constituting a whole action are usually different in its real

occurrences.

12. ACTION FUNCTION

Watching an action closely to its end, we can see diat its agent

successively changes its posture, during which die location in

motion shifts from one sets of parts to anodier to complete an

action. Thus, each action is defined as a sequence of sets of moving

parts. Totake the action of "nodding" as an example: first the head

gets bent forward, second the neck moves forward to some extent while the head is continuing the same movement, third the movement affects the shoulder with the other two parts continuing

the same, fourth all these parts halt for a moment, and they resume

this process backwards. The sequence ofmoving parts taking parts

in"nodding"canberepresentedas: nod: D„=<{head},{head, neck},

{liead, neck, slwulder}, ... >. The sequential specification of moving parts enables us to define

Action Function . At each interval of the whole duration of an

action, thi s al gori thm specifies a set ofdefining features and locates

their denotation on the placepoint set occupied by its agent:

<*i<tj. <t

q

> tf>u, KiX0(x, y), D\u))=z,j-£q+l-£h-£r,

where* EIND, y =th eT, z €2>>-{4>},

u=l: <q=j, T=fintvi(l)+j>,

u-l u u^2: <q= Zfinniiky+j, r= ?-fintvi(k)+j >.

k=l fc=l

If die base function, the first argument of die extended category

function, which is in turn the third argument of an action function,

takes an individual and die starting timepoint tj and calculates its

base, then the action function picks up the first interval(, which

contains diat timepoint and is of allowably arbitrary lengdi,) from

within the overall interval of the action a;, starting at ti andretum

as its value a subset of the base which corresponds to die first set of

features of the defining sequence for the action a,-. Similar

calculation is iterated until the relevant timepoint exhausts the first

interval. Switching to the second interval, the action function

returns a subset of die base for the second feature set of the defining

set and each timepoi nt of the second interval , si mil ar process being

iterated until the last interval is reached. Thus, the category

function embedded in this function plays a central role in

representing the meaning ofeach action by displaying sequentially

the denotations of die moving parts of its agent.

13. CATEGORY FULFILLMENT

Using Action Function, we set up Dynamic Category Fulfillment

Co/id/7/o/i.,aninteqirctationmecliaiiismwliichchecksifacandidate

situation falls under the relevant category of action. If, by

decomposing an action into several intervals, we can find that the

parts of its agent which have changed their positions during each idiinterval contain the parts specified by die value returned from an

action function widi diat / -di set of feature as its second argument,

dien we can decide that die movement belongs to die category

denoted by diat function:

474
{yl<*,y>G( {co(IND,0(inda

,tk+ l ))y-l

-aeo(IND,/3(inda,tk

)))'-i

2 a,{tjt <t

q,t^u, ic

, £0Qnda

,tk+ x ),Du J).

This is a recognition device which, given a complex of actions

performedbyanindividual judgeswhetherthecomplexcontains the

specified action. Then, how are we to represent actions in these

terms?

14. ACTION FORMULA

In contrast to the sequential specification of the subsets ofdefining

features denoting the parts involved in motion, we can set up

another algorithm, Action Formula. This specifies the defining

features as they are individually without reorganizing them into

their subsets:

ACTlONi \tv

t^ Vl (flL)

=<<^!«, ^Vt-l > l' <F"jq+l>P'jq+2>2< <F"p'l'P'jr>r-q>-

The domain of this function is limited to the set of the defining

features, which denotes the moving parts involved in the relevant

action. If any of the features for that action is taken as its value, the

function returns a sequence ofpairs of placepoint sets occupied by

the agent, over the maximal interval during which the part denoted

by that feature actually is continuing some motion. The settheoretical definition of this function is done by applying

recursively the adjacent movement function:

ACTlONi indJ'-tW^

=deji <*< < <y>Z>\Uwda <V<M>

(y)=Z > t_l

bc=( co '(INDIVIDUAL, j3(indaJi)))(y) t * <E D*

y € 2 8( -{ 4> },qj^k-£rr

1 ID.-I > }.

The returned value shows the series of changes in the figure of a moving part over the interval during which that subaction is ongoing, in terms of a sequence of pairs of place-point sets at adjacent timepoints. The relative order of the subactions of an

action is defined by the endpoints of die inner interval. Let us, here, define Set Trace Function, which, with its fixed

individual and time interval, takes any subset of content points for mecategoryrNDIVIDUAL.retunisasequenceofpairsdenotingthe

transition, over diat interval, of the part denoted by diat subset of

content points:

=«P'q>P'q+l>l> <F"q+\'P'q+2>2> r-\fr>r-q>

The transition shows the all possible changes in the figure of the relevant part.

15. ACTION CONTAINMENT

To check if an individual has performed an action over an interval

,

we have to find that for every sequence returned from the relevant

action formula with a feature as its argument, there is some

sequence whichis returned from the relevant set trace function with

its argument corresponding to the part denoted by the feature and

which includes the former sequence as a subset For a specific

individual over a specific interval, the following holds:

VydACTIONt \<k V(x)=y x

&yj£y2 & COXIND, 0(inda

,tk ), K £0(1,^), x))=z ] ],

where ^k^rj,

This denotes how the transition of each part of the agent, over the

interval of motion, is included into its transition over die whole

interval. Simplifying its notation by deleting the details, we can

express the universal quantification as an inclusion relation. See the

following:

For every dGDit ACTlONi K*h t^^ST^a K'HC),

where co '(IND, /3{indaJk ), Kt{/3(inda ,tk ),d))=C'.

16. CONCLUDING REMARKS

The above setting enables us to interpret sentences of action in two

compositional ways. Limiting to a simple intransitive case,

functions and conditions are to be applied roughly as follows:

•) a- ts [np agent's base] [vp [v Action Function] ] ]

b. [s [np agent's base] [yp Action Function ] ]

c. [s Dynamic Category Fulfillment Condition ]

ii) a- ts [np Agent's base] [yp [v Action Formula] ] ]

b- [s [np Agent's base] [yp Action Formula ] ]

c. [§ Action Containment ]

We have shown a possibility that human recognition process not only of static categories but also ofdynamic ones like action verbs

isperfonnedbysomeplace-locatingmechanismsignificantlybased

upon vision as its input. If this mechanism is to be fully

understood, then it will provide some evidence that the human

cognitive ability to categorize is actually driven or supported by a

comparatively simple physical system.

475
We have seen two alternatives based upon the categorization

algorithm in which several functions detect sequentially the parts

involved in ongoing actions by specifying them in terms of placepoint sets. Does the physical cognitive system, then, favor one

over the other? We have no biologically oriented data to choose

between those. From a linguistically semantic viewpoint, however, there is a

possibility that the first one provides a model for interpretation and

the second forms a representation which is at least partially

compositionally calculated from the syntax. We will discuss this

point elsewhere.

We have still more questions to answer and problems to solve. Some of them are the following: how to semantically represent

transitive cases, for which we have been developing an algorithm,

and what if an agent performs anaction ona independently moving

object?, for which we have to set up an embedding device where

Orientation Function applies multiply.

17. REFERENCES

[ 1 ] Barwise, J. and Perry, J. Situations andAttitudes. Cambridge,

Mass: MIT Press, 1983.

[2] Chomsky, N. LecturesonGovernmentandBinding .Dordrecht:

Foris, 1981.

[3] Chomsky, N. and Halle, M. The Sound Patterns ofEnglish.

New York: Harper and Row, 1968.

[4] Gruber, G. Lexical Structures in Syntax and Semantics.

Amsterdam: North-Holland, 1976.

[5] Jackendoff, R. Semantic Structures . Cambridge, Mass: MIT

Press, 1990.

[6] Jacobson, R., C. G. M. Fant and Halle, M. Preliminaries to Speech Analysis: Tlie Distinctive Features and Their Correlates

.

Cambridge, Mass: MIT Press, 1952.

[7] Lakoff, G. Irregularity in Syntax . New York: Holt, Rinehart &

Winston, 1970.

[8] Montague, R. 'The Proper Treatment of Quantification in Ordinary English," in Hintikka, J., Moravcsik, J. and Suppes, P.

(eds.),ApproacIiestoNaturalLai7guage . Dordrecht: Reidel,1970,pp.

221-242.

[9] Nishina, H "Describing Actions in Locational Terms," in Takahashi, S., Asao, K. and Matsumoto, R (eds.). Festschriftfor

Nobuyuki Higashi, Tokyo: Kenkyusha, 1995, pp.1 17-127.

[10] Nishina, H. 1996, "On the Spatiotemporal Semantic

DescriptionofAction VerbsUsing Features," Budapest: Workshop

12 "Representation and Processes between Vision and NL",

ECAI'96, August, 1996, pp. 84-90.

476
Solving the Forward Kinematics Problem for the Stewart

Platform by Focusing Attention and Searching

A. Lacaze*o, C. Tasoluk*, A. Meystel**

* National Institute for Standard and Technology,

o University of Maryland, • Drexel University

lacazeOcme . nist . gov

Abstract

This paper presents a new algorithm for solving the

forward kinematics of the Stewart Platform by us- ing Focusing Attention and Searching. Previous al- gorithms solve this problem by numerically finding the

solution for a 16th degree polynomial. We will show

that it is possible to drastically reduce the search space

by representing the system with three angles around

the circles formed by the given lengths. Then, we

search in a nonlinear equation with one unknown and

two roots. Reduction of computational complexity al- lows us to use the feed-forward kinematics transform

in a broader scope of practical cases.

I. Introduction

In this paper, we demonstrate that no matter how

complex the problem is local focusing of attention and

searching can be used to substantially simplify the effort. This paradigm of dealing with problems (outlined in [1, 2] can be implemented in many cases. The

Stewart Platform was introduced in [3] and further

developed in [4, 5]. It is a closed kinematic system

with parallel links which is consider to be far more

rigid than the serial counterparts of the same size and

weight. Its force-output-to-manipulator-ratio is generally an order of magnitude bigger than most industrial

robots [6]. This same closed kinematic structure that

gives its rigidity also complicates the solution of the

forward kinematics in such a way that no close loop

solution for this problem has been found. Some authors go as far as to say that "due to the kinematic

nature of this procedure, it is impossible to compute

the kinematics solution on line" [6]

.

To solve this problem, some researchers have transformed it into solving 30 non-algebraic simultaneous

equations in [7]. More recent results include the solution of 24th [8], 16th [9, 10], or 12th [11] order polynomial in a single variable. Finally, in [6] an algorithm

that involves three non-linear simultaneous equations

with three unknowns. [12] shows that some of these

Multiple Solutions

Length /

of the 6 edges

controled by

actuators

Forward

Kinematics

Inverse

Kinematics /

Position and

and orientation of the end effector

One Solution

Figure 1: Forward and inverse kinematics

parametric errors

Desired

Position and Onenlauon

trajectory

Controller

Inverse Kinematics Platform —©-

Length of the edges controlled byihe actuators

6

Forward

Position and

onentauon of

Kinematics

Figure 2: An example of using transformations of forward and inverse kinematics for control purposes

algorithms can be solved in parallel, thus reducing the

time of computation.

Our algorithm has a number of advantages in comparison with the existing solutions. It uses a nonlinear

equation with one unknown and two roots. It is not

necessary to solve all 16 mathematically possible solutions [11] for the platform. One should be sufficient,

considering that the structure of the platform is known

and that we make sure that we are inside of some re- gions of existence that we will later define

The results can be used for real-time control application in a variety of settings. Control structures are presently being developed.

477
Image Platform

Stabilizer and camera

Image

Image

Length of edges

controlled by actuators

Forward

Kinematics Camera position and orientation

Figure 3: An example of using inverse kinematics for

measuring purposes

II. Forward Kinematics and its Need for

Control and Measurement

Forward and inverse kinematics are terms to describe mapping from the space of inputs to the space of

outputs of a non-dynamic mechanical system as shown

in Figure 1. Figure 2 shows a typical application of

the forward and inverse kinematics algorithm. A tra- jectory such as a milling machine or a welding system

is to be followed. The controller, using the inverse

kinematics algorithm (and calculating desired changes

in position), computes the control signal given to the

actuators. At the output of the platform we measure

the lengths of the edges controlled by the actuators.

Then, the forward kinematics algorithm transforms

those length into positions. The position signal is compared to the assigned position and added to the controller's input. Because of its closed kinematic chain,

in the Stewart platform, the rigidity of the end effector

allows a reasonably accurate feed-forward assignment.

Due to the complexity of older forward kinematics al- gorithm, most Stewart platforms are controlled without using feedback. The proposed algorithm will allow

the calculation of the forward kinematics in real time.

This, opens an opportunity to increase the accuracy

of the control algorithms and broadening the current

uses of the platform.

There are other applications where the solution of

forward kinematics is mandatory. These are the cases when the Stewart platform is used as a component of a measuring device. These cases include:

• camera mapping where a camera is mounted on

top of a Stewart platform. For example, we let the

camera roam until it finds a target, and then we

ask where is the camera pointed. It is also usefull

when we have a fast control system to stabilize

the camera and then have the forward kinematics

algorithm tell where the camera is pointed (See

Figure 3). • positioning devices (6 degrees of freedom joysticks), and

• inspection systems mounted in Stewart platforms

that could be used to touch the part to inspect it.

We were unable to find any examples where the Stewart platform was used for any of these purposes in industry, although the uses of parallel manipulators for

sensing are very common in nature (i.e. our necks and

eyes). We can conjecture that these structural solutions did not emerge in industry because the previous

forward kinematics algorithms were not fast enough to

allow for real time operation of these devices.

In [13] and [14] new sensors were added to their parallel manipulators in order to find the forward kinematics in a faster way. We expect our algorithm to

decrease the manufacturing cost of these platforms by

solving the problem without the need to add extra sensors. In this paper, we will first show how this algorithm

is used to solve the forward kinematics of the 3-3 Stewart manipulator (three joints in the fixed platform and

three joints in the moving platform). See Figure 4. Later we show how this algorithm can be extended for

other parallel platforms.

In Figure 5, the RST triangle is the fixed platform

and the ABC triangle is the moving platform. The

length of the six edges controlled by the actuators of

the platform £i, . . . ,£6 , (Figure 4). The position of

R, 5, and T are constant and given. If we draw the

geometrical place of the point A (Figure 5), it will be

a ci rcle (o,4) since the segments RS, SA = £2 and

RA — C\ are given. This circle can be created by

rotating the triangle ARS around RS. In the same

manner, oB and oC are created by rotating B around

ST, and C around RT respectively. For simplicity, let AB = AC = BC = b and RS = RT ^ ST = a. By looking at Figure 5, it is possible to see that the

forward kinematics algorithm must find a point in

each circle such that the distance among these points

matches the dimension of the edge of the moving platform.

III. The Algorithm of Forward Kinematics

Therefore, the algorithm in the general form works

in the following manner (Figure 6):

1 . The subsequent procedures start with finding the

range of the real solutions. In order to explain

how this is done, we will outline the algorithm.

2. Pick a point A' in oA (See Figure 7). A' is completely defined by oA and 6a the polar angle inside that circle. For now, A' is an arbitrary point.

Later, we show that it is possible to analytically

find a region where the solutions must exist.

3. Analytically find a point B' in oB such that

A'B' — b. We will see that there are two analytical solutions. Let's name them B'+ and B'_

(for positive and negative slope of the A'B' versus 6a curve, top-left of Figure 9. For now, assume

that these are arbitrary labels).

478
B

Figure 4: 3-3 Stewart Platform showing the actuators

Figure 5: 3-3 Stewart Platform showing oA, oB, and

oC

4. Analytically find a point C in oB such that

A'C = b. Again, there are two analytical solutions. Let's name them C'+

and C'_ (for positive

and negative slope of the A'C versus 9b curve).

5. At this point, we found five points such that

~WB\ = A^W = ~AC\. = A^Cl = b, but

we are still not sure that B'+C+

lb, B'+

C'_lb,

B'_C+

Lb, and B'_C'_Lb. We can create four functions: Ji(0a) (length of B'+

C'+as a function of

9a), J2{9a) (length of B'+

C'_ as a function of

9a), /a (^a) (length of B'_C'+

as a function of 9A)

, and fi{0A) (length of B'_C'_ as a function of

#,4). Examples of these functions are shown in

Figure 8. The algorithm then individually uses Newton-Raphson search procedure and finds the

Find the range

of real solutions

in circle A

Choose a point A' in

circle A

Calculate B' so that A'B'=b

Calculate C so that A'C=b

Calculate B'C

Desired " hi0

accuracy?

Figure 6: A general view of the forward kinematics

algorithm

oC

Figure 7: Searching for the correct b lengths

value for 9a in each of the functions until B'C = b

to the desired accuracy. These functions are periodic, and they will have at most two roots in each

half period. Thus yielding 8 forward kinematic

solutions^-BC-)-.)-)- being the positive slope solution of the /i(#a), ABC+-\ being the negative

edge of the same functions. Similarly, ABC^ |_, ABC+__, ABC-++, ABC-+-, ABC +, and

ABC are the other six solutions, to a total

of eight solutions (for the half period of 9a see Figure 9).

479
Distance between Circles B-C (units) 6

50 100

Thetal (deg)

150 50 100 150

Thetal (deg) 200

50 100 150

Thetal (deg)

200 50 100 150

Thetal (deg)

200

Figure 8: h(0A), h(0a ) , h ) , and f4 (9A ) for a b = 5

example

It is unnecessary to search all four functions unless

we are interested in finding all 8 (top) solutions. The

reason is that if we know how our platform is currently

configured (i.e. in the ABC+ ), it is easy to prove

that the next solution will also be a ABC+ provided

that we have not gone through maxima which are ac- tually a singularity point. These singularity points can be easily derived from the expression for the A'B' and

A'C. For each concrete configuration, a search strat- egy can be assigned in such a way that the complexity

of computation is minimized.

IV. The Equations of the System

We can write the equations of the system in the fol- lowing way:

Ci = V (xa - x R ) 2 + (yA - yR ) 2 + (za -Zr)2 (1)

Ci = \J(XA - XS ) 2 + (yA -ys)2 + (za -ZS ) 2 (2)

c3 = \/(xc - xr)2 + (yc - vr) 2 + (zc -ZR)2 (3)

c4 = \J(x c - xt)2 + {yc - Vt) 2 + (zc -zt ) 2 (4)

c5 = a/(xb - xs) 2 + (yB - ys) 2 + (zb -zs ) 2 (5)

c6 = V (XB - xT ) 2 + (yB - VT) 2 + (ZB -zT ) 2 (6)

are the Euclidean equations between the three points

that define the lower platform R, S, and T and the

points of the upper moving platform A, B, and C. We

can also write the Euclidean equations of the top platform. Here, we assume that it is an equilateral triangle, but we are not making any simplifications based

Found analytically tl( 6 a)

4

4

vABC

\ABC_\

A_BC^

/3(*A)

Length of A'.C'

.ABC_ +

A /4 («a)

BC++

Figure 9: 8 solutions in the Stewart Platform

on this assumption.

b

2 = (xA - xB )

2 + (yA - yB)

2 + (zA - zb)' (7)

(8)

(9)

b

2 - (x A - xc )

2 + (yA - yc)

2 + (zA - zc) 2

b

2 = (x B - x c ) 2 + (yB - yc)

2 + (zb - zc)

2

where b is the length of the equilateral triangle of the

top platform. We create a new reference coordinate

system on S (Figure 10) to simplify the expressions as

follow:

XR = a yR = 0 ZR = 0 (10) xs = 0 ys = 0 ZS = 0; (11)

XT

a ~ 2 yr\/3a

2 ZT = 0 (12)

As shown in Figure 10, we define:

PA =

(ci - r

2 + a

2

) rA -

2a

PB =

(ci -cl + a

2

) rB =

2a

PC -

(Ci r

2

2a

+ a

2

) rc =

v^FTI (is)

By looking at Figure 10 and by using definitions (13)

through (15), we can easily write a polar parametric

equation of oA in the following manner,

xa = a — pa

yA = rA cos 6a

za = ta sin 9a

(16)

(17)

(18)

480
Figure 10: New coordinate system and some definitions

on

in a similar way, after some trigonometric transformations the equations for oB and oC:

XB

VB

y/3rs cos 9b + Pb

2 —tb cos 9b + V3pb

zb — tb sin 9b

y/Src cos(9c) - a +pc

xc = a —

yc - —rc cos(#c) + \/3(a — pc)

zc = tc sin 9c

(19)

(20)

(21)

(22)

(23)

(24)

(25)

Let's assume that we have chosen a 9a in oA using

equations (16) through (18) which uniquely defines a

point A in oA We are interested in finding the points

in oB that are a distance b away from A. We will

present two methods for accomplishing this.

Two methods where tested (both with positive results:

Method 1: Solving the 2nd order polynomial

and

Method 2: Intersecting a sphere and a circle

The intersection between the sphere and oB as shown in Figure 11. Note that the only way for a

platform to go from 9b+ to 9b_ is that:

• the platform has gone through a singularity point

{9b+ = These points are at the maximum

of the curves in Figure 8 or 9

• one of the cables (or more) has gone slack if the

Stewart platform has flexible members

• an actuator has broken if the platform has rigid

members.

It is only necessary to calculate one $b and one 9c

for a real platform. To start our search technique, we

Figure 11: A new coordinate system

calculate the distance between B and C which it is given by (9).

V. The Search Technique

Previously, we presented an expression that given 9a

will give the distance B'C\ or /(#a)- We need to find

9a such that /(9a) = b. There are several searching

techniques that can be used. The search problem has

the following features:

1 . the region of search is known

2. there are no more than two solutions

3. there is only one maximum

One simple way of finding 9a such that /(#a) = b

consists of the following steps:

1. find the maximum, using Newton-Raphson search,

2. divide the space of search in two parts: to the left and to the right of the maximum,

3. search for the root of the equation only in one of

the parts.

If we have the previous forward kinematics solution, we

can use that value as a starting point for our search,

thus avoiding the need to find the maximum.

VI. Implementation

The previous algorithm was compiled in two different computers: a Sun Sparc 2 and a Sun Sparc 20.

Table 1 shows the different average times of calculation. Table 2 shows the time that the algorithm takes

with respect to the desired accuracy of the result.

The algorithm of forward kinematics was tested us- ing data from a Stewart based milling machine. See

Figure 12. The trajectory is the spiral shown in Fig- ures 13 and 14, position trajectory and unit vectors,

show the direction of the end effector respectively.

481
Hardware average time

111 /XocCOIlClo

Sun Sparc 20 with

UiJIIl^JllCl vJ|J UlliilZiClitlUll

98

Sun Sparc 20 without

compiler optimization

121

Sun Sparc 2 with

compiler optimization

490

Sun Sparc 2 without

compiler optimization

512

Table 1: Comparative study of different hardware to

find the complete forward kinematic solution with an

accuracy of ±0.01 radians and the Newton Raphson

search method

Accuracy in (± radians) typical time (//seconds)

0.01 98

0.001 136

0.0001 250

0.00001 492

Table 2: Typical algorithm times using a Sun Sparc

20 and using the "-04 -msuperspark" compiling options with different accuracies and the Newton Raphson search method.

Figure 12: Ingersol-NIST Hexapod

Figure 13: Spiraling trajectory

0.2 0.1 0 -0.1 -0.2 j -0.2 -0.2 |

Figure 14: Angular trajectory

Figure 15 shows the four four sets of curves created

by plotting the distance BC when AC = AB — b as a function of 9a along the spiral trajectory. Each

different curve corresponds to the distance {BC) for a point along the trajectory shown in Figures 13 and

14. Note that the algorithm does not need to draw

this curve to find the solution. It is searching in these

solutions to find the BC = b solution that corresponds

to the current configuration of the platform. Figure 16

is a two-dimensional view of Figure 15 that shows the

found solutions marked in the bottom left curve.

VII. Conclusions

1. An algorithm of forward kinematics for Stewart

Platform which allows for substantial reduction

of computational complexity is proposed.

2. Unlike many of existing systems, this algorithm

knows the number of solutions in advance. Since

the previous configuration is considered part of

the assignment, we must only search for only one

root in most cases.

482
Figure 15: BC along the spiral trajectory

Figure 16: BC along the spiral trajectory in 2d

3. In addition to reducing complexity, the algorithm

is easy to implement.

4. Due to the constraint and monotonic character of

the functions in the search zone, the search algorithm is stable (it cannot jump roots).

5. The algorithm allows for real time applications.

Further reduction of computational time can be

achieved by introducing parallel computation.

6. Unlike some of the existing algorithms, the proposed one does not depend on the length of the

edges.

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[13] H. Hollerbach and D. Lokhorst. Closed-loop kinematic calibration of the rsi-6 hand controller. In

Proceedings of IEEE International Conference on

Robotics and Automation, volume 2, pages 142-

148, 1993.

[14] JP. Merlet. Closed-form resolution of the direct

kinematics of parallel manipulators using extra

sensor data. In Proceedings of IEEE International Conference on Robotics and Automation,

volume 1, pages 200-204, 1993.

483

XVIII BRAIN, MENTALITY, MEANING

A neurobiological interpretation of semiotics:

meaning, representation, and causality

Walter J Freeman

Department of Molecular & Cell Biology, LSA 129

University of California at Berkeley CA 94720-3200

wfreeman@socrates.berkeley.edu http://sulcus.berkeley.edu/

Abstract

That branch of semiotics called semantics

deals with the relationships between

meanings and representations. In my view

meanings exist only in brains without

representations there. A meaning is the focus

of an activity pattern that may occupy the

entire available brain. It is constructed by

intentional action followed by learning from

the consequences of the action.

Communication between brains requires

reciprocal construction of representations in

accordance with meanings, which elicit other

meanings in other brains. A representation, as a material object or process, has no

meaning in itself. EEG data indicate that

neural patterns of meaning occur in

trajectories of discrete steps marked by

cortical state transitions, served by rapid

exchanges of discrete wave packets between

interactive cortical domains. These wave

packets are made by self-organizing

dynamics that control behavior and shape the

sensitivities of sensory cortices to the

sequellae of actions. The nature of causality

must be analyzed and understood in

accordance with the questions: How do

meanings cause representations, and how do

representations cause meanings?

Introduction

Archeologists studying a petroglyph ask not

only who did it and when, but what does it mean? They conclude that no one can know

what it means now, and that they can only

speculate on the prior meanings in the minds

of the makers and viewers. The lesson is that

the petroglyph contains no meaning, even

though it was made by humans with intent to

communicate meaning by evoking the

formation of comparable meanings in other

humans.

Engineers who want to make semantic

machines are faced with the task of defining

meaning, which at present exists only in

brains, and then with the task of learning

how to make or cause meaning in machines,

as shown by Tani [1996] and Clark [1997].

The requirements on network models to

simulate the chaotic dynamics of brains

include global though sparse connectivity,

continuous time dynamics, and distributed

spatial functions in two-dimensional arrays of

nonlinear integrators. Digital hardware may

suffice to emulate the biological functions of

sensory cortex in brains by use of nonlinear

difference equations [Chang and Freeman,

1996; Shimoide and Freeman, 1995;

Freeman et al., 1996]. In this way, a next

step to machine intelligence may be to use a model of a sensory cortex as an interface

between the unconstrained real world, which

is infinitely complex, and the finite state

automata that constitute the main support for

contemporary artificial intelligence. That is,

models from brain dynamics can provide

eyes and ears for conventional computers.

However, this step will require that a major

problem be addressed: the relation between

representation and meaning in brain function.

Shannon-Weaver information theory, which

is representational, has divorced meaning

from information and therefore does not

apply to brains. The aim of this presentation

is to sketch some of the principal elements of

the problem, as a basis for discussing some

possible pathways toward solutions through

487
Representation A

>

Representation B

Figure 1

a better understanding of the biological basis

of meaning as relations between brain states

and behavioral actions, not between symbols

in syntactical systems.

Communication by representations

Operational discreteness is essential for

communication in dialogue. A pair of brains

can act, sense, and construct in alternation

with respect to each other, not merely as dogs

sniff, but as two humans speak, listen, and

hear. Consider brains A and B interacting

(Figure 1), where A-B are parent-child,

wife-husband, rabbit-dog, philosopherbiologist, neuroscientist-rabbit, etc. A has a

thought that constitutes some meaning M(a).

In accordance with this meaning A acts to

shape a bit of matter in the world (a trace of

ink on paper, a vibration of air, a set of

keystrokes on e-mail, movements of the face,

etc.) to create a representation (a sign or symbol for humans, merely a sign for

animals) directed at B, R(ab). B is impacted

by this shaped matter and is induced by

thought to create a meaning M(b). So B acts

to shape a bit of matter in accordance with

M(b) in a representation R(ba), which

impacts on A to induce M(a+1).

And so on. Already by this description there

is implicit recognition of a discrete ebb and

flow of conversation like recurrence of tides, so that meanings M(i)'s as constructions of

thoughts become the internal active states,

and the R(ij)'s as attributes of matter become

the external representations. By its nature an

external "representation can be used over

and over. It cannot be said to contain or

carry meaning, since the meanings are located

uniquely inside A and B and not between

them. Moreover, the same R's induces

different meanings M(i) in other subjects C

who intercept the representations. The

objects that are used to communicate are shaped by meanings that are constructed in A

and B iteratively and induce the constructions

of meaning in B and A alternately. If

communication is successful, then the

internal meanings will come transiently into

harmony, as manifested by cooperative

behavior such as dancing, walking in step,

shaking hands, exchanging bread, etc.

Symbols can persist like books and stone

tablets, while minds fluctuate and evolve until

they die.

Observations of

electroencephalograms

A biological approach to the problem of

meaning is to study the evolution of minds

and brains, on the premiss that animals have

minds that are prototypic of our own, and

that their brains and behaviors tell us what

essential properties are common to their

minds and to our own minds.

488
Experimental measurements of brain activity

(EEG) that follows sensory stimulation of

animals show that sensory cortices engage in

construction of activity patterns in response

to stimuli [Freeman, 1975]. The operations

are not those of filter, storage, retrieval, or

correlation mechanisms. Each construction is

by a state transition, in which a sensory

cortex switches abruptly from one basin of

attraction to another, thereby changing one

spatial pattern instantly to another like frames

in a cinema. The transitions in the primary

sensory cortices, visual, auditory, somatic

and olfactory [Barrie, Freeman and Lenhart,

1996], are shaped by interactions with the

limbic system, which establish multimodal

unity, selective attention, and the intentional

nature of percepts. The interactions of the

several sensory cortices and the limbic

system occur in conjunction with goaldirected actions in time and space. Each

cortical state transition involves synaptic

changes constituting learning throughout the

forebrain, so that cumulatively a unified and

global trajectory is formed by each brain over

its lifetime. Each spatial pattern appears to

reflect the entire content of past and present

experience [Skarda & Freeman 1987], that is,

a meaning.

The most important experimental finding is

that the neuroactivity patterns in sensory

cortex, which are correctly classified on

perception of conditioned stimuli by the

animals, are not invariant with respect to the

unchanging physicochemical stimuli. The

brain activity patterns are found to change

slightly but significantly with any change in

the significance of the stimuli, such as by

changing the reinforcement, or adding new

stimuli [Freeman, 1992]. From numerous

tests of this kind the conclusion is that brain

patterns reflect the value and significance of

the stimuli for the animals, not a fixed

memory store. Each pattern formed in

response to the presentation of a stimulus is

freshly constructed by chaotic dynamics in

the sensory cortex, in cooperation with input

from the limbic system enacting processes of

attention and intention, and it expresses the

history and existing state of the animal as much as or more than the actual incident

stimulus. The patterns cannot be

representations of stimuli or of meanings of

stimuli. They are active states induced by

stimuli, constituting evolution of the brains in

their growth of experience [Piaget, 1930].

The neural basis for intentional action

The making of a representation is an

intentional action. All intentional actions

begin with the construction of patterns of

neural activity in the limbic system, which

has been shown by use of lesions and by

comparative neuroanatomy and behavior to

be a product of the limbic system [Herrick,

1948; Roth, 1987; Freeman, 1995]. In

mammals all sensory input is delivered to the

entorhinal cortex, which is the main source of

input to the hippocampus, and the main target

of hippocampal output (Figure 2). Goaldirected action must take place in time and

space, and the requisite organ for these

matrices is the hippocampus with its 'short

term memory' and 'cognitive map' [O'Keefe

and Nadel, 1978].

For example, hunger is an emergent pattern

of neuroactivity that expresses the

requirements of brains and bodies for

metabolic fuel and building material. It induces a state transition in the neural

populations of the forebrain under the

influence of sensory stimuli from the gut and

the brain's own chemoreceptors for its

chemical state. It is also shaped by

neurohormones from nuclei in the brain stem.

The emergent pattern impacts the brain stem

and spinal cord, leading to stereotypic

searching movements that are adapted to the

immediately surrounding world. Feedback

from the muscles and joints to the

somatosensory cortex provides confirmation

that the intended actions are taking place.

The impact of the movements of the body on

sensory input is conveyed to the visual,

auditory and olfactory systems. All of these

perceptual constructs, that are triggered by

sensory stimuli and are dependent on prior

learning, are transmitted to the limbic system,

specifically to the entorhinal cortex, where

they are combined. When an animal detects

an odor of food, it must hold it, move, take

another sniff, and compare the two

concentrations in order to decide which way

to move next. The difference in strength has

no meaning, unless the animal has records of

489
DYNAMIC ARCHITECTURE OF THE LIMBIC SYSTEM

RECEPTORS «* ENVIRONMENT 4 SEARCHING

MOTOR LOOP

PROPRIOCEPTIVE LOOP —— BODY ~U

REAFFERENCE

LOOP

ALL

SENSORY

SYSTEMS

ENTDRHINAL

CDRTEK

SPACETIME LOOP

HIPPOCAMPUS

Figure 2

CONTROL

LOOP

* ALL

MOTOR

SYSTEMS

which way it moved, when the samples were

taken, and a basis for determining distance

and direction in its environment. These basic

operations of intentional behavior are

properties of the limbic system. The same

requirements hold for all distance receptors, so it is understandable that evolution has

provided multimodal sensory convergence in

order to perform space-time integration on the

Gestalt, not on its components.

In the description thus far the flow of neural

activity is counterclockwise through

proprioceptive and exteroceptive loops

outside the brain. Within the brain there is a clockwise flow of activity constituting

reafference. When a motor act is initiated by

activity descending into the brainstem and

spinal cord, the same or a similar activity

pattern is sent to all of the sensory systems

by the entorhinal cortex, which prepares them

for the impact of the movements of the body

and, most importantly, sensitizes them by

shaping their attractor landscapes to respond

quite selectively to stimuli that are appropriate

for the goal toward which the action has been

directed. These reafferent patterns have been

denoted as the senseof effort [Helmholtz,

1879], reafferent signals (vonHolst and

Mittelstaedt, 1950], efference copies [Sperry,

1950], and preafference [Kay, et al., 1995,

1996]. They are the essence of attention.

Linear versus circular causality in

self-organizing systems

The conventional view of sensory cortical

function holds that stimuli activate receptors,

which transmit to sensory cortex through a

linear causal chain, with the eventual outcome

of a motor response to the initiating stimulus.

Modeling with nonlinear dynamics shows

that the stimulus is typically not the initiating

event. Rather it is the search for the stimulus

that arises in the limbic system in a recurrent

manner from prior search and its results.

This is circular causality at the level of

intentional behavior [Merleau-Ponty, 1942].

Much lower in the hierarchy of brain

organization is the event in the primary

sensory cortex, which consists of the

destabilization of a macroscopic state by the

introduction of microscopic sensory input.

In this case the transition from a prior basin

of attraction to a new one, which has been

facilitated by limbic modulation, is guided by

the sensory input that activates a learned

nerve cell assembly comprising a small

subset of cortical neurons. The transition to a new state is global, so that this causal chain is

also circular. The stimulus-dependent neural

activity of a few neurons triggers the state

transition, and then the entire domain of the

490
primary sensory cortex transits to another

pattern, which in the words of Haken (1983)

"enslaves" the whole set of cortical neurons

by acting as an "order parameter". This new

active state has been characterized by Ilya

Prigogine (1980) as a "dissipative structure",

that constitutes the "emergence of order out

of chaos".

The similarity of the properties of neural

activity in the various parts of the limbic

system to those in the primary sensory

cortices [Kay et al., 1995, 1996] indicates

that populations of neurons there also

maintain global attractors, which are accessed

by nonlinear state transitions, and which are responsible for the genesis of motor patterns

controlling goal-directed actions and of

reafference patterns that prepare the sensory

cortices for the consequences of those

actions.

A hypothesis on the causal relations

of meanings and representations

The idea is proposed that representations are formed by the forward, counterclockwise

flow of neural activity, which emerges from a microscopic level by the interactions of

neurons and neuronal populations, and which

places the motor systems of the brainstem

and spinal cord into appropriate basins of

attraction, thereby changing the sensory

inflow in a goal-directed manner. The

making of a representation is an ordering of

the neural control systems of the

musculoskeletal apparatus, that is aimed to

elicit sensory feedback of a certain kind,

namely the patterns of receptor discharge

from representational stimuli transmitted by

other beings, that place the sensory cortices

into the expected basins of attraction. The

meaning of the representation is implicit in

the form that is given to the representation by

the limbic system.

The clockwise backflow of neural activity serves as an order parameter to modulate and

shape the neural activity patterns of the

sensory cortices, which transmit the states of

their neural populations before and after the

expected inputs have occurred, and also if

they do not occur as expected, or at all. It comprises not only the exteroceptive input

but the proprioceptive feedback as well. This

global active state, enslaving alike the limbic

system and the primary sensory cortices,

shapes the meaning not only of the unified

sensory input consequent to the transmitted

representation, but also of the emitted

representation.

The implication here is that the agent who is

constructing and transmitting the

representation cannot fully know its meaning

until after the immediate consequences have

been delivered through his or her own

sensory systems. More generally, a poet,

painter, or scientist cannot know the meaning

of his or her creation until after the act has

been registered as an act of the self, nor even

until the the listeners and viewers have

responded with reciprocal representations of

their own, each with meaning unique to the

recipients.

Conclusion

Why do brains work this way? Animals and

humans survive and flourish in an infinitely

complex world despite having finite brains.

Their mode of coping is to construct

hypotheses in the form of neural activity

patterns and test them by movements into the

environment. All that can be known is that

which has been constructed, tested, and

either accepted or rejected [Piaget, 1930;

Merleau-Ponty, 1942]. The same limitation

is currently encountered in the failure of

machines to function in environments that are not circumscribed and reduced in complexity

from the real world. Truly flexible and

adaptive intelligence operating in realistic

environments cannot flourish without

meaning.

This global state variable may be regarded as a mechanism supporting consciousness,

which in the neurodynamic view is a global

internal state variable composed of a

sequence of momentary states of awareness

[Hardcastle 1995]. Its regulatory role is

comparable to that of the operator in a

thermostat, that instantiates the difference

between the sensed temperature and a set

point, and that initiates corrective action by

turning a heater on or off. The machine state

variable has little history and no capacities for

491
learning or determining its own set point, but

the principle is the same: the internal state is a

form of energy, an operator, a predictor of

the future, and a carrier of information that is

available to the system as a whole. The

feedback device is a prototype, an

evolutionary precursor, not to be confused

with awareness, any more than tropism in

plants and bacteria is to be confused with

intentionality. In animals and humans, the

operations and informational contents of this

global state variable constitute the experience

of causation.

Acknowledgements

This work was supported by research grants

from the National Institute of Mental Health

MH06686 and the Office of Naval Research

N00014-90-J-4054. .

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Haken H (1983) Synergetics: An

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Perceptions of Vision (JPC Southall,

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Herrick CJ (1948) The Brain of the Tiger

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(eds.) Information Processing and Pattern

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system during odor recognition. Intern.

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of Behavior [AL Fischer, Trans.]. Boston:

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Prigogine I (1980) From Being to Becoming:

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492
INTELLIGENCE vs. MENTALITY:

Important but Independent Concepts

James H. Fetzer

Department of Philosophy

University of Minnesota

Duluth, MN 55812

Abstract

intelligence and mentality are frequently identified as though they were one

property designated by different predicates. That, however, appears to be a

misconception-aibeit one with many intriguing ramifications. The most common tendency presumably would be to identify intelligence with mentality of

a high order. But if some cognitive systems possess mentality of a low order,

then they have mentality without intelligence. Other systems, which may or

may not qualify as "cognitive", moreover, appear to have intelligence without

mentality. Since properties are the same only if they have the same class of

instances, evidently intelligence and mentality cannot be the same property.

t. Introduction. Perhaps the most common mistake that occurs within the context of theorizing about cognition is that

of treating intelligence and mentality as

if they were the same thing. If we were

to employ the term "system" to stand for

any entity-simple or complex-for which

specific kinds of input, causes, or stimuli

(probabilistically) bring about particular

kinds of output, effects, or responses, no

one ought to be tempted to suppose that

those entities are necessarily "cognitive",

"intelligent" or possess "mentality". The

concept of system thus defined is broad

enough to include sticks and stones along

with digital machines and human beings

within its extension or class of instances.

Since few would suppose that sticks or

stones-ordinary sticks and stones, at any

rate-are things that are capable of cognition, the intension or defining conditions

of "cognitive system" had better exclude

them on pain of demonstrating its

own inadequacy. If some systems

are cognitive, while others are not,

then that property, too. had better

be carefully defined, with consideration for whether or not it clarifies

and illuminates their differences as

well as their similiarites. It may be

that some systems properly qualify

as "intelligent" even though they do

not properly qualify as "cognitive".

Of course, if we are unable to define what it means for something to

be a "cognitive system", then we are

open to the charge that we literally

do not know what we are talking a- bout, My purpose here, therefore,

is to sketch a theory of the nature

of mentality that brings with it an

account of the nature of cognition.

The differences between mentality

and intelligence are then explored

493
with special concern for the prospects of

developing tests for mentality and tests

for intelligence, respectively, which tend

to support the distinctions drawn within

this context and their consequences with

respect to differentiating between them.

2. Minds as Semiotic Systems. The right

place to begin. I believe, is with a theory

of mind that builds on a foundation provided by Charles Peirce's theory of signs.

According to Peirce, a sign is a something

that stands for something else in some respect or other for somebody. There turn

out to be three basic classes of signs that

differ in the way in which they stand for

something else, namely: icons, which are

things that resemble other things; indices.

which are things that are causes or effects

of those other things; and symbols, which

are merely habitually associated with the

things for which they stand. Relations of

resemblance and of cause-and -effect provide natural as opposed to artificial signs.

Photographs, paintings, and statues (at

least, when they look like the things they

stand for) are therefore icons in this sense.

Ashes are indices of fire and fire of ashes,

because they are causally connected. The

words-such as "golf" and "tennis", that occur in ordinary languages, such as Englishhowever, are symbols, even when the habitual associations between such words and

that for which they stand happen to be reinforced by traditions, customs, and practices of a community. Attaining the goals

of a community requires cooperation, and

cooperation is facilitated by (the capacity

for) successful communication. Although

many words could have stood for things

other than those for which they happen

to stand, when they are thus reinforced,

they assume the standing of conventions.

The triadic character of the sign

relation-which connects signs with

what they stand for and sign -users

-suggests the prospect of defining

minds as sign-using lor "semiotic")

systems, where "minds" turn out

to be the kinds of things for which

something can stand for something

else in some respect or other. This

approach implies that there ought

to be at least three kinds of minds,

namely: those that have the capacity to use icons; those that have the

capacity to use indices; and those

that have the capacity to use symbols, as successively stronger kinds

of minds (Fetzer 1988. 1990. 1996).

3. Conditions of Adequacy. Among

the most important but least mentioned aspects of theory of mind is

the conditions that must be satisfied for a theory of mind to qualify

as adequate. These include (CA-i

)

explaining how mental states can

exert an influence upon behavior;

(CA-2) the differences between human minds, animal minds, and the

minds of machines, if such a thing

is possible; and (CA-3) how we can

tell-how it's possible to know-whether or not something has a mind.

These may not be the only desiderata an adequate theory of mind

must satisfy, but they are among

the most important. Whether or

not the theory of minds as semiotic systems can satisfy them is

thus a measure of its adequacy.

Because signs "stand for" that

which they stand in some resoect

or other, things that "stand for"

other things characteristically do

494
so oniy partially rather than completely.

Because everything resembles itself-by

"being like" itself in every property and

at every time-there is a trivial sense in

which everything stands for itself iconically. Typically, however, things "stand

for" other things only in certain respects,

as in the case of a driver's license photo,

which may resemble you (on a bad day)

when viewed from in front but not when

viewed from the side (since you are just

not that thin)! The use of even the least

complex kind of sign-an icon-thus presupposes the adoption of an appropriate

perspective, that is, of a "point of view"!

The theory of minds as semiotic systems supports a distinction between consciousness and cognition relative to signs

of various kinds. A system is conscious

(with respect to signs of specific kinds)

when it has the ability to utilize signs of

that kind and is not incapacitated from

the exercise of that ability. Even when

a person is familiar with the rules of the

road and understands traffic signs, that

does not guarantee they will be able to

perceive and respond to them. The conditions under which drivers fail to obey

signs include those in which, although a

sign was present, it was obscured from

vision, the driver suffered from (temporary) blindness, or was so intoxicated

that his attention span was abbreviated.

4. The Nature of Cognition. The phenomenon known as cognition appears to occur

as a consequence of the causal interaction

between signs and minds (or sign-users).

When a sign-user is conscious in relation

to signs of a specific kind, then the presence of a sign of that kind within suitable

causal proximity (probabilistically) brings

about the occurrence of cognition, during

which the sign is taken as standing for something in some respect

or other by that user. Thus, consciousness combines ability and

capability, while cognition arises

as an effect of consciousness and

opportunity, where both notions

are relative to signs of fixed kinds.

The meaning of signs for signusers may be captured most adequately by their causal influence

upon behavior. This influence is

affected by the causal interaction

of every other factor whose presence or absence makes a difference

to the behavior of that system. In

the case of human beings, the full

range of kinds of factors that tend

to affect behavior would appear to

be exhausted by motives, beliefs,

ethics, abilities, capabilities, and

opportunities. The role of oppor -

tunities differs somewhat relative

to factors of these other kinds insofar as they represent the actual

situations that obtain for systems

themselves as opposed to the situations they believe they are in.

If we refer to some particular

combination of motives, beliefs,

ethics, abilities and capabilities

as a "context" CL then the meaning of a sign S for a system z is

the totality of behaviors (actual

or potential) BL B2, . . . that the

system would (probabilistically)

display in the presence of that

sign, relative to various contexts

CL C2, Thus, if we employ

". . . => " as a subjunctive conditional and ".

. . =n=> " as the

causal conditional, the meaning

of sign S for z, relative to CL is:

495
(MSI) Clzt-j (Szt «n->Bl.zt*)&

(MS2) C2zt => (Szt=m=>B2zt*)&

where the causal influence of S within

context Ci would (with the strength n)

bring about behavior of kind BJj within context C2 would (with the strength

m) bring about behavior of kind B2; etc.

5. Meaning and Behavior. Thus, when

a little old lady from Pasadena reaches

a traffic intersection and fails to notice

a stop sign because her vision is not as

good as it used to be, she may run the

stop sign and cause an accident, but it

would not have been on purpose. If a

felon fleeing with police in hot pursuit

notices a stop sign but runs it anyway,

he may cause an accident, but because

it was a risk that he was willing to run.

When an expectant father decides that

he cannot take the time to obey a sign

because his wife has begun labor in the

back seat, he might pray no accident is

about to happen, because that would be

the worst possible outcome. And so on. The same sign (such as an octagonal

red surface with the letters "S-T-O-P"

inscribed) thus has the same meaning

for different systems when their (actual or potential) behavior in the presence of that sign- more precisely, the

strength of their tendencies toward behavior of various kinds-are the same

across different contexts. This does not

mean their actual behavior is the same,

because they may have been in different contexts, but only that, if they had

been in the same context, then the behavior they displayed-more precisely,

the strength of their tendencies toward

behavior of various kinds-would have

been the same, under those conditions.

Similarly, different signs have

the same meaning for a system

when the (actual or potential) behavior it would display-more precisely, the strength of its tendencies toward behavior of different

kinds-would be the same across

different contexts. It can turn out

that sameness-of- meaning differs

in some contexts even though not

in others. With regard to purchasing power, four quarters, two halfdollars, and a dollar bill would be

the same; from other perspectives,

such as convenience of carrying in

a wallet, they would differ. Sameness of meaning thus seems to be a

property that can vary by degrees.

6. Animal Mentality. The theory

of minds as semiotic systems also

implies that there should be a correlation between lower species and

lower mentality and higher species

and higher mentality. Indeed, symbolic mentality presupposes indexical mentality, and indexical mentality presupposes iconic. It would be

predictable on the basis of the semiotic account, therefore, that there is

some corresponding progression in

nature from iconic mentality up to

symbolic, where each kind might be

instantiated in nature in more than

one variety, depending on the number and types of signs a system uses. The lowly E. coli bacterium, for example, has the tendency to swim toward twelve different chemo-tactic

substances and to swim away from

eight more (Bonner 1980, p. 63). It

should be evident, from the semiotic

perspective, that E. coli possess the

496
ability to recognize different instances

of each of these twenty che mo- tactic

substances, since otherwise they would

be unable to respond to them properly.

Somewhat surprisingly, therefore, E. coli

appear to possess iconic mentality. It is

not necessary that E. coli should also be

aware that twelve of these are beneficial and eight of these are harmful, since

the tendency to avoid harmful stimuli

and to encounter beneficial ones would

evolve as a function of natural selection

even in the absence of indexical ability.

Another (no doubt, less controversial)

example of animal mentality arises with

the vervet monkey, who makes at least

three different alarm calls, one for eagles

(or air-born predators), one for leopards

(or earth-bound predators), and one for

snakes (or earth-bound curiousities). A

call of the first kind tends to cause them

to hide in thick bushes; a call of the second kind, to run up into trees; and a call

of the third kind, to look down for something interesting to watch (Slater 1985,

pp. 155-157). Observe how beautifully

this example satisfied the conception of

minds as sign-using systems, where the

meaning of a sign is given by the act ual

and potential behavior it induces within

a context. Here clearly at least indexical

and perhaps even symbolic mentality is

displayed, since the alarm calls even appear to possess elements of conventions.

7. Machine Mentality. It may come as a disappointment to some that the theory

of minds as sign-using systems implies

that ordinary computers-von Neumann

or digital machines, at least-are not the

possessors of minds. This follows from

the realization that these machines are

designed to process marks or to manipulate syntax, where syntax" consists

of strings of marks that are subject

to interpretation. Since digital machines are capable of processing syntax,

it may be tempting to suppose they

must be possessors of mind. But the

capacity to processs syntax is merely

a necessary and not a sufficient condition for a system to be ' se miotic",

since it must also be the case that

the marks that are processed stand

for something for that system rather

than just for the users of that system.

The principal difference between

se miotic systems and syntax- processing systems (such as digital machines)

is that the syntax that is processed by

a se miotic system stands for something

for that system itself, while the syntax

that is processed by a digital machine

instead stands for something for users

of that system . Since a mind is a something for which something can stand for

something else for that system, clearly

systems that lack the ability of taking

something to stand for something for

itself cannot properly qualify as minds.

This might be described as the "static"

difference between minds and digital

machines. (Fetter 1988, 1990, 1996.)

Another difference that some may

consider to be at least equally instructive might be described as a "dynamic" difference between them, which is

that digital machines are governed by

algorithms implemented in the form

of programs, because of which transtions between machines states assume

the character of (what has sometimes

been called) "disciplined step satisfaction". A se miotic analysis of the transitions that typify human thought, by

contrast, suggest that human thought

497
has an associationislic dimension thai

disciplined step satisfaction lacks (Fetzer 1994). The potential for the same

sign to function iconicaily, indexically,

or symbolically-possibly probabilisticaily-in the same or different contexts

poses apparently insuperable problems

for those who would reduce thinking to

computing. They are just not the same.

8. Mentality and Intelligence. Perhaps

the gravest blunder that has occurred

in discussions of machines and mentality has been to ignore the difference between systems that yield the same out -

put given the same input and systems

that yield the same output given the

same input by means of the same processes. A simple illustration arises in

the case of question-answering mechanisms. The prospect that a machine

might be able to answer questions by

providing the same answers that a human being might provide not only does

not prove it is human but also does not

prove it has a mind. The critical difference concerns the issue cited above between systems for which things stand

for other things for those systems themselves and those for which things stand

for the users of those systems. No one

should doubt that digital machines can

simulate thought processes; the serious

issue is whether they can replicate them.

The difference between intelligence

and mentality arises again at this juncture. The appropriate criterion for mentality, given the theory of minds as semiotic systems, appears to be the ability to

make a mistake (Fetzer 1988, 1990, and

1996, for example). Things that have the

ability to make mistakes, after all, have

the ability to take something to stand for

something, while doing so wrongly.

This is an ability that appears to be

wide-spread among animals, moreover, but impossible for digital machines, which can malfunction, but

whose "mistakes" are attributed to

those who design, program and use

them rather than to those machines.

In the case of intelligence, however, it would be at least faintly ridiculous to suppose that a suitable

test would be the ability to commit

mistakes! Something more like the

opposite-the ability to avoid themwould seem to be a more appropriate criterion. But this is because intelligence is commonly understood

to be akin to a high order of mentality. Machines that are incapable of

committing mistakes may still be entitled to be described as "intelligent",

especially when they are capable of

the successful performance of complex tasks, such as the manipulation

of syntax. Digital machines thus exemplify intelligence without mentality,

where the conflation of these properties seems to be a significant mistake.

References

Bonner, J. ( 1 980), The Evolution of Culture in Animals (Princeton).

Fetzer, J. H. (1988), "Signs and Minds", in

J. Fetzer, ed„ Aspects of A

I

(Kluwer).

Fetzer, J. H. (1990), AI: Its Scope and

Limits (Kluwer).

Fetzer, J. H. (1994), "Mental Algorithms",

Pragmatics and Cognition 2/1.

Fetzer, J. H. (1996), Philosophy and Cognitive Science. 2nd ed. (Paragon).

Slater, P. J. B. (1985 ), An Introduction

to Ethology (Cambridge).

498
Functional Organization of Cortico-Basal Ganglia-Thalamocortical Loops

K.V. Baev

Barrow Neurological Institute

350 West Thomas Road, Phoenix, AZ 85013

ABSTRACT

A hypothesis is proposed that each cortico - basal ganglia -

thalamocortical loop is a control system that possesses a model of

behavior of its controlled object. The control system utilizes error

signals that are distributed via dopaminergic neurons of the

substantia nigra pars compacta and ventral tegmental area to adjust

both the control law and the model, i.e., for learning. The whole

system of cortico - basal ganglia - thalamocortical loops is considered as a system with nested hierarchies of functional loops.

Movement toward higher hierarchical levels is accompanied by

generalization of encoded parameters. An error signal computed at a

particular level is sent to the model of the same level and to the

higher loop as well. Within the proposed theoretical framework,

Parkinson's disease that is caused by a substantial loss of substantia

nigra dopaminergic neurons can be conceptualized as a disorder of

the error distribution system. Necessary experimental data

supporting the proposed hypothesis are discussed.

KEYWORDS: Optimal Control System, informational

signal, initiating signal, error signal, basal ganglia

1. INTRODUCTION

Cortico - basal ganglia - thalamocortical circuits are considered to be the major component of the highest brain

hierarchical levels. Five such circuits were distinguished: the

"motor" (or "skeletomotor"), the "oculomotor", the

"dorsolateral prefrontal", the "lateral orbitofrontal", and the

"anterior cingulate" [1]. According to the existing views,

each basal ganglia - thalamocortical circuit receives its multiple corticostriate projections only from functionally

related cortical areas. Moreover, each circuit is formed by

partially overlapping corticostriate inputs which are progressively integrated in their passage through pallidum

and substantia nigra (pars reticulata) to the thalamus, and

from there to a definite cortical area. Usually the target area

is one of those which sent projections to the basal ganglia.

That is why the hypothesis appeared that the characteristic

feature of all basal ganglia - thalamocortical circuits is the

combination of "open" and "closed" loops.

According to current views, similar neuronal operations are performed at comparable stages of each of the five mentioned

loops; the apparent uniformity of synaptic organization at corresponding levels of these loops and the parallel nature of

these circuits are indirect proof of this opinion.

Classical neurobiological theoretical views are not capable of

providing a reasonable explanation of how these loops

function and why they were created in the course of

evolution. However, it is relatively easy to create a conceptual

theory of function of these loops by utilizing modern control

theory.

2. A NOTION OF GENERIC NEURAL

OPTIMAL CONTROL SYSTEM

Experimental studies of spinal Central Pattern Generators

(CPG) for locomotor and scratching hindlimb movements in

cats have demonstrated that these CPGs possess a model of

object behavior [2], and CPG treats model flow as a component of peripheral afferent flow. The latter means that

both flows interact on a parity basis. A CPG deprived of

afferent flow (after deafferentation) can generate "proper"

rhythm by utilizing model afferent flow.

Later theoretical developments led to the conclusion that a CPG is a regime of work of spinal Optimal Control System

(OCS), and every neuronal OCS is constructed according to the same functional principle, regardless of its location in the

hierarchy of the nervous system (Fig. 1). Such neural

controlling system contains two distinct functional

subdivisions: (1) a controller, the subsystem providing a governing set of rules or commands - a controlling law - that

directs the action of the recipient of these rules - the

controlled object; and (2) a model, the subsystem that

generates a model of object behavior, i.e., expected afferent

flow from the controlled object. The function of the model is

to predict with high probability any given state of the

controlled object that can result from influences on it from its controlling system.

There are two main reasons for the control system to have a model of the object behavior - incomplete observability and

incomplete controllability of the controlled object. The

presence of the model within any neural control system is a consequence of its optimality. Model afferent flow is used by

the system to determine the most probable current state of the

object by using the mechanism of filtering of afferent

information (for simplicity, the filtering mechanism is put in

the control law box and is not shown in the Fig. 1). Another

advantage of having a model is the ability of a control system

to receive very important information such as mismatch or

error signals. A mismatch signal between real and model

499
controlled object

flows is necessary for the process of learning (see below) and

is also computed during filtering process (Fig. 1).

Figure 1. Functional

architecture of a generic

neural optimal control

system (OCS). Types of

signals - informational and

initiating - that controlled

object and subunits of OCS

send to each other are shown by single and

double arrows,

respectively.

It is necessary to note that

the described above two

functional subdivisions of

any given OCS may be

inseparable anatomically.

Both the control law and

the model can be realized within the same neural circuit in

the simplest of control systems. These two functional

subdivisions can be more clearly separated anatomically in

complex control systems.

It is rather easy to imagine a hierarchy of neuronal OCSs.

Lower OCS becomes a controlled object for higher OCS. Fig.

1 illustrates what signal types are sent by one hierarchical

level to another. It is well seen that the controlled object

sends to its controlling system, lower OCS, the same types of

signals that the lower OCS sends to a higher OCS. Those are

initiating and informational signals. The latter are used by a

control system to compute a control output that minimizes

the initiating signals. An initiation of lower automatism is performed by a simple tonic command that means that a

trajectory at the lower level corresponds to a point within a given system state at the higher command OCS. Therefore,

movement toward higher hierarchical levels is accompanied

by generalization, increase in parameters' abstraction, of

encoded parameters. It is clear that there should be a match

between the control level and its detectors, because the latter should properly describe the corresponding space state coordinates of the controlled object. The hierarchy of

detectors is created in such a way that lower detectors

become controlled objects for the higher detectors.

The above-mentioned theoretical conclusions created a foundation for theoretical analysis of organization of the

highest brain levels. Cortico - basal ganglia - thalamocortical

loops are the major anatomical substrate of the highest brain

levels, and let us try to analyze the available anatomical and

physiological data by utilizing the language of control theory.

It is easy to identify in these loops corresponding functional

subdivisions and types of signals.

3. SKELETOMOTOR CORTICO - BASAL

GANGLIA - THALAMOCORTICAL LOOP

The skeletomotor circuit is largely projected on the putamen,

which receives projections from the motor and somatosensory

circuits (Fig. 2a). In addition to these projections, the

control law

(cerebral cortex)

complex

informational

/ context

model of object behavior

(basal ganglia and

thalamus)

controlled object

Figure 2. Structural and functional organization of the

skeletomotor circuit, a - "closed" and "open" cortico - basal

ganglia - thalamocortical loops. Abbreviations: APA -

arcuate premotor area; GPi - internal segment of globus

pallidus. MC - motor cortex; PM - premotor cortex; SC -

somatosensory cortex; SMA - supplementary motor area; SNr

- substantia nigra pars reticulata; tn - thalamic nuclei, b -

cortico - basal ganglia - thalamocortical circuit is a control

system which has a model of the controlled object.

putamen also receives projections from area 5, from lateral area 6 including the arcuate premotor area, and from the

supplamentory motor area. While the most prominent

projections of each of these cortical areas go to the putamen,

there is slight encroachment of each projection upon

neighboring regions of the caudate nucleus. Additional

corticostriate inputs to the "motor" circuit from other

functionally related regions - precentral, ventral cingulate

premotor area, the supplamentory somatosensory area and

certain parts of superior and inferior parietal lobules, are still

in question. The putamen sends topographically organized

projections to discrete regions of the globus pallidus (e.g.,

ventrolateral two-thirds of both the internal and the external

segments) and to caudolateral portions of the pars reticulata

of the substantia nigra. The above mentioned internal

pallidal regions and substantia nigra send topographic

projections to specific thalamic nuclei including nucleus

ventralis lateralis pars oralis (VLo), lateral part of nucleus

500 I
ventralis anterior pars parvocellularis (VApc), lateral part of

nucleus ventralis anterior pars magnocellularis (VAmc), and

the centromedian nucleus (CM). The motor circuit is closed

by a means of thalamocortical projections from VLo and

lateral VAmc to the supplementary motor area (SMA), from

lateral VApc (from VLo as well) to premotor area (PM), and

from VLo and CM to motor cortex (MC).

Thus, the general rule of connections between the cortex and

the basal ganglia may be formulated in the following way:

each part of the basal ganglia that comprises a specific basal

ganglia - thalamocortical loop receives inputs from much

bigger regions of the cortex than those to which they project

their signals.

The Basal Ganglia is the Major Substratefor the Model

Closed neuronal loops are the substrate for the model.

Therefore, it is possible to redraw Fig. 2a in the other way

(Fig. 2b). It is necessary to note that the functional

subdivision shown in Fig. 2b should not be completely

identified with anatomical subdivision. This identification

may be done only to a certain extent (see Introduction). But

for our purpose we may do this as a first approximation and

consider the basal ganglia as a system which models the

controlled object.

It is not difficult to determine what is the controlled object

for the controlling system of the skeletomotor basal ganglia -

thalamocortical circuit. It is the body of the animal and the

environment. This model describes the behavior of the body

and the environment during animal movements.

To predict the behavior of the object, the model uses the

language of afferent signals that enter the system. For the

spinal OCS, it was the language of peripheral afferents. At

the level of the basal ganglia - thalamocortical circuit, the

situation is different. Lower OCSs are responsible for

different motor automatisms and the problem of basic

movement coordination is solved at those lower levels. Various motor control levels such as initiating systems of the

brainstem, the cerebellum, and even cortical level (motor

cortex) are controlled object for cortico - basal ganglia -

thalamocortical loop. The latter is a hierarchical control

system. Additionally, cortical area to which the basal ganglia

project their signals receives inputs from other cortical areas

that means that a great variety of cortical detectors (including

very complex ones) send signals to this area. These detectors

determine what values have relevance to parameters

describing the state of the object or its parts for any given

moment in time. The model predicts the behavior of these

detectors as well.

Fig. 3 illustrates how different levels of skeletomotor cortico

- basal ganglia - thalamocortical loop are functionally

interconnected with each other. Numerous subloops

subordinated to one another can be separated within

skeletomotor cortico - basal ganglia - thalamocortical loop.

The higher the subloop in the hierarchy, the more abstract

parameters are processed by this loop. Clearly, each subloop

has to receive corresponding afferent inputs to function

properly. This is why all types of afferent information have to be processed by different cortical regions before afferent

signals arrive in the corresponding subloop. For instance, the

information from the skeletomotor subloop that supplies the

motor cortex is not directly intermingled with information

from the cerebellum that arrives in the sensorimotor cortex. Cerebellar projections go to the cortex that is located between

motor and sensorimotor cortices.

higher level loop lower level loop

control law model

7T

control law model

dopaminergic error

(higher compartment)

distribution system

(lower compartment)

Figure 3. Hierarchy within the skeletomotor loop.

Dopaminergic neurons are included in error distribution

system.

The model for which the basal ganglia - thalamocortical

circuit is the substrate is used in two ways. First, as mentioned above, it is used during execution of the

movement to predict the transition to a new state. Second, it

is used during planning of a movement that needs the model

in a full scale because of a lack of afferent information about

future states. It is hard to imagine this process without using

a model. Moreover, a cause-effect model is not constrained

by real time and may function at rates faster than real time

that are necessary for multistep planning. It is obvious that

using the model without the constraint of real time requires

efferent and afferent channels to be cut off until a correct decision is found. It is not difficult to imagine how

deafferentation or deefferentation can be done at this level; different inhibitory mechanisms can be used.

The reasoning made above helps to better understand the

circuitry in the basal ganglia and shows the way to future

investigations. Several simple suggestions may be made

about basal ganglia circuitry. A few examples will be

discussed below. The system at the higher level has to "jump"

from one state to another while performing controlling

501
functions. The optimal (easiest) way to create such a system

is to build it on the basis of pacemaker neurons or neurons

possessing bistable properties. It is easy to create a system

which is able to switch from one stable state to another while

simultaneously counting time intervals by using simple

trigger elements, i.e. neurons having the above described

properties. For instance, it is well known that such neurons

are frequently a part of central pattern generator circuitries in

many animal species. They model the period of rhythm

generation during locomotion, breathing, etc. Such neurons should be included in the basal ganglia

circuitry. Otherwise basal ganglia circuits that include

inhibition of inhibitory neurons will not work. Such

processes take place in striatum, GPe (external segment of

globus pallisus), GPi (internal segment of globus pallidus),

and pars reticulata of the substantia nigra. Moreover, there

could be one additional interesting mechanism: more

complex circuit triggers. A system having a large number of

such triggers, each of which may be only in two stable states, can encode the whole variety of possible states of the object.

Therefore, a hierarchy of states may be encoded so that

higher level triggers change less frequently than lower level

triggers.

Dopaminergic Neurons are a Part ofAn Error Distribution

System

It was implied above that control system uses the model

while performing its function. Such systems have to have an

error distribution system in order to properly tune the model on the object. It is easy to find it in skeletomotor cortico -

basal ganglia - thalamocortical circuit. Error distribution

system includes dopaminergic neurons of the substantia nigra

and adjacent mesocorticolimbic group (Fig. 3). The complex

organization of the cell body subgroups, the one located in

the substantia nigra pars compacta and the other in the

ventral tegmental area, are no longer defined in terms of

striatal or mesocorticolimbic projections. These subgroups

are intermingled, and some mesocorticolimbic projections

have their origin in the substantia nigra and vice versa [3]. This view is in good agreement with numerous experimental

data. Dopaminergic neurons of pars compacta and

mesencephalic tegmentum react to any behavioral or environmental change, i.e., to stimuli which are not

predicted by the model. If the stimulus can be predicted,

situation is different. For instance, in conditioning paradigm,

dopaminergic neurons respond to unconditioned stimulus in

the beginning of learning. Later, as the animal learns the

task, the cells respond to conditioned stimulus that can not be

predicted and do not respond to unconditioned one [4],

However, they will fire if the unconditioned stimulus is not

presented at its previously predicted time interval, for

instance, the stimulus appears earlier than expected. Any

previously described patterns of dopamine neuron firing

could be misleading in terms of stimuli that activate this

neuronal system and some authors suggested that signaling

of dopamine neurons predicts future reinforcement [5]. Although the idea of prediction is still the major feature of

their model, the authors ascribe this function to a circuit that

includes dopaminergic neurons. As we have seen above, it is more appropriate to consider the whole basal ganglia circuit as a substrate for predictions. In this case, a preceding firing

of dopaminergic neurons in response to unpredicted

conditioned stimulus can play a role of tuning the basal

ganglia circuitry on correct future prediction of

unconditioned stimulus.

There are three possible locations where mismatch signals

between model and real flows may be calculated. This

mismatch signal goes to dopaminergic neurons mentioned

above. First, in the cortex, from which signals about

mismatch go to those putamenal and caudate neurons which

project to dopaminergic neurons. Second, in the putamen and

the nucleus caudatus. Third, in both places. But it is necessary to note that there are no principle differences

between these possibilities. In all cases error signal resulting

from mismatch between model and real flows, will reach

dopaminergic neurons.

In addition to the described above mismatch signals,

dopaminergic neurons also receive less numerous initiating

inputs from other sources: from, entopeduncular nucleus,

dorsal nucleus of raphe, the central nucleus of the amygdala,

and the bed nucleus of the stria terminalis. There are also some indications about direct cortical inputs to the substantia

nigra [see 6]. The existence of multiple inputs to the error

distribution system does not contradict to the theory. They

can create new minimization criteria for the system.

Thus, mismatch signal computed at the level of one subloop

goes through dopaminergic neurons to the model of the same

level and to the controlling network (corresponding cerebral

cortex) of higher subloop.

Learning in the basal ganglia starts when initiating signals

become larger than minimal and stops when they are minimized. It is possible to suggest that very complex

strategies may be used at this level to minimize initiating

signals. The strategy of random search may be used in early

ontogenesis when there is no knowledge of object behavior.

Later, more complex and more advanced learning strategies

may be used. These strategies can be based on some specific

mechanisms, for instance, memorization of informational

context, memorization of incorrect decisions, etc. The

complexity of cortical and basal ganglia networks makes

such a suggestion reasonable. Moreover, in this system error

signal possesses a sign: Dopaminergic influence excites

direct pathway from the putamen to the globus pallidus and

inhibits the indirect one. Clearly, the sign accelerates

significantly the process of learning, and fast tuning of the

model on the object becomes possible. It was already

mentioned that a hierarchy of parameters exists at this level,

502
and it is possible to mention the simplest analogy. Suppose

the predictive mechanism is built on the basis of a counter

that encodes object states. In this case, if this predictive

mechanism is working quite well it will be necessary to

adjust only lower digits by changing thresholds of their

switches.

Parkinson 's Disease

Parkinson's disease is one of the most studied

neurodegenerative disorders. Clinical studies and

experimental data from animal models of parkinsonism have

convincingly shown that death of dopaminergic neurons of

the substantial nigra leads to Parkinson's disease. Akinesia,

muscular rigidity and tremor are the main symptoms of this

disease [see 7, 8].

Thus, based upon the proposed theoretical approach it is

possible to conclude that Parkinson's disease is the

consequence of disorders of learning processes in the basal

ganglia (in its skeletomotor loop), a disorder of error

distribution system. As a result of this, the model incorrectly

predicts the state of the object in these patients (Fig. 4)

normal subject Parkinson's disease

object state

Figure 4. Probability of the controlled object to be in a

definite state. When the model functions correctly, the

prediction coincides with the probability distribution

generated by real afferent flow. In case of Parkinson's

disease, predicted and real probability distributions do not

coincide when the model functions incorrectly.

Let us analyze how incorrect prediction leads to symptoms in

Parkinson's disease. It is clear that symptoms depend on what

parameters of the object are predicted incorrectly (what digits

of a "counter", lower or higher, are set improperly). When

the state of antagonistic muscles is predicted incorrectly,

there will be rigidity or tremor. In the latter case, it looks like

overregulation when the model always misses the

equilibrium point. More complex explanations should be

used for bradykinesia. In this case higher level subloops are involved, and the prediction of the model differs significantly

from the real state of the object. The model may predict also

several states with equal probabilities. Therefore, it takes

much more time for the system to choose from these states, to decide which of them is more probable.

Let us consider one of the simplest analogies - interaction of

antagonistic reflexes at the spinal level. It is well known that

when receptive fields for antagonistic reflexes are stimulated

simultaneously it is impossible to predict which of these

reflexes will be evoked. The latent period of the evoked reflex

is usually much longer than in the normal situation.

Moreover, sometimes none of these reflexes appear at all. Severe akinesia is the result of an absolutely unreal

prediction of the model.

The most curious problems unearthed by observations

generated by functional neurosurgery for Parkinson's disease

still remain unclear. For example, why do partial lesions of

particular structures within the neural network of the basal

ganglia - thalamocortical loop, globus pallidus pars interna

and some thalamic nuclei, improve symptoms. This

observation contradict common sense: How is it possible to improve the network function by destroying its part?

Moreover, chronic stimulation of some of the same structures produce identical effect. This is a fundamental paradox that

until now has not been reasonably explained by reflex theory

or the balance of excitation and inhibition that is postulated

to occur in the basal ganglia. In the case of stimulation, two

possible mechanisms exist: (1) Stimulation produces a

functional block in regions immediately adjacent to the

electrode tip; and (2) spreading of influences to other brain

regions occurs via both fibers passing through the stimulated

region and axons of neurons excited during stimulation.

However, these latter influences do not provide the system

with meaningful information for signal processing. Thus, the

second mechanism simply introduces noise into the network.

Therefore an obvious question appears: Why does noise

added to such a system improve its function? At last, it is well known that such parkinsonian symptom as tremor can

be effectively removed by placing a lesion in thalamic

nucleus that conveys information from the cerebellum to the

cortex, that means that the real afferent flow is changed by

this procedure.

From the point of view of the developed theory explanation

of these medical facts can be the following. When the

network generating model afferent flow is partially

destroyed, probability distribution of possible object states become lower and wider. Obviously, predicted states can

partly overlap with possible real states of the object after this

procedure. As a result, system does not find an error in its prediction anymore, and does not try to correct the object

position in it state space. Situation is symmetrical in case of

placing the lesion in the network processing afferent flow.

Model flow is not changed. What is changed is the

probability distribution predicted by real afferent flow, and

two distributions generated by model and real flows start to

503
overlap. The latter leads to alleviation of parkinsonian

symptoms, for instance, tremor.

An explanation for the effects of chronic stimulation becomes

transparent after what was said above. Functional block

works as partial destruction of the structure. Therefore, the

mechanism of chronic stimulation is partly similar to placing a lesion. Concerning noise, another possible factor that can work in the case of chronic stimulation, it is well known that

adding noise effectively helps the system to slide down the

error surface to its global minimum, much like shaking an uneven declining surface helps a ball slide down to the

lowest point on that surface. While the results of chronic

stimulation are similar to the clinical results of placing a

lesion, they do not produce immediate neural tissue

destruction. Furthermore, one can stop stimulating tissue by

turning off the source of current, thus producing a reversible

type of functional lesion.

One critical aspect of this explanation should be always kept

in mind. Placement of a lesion or chronic stimulation within an OCS network improves symptoms, but does it make the

controlling system function normally? The answer is no! After the lesion has been placed, the system is effectively

tricked and does not find any errors in its prediction.

However, normal function of the controlling system is not

restored. Therefore, functional neurosurgical procedures in

PD should be considered merely as palliative, symptomatic

interventions and not curative because they do not stop the

fundamental degenerative process. Only restoration of the

structural integrity of the system by rewiring of lost connections, or at least prevention of further dopaminergic

cell loss, will be the most effective form of treatment for PD.

Therefore, functional neurosurgical procedures have to be

considered as methods of treatment based on holographic

properties of biological neural networks, that means that

system can function being partially distructed. Like in

holography when complete three-dimensional image of an

object can still be reproduced after partially destruction of the

photographic plate, but with a lesser resolution.

4. OTHER CORTICO - BASAL GANGLIA - THALAMOCORTICAL CIRCUITS

Skeletomotor loop described above controls movement of

such objects as the animal's body and the environmental

objects. Oculomotor loop is principally very similar to the

skeletomotor loop. Obviously, if the level of parameters'

abstraction in such a system as the cortico - basal ganglia -

thalamocortical circuit became sophisticated enough to perform "movement" of abstract objects in an abstract state space out of real time, there would clearly be the creation of a

principally new functional feature, and the process of

elaborately detailed multistep planning would be possible,

i.e., the capacity for thought. Prefrontal loops are the

substrate where such operations take place.

The above-described theoretical approach can be utilized for

explaining the functional role of the cingulate gyrus and its cortico - basal ganglia - thalamocortical loop. The latter loop

is often referred as the "limbic" loop. It is a part of the limbic

system. According to numerous experimental data, the limbic

system controls: Activities essential for the self-preservation

of the individual, including emotional ones (e.g., feeding

behavior and aggression, behaviors that are often

accompanied by emotions); activities essential for the

preservation of the species (e.g., mating behavior,

procreation, and the care of the young); visceral activities

associated with both of the above and numerous other

activities of the hypothalamus; mechanisms for memory.

REFERENCES

[1] Alexander, G.E., DeLong, M.R. and Strick, P.L. (1986):

Parallel organization of functionally segregated circuits

linking basal ganglia and cortex. Ann Rev Neurosci 9: 357-

381

[2]Baev, K.V., and Shimansky, Yu.P. (1992): Principles of

organization of neural systems controlling automatic

movements in animals. Progr Neurobiol 39: 45-1 12

[3] Le Moal, M., and Simon, H. (1991): Mesocorticolimbic

dopaminergic network: functional and regulatory roles. Physiol Rev 71: 155-234

[4] Ljungberg, T., Apicella, P., and Schultz, W. (1992):

Responses of monkey dopamine neurons during learning of

behavioral reactions. J Neurophysiol 67: 145-163

[5] Houk, J.C., Adams, J.L., and Barto, A.G. (1995): A

model of how the basal ganglia generate and use neural

signals that predict reinforcement. In: Models ofInformation

Processing in the Basal Ganglia, Houk, J.C., Davis, J.L., and

Beiser, D.G., eds. Cambridge, Massachusetts, London,

England: Bradford Book, The MIT Press, pp. 249-270

[6] Brodal, A. (1981): Neurological anatomy. In relation to

clinical medicine. New York, Oxford: Oxford University

Press

[7] Bergman, H., Wichmann, T., and DeLong, M.R. (1990):

Reversal of experimental parkinsonism by lesions of the

subthalamic nucleus. Science 249: 1436-1438

[8] Greene, K.A., Marciano, F., Golfinos, J.G., Shetter, A.G.,

Lieberman, A.N., and Spetzler, R.F. (1992): Pallidotomy in

levodopa era. Adv Clinical Neurosci 2: 257-281

504
Learning How To Know:

Semiotics and Multiscale Cybernetics

A. Meystel

Drexel University

National Institute of Standards and Technology

Abstract. In this paper a comparison is made of

Semiotics and Cybernetics. It was found that

semiotics can be considered a cybernetics of the mth order. The latter can be characterized by the

phenomena of self-reflection and multiscale

representation. A syllabus for the corresponding course is outlined.

Key words: cybernetics, m-th order, multiscale

representation, reflection, semiotics

Knowledge Acquisition. Intelligent systems

acquire knowledge through preprogramming and

learning. These processes deal with information

represented in signs (labels, elementary codes) and

symbols (generalizations of signs). The synapses of our nervous system generate signs and symbols,

and are signs and symbols themselves. The

formation and use of signs and symbols is analyzed

within the discipline of semiotics. In semiotics, the

central process under consideration is called

semiosis. This process takes the form of an elementary loop of acquisition and processing

which represents both functioning and learning.

Semiosis is combined of the following

subprocesses [1,2]:

a) encoding of the sensations (sets of signals from

transducers interpretable as states of the reality)

by using elementary signs

b) associating encoded sensation with codes of

actions (sets of phenomena which entail the

commands generated by the system)

c) constructing strings of codes for "states-actions-

..." (S-A-S-A...) stored in the memory

d) assigning to these strings of signs values of

goodness J interpretable under specific goals G,

which allow interpretation of "experiences" E:

[G,(S-A-...)]-->J

e) discovering classes of experiences {E},

assigning labels (signs, symbols) to them,

assigning signs to their components (generation

of the concepts of objects and actions)

f) forming hypotheses of new behavioral rules

using previously stored results of prior processes

of semiosis.

Statements "a" through "f can be formed

only for a particular "level of resolution" (or

"granularity".) The level is characterized by two

major constraints in focusing attention (from above

and from below.) The first constraint corresponds to the scope of view, the second - to the minimum

"granule" (the "indistinguishability zone"

introduced in [3].)

All semiotic processes contain an operation

of generalization which is typical for all processes

of knowledge acquisition. The need in

generalization is determined by the orientation

toward complexity reduction. All algorithms of

generalization consist of procedures of grouping,

focusing attention, and combinatorial search (see,

GFACS in [2].) A special feature of the semiotic

system is that GFACS is being applied to the

results it produces at its output. Thus, the

multigranular systems emerge.

Cybernetics vs Semiotics. The loop of semiosis

has a striking similarity with a cybernetic views of the

system. The sequence "a" through "f describes

computational activities at a singe level of granularity

in a system for knowledge acquisition, generalization,

and utilization (e.g. "action") i.e. in a semiotic system.

Unlike a classical cybernetic system the semiotic

system generalizes the acquired information and

processes it again many times, thus building up a system of multiresolutional nested loops. Each of

these loops is a classical cybernetic loop. A system of

these loops allows for considering m levels of

granularity. In classical cybernetics, the issues of granularity

are considered to be a source of special effects (e.g.

nonlinearity) but does not interfere with the

architecture of the "loop": "...vibrations of the

molecules in the nucleic acid complexes may be

responsible for their behavior as organized systems

...in dynamical systems of a much coarser texture the

vibration properties play a large part in their

organization. This is true both with biological and

with engineering systems." [4]

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It is typical for the analysis of semiotic

system to be focused upon the meaning of the

system and the process: after answering the What?

question, Why? is the question that the

semiotician attempts to answer. In cybernetics, the same elementary signal processing loop is a source of different insights. How? and How to control?

are the typical questions for the cyberneticist . As a

result, a semiotic system turns out to be equipped

by the means of generating feedforward commands

which contain the goals and tasks, and it becomes a conventional cybernetic system.

Levels of various granularity. In other

words, the cybernetic loop of system functioning is almost equivalent to the semiotic loop of semiosis

with the following difference: the first describe

control processes in physical terms while the

second analyzes the processes in the multigranular

sign-symbol domain. A more serious difference is

in the emphasis: since semiotics is pursuing the

meaning of the system, the goal is always

questioned, and another loop should be discussed at which the goal is just a variable. This new loop (a coarser granularity loop) has a different goal, and

the goal of the first loop is just a variable for this

new loop. The pursuit of meaning leads us to discovery of loops of different granularity.

(Actually, emergence of the objects and processes

of coarser granularity was ingrained in the stage "g"

of the description of the process of learning.

When m levels of granularity (resolution,

scale) emerge as a result of learning in the semiotic

system, similar levels emerge in the corresponding

cybernetic system. A cybernetic system of the m-th

order emerges, or multiscale cybernetics. The

multiscale cybernetic systems can be characterized

by a multigranular (m-loops) semiosis which

invokes a variety of interesting and important

phenomena including reflection ("reflexia"), self- organization and emergence (usually attributed to the situation of "complexity") and others.

Can we talk about virtual equivalence of

semiotic and cybernetic systems just by considering

a single level loop? We can but the powerful

concepts of the semiotic-cybernetic scientific

paradigm will be wasted. We do not need the tools

and techniques of either in a single loop case. On

the other hand, if learning is involved, if planning

is of interest, if processes of self-organization and

self-description are of significance, no single loop

(single level) discussion can be productive: such a

simplification will have hidden mistakes.

At a single level of resolution, the relation

between the constructive mathematics and nonstandard analysis can be demonstrated. Both are characterized by illustrative paradoxes which

demonstrate that movement to another level is

required.

The joint semiotic-cybernetic paradigm

allows us to address all these issues and explore the

research developments implied, and the applications

of the expected theoretical results.

Semiotic Architectures. A long time ago

people discovered that intelligent systems and

learning processes depend on architectures of signsymbol processing. These architectures determine

how intelligent systems perceive the world,

recognize objects in it and interpret the results of

recognition for the subsequent actions. The

multigranular architectures of our intelligence and

the multigranular representations generated by our

intelligence are affected by the processes of single

and multi-level self-reflection.

Architectures of sign processing affect the

ways intelligent systems behave in the world. They

depend on the way these systems think they

behave. Careful analysis demonstrates that all our knowledge depends on our self-reflection. Our own

brain-architectures are reflected in all the knowledge

we acquire, even when we think that we analyze an

electron, a spray casting, or a bacterium. All our

representations reflect the architecture of our brain.

Architectures of intelligent systems incorporate the

recursion of self-reflection which becomes crucially

important for describing interactions among

multiple intelligent systems.

In intelligent systems knowing always

presumes changing resolution or granularity or scale (which is the same). Therefore, learning

brings on changing the scale of representation and

subsequent changes in processes of decision

making, planning, and error compensation within

this scale of representation. Each next step of

learning leads to the generation of a next order of

cybernetic analysis. Once a higher level (level of

coarser granularity) is achieved, all previously

known (finer resolution) subsystems are subsumed

by (aggregated within the model of) the level of

coarser granularity.

Cybernetics was a step in learning how to know. We have discovered the phenomenon of self- organization via planning and error compensation

during functioning. Self-organization was a step

toward self-reflection. With realization of the

phenomenon of self-reflection we started paying more attention to the techniques of interpretation.

The results of our interpretation are strongly

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affected by our "self hidden in the techniques of our intelligence. Then, the cybernetics of the

second order emerged (this term was introduced by

H. von Foerster to describe the level produced by

self-reflection).

Socio-scientific Aspect of Knowledge

Acquisition. People were always respectful to and

comfortable with activities related to knowledge

acquisition and organization, all of them starting from

broadminded Aristotle and ending with narrowly trained

professionals of the XX Century. Problems related to knowledge emerged when we entered the era of

intelligent systems:

a) we realized that within a single problem

we should address modeling of the system at several

levels of resolution (granularity, scale)

b) we started analyzing processes of selfreflection when in addition to the world produced by

sensations we encountered a world produced by our own representations which included representation

of ourselves.

How Is Semiotics Related To Other

Disciplines. The gist of the movement toward

Unified Science was rejected by the reality of socioscientific process. However, the essence of it cannot be discarded because of the following

reasons:

• all sciences are based upon the system of

symbols and their transformation induced by our

brain architecture

• thus all phenomena of the world perceived

and reasoned by us are preprocessed so as to fit

to be interpreted by these architectures

What makes the natural sciences distinct is something that can be called "legacy issues": this is

the way how people in the particular socioscientific niche are used to talk about their

subdomain entities, so do not interfere with this

legacy. Nevertheless, it seems to be prudent, to study the invariance of the natural sciences before

we embark on doubtful enterprise of

unconditionally solidifying obstacles for generalization which are copiously collected within

the bulk of legacy issues. The following temporal

sequence of knowledge acquisition can be

recommended in the imaginary syllabus of the course on "Semiotics of Knowledge":

I. Science of Signs Formation which includes:

• Energy and Complexity

• Entity formation techniques

Grouping, Focusing Attention,

Combinatorial Search (GFACS)

• Generalization and formation of the entityrelational structure

• Continuity and discretization

• Granularity and Resolution

• The phenomenon of recognition

• Equivalence, Resemblance, Similarity

A significant issue (among others) is the skill and

the habit of notations: they carry with themselves

premises, assumptions and prejudices.

2. Science of representation including Syntactics

and Semantics.

3. The Phenomenon of Interpretation

4. Sciences of Generalized Reasoning including

Logic , Mathematics, and Computer Science

5. Knowledge Engineering and Epistemology

6. Science of Value Judgment including methods of

evaluation and optimization of Goodness and

Beauty.

7. [Intuitive] World Modeling in Art and Literature

8. [Weak] World Modeling (Experimental

Knowledge Classification) in Zoology, Botany,

Medicine, Geography, History, Economics

9. [Strong] World Modeling (Architecture Analysis)

with the legacy disciplines of Physics,

Chemistry, and Biology

10. Problem identification and creative solving:

Theory of Design

1 1 . Philosophy and Psychology: Theory of Mind

12. Control Theory

13. Information Theory

14. Science of Learning including Process of

Semiosis, Adaptation, Evolution, Machine

Learning

15. Engineering

16. Life Science, Evolution, Genetics

17. Large Complex Systems (including Sociology

and others)

18. General Pragmatics and Symbol Grounding

A special role of Control Theory. In 60s, the

ideas surfaced that theory of control should go further

than just constructing mathematical models of dynamic

systems (K. S. Fu, G. Saridis.) The annual

symposium on intelligent control has been initiated in 1984 when it became clear that Control Theory

benefits from unified application of techniques and

ideas typical for Operation Research (OR) with its search, and Artificial Intelligence (AI) with its logics

and linguistics. In the course of events, it became clear

that there is more to the situation than just merger of:

Control Theory+OR+AI.

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Some groups persistently associated intelligence

with neural networks, fuzzy set theory, and

evolutionary computation. This wing of

control/computational science exists now as a community of Soft Computing for whom the body of

intelligent control is a sum:

NN+Fuzzy Sets+Evolutionary Computation.

Finally, many people believe that it is very

important to determine everything by the

architectural issues which makes problems

dependent of the cases of intelligent systems known

from the biology of nervous systems in living

creatures, laws of language, physics, and technical

solutions in autonomous robotics. Thus, a new set of interrelated domains was added to the area of

Intelligent Control:

Architectures+Brain+Semiotics

One can see that these three communities are not independent, they rather overlap a lot. It is tempting to say that the truth is in the middle.

However, in this situation finding a "middle" is a formidable problem by itself.

Conclusions. Various disciplines, including

knowledge engineering, artificial intelligence,

intelligent control, and semiotics, are stages in the

exciting search within and traveling toward

multiresolutional cybernetics, or cybernetics of the mth order. Such systems produce representations in multiple scales, supplement control with self- organization and throw us into a totally new world, a multigranular world, in which we always live even though we do not pay too much attention to its multiresolutional nature. Various artifacts of life and technology

should be discussed from the point of view of

multiscale cybernetics. In engineering problems and

poetry, scientific research and visual arts, everywhere we will continue to discover the

multiresolutional world of semiotic-cybernetic

models.

References

1. R. Carnap, "Foundations of Logic and

Mathematics", in International Encyclopedia of

Unified Science, eds. O. Neurath, R. Carnap, C.

Morris, U. of Chicago Press, Chicago and London,

1955, pp. 139-213

2. A. Meystel, Semiotic Modeling and Situation

Analysis: An Introduction, AdRem, Bala Cynwyd, PA

1995, pp. 81-91

3. A. Meystel, "Planning in a hierarchical nested

controller for autonomous robots," Proc. IEEE 25th

Conf. on Decision and Control, Athens, Greece, 1986

4. N. Wiener, "Perspectives in Cybernetics", in Eds.

N. Wiener, J. Shade, Cybernetics of the Nervous

System, Elsevier, Amsterdam, 1965

508
XIX SEMIOTICS IN INTELLIGENT

CONTROL

Semiotics: a Key to Intelligent Control

Tariq Samad

Honeywell Technology Center

3660 Technology Drive

Minneapolis, MN 55418

samad@htc.honeywell.com

ABSTRACT

As the discipline concerned with communication and

signification in their broadest senses, semiotics has much to

offer for the development of truly intelligent systems. This

paper explores the relevance of semiotics to intelligent

control. I focus in particular on the role of the semiotic sign

in control systems, distinguishing several types of signs

involved. These include signs used to communicate system

states, human user inputs, and environmental variables to the

control system, signs used to communicate control actions to the system, and signs used internally by the control system

for its functioning. Viewing these various flows of

information as general signification activities broadens our

conventional notion of control, and renders it more relevant to

large-scale, complex processes. Several technologies that can

contribute to the "semioticization" of control are noted:

multiscale representations, fuzzy logic, learning and

adaptation, computational linguistics, and classical control.

Keywords: control systems, multiresolution models,

fuzzy logic, learning systems, computational linguistics.

1. Visions of Intelligent Control

The successes that have been achieved with our existing

control technology over the last few decades are a mixed

blessing. On the one hand, control technologists can take

justifiable pride in contributing to the technological progress

of our societies. On the other hand, further research in

classical control appears to be a path of incremental,

evolutionary improvements. Yet challenging control

problems are still far from being solved—practical

learning/adaptive systems for real-world applications are still

far from reality, to take one example. The interest in

"intelligent control" reflects both the recognition of the

outstanding research needs in control and the view that

classical control methods cannot by themselves satisfy these

needs. There remains, however, a considerable mismatch

between the motivation for intelligent control and much of

the research that is currently being conducted under its aegis.

Single-loop neural and fuzzy controllers are only a small part

of the solution—at best.

One critical limitation of most research—whether in a

classical or intelligent control vein—is the simplistic, highly

restricted code theory that is assumed to underlie

communication and signification in control systems. Aspects

of this communication include: a user's command to the

control system, the representation of sensory measurements,

controller design parametrization, system models as used in the controller, and the control action itself. In each of these

cases, current control systems only permit simple types of

information structures, such as numerical vectors.

As the discipline concerned with communication and

signification in their broadest senses, semiotics has much to

offer control science and engineering. This "position paper"

attempts to demonstrate this relevance. The next section

discusses how a control system can be viewed as a semiotic

system, the latter being taken to mean a system in which the

Peircean triad of object/sign/interpretant is realized. Section 3

outlines several possible roles for signification, noting how

they extend our current thinking in control. Semiotics is not,

at least not yet, a technology with packaged solutions to

offer, but several technological fields have significant

connections with it. Some of these are briefly discussed in Section 4. Section 5 contains some concluding remarks.

This paper is speculative. It presents no crisp technical ideas.

I am hoping that it can serve as grist for discussing the role of

semiotics in intelligent systems in general, and intelligent

control systems in particular. The majority of the exposition

is abstract, but I occasionally refer to some examples. These

are taken from domains I have some familiarity with

industrial process control and building control—but the

exposition is intended to apply to control systems generally.

2. Roles for Semiosis in Intelligent

Control Systems

I discuss in this section how a control system can be viewed

as a semiotic entity, placing particular emphasis on the role

of the sign as the linchpin of semiosis. The notion of the

sign has been adapted considerably over the history of

semiotics, and it is relatively recently that the possibility of

artificial entities generating and interpreting signs has been

acknowledged. The very thought that a control system can engage in semiosis may still seem a novelty to some.

Nevertheless, a semiotic explication of a control system can be suggested: A control system receives signs from its environment, interprets and processes them according to models explicitly or implicitly embedded in it, and produces

other signs. The question arises: What, if any, advantage is gained by this potentially confusing reformulation over our conventional understanding and articulation of a control

system?

511
For the lowest level of controllers—which comprises the

majority of them—the benefits may appear to be few. I do

not, for example, see how our understanding of the PID

algorithm can be improved given the semiotic insight relative

to its explication as u = Kce(t) + Kije(t)dt + Kd^- .

1 Even for

dt loop control, though, the core algorithm is but one piece of

the puzzle. The functioning of a PID controller also requires

integral windup protection, a bumpless transfer mechanism,

tuning procedures, manual override capability, etc. These

functions may be ancillary, but the complexity of most

exceeds that of the controller's "primary" element.

In this larger picture, a semiotic perspective is meaningful,

and a semiotic triangle associated with detecting a poorly

tuned process is presented in Fig. 1 . One manifestation of a poorly controlled process is high variance in the process

output, here assumed to be temperature. In the figure, this

sign has an interpretant, a consequence of a human operator

observing, for example, the temperature versus time trend on

a display. The interpretant is itself a sign—perhaps a command to the control system to initiate a retuning of the

PID controller. There are many other signs of the considered

object: large overshoot in step responses, high control

action, poor quality product downstream, etc. There are also

many potential interpretants, which could be generated by

manual or automatic systems.

Large Temperature

Variation(Sign)

Poorly Controll ed Effect onOperator

Process (Object) (Interpretant)

Fig. 1. A semiotic triangle for a simple control

application.

The chain of semiosis—a sign resulting in an interpretant

which, being a sign itself, leads to another interpretant, and so on—exists in control systems no less than in general

semiotic systems. At some point, the chain terminates and a

physical action is taken—the retuned controller starts operating a valve differently than before. At this limit of the

semiotic activity, its triadicity is replaced by the dyadic action

of the physical world. Since a control system operates by

feedback, the semiotic regression ultimately affects its object,

'For those readers unfamiliar with PID controllers, the control

output u is computed as a weighted sum of three error terms:

the instantaneous error e(t) (i.e., the difference between the current system output value and the desired value), the

integrated sum of this error, and the rate of change of this

error. Kc, AT,-, Kj are the respective weights and are generally

referred to as the proportional, integral, and derivative gains.

the system under control, thereby initiating another chain of

interpretants.

There is as yet no consensus on a typology of signs. Eco

(1984) analyses various historical treatments of the concept of

the sign, stressing its generality. Peirce's initial classification

differentiated between indices (signs in physical adjacency to

their objects), icons (signs similar to their objects), and

symbols (in which the sign/object connection is arbitrary).

Eco (1976) labels this classification "untenable" and suggests

that signs can be classified from different perspectives (e.g.,

relative to the channels of communication, the gradation of

the sign, and its origin). Sebeok (1994) extends Peirce's

tripartite scheme with three additional types: signals,

symptoms, and names.

What types of signs are appropriate for control systems? It is useful to adopt Eco's distinction between a signal and a sign

(Eco, 1976; p. 46)2. A signal, by his definition, is "a pertinent unit of a system that . . . could also be a physical

system without any semiotic purpose. ... A signal can be a stimulus that does not mean anything but causes or elicits something." In our earlier example, we described the

operation of a PID algorithm as lacking a semiotic character. We can thus say that, when the process output error signal serves only as input to a PID controller, it is solely a signal.

It assumes a semiotic role, and the status of a sign, only

when a semiotic triangle is configured through the operation

of a (human or machine) interpreter that is capable of

generating an interpretant for further signification.

Some signs relevant to intelligent control systems are shown

in Fig. 2, which also differentiates between mandatory and

optional signs. In the general case, a control system will

receive inputs, and these may have signification potential,

from its environment, its human users, the system to be

controlled, and other automated systems. Its outputs, again

potentially signs, will be communicated to human users (some of these may be identical to the human users that provide input to the control system, but others will not be),

the controlled system, and other systems. Semiosis is not

limited to the interface between the control system and the

world; signification occurs internally as well. I am assuming

in this figure that any device that can be directly effected by

the control system is by definition part of the controlled

system. The environment is therefore not an output.

This figure is not intended to represent a far-off, futuristic

vision in which intelligent control systems may operate with

complete, unmitigated autonomy. Semiotics can play a

revolutionary role in control systems in the considerably

nearer-term. Some role for the human will undoubtedly exist

in this case—at a minimum, in the start-up, shut-down, and

maintenance of the control system. For a practical intelligent

control system, the human interaction is not optional.

2 "Signal" is also one of the six types of signs classified by

Sebeok (1994). In this paper, I follow Eco's usage since it conforms to the common notion of signal in control systems.

512
3. Sign Functions in Control

Systems

Next, I briefly discuss the signification potential for some of

the interactions shown in Fig. 2. None of these inputs and

outputs are completely absent in today's control systems.

However, I hope to show how considering the

communications depicted in Fig. 2 as significations in a general sense naturally results in a broadening of what we

mean by a control system, with the potential for dramatic

advances in control technology.

3.1. Signs referring to states of the controlled

system

Most industrial control systems are configured to expect sensor readings to consist of raw numeric information:

temperatures, pressures, flows, forces, etc. Sensor readings

are only intended to be signals. There is now increasing

interest in the use of unconventional modalities in feedback

systems, extending the notion of a sensor in novel ways.

Control engineers are actively exploring the integration

within control systems of "artificial noses" for fugitive

emissions detection, pattern recognition devices for visual

quality control, vibration signature analyzers for rotating

machinery, etc. However, this exploration is proceeding in an

ad-hoc, piecemeal manner that does not recognize the

fundamental signification function that these innovations have

in common. In most of these cases, the control system may

provide the capability for a human to view the sensor output

and for a human or a separate stand-alone system to process

the sensory information, but this limits the role of the control

system to a transmission medium. The video image or vibration spectrum may be a sign for the human, but it is not

a sign for today's control system.

The growing use of neural networks and related technologies

is also providing a limited semiotic capability to control

systems, but much more can be done. A sensor complex that detects the number and distribution of people in a conference

room could, in principle, be used for more effective and

efficient temperature, humidity, and air quality control. In current systems, realizing these improvements would

necessitate one-of-a-kind encoding strategies. In contrast to sensor signals, where (for example) the 4-10 mA standard is universally accepted, there is no standard for representing

complex information regarding system state.

These shortcomings can be attributed, not entirely but in large

part, to a failure to recognize that control systems can be

semiotic entities.

The Envi ronment

Human Users

The Controlled System

Other Systems

Human Users

The Controlled System

Other Systems

Fig. 2. The roles of signs as input to, output from, and internal to, an intelligent control system. The lighter arrows imply

optional significations.

3.2. Signs from human users

Another critical aspect of communication to a control system

is user commands. Current systems adopt unstructured, flat codes, a limitation that is not problematic for the tasks

demanded of them, such as regulating the temperature of a room to a fixed setpoint. But this limitation is incompatible

with revolutionary advances in control. In the foreseeable

future, we would like to have automatic control systems that can respond to commands such as (for a building cooling

system): "Attempt to reduce energy consumption by 10%

without permitting temperatures to rise more than 1°C from

nominal settings in any zone and without resorting to full lighting setback except in unoccupied areas." The expression

need not be in a natural language, although that is a worthy

goal, but in either case the intelligence required to effect such

commands requires a semiotic sophistication well beyond

what current control technology offers, or even seeks to offer.

Other types of signification from users can also be catalogued:

commands that relate to controller operation (such as switching from manual to automatic control), the

communication of prior knowledge about the controlled

system (such as model order or parameter estimates), the

communication of application-specific heuristics for control

(such as fuzzy rules), etc.

3.3. Signs referring to controller commands

The common valve today is restricted in its control input to a stem position command, which it receives every sample and

executes with a small actuational delay. Consider, however, a valve that can take as input a schedule of position or position

513
change commands. Such a device would enable more efficient utilization of control system resources. Valve technology is not a stumbling block: smart valves with self-diagnostic and

self-calibration features are becoming available (adequately

dealing with these also requires a sign-function capability). A

primary obstacle is the highly restricted code used to communicate the controller output to the valve.

Even today, control systems for industrial applications are hierarchically structured (a multivariable controller will

typically generate setpoints for PID controllers). Thus it is already commonplace for the output of a control system to be an input to another control system. The remarks above

regarding the signification potential for controller inputs (in

particular, signs that refer to users' expectations of the

system) suggest that controller outputs should be viewed in the same light.

3.4. Signs referring to controller structures

This category hides considerable complexity. For those of us involved in the design and analysis of intelligent control

systems, as distinct from their black box operation, it is also

the most interesting one.

The key point here is that some sort of modularity is inevitable in a control system of any sophistication.

Controllers for large-scale systems will comprise ystem

models (often compositional themselves), optimizers,

parameter estimators, state estimators, constraint handlers,

diagnostic modules, schedulers, planners, performance

monitors, adaptation blocks, and many other separable but

synergistic. Modularity does not imply a commitment to any

specific structure, such as a strict hierarchy. On the contrary, more amorphous compositions may well be preferable. One

general way to view an intelligent control system is as an agent architecture, with the agents representing different

(although possibly overlapping) functionalities.

Communication between agents can occur through shared

"blackboards" or by message-passing. This communication

must embody a semantic richness that is, in all likelihood,

incompatible with representing the input/output parameters of

the modules or agents as unstructured numerical variables.

4. Elements of a Semiotic Approach

to intelligent control

Semiotics is not a technology in the sense that it can provide

algorithms or devices ready for implementation in intelligent

systems. However, as a discipline that focuses on

signification and communication in general, it can be

considered to subsume aspects of several technologies. In this section, I briefly discuss some of these connections, and their

relevance to endowing intelligent control systems with

semiotic capabilities.

4.1. Multiresolution models

Intelligent controllers need to handle target systems of all scales, from single-loop to system-wide. Representations that are appropriate for this breadth of scope are needed. A naive

view may presume that one large "flat" model will serve the

purpose, but this strategy is hardly efficient, or even feasible

for large-scale systems.

Current control schemes already exhibit some

compositionality, with a hierarchy of implicit or explicit

models:

• At the single-loop level, PID or (occasionally) more

sophisticated controllers are implemented with heuristic

knowledge of elementary process dynamics and little consideration of variable couplings.

• Multivariable controllers explicitly take into account the

interactions between different components of a small or moderate scale system. In most cases, multivariable

controllers provide setpoints for PIDs rather than directly

commanding actuators.

• There is now increasing interest in higher levels of

control—unit-wide or plant-wide optimization in industrial

processes, for example. At these levels, unlike the

preceding two, models often attempt to capture

nonlinearities, but sacrifice detailed knowledge of

dynamics.

Conventional control schemes make little or no attempt to integrate these various control and modeling scales. Ensuring

consistency among models of different scales is the task of the

human control engineer.

Multiple scales of representation are also required on the

temporal level. In most large-scale systems, both external

disturbances and intrinsic dynamics will occur over a wide

range. Energy consumption in commercial buildings, for example, will show variations that are correlated with a) day/evening, b) weekday/weekend, and c) seasonal cycles. In setting interior lighting levels and lighting setbacks on a daily

basis, knowledge of the (seasonal) daylight hours can be used

to optimize energy efficiency.

Wavelets are an obvious candidate for a medium that can

represent a wide range of temporal and spatial phenomena. A

few intriguing research results at incorporating wavelets in control schemes have been reported, and more work in this

direction is needed. One limitation of current work in this area is also notable: it assumes that wavelets are inherently a

univariate representation scheme, well suited for capturing

variations at multiple time scales of a single signal (such as building energy consumption). Their value for representing

multi-scale multivariable input-output models is still in question.

4.2. Fuzzy logic

A distinguishing feature of intelligent control systems, as

distinct from many other intelligent systems, is the

requirement that they function both in the symbolic and

numerical domains. Fuzzy logic is useful in intelligent

control systems in large part measure because it fulfills some

part of this requirement. Through the use of fuzzy

membership functions, raw numeric data can be translated into

514
linguistic labels. Furthermore, fuzzy rules allow heuristic

(and symbolic/linguistic) control information gained from

human experts to be used for continuous control applications.

These features are often noted from the standpoint of systemhuman communication, but they are also important for inter- module (or inter-agent) communication in intelligent control

systems. Reasoning processes in these systems may be

symbolic, but, for most control applications, their outcomes

will need to be translated into continuous quantities.

The relevance of fuzzy logic to intelligent control is unquestioned, but the current state and directions of this

technology have some significant limitations. In particular,

popular fuzzy rule formalisms are inconvenient to use for more than small-scale applications. A rule in a fuzzy

controller maps conjunctions of sensor readings to a controller

output through a simple conditional relationship. More

complex rules are rarely considered.

4.3. Self-organization and learning

The alternative to some ability for self-organization/

learning/adaptation in a control system is to have every facet of the control scheme manually specified. Whether or not

this is seen as a feasible option depends largely on what we

mean by learning, or conversely what we mean by manual

specification. Current usage betrays some inconsistencies.

For example, training a neural network (even off-line) is typically classified as learning, whereas linear system

identification is not.

It is neither accurate nor helpful for promoting intelligent

control to view learning and adaptation as capabilities that

control systems either do or do not exhibit. Rather, there is a spectrum of possibilities. Towards the simpler end of this

spectrum, the widespread use of system identification, gain

scheduling, and even feedback linearization demonstrates the

feasibility of learning and adaptation in some form. The issue

then is not whether to include learning capabilities in future

control systems, but how to increase their learning

capabilities in order to reduce the level of manual effort currently involved in control design, system modeling, and

controller modifications in the face of unexpected variations.

It is inconceivable that human involvement can be completely

dispensed with, just as it is inconceivable that our current control technology would have progressed to the point it has

without some element of learning.

In intelligent systems research, the interest in learning has

been predominantly geared toward improving the performance

of individual modules in the system. Learning in a semiotic

system has another important implication: the generation of

new communication and signification capabilities. Thus

languages for inter-agent communication can be evolved to allow the communication of appropriate information in a

sufficiently expressive yet easily interpreted form.

4.4. Computational linguistics

As we broaden our view of control, a fundamental insight to contemplate is that human users of control systems need to be

part of the picture. The importance of human-system

interaction increases in proportion to the functionality of the

control system. Further, different classes of users must be

considered, including operators, control engineers,

maintenance supervisors, and others.

Effective human/control-system interaction requires

appropriate communication mechanisms. The control

community's view of user communication needs has generally

been limited to graphical and tabular displays of numeric data. These are sufficient for most low-level control functions, but

not for higher levels. Commands from users at these levels,

for example, will not be setpoint changes but more complex

instructions which may be most naturally expressed in some

limited linguistic form (as illustrated in Section 3.2).

Current research in theoretical linguistics is largely in the

Chomskyan generative tradition. The hard distinctions drawn

in this research, such as competence versus performance and

syntax versus semantics, with the subject of linguistic study

limited to syntactic competence, limits its direct relevance to engineering systems. The discipline of computational

linguistics, however, addresses all aspects of linguistic signs

and signification—syntactic, semantic, and pragmatic.

Computational linguistics exploits insights from modem

linguistics, along with developments in less analytic

approaches (e.g., statistical and connectionist natural language

processing), and shows considerable promise for the

development of effective language understanding and

generation systems for focused applications.

The immediate relevance of computational linguistics to control systems is in the pursuit of more effective and

efficient human-system interaction. However, there is another

intriguing connection. As noted earlier, an intelligent control

system will not be an undifferentiated block of software, but

will be composed of numerous subsystems many of which

will exhibit some aspects of intelligent behavior. Natural

language is the preferred means of human communication

because it has evolved to satisfy the communication needs

between individual intelligent beings. As control systems

increase in sophistication, functionality, complexity (and

intelligence), their component modules will too. Parameter

or signal vectors will not provide an adequate communication

mechanism between these modules. A full-fledged natural

language capability is neither required nor desirable, but the

discipline of computational linguistics has much to offer towards devising a more limited language, one that is qualitatively richer than current mechanisms.

4.5. Classical control

Neither humans nor intelligent controllers are directly

responsible for the control of today's aircraft, manufacturing

plants, automobiles, or any of the other domains that represent the true successes of control. The credit, in large

part, goes to our classical control technology. Intelligent

control must build on this proven foundation, and it must

provide the framework for classical control techniques to continue to serve their many useful purposes. As we discuss

the need for semiotically-sophisticated control, and for new

515
codes and signification capabilities, it is important to remember that such semiotic capabilities as are incorporated

in current control systems must be maintained. Even as we

suggest the need for linguistic communication, for example,

at some level of an intelligent controller there will still be a need to communicate linear transfer function matrices.

Analogously, the imprecision of fuzzy logic can supplement,

but it cannot supplant, the expression of model uncertainty in the jj. framework.

6. Concluding Remarks

A matter of definition lurks behind the scene in this paper: is the broader vision of control sketched above overstepping the

boundaries of the discipline? In fact, the vision of control has

always been a broad, overarching one. Any introductory

control textbook will first present some examples of target

systems for control technology, and these can encompass

national economies, global ecologies, and similarly largescale, complex domains (see Fig. 3). Unfortunately, the logic

of control often belies its rhetoric. A semiotic perspective is

fully compatible with the classical vision of control, even if the practice of control science and engineering shows little evidence of this connection.

Although in this paper I have focused on the role of semiotics

in intelligent control systems, I have attempted neither to define intelligent control nor to separate it from any other

adjectival variation—definitions of intelligence in any context

are of problematic value. I propose not a definition but a guiding principle: the degree of intelligence in a control

system is in direct proportion to the sophistication of its semiotic character.

Acknowledgement:

review and criticism.

I am grateful to Hannah Blau for

Bloomington, IN:

Bloomington, IN:

References

Deely, J. (1990). Basics of Semiotics.

Indiana Univesity Press. Eco, U. (1976). A Theory of Semiotics.

Indiana Univesity Press. Eco, U. (1984). Semiotics and the Philosophy of Language

Bloomington, IN: Indiana Univesity Press. Sebeok, T.A. (1994). Signs: An Introduction to Semiotics

Toronto, Canada: University of Toronto Press.

-^Births per year

Fig. 3. Visions of Control. From

Richard C. Dorf, Modern Control

Systems, Addison-Wesley, 1974. As

adapted from The Limits to Growth:

A Report for the Club of Rome's

Project on the Predicament of

Mankind, 2nd ed., D.H. Meadows et

al. New York: Universe Books,

1972. Used with permission of

Potomac Associates, Washington,

D.C.

Fertility Food

Deaths per year -^-

(-)

Desired food per capita

(-)

per capita

Cultivated > land

Mortality

Average lifetime of capital

516
INTELLIGENT VS REFLEX CONTROL

FOR COMPLEX DYNAMICAL SYSTEMS

Michel Cotsaftis, Professor

LTME/ECE, 53, Rue de Grenelle, 75007 Paris, France

email : mcot@ece.fr

ABSTRACT

Direct consequence of systems complexity increase is more

complicated, less observable and less controllable trajectory in phase space in a classical sense. Control adequacy should imply more freedom in decision process to balance system modeling unpreciseness and inadapted in- formation flux handling when too much centralized. More

global approach than classical state space is now required

to fit reality of larger trajectory wandering and their natural organization along invariants in phase space inside

which they become undistinguishable. Most elementary

is function space approach, where the "unit" is a whole

trajectory, and control problem becomes embedding sy- stem solution into initially prescribed function space from

asymptotic stability and monotonicity conditions. This

"functional" control strongly reduces information fluxes

up and down inside system structure by taking advantage

of internal system selforganization consecutive to complexification. Hierarchical structure is here satisfied within

subsidiarity principle, by delegation of more "intelligence"

toward lower levels and by leaving more freedom for decisional processes at higher levels where fuzzy controllers are mostly adapted, opening the way to intelligent self- deciding systems.

KEYWORDS: Complex System, Intelligent Control,

Stability, Functional Control

I. INTRODUCTION

To accomplish more complex technical tasks with more

complex systems[l] as required in modern industries to survive in world spreadout economy, one might rely upon

technology advance of the various system components and

augment in parallel control complexity with larger sensor information. Independent of failure increase with all its consequences, this approach is different from existing li- ving systems, exhibiting remarkable ability to decide and

to perform extremely complex tasks with their complex

"living" machine. This suggests that another less strictly

computerized and more qualitative way is possible, and some elements in this direction are given in the following.

For Lagrangian dynamical systems, classical PD-type controllers locally give system trajectories a stable fo- cus- type structure guaranteeing trajectory asymptotic stability. For more complicated systems, concepts of "adaptiveness" [2] and of "robustness" [3] have been analyzed.

They can be represented with symbolic "co- ordinates"

(system complexity-performance level) as arrows along a

xisses from initial simple PID control domain, see Fig.l.

Adaptiveness is asymptotically stable by construction, but

at some level system complexity and performance analysis cannot be handled together in real time, leading to a

tradeoff. In robustness approach, simple stability resul- ting from system simplification forbids higher preciseness

required for more advance performance quality, so that

both extensions are mainly localized along the two axisses. On the other hand, as elementary performance is not

worth from a complex system, nor high level performance

is usually output from a simple system, real system repre- sentative point should stay inside a band along the first diagonal.

This means that both previous approaches are suffering

from the defect of not changing system structure which

cannot remain too centralized beyond some level of complexity. Improvement of information flux circulation re- quires more delegation of decisional capability to system

parts themselves with system complexity increase, ie to subsidiase more intelligence into local controls which be- come of reflex type, so that upward information flux is strongly reduced for higher level controllers to deal with

affordable amount of material. Here Fuzzy controllers[4] are singled out as they would provide very adequate rela- tions between quantitative description at system dynamics

level and qualitative representation at decision intelligent

higher level. So as they split off the diagonal band, previ- ous control approaches are not adapted for extension to intelligent higher controls due to the gap between their (too

much detailed) representative variables and the (more global) ones adapted to intelligent controls, leading to unaffordable explosion of logical rules with system complexity

from combinatorics.

Convergence toward the diagonal band is nevertheless possible, as living systems are showing it everyday by changing the nature of control from trajectory space to task

space, which is made possible by the huge experience coll517
ected by each individual. For complex mechanical or technical systems, it is also possible to converge toward the

diagonal band with a new type of control, called functional

control[5], based on intermediate "natural" variables filling

this gap, and with which a multilevel control allowing integration of decisional functions into system control can be

constructed. The main idea is that when system complexity increases, its trajectory in phase space becomes more

complicated, but at the same time the information content in its observation decreases, because trajectories are becoming less distinguishable, ie are becoming equivalent

in a dynamic sense. They are filling more and more regularly domains in phase space, and initial conditions (local

invariants) cannot be used as before to define a trajectory.

Only more global invariants[6] can be used to classify tra- jectories in groups within which single trajectories cannot

be distinguished anymore. Examples are for instance magnetic field lines which are not distinguishable on their flux

surfaces, and extreme case is a gas in thermodynamics the

trajectories of which on energy surface are all equivallent.

Another quite frequent situation occurs when, due to nonlinearities, there exists bifurcation points at which system

dynamics branch off toward more complicated trajectories

up to chaotic ones[7]. In all cases, invariants are no longer

initial trajectory coordinates as for classical mechaical problem, but the corresponding invariants, for instance flux

surface for magnetic field and energy surface for gas. Here

part of trajectory behavior escapes from direct control in the sense that because the number of DOF of state vector

is much larger than control vector, system dynamics organize themselves on invariant surfaces. It is interesting to note that in this case, state vector may still be observed,

but all its components are not controllable. In consequence

control problem transforms into acting more globally onto

system trajectory as a whole rather than correcting it locally, and to impose the solution of system dynamics to belong to a prescribed function space, chosen from general

desired properties in their functional behavior (overshoot,

decay, monotonicity,..), and compatibility with system dynamical behaviors which should belong to this function

space. This is the only way to take advantage of system

selforganization resulting from its complexification, and to eliminate risk of antagonizing this selforganization by inadequate control. The resulting "embedding" problem fits into Fixed Point Theorem[8] framework, and asymptotic

stability toward desired trajectory may be guaranteed.

To technically deal with system dynamics complication

and difficulty of correct physical phenomena representation, an efficient way would be to combine both advantages of functional and robust controls, ie asymptotic stability and simplicity. From analysis of regular robustness

approach, simple stability is due to narrowness of allo- wed function space when applying Lyapounov Theorem,

and forbids application of Fixed Point Theorem, whereas

adequate function space enlargement leads to asymptotic stability property without requiring extra system in- formation. In next part reduction of dynamical system

equations to canonical form is given. Structure of classical

robust control is analyzed afterward with its inherent defects, and improved robust control is explicitely constructed. Resulting asymptotic robust control is of simple form

and is easily implementable. In contrast, fuzzy control law, even when analytically explicited in terms of system variables to save basic combinatorics computation, requires

their approximate evaluation, making the approach unusable at this detailed level for complex large dimension

system. Application to N-link actuated compliant and deformable mechanical system is given as an example.

II. CANONICAL ERROR EQUATIONS

Let for t > to the dynamical system

with state vector X = col(X\ , X2, --Xn and control vector U . F(.,.,.) is supposed smooth enough to appropriate

order in its arguments so that a solution X = X(t,Xo)

exists for a fixed U = Uj(t) with initial condition Xq =

X(to), and with possible different behaviors for t — 00

for different Xq. For a fixed X = Xd(t), there conversely exists for U one (or more) solution of eqn(l) Ud =

F~ 1 (Xd,dXd/dt,t), so in principle U may be determined

for eqn(l) to have a solution behaving in a prescribed way.

System trajectories close to Xd{t) have to be analyzed to determine the conditions for their convergence to Xd{t)

for large t. To deal with in not well known functional dependence of F(.,t, .) in real cases, much simpler structural

stability analysis is called for. To proceed, the RHS of

eqn(l) is splitted into a "simple" part for which a control

exists guaranteeing asymptotic convergence, and a "rest" with upper bounded effect. An equivalence class with re- spect to this " rest effect" is realized if an additional control

exists giving also the complete system asymptotic conver- gence property, thus reducing the analysis to "skeleton"

systems out of which these equivalence classes are constructed. This will be called a canonical reduction.

With X = Xd + x, U = Ud + u, variational error system

from eqn(l) is—dx = A0 .x + B.{u0 + Att) + 77 (2) at

splitting variational control u into uo guaranteeing as- ymptotic convergence of "skeleton" equation with 77 = 0, and

additional part Au to annihilate the action of extra term

77 containing both nonlinear and error terms when passing from eqn(l) to eqn(2). Eqn(2) is useful if there exists

for skeleton equation a P-type, possibly time dependent,

518
control such that, with uq = —Kx, there exist positive definite matrices (P, Q) satisfying (Ag + KT BT )P + P(A0 +

BK) + dPfdt = —Q and Lyapounov stability theorem applies with V = xT Px, dV/dt = —xT Qx. Au should now

be found such that with extra term 77, asymptotic conver- gence property is maintained for eqn(2).

III. IMPROVED ROBUST CONTROL

ANALYSIS

Derivative of V = xT Px along trajectories of eqn(2) writes

^ = -xT Qx + 2{BT PxfAu + 2(Px)T r, (3) dt

With the bound \t)\ < p > 0, not specified for the moment,

usual robust method is defined by additional control[9]

AuR = -p(BT B)- 1 B

T Px

1

[Sup(e,||P*|

where e is small > 0, leading to the bound

(4)

(5)

with y - = Supt p{y,t), and Ami „ = Minj<t Xj

(<). For bounded pl with pl(0) ^ 0, there exists y = ym

below which dV/dt becomes positive, defining an attractor

inside the ball xm = P~ 1 ym [f]- All trajectories will hit its surface after a finite time, and remain captured inside for larger time. Its size is small for e small and Am:n (<5) large,

ie for large gains. So with usual robustness approach,

initial system uncertainty due to nonzero norm bounded

terms 77 cannot be completely removed and leads to state uncertainty inside a finite ball ||£ m || on system error dynamics, giving simple stability result after a first exponential

decay period. Due to conservativeness of sufficient stability condition in Lyapounov method this decay cannot be

satisfied for all time. Also, for (AUra = 0) and 77 ^ 0, one gets dV/dt < -xT Qx + 2p\\Px\\ < -XV + 2kpL V^2

with A and k from bounds on eigenvalues of P and Q. V is

upper bounded by t = /yi/2 [kpL(x2

) — (X/2)x]~ 1 dx with

exponential behavior Aa; ~ exp(2kxmp'Lm — \/2)t close to a zero xm of integrand denominator, stable or unstable

depending on the sign of coefficient oft. Final behavior of

Y(t) depends on the number of possible xm . Thus classical

robust control only changes the size of induced uncertainty

ball, but not its existence.

Less conservative condition follows from using different

additional control algebraic form. Instead of Aur from

eqn(4), let

Au/m = -

p(BT B)- 1 BT Px

a\\Px\\ + ef(t)

(6)

with a < 1, and "driving" function f(t) to be discussed

later. V(t) is bounded above by the solution of majorant

equation

TM=-\Y + 2^pf(i) (7)

a

where f(t) is determined such that, for given functional

form of p(Y, t), the solution Y(t) of eqn(7) exhibits a pre- scribed time dependence Yd(t). Note that with f(t) much

larger freedom exists now than in eqn(5) with only number e, and simple calculation would give f(t) for prescribed

Yd(t) from eqn(7). However it is more appropriate in ro- bustness context to solve an embedding problem where a correspondance is researched between function spaces T

and y for various possible functional forms of p(Y, t), with

f(t) G T and Y £ y, and where y is fixed by general properties such as continuity and behavior (decay) for large

t. Usual approach is to determine y from T and p(Y, t) via Fixed Point Theorem. Specific applications are obtained when y is usual Lebesgue £p or Sobolev W£ space

and p(Y, t) ranges in a similar space, as when p(Y(t),t)

satisfies Caratheodory condition[10]

p(Y(t),t)<a(t) + b(t)Y(ty (8)

with a(t) and b(t) in adapted spaces, by use of Holder in- equality onto eqn(7) to determine the order of J

7

, ie the

power q in /(<) = kiY(t) 9

, chosen to eliminate control

explicit time dependence. Eqn(8) follows from thermodynamic properties in natural systems, and is obtained for systems with real, physical or technical, origin. Asymptotic stability is now obtained for a large class of functions

p(Y(t),t), in contrast to previous robust result, but with

decay weaker than exponential.

When inequality p(Y(t)exppt,t) < p(Y(i))h(t) holds with

nondecreasing function /?(.), one gets

Y(f) < exP -pt.G- 1 {G{Y0 ) + 2sgn(G)I(t)) (9)

with I(t) = (c/a)fiexpirt' f(t')h{t')dt' where G(x) =

f

x dv/p(v). When G(.) is sublinear, sgn(G(.)) > 0, and

Y(t) is defined for any [Y(0),t], whereas if G(.) is superlinear, sgn(G(.)) < 0, and Y(t) is only defined for Y(0) G

[0, Yc] such that the argument of G~ l does not change sign

for t < +00, ie G(Y0 ) = 2^ /0°° exppt'f(t')h(t')dt' in order

to avoid finite time Lagrange instability. Here Y(t) may

decay faster than exponential but in a limited ball of initial conditions depending on /(<). When p. = 0,h(t) = 1, Y(t)

in eqn(7) is bounded by — Lp{u)uq ]~ 1 du = —Xt in

implicit form with L = (2ek\/aX), and decays asymptotically to 0 for large t under the simple explicit conditions

q > 1 > L-p{Y0 )Y*- 1 (10)

519
relating system and control parameters for given initial ball Yb, best satisfied for large linear gains and small initial

ball. In all cases, with control of generic canonical "triplet"

form U = Ud + uo + Au, asymptotic stability can be found

in conjunction with robustness constraint, in contrast to

classical approach, and the role of f(t) which drives the

behavior of Y(t) is clearly shown.

IV. EXPLICIT FUZZY CONTROL

To escape from detailed dynamical system description another way would be to set conditional "linguistic" state- ments in the form of if-then rules[ll] allowing to directly

pass to generic descriptive representation of system tra- jectories in geometric space. However this is only possible

when their qualitative nature is already known, which rests upon the correspondance between the minimum number of

rules in rule space (71) and types of trajectories in geometric space (T), only known in very few cases, despite a

global relation from universal approximator property [12]. One case corresponds to simple "driving car" rules[13], and

applies for focus-type (or node-type) trajectories, produced at least locally by lagrangian equations[14]. Again in this case, combinatorics explosion for large enough dimension number renders this approach useless, indicating that

the variables on which control method is applied are not

good ones because too much detailed, suggesting direct

search of explicit final defuzzyfied control law to avoid all intermediate steps.

Consider for simplification fuzzyfication under translationally invariant membership functions fi(x) = f(x — iAi)

over normalized interval and such that /j_i(Ai) = 1, /»(Ai) = 0, guaranteeing always only two nonzero membership values m,_i and m,- for any 0 < x <

Ai, see Fig. 2. Similarly after usual max-min compositional rules of inference, defuzzyfication by centroid method

with translationally invariant output membership functions gj(y) = g(y—jA2 ) gives analytic crisp output control u = upd + Aupuz with usual PD part upd = l/2[t/fc— l +

j/t] in normalized form and fuzzy contribution Aupuz =

(A2/2)(l+.4fc_i/.4jfc)~ 1 with domains Ak-i and Ak shown

on Fig. 2 and

Ak-i _ TM.i[zi +Inf(y0 ,zi) + 2Sup(701 ,0)]

Ak ~ In + z9(A2 y)\H

{

>

renormalizing y to A2, with y(m; ) = yj, zj = 1 — j/y, Ij k = f£

k g(A2 y, and intersection point j/o = 1/2 bet- ween two contiguous membership functions corresponding

to g(A2 y0 ) = rn0 and g(A2 y(mk )) = g(A2 )mk writing

mjt_i = mi, mk = m2 with translational invariance pro- perty of membership functions. Note that Fk(mk,0) — 1 and Fk{m,m) = 0. With the constraint rrik-i + = mi + m2 = 1, and f(A\x) = m from input with nor- malized x, Fk(l — m,m) can be thoroughly studied for m € [0, 1/2] with slopes -2(/„

1 g(A2 t)dt)~ : at m = 0 and

0 at m = 1/2. With for instance generic membership function g(y) = y

a and a > 0, the steepening increases with a

ie with pitching.

So one may only use the final explicit control expression in eqn(ll) once system variables are properly located in their

membership domains. This only requires inverse functions X = /

-1 (m) and Y = <7 -1 (m), but the problem

still lies in evaluation of all system coordinates with flags

when crossing membership domain. Here the advantage

in unpreciseness is unfavorably balanced by the number

of variables to treat, showing again that high quality of

fuzzy controller is not fully exploited at this too detailed

description level, as compared to very global and limited

knowledge required in robust control given in eqn(6).

V. APPLICATION TO N-LINK MECHA

NICAL SYSTEM

Canonical error equations for actuated mechanical systems

with compliance at joints and flexion and torsion link deformations can be exactly cast into the form[15] of eqn(2)

with x = col(e,de/dt, Z,dZ/dt), jj = 00/(771,

772), Au = co/( Auo, Aui), A = Ao — BK and error terms

with regressors associated to both system parameters and

deformations parameters and obtained as difference bet- ween exact and estimated quantities in initial system. Application of control Aupuz is only possible here if all elements in column vector x are evaluated which is difficult for the last component. On the contrary, from analysis of previous expressions one gets the bound ||77j|| <

Aj\\\X\\\ + Bj = pj of Caratheodory form allowing

direct application of eqn(10). With f(t) = asymptotic stability of is obtained if the conditions

?>1. l>L(l + (3\\X(0)\\)\\Xm\9~l (12)

are satisfied by proper choice of parameters a, e, k, q with L = 2eak/\a, f3 = b/a, and a, b > 0 obtained from

Aj, Bj and supposed constant in time with appropriate

upperbounding. So for A^-link mechanical system a large

class of decaying driving functions is found, which monitor

system decay guaranteeing both robustness and asymptotic stability with only knowledge of basic skeleton parameters and error ball for uncorrectly estimated parameters,

in contrast to usual robust analysis showing simple stability property, and to other control approaches requiring more detailed knowledge of system parameters. Present

better result is due to taking full advantage of Caratheodory type constraint and to less stringent conditions on the

majorant of error vector norm, used as a Lyapounov function. Lyapounov conditions for asymptotic stability are not satisfied, but the majorant still fulfills (weaker) conditions leading to asymptotic (not necessarily exponential)

decay. Numerical application to a 3-dof is given in [16]. VI. CONCLUSION

520
Error equations for dynamical system equations are canonically reduced to a generic form composed of a (usually

linearized) part coming from linear known terms, and a

residual nonlinear one coming from unavoidable mismatch

between system representation and its actual (unknown)

form, both at parametric level and at functional form of

functions modeling physical phenomena (friction, contact

interactions). Control should give for solution of error equations best convergence to origin. A first component

from linearized part is of PD type, usually giving locally

weakly damped oscillatory behavior from power limitati- ons restricting allowed gains. Resulting asymptotic con- vergence is not structurally stable because residual part,

when norm-bounded, leads to simple stability of error sy- stem solution. So an additional controller is needed for further improvement. Simplest form is a robust one re- quiring the knowledge of norm-bound, classically leading

to simple stability result because of unmaintainable condition for all time that error norm vector is majorized by

exponentially decaying function.

New form of robust controller allowing larger functional

space results from introduction of a driving function f(t),

whose proper design guarantees asymptotic decay depending on functional form of norm bound, even when Lyapou

nov conditions are not satisfied. The controller combines

simplicity of previous conventional robust controller requiring only information on norm bound of residual terms,

with efficiency and preciseness of trajectory tracking by

maintaining structurally stable asymptotic convergence.

So here results are in real systems obtained at lowest le- vel of mechanical structure. Contrary to fuzzy controller even in explicit final form after application of logical rules demanding evaluation of complete system state vector,

very few informations are required in new proposed robust

controller, so its description at higher level is extremely

simplified, easing the role of higher loop decisional fuzzy

type adapted controllers[14].

REFERENCES

[1]-B. Cohen, W.T. Harwood, M.I. Jackson : The Specification of Complex Systems, Addison-Wesley, N-Y, 1986;

M. Gell-Mann : What is Complexity, Complexity, Vol. 1(1)

p. 16, 1995; H. Morowitz : The Emergence of Complexity,

ibid, p.4; G. Nicolis, I. Prigogine : A la Rencontre du

Complexe, PUF, Paris, 1992

[2]-J.J. Craig : Adaptive Control of Mechanical Manipulators, Addison-Wesley Pub., Reading, 1987; S. Sastry, M.

Bodson : Adaptive Control, Stability Convergence and

Robustness, Prentice-Hall, Englewood-Cliffs, N.J., 1989

[3]-M.W. Spong, M. Vidyasagar : Robot Dynamics and

Control, J. Wiley and Sons, New-York, 1989

[4]-C.C. Lee : Fuzzy Logic in Control Systems : Fuzzy

Logic Controllers, 1,11, IEEE Transac. on SMC, Vol.20

p.404,435, 1990; R.R. Yager, D.P. Filev : Essential of

Fuzzy Modeling and Control, Wiley and Sons, N-Y, 1994;

L.X. Wang : Adaptive Fuzzy Systems and Control, PTR

Prentice-Hall, Englewoods-Cliffs, N.J., 1994

[5]-M. Cotsaftis : Functional Control of N-Link Deformable Mechanical Systems, Proc. lrst MOVIC Conf., Yokohama, Sept. 7-11, 1992

[6]-H. Poincare : Les Methodes Nouvelles de la Mecani que

Celeste, Gauthier-Villars, Paris, 1897, 1899; M. Hirsch, C.

Pugh, M. Shub : Invariant Manifolds, Lecture Notes in Math. 583, Springer-Verlag, Berlin, 1977

[7]-T.S. Parker, L.O. Chua : Chaos, a Tutorial for Engineers, Proc. IEEE, Vol.75(8), p.982, 1987; S.H. Stro- gatz : Nonlinear Dynamics and Chaos with Applications

to Physics, Biology, Chemistry and Engineering, AddisonWesley, N.Y., 1994; E. Ott : Chaos in Dynamical Systems,

Cambridge University Press, Cambridge, Mass. 1993

[8]-E. Zeidler : Nonlinear Functional Analysis and its Applications : Tome I, Springer- Verlag, New-York, 1986

[9]-G. Leitman : On the Efficacy of Nonlinear Control in Uncertain Linear Systems, J. Dyn. Syst. Meas. Control,

Vol.103 (1981) p.95

[10]-J. Appell, P.P. Zabrijko : Nonlinear Superposition

Operators, Cambridge University Press, Cambridge, Mass.

1990

[11]-R.R. Yager, D.P. Filev : Essentials of Fuzzy Modeling

and Control, Wiley ans Sons, New-York, 1994

[12]-L.X. Wang : Adaptive Fuzzy Systems and Control,

Prentice-Hall Inc., New-York, 1994

[13]-M. Sugeno : Industrial Applications of Fuzzy Control,

North Holland, Amsterdam (1985)

[14]-S. Lefschetz : Stability of Nonlinear Control Systems,

Acad. Press, New-York (1965)

[15]-M. Cotsaftis : Global Control of Deformable N-Link

Mechanical Systems, Proc Winter Annual Meeting ASME

New-Orleans, Louisiana, Nov.28-Dec.3, 1993

[16]-M. Cotsaftis : Asymptotic Robust Control for Mechanical Systems, Proc. 1994 Japan-USA Symposium on Flexible Automation, Kobe, Japan, July 11-18, 1994, Vol.11,

p.671

[17]-M. Cotsaftis : Intelligent Control for Complex Systems, Proc. 1993 IEEE Intern. Conf. on Robotics and

Automation, Atlanta, Georgia, Vol.11, p. 75, 1993

521
"Performance"

a Level

"new domain

Adaptath e Tj\£

Controls

Controls

—Logical Rules

—Fuzzy Controls

—Neural Nets

System Structure

Complexity

Fig.l : System Performance vs Structure

Complexity with Various Controls

Fig. 2 : Membership Functions and Areas Ai

Domain(A, B, C, D), A2 = Domain(E, F, G, C)

522
Introduction to Integrated Learning/Planning Paradigm

A. Meystef°, A. Lacazeto

*Drexel University

^University of Maryland

°National Institute of Standards and Technology, Intelligent Systems Division

Abstract.

This paper is an effort to address the issues of

planning and learning as two components of the same

process of intelligent system functioning.

Key words: behavior, goal, path,

planning, redundancy, resolution, representation,

tessellatum, trajectory

1. Planning Problems of Behavior

Generation

Behavior Generation [1] can have many

mechanisms of planning and execution. At the

present time, these mechanisms cannot be

considered as thoroughly known, and the general

theory of planning can hardly be attempted. We will

discuss a subset of problems in which the goal is

defined as attainment of a particular state. Other

types of problems can also be imagined: in chess

the goal is clear (to win) but this goal cannot be

achieved by achieving a particular position in a space (even in a descriptive space.) Most of the

problems related to the theory of games and linked

with pursuit and evasion are characterized by a

similar predicament and are not discussed here.

Planning is understood as searching for appropriate future trajectories of motion leading to the goal. Searching is performed within the system

of representation.

2. Planning in a Representation

Space with a Given Goal

The world is assumed to be judged upon by

using its Space of Representation which is

interpreted as a vector space with a number of

properties. Any activity (motion) in the World

(Space of Representation) can be characterized by a

trajectory of motion along which the "working

point" or "present state" (PS) is traversing this

space from one point (initial, or state, IS) to one or many other states (goal states, GS.) The goal states

are given initially from the external source as a "goal region", or a "goal subspace" in which the

goal state is not completely defined in a general

case. One of the stages of planning (often the initial one) is defining where exactly is the GS within the

"goal region." In this paper, we will focus upon

planning problems in which one or many GS

remain unchanged through all period of their

achievement. Traversing from IS to GS is associated with consuming time, or another

commodity (cost.)

6i 1 1 1 1 1 1 1 j r

Figure 1. The general paradigm of planning

3. Learnable Representations

All Representation Spaces are acquired

from the external reality by the processes of

Learning. Many types of learning are mentioned in

the literature (supervised, unsupervised,

reinforcement, dynamic, PAC, etc.) Before

classifying a need in a particular method of learning

and deciding how to learn, we would like to figure

out what should we learn. Now, it is not clear whether the process of learning can be separated into

two different learning processes:

• that of objects representation, and

• that of the rules of action representation, or are these two kinds of learning just two sides of

the same core learning process?

The following knowledge should be

contained in the Representation Space. If no GS is given, any pair of state representations should

523
contain implicitly the rule of moving from one

state to another. In this case, while learning we

inadvertently consider any second state as a provisional GS.

We will call "proper" representation a

representation similar to the mathematical function

and/or field description: at any point of the space, the derivative is available together with the value of

the function; the derivative can be considered an

action required to produce the change in the value of

the function.

We will call "goal oriented" representation

a representation in which at each point a value of

the action is given required for describing not the

best way of achieving an adjacent point but the best

way of achieving the final goal.

Both "proper" and "goal oriented"

representation can be transformed in each other.

0

-1

-2

-3

! ! ! !

-Sirtes • I--

1

0 123456789

Figure 2. Knowledge of state, and knowledge of

action which produces changes

4. The Artifacts of Representation

Space

Representation (that of the World) can be

characterized by the following artifacts:

• existence of states with its boundaries

determined by the resolution of the space each state

is presented as a tessellatum [2], or an elementary

unit of representation, the lowest possible bounds

of attention)

• characteristics of the tessellatum which is defined as an indistinguishability zone (we consider

that resolution of the space shows how far the

"adjacent" tessellata (states) are located from the

"present state" (PS)

• lists of coordinate values at a particular

tessellatum in space and time

• lists of actions to be applied at a particular

tessellatum in space and time order to achieve a

selected adjacent tessellatum in space and time

• existence of strings of states intermingled with

the strings of actions to receive next consecutive

tessellata of these strings of states

• boundaries (the largest possible bounds of the

space) and obstacles

• costs of traversing from a state to a state and

through strings of states. In many cases, the states contain

information which pertains to the part of the world

which is beyond our ability to control it, and this

part is called "environment." Another part of the

world is to be controlled: this is the system for which the planning is to be performed. We will

refer to it frequently as "self." Thus, part of the

representation is related to "self including

knowledge about actions which this "self should

undertake in order to traverse the environment.

It is seen from the list of artifacts that all knowledge is represented at a particular resolution.

Thus, the same reality can be represented at many

resolutions and the "multiresolutional

representation" is presumed.

D 12345679

4 1 1 ) 1 1 1 1 ) n 1 1 1 n n i n 1 1 1 1 1 1 1

1

1 1

1

) 1 1 1 1

1

1 1 1 ii 1 1 1 1 1 1 1 1 1 m I m I ) 1 1 1 1 1 1

1

) 1 1 1 1 1 n 1 1 11 1 1

1

_4 1 i ; j

> i i i i i i i i i i i i i i i i i > ji 1 1 1 1 . i . i i . i . i

Figure 3. Multiresolutional representation

5. Planning in Redundant Systems

Non-redundant systems have a unique

trajectory of motion from a state to a state. Redundant system is defined as a system in which

there is more than one trajectory of motion from one state to another. It can be demonstrated for many realistic couples "system-environment" that

• they have a multiplicity of traversing

trajectories from a IS to

524
0 0

Figure 4. Multiplicity of plan alternatives

• these trajectories can have different costs. These systems contain a multiplicity

of alternatives of space traversal.

Redundancy grows when the system is considered to be a stochastic one. The number of available

alternatives grows even higher when we consider

also a multiplicity of goal tessellata of a particular

level of resolution under the condition of assigning

the goal at a lower resolution level which is the fact

in multiresolutional systems (such as NIST-RCS.)

In on-redundant systems there is no

problem of planning. Since the trajectory of motion

to be executed is a unique one, the problem is to find this trajectory and to provide tracking of it by

an appropriate classical control system.

6. Learning as a Source of

Representation

Learning is defined as knowledge

acquisition via experience of functioning. Thus,

learning is development and enhancement of the

representation space. The latter can be characterized

in the following ways:

• by a set of paths (to one or more goals)

previously traversed

• by a set of paths (to one or more goals)

previously found and traversed

• by a set of paths (to one or more goals)

previously found and not traversed

• by a totality of (all possible) paths

• by a set of paths executed in the space in a random way.

One can see that this knowledge

contains implicitly both the description of the

environment and the description of the actions

required to traverse a trajectory in this environment.

Moreover, if some particular system is the source of

knowledge, then the collected knowledge contains

information about

properties of the system which moved in the

environment.

All this information arrives in the form of

experiences which record states, actions between

each couple of states, and evaluation of the

outcome. The collection of information obtained in one or several of these ways forms knowledge of

space, KS.

If the information base contains all

tessellata of the space with all costs among the

adjacent tessellata - we usually call it the

representation.

Ergo: the representation is equivalent to the multiplicity of explanations how to traverse, or how to move. In other words: all kinds of learning

mentioned in p. 3 are equivalent.

Comments: a) remember Albus' question

about knowing states, or knowing derivatives"

(actions) from a state to a state; b) apparently, each

state can be characterized by some cumulative cost

(value), while each traversal from a state to a state can be characterized by some incremental cost {goodness of a move or a set of moves.)

7. Types of Problems of Planning

Any problem of planning is associated

with

• actual existence of the present state

• actual, or potential existence of the goal state

• knowledge of the values for all or part of the

states as far as some particular goal is concerned.

From this knowledge the cumulative costs of trajectories to a particular goal (or goals) can be

525
deduced. On the other hand, the knowledge of costs

for the many trajectories traversed in the past can be

obtained which is equivalent to knowing cumulative

costs from the initial state (PS) to the goal state (GS) (from which the values of the states can be

deduced.)

In other words, any problem of planning

contains two components: the first one is to refine

the goal (bring it to the higher resolution.) The

second one is to determine the path to this refined

goal. These two parts can be performed together, or

separately. Frequently we are dealing with them

separately. In the latter case they are formulated as follows:

a) given PS, GS and KS (all paths) find

the subset of KS with a minimum cost, or with

a prearranged cost, or with a cost in a particular

interval.

b) given PS Gs from the lower resolution

level and KS (all paths) find the GS with a

particular value

8. The Duality of Planning and

Learning Algorithms

Finding solutions for these problems is done by a process which we will call planning. In other words, planning is construction of the goal

states, and/or strings of states connecting the

present state with the goal states. As we analyze the

desirable processes of planning, we notice a striking

similarity between planning and learning, actually

their inseparability.

O GS

Submitted to HR

level as a result

Where is the goal for the HR level? Which trajectory to choose?

a b

Figure 5. Two parts of planning problem

Indeed, the first component of the planning

algorithm is translation of the goal state

description from the language of low resolution to

the level of high resolution. We must learn where

the goal is located, and it is done by consecutive

refinement of the initial coarse information.

Frequently, it is associated with increasing of the

total number of the state variables. In all cases it is associated with reduction of the indistinguishability zone, or the size of the tessellatum associated with a

particular variable. We plan and learn by testing: in

the representation, for planning, and in the reality,

for learning.

The second component is the simulation of

all available alternatives of the motion from the

initial state, IS to one or several goal states, GS and

selection of the "best" trajectory. Procedurally, this

simulation is performed as a search, i.e. via

combinatorial construction of all possible strings

(groups). To make this combinatorial search for a

desirable group more efficient we reduce the space of

searching by focusing attention.

The need in planning is determined by the

multialternative character of the reality The process

of planning can be made more efficient by using

appropriate heuristics which is not considered in

this paper.

9. The Unified System of Planning

and Learning

Planning is performed by searching within

a limited subspace

• for a state with a particular value

(designing the goal)

• for a string (a group) of states connecting SP and GP satisfying some conditions on the cumulative cost (planning of the course of

actions.)

The process of searching is associated ether

with collection of addition information about

experiences, or with extracting from KS the

implicit information about the state and moving

from state to state, or learning. In other words,

planning is inseparable from and

complementary to learning.

This unified planning/learning process is always oriented toward improvement of functioning

in engineering systems (improvement of accuracy in an adaptive controller) and/or toward increasing of

probability of survival (emergence of the advanced

viruses for the known diseases that can resist various medications, e.g. antibiotics.)

Thus, this joint process can be related to a system as well as to populations of systems and

determines their evolution.

LPA is a tool which allows for jointly

exploring these two fundamental processes of

intelligent systems.

526
represent tfl

represent

represent i-1

1

GPACS GFACS

goal ±

OFACS

I

t

OFACS * Plan

OFACS OFACS * Plan

T

OFACs"^"phm

Plan PLANNING

search M

search

i

search i-1

info LEARNING

Figure 6. On the relations between planning and

learning

10. The Elementary Components of

Planning and Learning

Search is performed by constructing

feasible combinations of the states within a subspace (feasible, means: satisfying a particular set of conditions.) Search is interpreted as exploring

(physically, or in simulation) as many as possible

alternatives of possible motion and comparing them

afterwards.

Each alternative is created by using a

particular law of producing the group of interest

(cluster, string, etc.) Usually, grouping presumes

exploratory construction of possible combinations

of the elements of space (combinatorial search) and

as one or many of these combinations satisfy

conditions of "being an entity" - substitution of this

group by a new symbol with subsequent treating it

as an object (grouping.)

The larger the space of search is the higher

is the complexity of search. This is why a special

effort is allocated with reducing the space of search.

This effort is called focusing attention and it results

in determining two conditions of searching, namely,

its upper and lower boundaries:

a) the upper boundaries of the space in

which the search should be performed, and

b) the resolution of representation (the

lower boundaries)

11. Planning and Intelligence

Formation of multiple combinations of

elements (combinatorial search, CS) satisfying

required conditions of transforming them into

entities (grouping, G) within a bounded subspace

(focusing attention, FA) is a fundamental procedure

in both learning and planning. Since these three

procedures work together we will talk about them as about a triplet of computational procedures

(GFACS.) Notice, that in learning it creates lower

resolution levels out of higher resolution levels

(bottom-up) while in planning it progresses from

the lower resolution levels out of higher resolution

levels (top-down.)

This triplet of computational procedures is characteristic for intelligence and probably is the

elementary computational unit of intelligence. Its purpose is transformation of large volumes of

information into a manageable form which ensures success of functioning. The way it functions in a

joint learning-planning process explains the

pervasive character of hierarchical architectures in all domains of activities.

Input

Info

STATES

Ooal

Plan

Simulation

Figure 7. Functioning of GFACS in the joint

learning-planning process

The need in GFACS is stimulated by the

property of knowledge representations to contain a

multiplicity of alternatives of space traversal (which

is a property of representations to be redundant.)

Redundancy of representations determines the need

in GFACS: otherwise the known systems would

not be able to function efficiently (it is possible

that redundancy of representations is a precondition

for the possibility of Life and the need in

Intelligence)

12. Planning, Learning, and Control

Theory

Representations reduce the redundancy of

reality. Elimination of redundancy allows for having

problems that can be solved in a closed form (no

combinatorics is possible and/or necessary).

Sometimes, this ultimate reduction of redundancy is impossible and the combinatorial search is the only

way of solving the problem). If the problem cannot

be solved in a closed form, we introduce redundancy

intentionally to enable functioning of GFACS.

527
At each level of resolution, planning is done as a reaction for the slow changes in situation

which invokes the need in anticipation and active

interference

a) to take advantage of the growing

opportunities, or

b) to take necessary measures before the

negative consequences occur. The deviations from a plan are compensated for by the compensatory mechanism

also in a reactive manner. Thus, both feedforward

control (planning) and feedback compensation are

reactive activities as far as interaction systemenvironment is concerned. Both can be made active

in their implementation. This explains different

approaches in control theory.

Examples: a) Classical control systems are systems

with no redundancy, they can be solved in a closed

form. Thus, they do not require any searching.

b) Any stochastics introduced to a control system

creates redundancy and requires either for elimination

of redundancy and bringing the solution to a closed

form, or performing search.

c) Optimum control allows for the degree of

redundancy which determines the need in searching.

In Figure 8, the process of

multiresolutional planning via consecutive search

with focusing attention and grouping is demonstrated for the control problem of finding a minimum-time motion trajectory.

The space is learned in advance by multiple

testing, and its representation is based upon

knowing that the distance, velocity and time are

linked by a simple expression which is sufficient

for obtaining computationally the theoretically

correct solution with an error accepted to be

admissible. Several methods of construbting the

envelopes of attention can be applied.

References

1 . J. Albus, A. Meystel, "A Reference Model

Architecture for Design and Implementation of

Intelligent Control in Large and Complex

Systems", International Journal ofIntelligent

Control and Systems", Vol. 1, No. 1, pp. 15-30

2. A. Meystel, "Architectures, Representations, and

Algorithms for Intelligent Control of Robots", in

Intelligent Control Systems: Theory and

Applications, eds. M. M. Gupta, N. K. Sinha,

IEEE Press, New York, pp. 732-788

3. J. Albus, A. Lacaze, A. Meystel, "Autonomous

Learning via Nested Clustering", Proc. of the 34th

IEEE Conference on Decision and Control, Vol.3,

New Orleans LA, pp. 3034-3039

a)

Figure 8. Solving a minimum-time control

problem by multiresolutional with grouping and

consecutive focusing attention

528
XX ISAS'96 UNPUBLISHED PAPERS
rl
A Road Map to the Future

for

Intelligent Systems

and Semiotics

by

James S. Albus

Intelligent Systems Division

Manufacturing Engineering Laboratory

National Institute of Standards and Technology

Introduction

In common usage, a road map is a piece of

paper with lines that indicate roads and dots that

represent cities. More technically, a road map is an iconic representation of the surface of the earth

with roads represented as lines, and destinations

(or goals) represented as points, or regions on the

map. In the context of the title of this paper, a road map implies a planned route on the map

from our present position to some future goal.

What is the goal for intelligent systems and

semiotics? What should it be? What could it be?

In order to decide on a goal, one must

choose a cost/benefit function. What are the

factors that go into a cost/benefit function?

What is important? Important for what?

I will argue that intelligent systems and

semiotics are important for science, economic

prosperity, military strength, and human well

being.

Intelligent systems and semiotics are important to science because they extend human

knowledge into a rich and largely uncharted

region -- the mind. Intelligent systems theory

has much to contribute to a fundamental

understanding of the mind and of the nature of

perception, cognition, and behavior.

Intelligent systems and semiotics are important to economic prosperity because they

enable productivity improvements in the

production of wealth. Intelligent systems

applications have the potential to reduce the cost

and improve the quality of almost every kind of

product and service.

Intelligent systems and semiotics are important to military strength because they will

enable a whole new generation of battlefield sensors and weapons that will revolutionize the

art of war. Information dominance and unmanned

weapons systems have the capacity to increase

the effectiveness and reduce the risk of projecting

military power to trouble spots throughout in the

world.

Intelligent systems and semiotics are important to human well being because they will

enable us to clean up the environment, to switch

to more efficient means of production, and to improve health care, education, public safety, and

personal security for everyone. In short,

intelligent systems have the potential to provide

the means to end poverty and bring about a golden age for human kind.

Important for Science

I would argue that all of science can be

summed up in three great questions:

1 . What is the nature of matter?

2. What is the nature of life?

3. What is the nature of mind?

Over the past 200 years, research in the

physical sciences has produced a wealth of

knowledge about the nature of matter, both on

our own planet and in the distant galaxies. We

now understand the forces and particles that make

up atoms and their constituent parts: what holds

531
them together, and what gives them their

properties.

Over the past half century, the biological

sciences have produced a revolution in knowledge

about the nature of life. We have a profound

understanding of the molecular basis of life. We

are well on our way to mapping the human

genome. We may soon understand how to cure cancer and prevent AIDS. We will see the

development of new drugs and new sources of

food. Within the next century, we may eradicate

most genetic diseases.

However, of all the questions in science,

the deepest and most profound may be ~ "What

is mind?"

This question can be asked in a number of

different ways. From the time of Moses,

prophets and priests have asked, "What is the

nature of the soul?" Since the time of Aristotle,

philosophers and theologians have asked, "What

is the relationship between mind and body?" For

at least a century, psychologists have asked,

"What is a thought? What does it mean to think

about something? How do we imagine things?"

Psychophysicists ask, "What is perception, and

how is it related to the world that is perceived?"

Psychiatrists ask, "What are emotions and

dreams, and why do we have them?"

Psychologists want to know, "What is motivation and intention, and how do we decide

what we intend to do?" Neurophysiologists ask,

"How do we convert intention into action and

sensation into feeling?" Researchers in

linguistics and semiotics ask, "How do we

generate and use language and how do we

represent knowledge about the world in our minds?" Researchers in artificial intelligence

and operations research ask, "How do we plan,

and how do we solve problems and reason about

the world?"

Intelligent systems from a semiotic

perspective is the study of mind. The study of

intelligent systems addresses what is arguably

THE most important question in science — What

is the nature of mind?

But let me move on to the issue of the

importance of Intelligent Systems and Semiotics

to economic prosperity.

Important for Economic Prosperity

Intelligent manufacturing systems are important economically because they can

dramatically increase productivity.

Toffler has suggested that there have been

three pivotal groups of inventions that shaped the course of human history. The first was the

invention of agriculture, which made it possible

to augment hunting and gathering with the more

efficient and less dangerous processes of

cultivation of crops and husbandry of animals.

This brought about the development of cities, the

organization of nations, and the rise of

civilization.

The second group of inventions was the

invention of the steam engine, the discovery of

electricity, and the development of the internal

combustion engine. These made possible the

augmentation of muscle power with mechanical

energy in the production of goods and services.

This caused the demise of slavery and the rise of

middle-class prosperity.

Toffler's Third Wave is based on the

invention of electronics and the digital computer.

This is enabling the augmentation of brain power

with computer power in the production of goods

and services. Intelligent systems have the

capacity to increase industrial productivity by

orders of magnitude. This could reduce the cost of production and enable wealth to be generated at a rate sufficient to eliminate both poverty and

pollution and create a world of prosperity in

which everyone could be economically secure and

financially independent. Intelligent machines

could become the economic equivalent of

mechanical slaves. Machine owners would

become the modern equivalent of an aristocracy,

and with the proper economic policy, everyone

could become an owner of wealth producing

machines.

Let me be more specific about how

intelligent machine and semiotics can be

important for economic prosperity.

Manufacturing

Intelligent manufacturing systems can

dramatically reduce the cost and improve the

quality of cars, trucks, airplanes, appliances,

furniture, clothing, food products, electronics,

optics, drugs, chemicals, construction equipment,

532
mining and drilling equipment, farm machinery,

railroads, ships, and weapons systems.

For example, intelligent machine

controllers based on inexpensive personal

computer technology will soon make it possible

to automatically generate programs for lifting,

positioning, cutting, joining, machining,

forming, finishing, and assembly operations in

factories and shops throughout the world. Online monitoring of material flow and machine

availability will enable real-time production

planning and scheduling. Advanced sensory

perception systems will enable on-line inspection

and testing. Intelligent adaptive control systems

will increase the efficiency and reduce the cost of

plants, processes, and machines.

The manufacturing industries produce $1.1

trillion of goods and services each year in the

United States. Every percentage point

improvement in manufacturing productivity

produces over $10 billion increase in the nation's

wealth production.

Business management

Intelligent systems technologies are becoming increasingly important for business

management. Computers are already involved in

design, planning, scheduling, word processing,

business management, financial services,

marketing, and customer services.

Transportation Safety and Efficiency

Intelligent systems technologies are about

to have a revolutionary impact on cars and

highways around the world. For more than a

decade in Europe and Japan, and now in the

United States, serious efforts are being directed

toward Intelligent Highway and Vehicle Systems.

In Germany, experimental vision-guided

automatic automobiles are undergoing regular

tests driving the streets and highways in traffic at normal speeds, almost completely without

human assistance. A sedan recently drove from

Munich to Copenhagen under automatic control over 95% of the time. In Japan, drivers can view

detailed maps of streets with directory assistance,

on-line traffic information, and voice

input/output. In the U.S., an automobile under

computer control recently drove from the east

coast to San Diego largely without human

assistance.

Advanced cruise control with collision

avoidance will enhance safety by alerting drivers

that have gone to sleep or whose attention has

wandered. Automatic lane following and

distance keeping will improve throughput and

increase safety on congested freeways. This may

significantly reduce the need to build additional

lanes in areas where construction is restricted by

the availability of space.

Intelligent systems can also improve airline

safety and prevent most rail and ship collisions.

A large percentage of accidents are caused by

human operator errors. Most of these could be

prevented by intelligent systems technology.

Communications

Intelligent systems technologies are already

having a profound impact on the

communications industries. The internet,

satellite and cable television, and cellular phone

systems are creating a communications network

that rivals in bandwidth, complexity, and

sophistication the network of neural fibers that

interconnect various parts in the human brain.

The potential for productivity improvements

from these new technologies is beyond our

ability to predict.

Construction

Studies of the construction industry have

suggested that significant benefits can be

achieved from integrating computer design data

with on-site measurements to enable real-time

planning and scheduling and inventory tracking.

Intelligent measurement systems can assure that

construction tolerances are met and parts fit together without modification. Intelligent

planning systems can assure that parts, tools, and

materials arrive at the right place, at the right

time, and in the right order for construction

operations to flow seamlessly. Complete "as- built" records can be kept for future reference

during maintenance, repair, and future

modifications.

Intelligent systems technology for construction can result in improved productivity,

lower cost, and higher quality in the construction

of factories, plants, high rise buildings, homes,

highways, bridges, tunnels, port facilities, sewer,

water, electricity, and gas utilities, and homes.

533
The construction industry produces about

$460 billion per year. Each percentage point

improvement in construction productivity growth

rate produces a $4.6 billion increase in the

nation's rate of wealth production.

Waste Management

Intelligent systems will enable improved

methods for toxic and radioactive waste handling

and cleanup of waste dumps. New approaches to

trash collection, recycling, and pollution

monitoring will enable environmental restoration

and preservation.

Hospital and Nursing Support

Intelligent fetch and carry robots are already

used every day in hospitals. Computers are used

for patient record keeping, patient monitoring,

and diagnostic aids. Intelligent systems can be

used in laboratory analysis, drug manufacturing,

and prescription filling. These applications could

reduce costs and improve care for hospital

patients.

In-home Patient Services

Intelligent systems could be developed for

lifting and positioning invalid and infirm patients

in and out of bed, on and off of the toilet, and in

and out of the bath. Intelligent systems can provide mobility, food preparation, physical

therapy, security and health monitoring,

telecommuting for work and shopping, and

entertainment and education for the home patient.

This can reduce the cost and improve the life of

patients that prefer to remain at home rather than

be institutionalized in nursing care facilities.

For example, around 100,000 persons enter nursing homes every month in the United States

at a cost of more than $2000 per month.

Delaying the average date of entry of the elderly

to nursing homes by only one month would save

the country about $2.4 billion per year.

Physical Security

Intelligent systems will enable advanced

security systems for the detection and tracking of

intruders with a minimum of false alarms.

Agriculture and Food Processing

Robotics and intelligent machine systems

have only begun to enter the field of agriculture

and food processing industries. The application

of intelligent systems technologies to farming

the oceans has not even begun to be explored.

Mining and Drilling

Three-fifths of the earth's surface is too

deep beneath the oceans for mining or drilling

operations using conventional techniques. This means that most of the earth's mineral resources have never been touched. Intelligent undersea

robots offer significant potential for productivity

improvements in deep sea mining and oil drilling

operations.

Space and Undersea Exploration

Outer space, planetary surfaces, and the

bottom of the ocean all share the characteristic

that manned exploration is extremely expensive

and hazardous. Intelligent systems and robotics

promise to decrease the cost and risk and increase

the amount of data that can be gathered from

space and undersea exploration.

Important for Military Strength

Intelligent systems technology promises to revolutionize warfare through a new generation of

sensors, machines, decision aids, and weapons

systems. Intelligent weapons are already highly

advanced. Cruise missiles, smart bombs,

unmanned vehicles, and computer augmented

command and control systems are currently being

developed and deployed. These are but the

vanguard of a whole new generation of military

systems that will become possible once

intelligent systems becomes a mature

engineering discipline.

In future wars, unmanned air vehicles,

ground vehicles, ships, and undersea vehicles will

be able to outperform manned systems. Many

military vehicles are limited in performance

because of the acceleration, vibration, or pressure

limits of the human body, or the need of humans

to consume air, water, and food. A great deal of

the weight and power of current military vehicles

is spent on armor and life support systems that

are necessary to protect and maintain human

operators.

Intelligent military systems will reduce

both the risk to human personnel and the cost of

training and readiness. Unmanned vehicles and

weapons systems put fewer humans in harms

way and require little or no training to maintain

534
readiness. Unmanned systems can be stored in

forward bases or at sea for long periods of time at low cost. They can be mobilized quickly in an emergency. They operate without fear under fire,

the first time and every time.

Intelligent systems can be fast and effective

in gathering, processing, and displaying

information. They can enable human

commanders to be quicker and more through in

planning operations and in replanning for unexpected events as the battle evolves.

In short, intelligent systems promise to multiply the capabilities of the armed forces,

while reducing casualties and hostages and

lowering the cost of training and readiness.

Important for Human Well Being

Productivity growth depends on technology.

Intelligent systems and semiotics have entered a new phase of rapid development that will produce

rapid growth in productivity. Intelligent

machines represent a new breed of workers that

will be able to produce more and higher quality

goods and services at lower cost. There is every reason to believe that we are on the cusp of an S-curve where productivity can grow

exponentially for a long period of time. Given

adequate investment, there is no reason to doubt

that productivity growth could return to 2.5%,

which is the average for the 20th century. Or, it could rise to 4% which is the average for the

1960-68 time frame, or even to 12% which

occurred during the period of World War II between 1939 and 1945. If this were to occur, many of the problems of poverty, disease, and

pollution that result from stagnant economic

growth would disappear. Society could afford to improve health care and education, to clean up

the environment, to adopt less wasteful forms of

production and consumption, to reduce taxes, and

provide a minimum income for all.

Charting the Route

At this point, a goal destination for our

road map has been established. Our goal is to understand the nature of mind and to build

intelligent systems that will improve economic

prosperity, strengthen military security, and

improve human well being. I believe this is a worthy and desirable goal.

Let me now turn to the issue of finding a

route from where we are today to the goal

destination.

First, let me say that we have already made

a good start and progress is rapid. The study of

intelligent control systems is an extremely active

field. Research in neural nets, fuzzy logic, and

genetic algorithms is showing how to recognize

patterns, discover control laws, and control

complex industrial processes. Computer science,

artificial intelligence, semiotics, and linguistics

are probing the nature of language and image

understanding. Significant progress has been

made in expert systems, rule-based reasoning,

planning and problem solving. Game theory and

operations research have developed methods for decision-making in the face of uncertainty.

Research in sonar, radar, and optical signal

processing has developed methods for fusing

sensory input from multiple sources, and

assessing the believability of noisy data.

Robotics and autonomous vehicle research

has produced advances in real-time sensory

processing, world modeling, navigation,

trajectory generation, and obstacle avoidance.

Research in computer integrated manufacturing

and process control has produced intelligent

hierarchical controls, distributed databases,

representations of object geometry and material

properties, data driven task sequencing, network

communications, and multiprocessor operating

systems. Modern control theory has developed a

precise understanding of stability, adaptability,

and controllability under various conditions of

feedback and noise. Intelligent control closes

the loop between sensing and acting through

perception, world modeling, planning, and

control. Intelligent control enables large

complex systems with many sensors and

actuators to pursue and achieve sophisticated

goals in an uncertain, competitive, and

sometimes hostile environment. Intelligent

control enables a system to analyze the past, to perceive the present, and to plan for the future.

Intelligent control enables systems to assess the

cost, risk, and benefit of past events and future

plans and to make choices between alternative courses of action.

In the neurosciences, much is known, both

about the machinery of the brain and the

processes that run in it. Neuroanatomy has

produced extensive maps of the interconnecting

535
pathways making up the structure of the brain.

Neurophysiology is demonstrating how neurons compute functions and communicate

information. Much is known about the

functionality of specific areas of the brain. For

example, the areas responsible for vision,

hearing, manipulation, locomotion, emotions,

hunger, thirst, and sexual drive are well explored.

Within the vision system, there are modules and

pathways that specialize in analysis of motion,

and others that specialize in recognition of shape.

The brain has neuronal mechanisms for estimating distance to visible surfaces, for tracking objects, anticipating movement, and for fusing information derived from eyes and ears.

Neuropharmacology is discovering many of

the transmitter substances that activate and

modify behavior, that enable learning, that dispense reward and punishment, and that assign

value to perceived objects and events.

Psychophysics provides many clues as to how individuals perceive objects, events, time,

and space, and how they reason about

relationships between themselves and the external

world. Neuropsychology adds information about

mental development, feeling, emotions, and

behavior.

Technology is Accelerating

The latter half of the 20th century has seen a number of fundamental breakthroughs that

have radically altered the landscape of

technological possibilities. Technological

knowledge is not just increasing, it is

accelerating. There is an exponential growth in

technological progress that shows no sign of

saturation. For example:

1. The power and speed (per unit cost) of

electronic computing has risen exponentially by more than a factor of ten per decade for almost

fifty years. This rate of progress shows no sign

of slowing. This means that computing power

comparable to that which exists in the brain

could be assembled in the foreseeable future.

2. The store of knowledge about how the

biological brain works has also increased many

fold over the last half century. The neurosciences

show no sign of running up against a fundamental barrier to understanding.

3. The number of scientists and engineers

is increasing exponentially. Over half of all the

scientists and engineers that ever lived are alive

and working today.

4. Perhaps of most importance, the nature

of knowledge is such that it is not subject to diminishing returns. The more that is known,

the easier it is to discover new things. There is no limit to what there is to know. There is only

a limit to the amount of time and resources we

dedicate to the pursuit of knowledge.

So what is lacking?

The main thing that is missing is a widely

accepted theoretical framework that ties together

all of the diverse fields related to intelligent

systems, semiotics, and the neurosciences. There

is little symbiosis between fields. Things are constantly being rediscovered in different fields and called by different names.

Also missing is a widely accepted reference

model architecture that can support an

engineering methodology for designing and

building intelligent systems. Several

architectures have been proposed, but none is widely adopted. There are no standardized metrics

for measuring performance that can scientifically

evaluate experiments and test theories. There are no interface standards so that intelligent systems

can be easily assembled from component parts.

Finally, there is no educational curriculum for producing scientists and engineers skilled in the

art of designing and building intelligent systems.

An Outline for a Theory of

Intelligence

As a result of our research in the Intelligent

Systems Division here at NIST, an outline for a

theory of intelligence has been published. (Albus

91) In this paper, the functional elements of

intelligence are defined as behavior generation,

sensory processing, world modeling, and value

judgment. Behavior generation provides the

functions of planning and control. Sensory

processing filters data from sensors, detects

events, recognizes patterns, and analyzes

situations. World modeling stores and maintains

a knowledge database and uses knowledge about

the world to predict the future and simulate the

results of hypothesized plans. Value judgment

536
functions compute cost, benefit, risk, and

uncertainty.

These functional elements are supported by

a distributed knowledge database where

knowledge about the world and the system is represented in terms of state variables, event and

entity frames, attributes, maps, lists, tasks,

rules, equations, and processes.

The functional elements and knowledge

database are integrated by a system architecture

that provides communications, timing, and an operating system.

Based on this theory, a reference model

architecture has been developed.

A diagram of the relationship between the

functional elements, and the knowledge database

in this reference model architecture is shown in

Figure 1.

— — Perception — — — y — — — Behavior Generation — — — —

|

VALUE

JUDGMENT

PERCEIVED

OBJECTS &

EVENTS

COMMANDED

TASK (GOAL)

OPERATOR

INTERFACE

TASK

DECOMPOSITION

OBSERVED

INPUT

COMMANDED

ACTIONS (SUBGOALS)

Figure 1 . Relationships between the functional elements and the knowledge database within

the NIST reference model architecture for intelligent systems.

Computational modules and a knowledge

database are interconnected by communication

pathways that transmit information so as to close

control loops, enable perception and planning,

and facilitate knowledge acquisition and learning.

In the intelligent system, values and cost functions control the selection of goals and

optimization of behavior. Hypothesized plans are communicated from Behavior Generation to World Modeling for simulation and the results of

simulation to Value Judgment for evaluation.

Evaluations are communicated back to Behavior

Generation for decision-making in selecting

goals, setting priorities, focusing of attention,

organizing perception, and controlling behavior.

World Modeling uses information in the

knowledge database to predict incoming data.

Sensory processing compares predictions with

observations and computes correlations and

differences. Differences are returned to the world

to update the knowledge database. This is a Kalman filtering loop for recursive estimation.

Correlations between predictions and

observations signal recognition of events and

objects. Value judgment facilitates learning by

computing what is important or trivial, and what

is rewarding or punishing. Real-time data in the

world model closes a control loop between

sensory feedback and task execution. Within this

system the deliberative is integrated with the

reflexive, enabling a real-time intelligent control

system to be both goal driven and sensory

interactive.

Figure 2 is a reference model architecture

for an intelligent shop controller within a

537
manufacturing enterprise. Each node in the

hierarchical architecture shown in Figure 2

consists of the set of functional elements shown

in Figure 1.

In each node of the architecture shown in

Figure 2:

a World Modeling function maintains the

Knowledge database, answers queries, predicts

sensory input, and simulates the result of

hypothesized plans;

a Sensory Perception function scales and

filters input from sensors, detects events, and

recognizes objects and situations;

a Value Judgment function computes cost,

risk, and benefit, and assigns values to recognized

objects and events and the results of simulated

plans;

a Behavior Generation function uses the

information provided by the World Modeling and

Value Judgment functions to find the best

assignment of tools and resources to agents, to find the best plan from the current state to a goal

state, and to execute that plan.

SHOP Plans for next day

CELL Plans for next hour

WORKSTATION Plans for next 5 minutes

Tasks to be done of tray of parts MACHINE Plans for next 30 seconds Task to be done on one object

*Tool Motion E-MOVE

3 second plans - Subtask on object part Obstacle-free paths

Points,

PRIMITIVE

0~3* second plan Tool trajectory

S£R.VO 103 second plan

J

J Actuator output

O

gcd. LU

O

H

o

SENSORS AND ACTUATORS

Figure 2. An intelligent system architecture for manufacturing.

Typically, control loops are closed in each

node. Each layer of this hierarchical architecture

has a characteristic servo loop bandwidth and a

characteristic planning horizon. For example, at

the servo level the feedback loop might be closed

every 3 milliseconds with a planning horizon of

30 milliseconds. At the primitive level, the

feedback loop may close every 30 milliseconds

with a planning horizon of 300 milliseconds. At

the elemental move level the feedback loop is closed every 300 milliseconds with a planning

horizon of 3 seconds. At the individual machine

level, the planning horizon may be 30 seconds.

At the workstation level, the planning horizon

may be 5 minutes, and at the cell level an hour.

At the shop level, the planning horizon may

extend a day into the future.

The architecture is hierarchical in order to

deal with complexity. The hierarchical structure enables a manufacturing system of arbitrary

complexity to be decomposed into manageable

units. Each level of the hierarchy has a

characteristic range and resolution in time and

space. Each chain of command within the

538
hierarchy generates a hierarchy of tasks and plans

for a hierarchy of agents. The world model and

knowledge database in the nodes contain a

hierarchy of entities and events. This hierarchical

decomposition enables the development of an engineering methodology within a systematic

framework of modular components, standard

interfaces, that enable designers to easily add sensors and upgrade processing capabilities.

The intelligent system architecture for manufacturing shown in Figure 2 is a derivative

of the Real-time Control System (RCS) reference

model architecture for intelligent systems that

has been developed at NIST and elsewhere over

the past two decades. RCS has been used to develop a wide variety of applications including

robots for machine loading and unloading using

vision and tactile sensors, deburring and

chamfering using active force control, integration

of an Automated Manufacturing Research

Facility including robots, machine tools, a turning machine, a coordinate measuring

machine, and automatic guided vehicles. RCS

also has been used to control multiple

autonomous undersea vehicles, a space station

telerobotic system, a simulated nuclear

submarine operating under ice during a transit of

the Bearing Straits. Intelligent controllers have

been developed for coal mine automation, post

office automation, a RoboCrane system, a next

generation inspection system, and an Enhanced

Machine Controller for a five axis machining

center. (Albus 97)

Current work at NIST is concentrating on

developing an systematic engineering

methodology for developing intelligent systems

applications. We are working on generic

templates and software development tools. We

are working with our four sister divisions in the

Manufacturing Engineering Laboratory to develop a National Advanced Manufacturing

Testbed (NAMT) which will perform research in

virtual and distributed manufacturing. The

NAMT will be a place where advanced laboratory

equipment such as the Hexapod machine tool, the

Next Generation Inspection Systems, and the

RoboCrane, the Advanced Deburring and

Chamfering System, and the HMMWV

Unmanned Ground Vehicle can be accessed and

used by experimenters at remote locations

anywhere in the world. Through the NAMT

facilities, experimenters will also be able to access experimental equipment in other divisions

at NIST, as well as at universities, industry labs,

and other government labs such as Sandia and

Oak Ridge.

Our Intelligent Systems Division is planning to distribute RCS software as freeware

to universities and to work with professors to develop lecture material and lab experiments that can be used for course work in intelligent

control. Through the NAMT virtual and

distributed testbed, we will work with professors

and students to develop algorithms and do

experiments and perform thesis research in

intelligent manufacturing, construction, and

unmanned vehicle systems. We also hope to collaborate with the National Science Foundation

and other sources of funding to support users groups, promote student competitions, and fund

collaborative research.

If this is successful, we intend to solicit

industrial partners to propose an Advanced

Technology Program targeted thrust area for

industry research in intelligent systems.

Conclusion

So this is my proposed road map for the

future. The goal of the roadmap is to understand

the nature of mind and to build systems that will

improve economic prosperity, strengthen

military security, and improve human well

being.

The suggested route is:

(1) to develop a theory and reference model

architecture for intelligent systems,

(2) to develop an engineering methodology

and educational curriculum,

(3) to distribute freeware and provide user support,

(4) to build a virtual and distributed testbed

environment so that researchers in many different

locations can work together, and

(5) to solicit partners and pursue additional

funding to advance the theory and practice of

intelligent systems and semiotics.

In closing, let me reiterate that intelligent

systems are important for a wide variety of

scientific, economic, and military reasons. The

technology of intelligent systems is moving

rapidly, but there are some gaps that impede

539
10

progress. Some suggestions have been made to

fill in these gaps and achieve the ultimate goal

of human well being.

As a final thought, I want to suggest that

intelligent systems represent a fundamentally

new technology that will create a new industrial

revolution. The impact of this new industrial

revolution will at least equal, and may far exceed,

that produced by the invention of the steam

engine and the discovery of electricity. The

ultimate result could be a breakthrough in

productivity growth that would bring an end to poverty and introduce a golden age for human

kind.

References

Albus, J.S., "Outline for a Theory of

Intelligence," IEEE Transactions on Systems, Man

and Cybernetics, Vol. 21, No. 3, pgs. 473-509,

May/June, 1991

Albus, J.S., "The NIST Real-time Control

System (RCS): an approach to intelligent systems

research", J. Expt. Theor. Artif. Intell. 9, p. 157-

174, 1997

540
Computational Semiotics and Fuzzy Linguistics

On Meaning Constitution and Soft Categories*

Burghard B. Rieger

FB II: Department of Computational Linguistics - University of Trier

riegerfildvOl . Uni-Tner . de

Abstract

Whereas most cognitive approaches in the study of language have been developing hypotheses concerning the

principles of knowing and understanding natural languages (i.e. competence) without bothering too much

about communicative language usages in realworld sit- uations (i.e. performance), new semiotic approaches

in cognitive computational linguistics explore the procedures believed to underlie processes of language learning and understanding. They do so by simulating these

capabilities as system behaviour under recourse to modeled structures, observable in very large samples of situated natural language discourse and represented in vec- tor space formats via numerically specified quantitative

methods of dynamic (re-)construction. It will be argued

that the ecological understanding of informational sys- tems in Computational Semiotics corresponds well to the procedural modeling and numerical reconstruction

of processes that simulate the constitution of meanings

and the interpretation of signs fsemiosis^. The theories

of fuzzy sets [24] and possibility distributions [23] to- gether with their derivatives in soft computing [25] appear to be promising in providing suitable formats for

computational approaches to natural language processing without the obligation neither to reject nor to accept

traditional formal and modeltheoretic concepts or ontologies. Examples from fuzzy linguistic research [10]

[18] will be given to illustrate these points.

1 Cognitive Information Processing

For the majority of researchers in knowledge representation and natural language semantics the common

ground and widely accepted frame for their modeling

may be found in the dualism of the rationalistic tradition of thought as exemplified in its matter-mind notion

of an independent (objective) reality and some (subjective) conception of it. 1.1 The traditional approach

According to the realistic view, the meaning of any portion of language material (like e.g. discourse, utterance,

word(token), morph, phone, etc.) is interpreted as being an instantiation of (or partly derivable from) cer- tain other entities, called linguistic categories (like e.g. text, sentence, word(type), morpheme, phoneme, etc.),

•presented at the NIST/NSF/IEEE/DARPA Interntl. Multidisciplinary Conference INTELLIGENT SYSTEMS: A SEMIOTIC

PERSPECTIVE, Oct. 20-23, 1996, Gaithersburg, Md, USA

with the understanding that these categories structure natural language material according to their compositional functions. It is by these functions that language material (strings of terms) appear to be composed of linguistic entities (aggregates of categories) to form structures and it is also by these functions that

the quality of language structures (having meaning) is conceived as being part of both, the physical reality of

language material and the semantic significance of lin- guistic signs. Illustrating this twofold membership are the graph-theoretical formats which have become stan- dard representations for natural language meanings,

both as reiationaJ structure and as re/erentiai denotation. Thus, relating arc-and-node configurations with

sign-and-term labels in graphs like trees and nets appears to be but another aspect of the traditional mindmatter-duality according to which a realm of meanings

is presupposed very much like the assumption of the

pre-given structures of the reai world related by signs.

Accepting this duality has neither allowed to explain

where the structures or where the labels come from

nor how their mutual relatedness as meanings of signs can be derived. The emergence of the meaning reiation, therefore, never occurred to be in need of some

explanatory modeling because the existence of signs,

objects and meanings were taken for granted and hence

seemed to be out of all scrutiny. Under this presupposition, fundamental semiotic questions of semantics

simply did not come up, they have hardly been asked

yet, and are still far from being solved.

1.2 Modeling cognition

Extending an earlier attempt [22] to classify approaches

in cognitive science, we may roughly discern four1 types

of approaches in modeling cognition:

> the cognitive approaches presuppose the existence

of the external world, structured by given objects

and properties and the existence of representations

of (fragments of) this world internal to the system,

so that the cognitive systems' (observable) behaviour

of action and reaction may be modelled by processes

operating on these structures; > the associative approach is described as a dynamic structuring based on the model concept of

self-organization with cognitive systems constantly

^here were only the first three of these four approaches dis- tinguished by Varela/Thompson/Rosch (1991).

541
adapting to changing environmental conditions by

modifying their internal representation of them.

Whereas both these approaches apparently draw on

the traditional rationalistic paradigm of mind-matterduality

static the former, dynamic the latter—in presupposing the externa] world structure and an interna]

representation of it, the third and fourth category do

not: > the enactive approaches may be characterized as being based upon the notion of strcuturai coupling.

Instead of assuming an external world and the sys- tems' internal representations of it, some unity of

structural relatedness is considered to be fundamental of—and the (only) condition for—any abstracted

or acquired duality in notions of the external and in- ternal, object and subject, reality and its experience;

> the semiotic approaches focus on the notion of semio'

sis and may be characterized by the process of en- actment too, supplemented, however, by the representational impact. It is considered fundamental to the distinction of e.g. cognitive processes

from their structural results which—due to the traces these processes leave behind—may emerge in some

form of knowledge whose different representational

modes comply with the distinction of interna] or tacit

knowledge (i.e. memory) on the one hand and of externa] or declarative knowledge (i.e. ianguage) on

the other.

According to these types of cognitive modeling, computational semiotics can be characterized as aiming

at the dynamics of meaning constitution by simulating processes of multi-resolutional representation [5] within the frame of an ecological information processing paradigm [18]. As we take human beings to be systems whose

knowledge based processing of represented information

makes them cognitive, and whose sign and symbol generation, manipulation, and understanding capabilities

render them semiotic, we may do so due to our own

daily experience of these systems' outstanding ability

for representing results of cognitive processes, organize

these representations, and modify them according to changing conditions and states of system-environment

adaptedness.

2 Computational Semiotics

For the semiotic approach to human cognition (constituting computational semiotics) such representations

resulting from complex semiotic cognitive information

processing may be found in any natural language dis- course. In an aggregated form of pragmatically homogeneous text corpora [7] communicatively performative natural language discourse provides a cognitively

highly interesting and empirically accessible material

whose extreme structuredness may serve as a guideline

for the cognitively motivated, empirically based, and

computationally realized research in the semiotics of

language, too. Following this line, however, will necessitate to pass

on from traditional approaches in competence ori- ented linguistics analysing introspectively the propositional contents of singular sentences as conceived by

ideal speakers/writers towards a new understanding of

meaning constitution as a dynamic process based upon

the semiotic cognitive information processing the traces of which are to be identified and systematically recon- structed on the basis of empirically well founded observation and rigorous mathematical description of universal regularities that structure and constitute different

levels of representations in masses of pragmatically homogeneous texts produced by reaJ speakers/writers in actual situations of either performed or intended communicative interaction. Only such a performance ori- ented semiotic approach will give a chance to formally

reconstruct and model procedurally both, the signifi- cance of entities and the meanings of signs as a function

of a first and second order semiotic embedding relation

of situations (or contexts) and of language games (or

cotexts) which corresponds to the two-level actualisation of cognitive processes in language understanding

[18].

2.1 Ecological information systems

Life may be understood as the ability to survive by

adapting to changing requirements in the real world. In terms of the theory of information systems, fac- ulties like perception, identification, and interpretation of structures (external or internal to a system)

may be conceived as a form of information processing which (natural or artificial) systems—due to their

own structeredness—are able to perform. Thus, living

systems receive or derive information only from rele- vant portions of their surrounding environments, they

learn from experience, and change their behaviour ac- cordingly. In contrast to other living systems which

transmit experiential results of environmental adaptation only biogenetically2 to their descendants, human

information processing systems have additional means

to convey their knowledge to others. In addition to the vertical transmission of system specific (intraneous)

experience through (biogenetically successive) generations, mankind has complementally developed horizontal means of mediating specific and foreign (extraneous) experience and knowledge to (biogenetically unrelated) fellow systems within their own or any later generation. This is made possible by a semiotic move that

allows not only to distinguish processes from results of

experience but also to convert the latter to knowledge

facilitating it to be re-used, modified and improved in learning. Vehicle and medium of this move are repre- sentations, i.e. complex sign systems which constitute

languages and form structures, called texts which may

be realized in communicative processes, called acfcuaii- sation.

2 According to standard theory there is no direct genetic coding of experiential results but rather indirect transmission of them by selectional advantages which organisms with certain ge- netic mutations gain over others without them to survive under

changing environmental conditions.

542
In terms of the theory of information systems,

texts—whether internal or external to the systems

function like virtual environments3

.

2.2 Modes of Representation

Considering the system-environment relation, virtuality may be characterized by the fact that it dispenses

with the identity of space-time coordinates for systemenvironment pairs which normally prevails for this re- lation when qualified to be indexed real. It appears,

that this dispensation of identity—for short: spacetime-dispensation—is not only conditional for the possible distinction of (mutually and relatively independent) systems from their environments, but establishes

also the notion of representation. Accordingly, immediate or space-time-identical system-environments existing in their space-time-identity may well be distinguished from mediate or space-time-dispensed systemenvironments whose particular representational form

(texts) corresponds to their particular status both, as language material (being signs), and as language struc- ture (having meaning'). This double identity calls for a

particular modus of actualisation (understanding) that

may be characterized as follows:

For systems appropriately adapted and tuned to such

environments actuah'sation consists essentially in a

twofold embedding to realize > the spaciotemporal identity of pairs of immediate

system-environment coordinates which will let the

system experience the material properties of texts

as signs (i.e. by functions of physical access and

mutually homomorphic appearance). These properties apply to the percepts of language structures presented to a system in a particular discourse situation, and

> the representational identity of pairs of mediate

system-environment parameters which will let the

system experience the semantic properties of texts

as meanings (i.e. by functions of emergence, identification, organisation, representation of structures).

These apply to the comprehension of language struc- tures recognized by a system to form the described

situation

Hence, according to the theory of information sys- tems, functions like interpreting signs and understanding meanings translate to processes which extend the

fragments of reality accesssible to a living (natural and

possibly artificial) information processing system. This

3 Simon's (1982) remark "There is a certain arbitrariness in drawing the boundary between inner and outer environments of

artificial systems. . . . Long-term memory operates like a second

environment, parallel to the environment sensed through eyes and ears" (pp. 104) is not a case in point here. Primarily con- cerned with where to place the boundary, he does not seem to

see its placing in need to be justified or derived as a consequence

of some possibly representational processes we call semiotic. As

will become clear in what follows, Simon's distinction of inner

(memory structure) and outer (world structure) environments is not concerned with the special quality of language signs whose

twofold environmental embedding (textual structure) cuts ac- cross that distinction, resolving both in becoming representational for each other.

extension applies to both, the immediate and mediate

relations a system may establish according to its own

evolved adaptedness or dispositions (i.e. innate and

acquired structuredness, processing capabilities, repre- sented JcnowJedge).

2.3 Semiotic enactment

Semiotic systems' ability to actualize environmental

representations does not merely add to the amount of

experiential results available, but constitutes also a significant change in experiencial modus. This change is characterized by the fact that only now the processes

of experiencing may be realized as being different and

hence be separable from the results of experience which

in immediate system-environments appear to be in- distinguishable. Splitting up experience in experiencial processes and experiencial results—the latter being

representational and in need for procedural actualisation by the former—is tantamount to the emergence of

virtual experiences which have not to be made but can

instead just be tried, very much like hypotheses in an

experimental setting of a testbed. These results—like in immediate system-environments—may become part

of a system's adaptive knowledge but may also—other

than in immediate system-environments—be neglected

or tested, accepted or dismissed, repeatedly actualized

and re-used without any risk for the system's own survival, stability or adaptedness.

This in a way experimental quality of textual rep- resentations which increases the potentials of adaptive

information processing beyond the system's lifespan, is constrained simultaneously by dynamic structures cor- responding to knowledge. The built-up, employment,

and modification of these structural constraints4is controlled by procedures whose processes determine cognition and whose results constitute adaptation. Systems properly attuned to textual system-environments

have acquired these structural constraints (language

learning) and can perform certain operations efficiently on them (language understanding). These are prerequisites to recognizing mediate (textual) environments

and to identify their need for and the systems' own

ability to actualize the mutual (and trifold) related- ness constituting what Peirce called semiosis5

. Systems capable of and tuned to such knowledge-based

processes of actualisation will in the sequel be referred to as semiotic cognitive information processing systems

(SCIPS) [17, 19].

Representation, therefore, has to be considered fundamental to the distinction of the processes of cognition from their results which may emerge—due to the

traces these processes leave behind—in some structure (knowledge). Different representational modes of this

*What Simon (1982) calls memory in accordance with his questioning of the inner-outer-distiction of cognitive systems and

their environments.

8 By semiosis I mean [. . .] an action, or influence, which is, or

involves, a cooperation of three subjects, such as sign, its object,

and its interpretant, this tri-relative influence not being in any way resolvable into actions between pairs. (Peirce 1906, p.282)

543
structure not only comply with the distinction of interna] or tacit knowledge (i.e. memory) on the one hand and of externa/ or declarative knowledge (i.e.

texts) on the other6

, but these modes also relate to dif- ferent types of formats (distributional vs. symbolic),

modeling (connectionist vs. ruie- based) and processing

(stochastic vs. deterministic). It is this range of cor- respondences that Fuzzy Linguistics is based upon and

tries to exploit to come up with a unifying framework

for most of the different approaches followed sofar. Soft categorising appears to be a prerequisite for fuzzy

linguistic modeling, examples of which will illustrate

the notion of dynamic structures emerging from cor- pora of natural language discourse when processed.

3 Fuzzy Linguistic Modelling

It is far from certain yet whether—and if so, how

semiotic models will help to understand how struc- tures may emerge from orders of some kind and how

these orders evolve from regularities which multitudes

of repeatedly observable entities show. Recent re- search findings, however, give rise to expect that processes which determine regularities and assemble them

to form (intermediate) representations whose properties resemble (or can even be identified with) those

of observable entities may indeed be responsible for

(if not identical with) the emergence and usage of

sign-functional structures in language understanding

systems, both natural and artificial. As more abstract (theoretical) levels of representation for these

processes —other than their procedural modeling—are not (yet) to be assumed, and as any (formal) means

of deriving their possible results—other than by their

(operational) enactment—are (still) lacking, it has to be postulated that these processes—independent of

all other explanatory paradigms—will not only relate

but produce different representational levels in a way

that is formally controlled or computable, that can be modeled procedurally or algoritbmized, and that

may empirically be tested or implemented [4]. Procedural models are understood to denote a class of

(re-) presentational or modeled (re-)constructions of entities whose interpretation is not (yet) tied to an underlying theory which would provide the semantics for

the entities (or expressions) that these type of models present. Instantiating their defining procedures as implemented algorithms will result in processes which

produce some observable structures that can only then

be compared to those of the modeled original.

As some of these procedural characteristics have

6 Whereas tacit knowledge cannot be represented other than

by the immediate system-environments' corresponding states, explicit knowledge is bound to acquire some formal properties

in order to become externally presented and thereby part of mediate system-environments. Natural languages obviously pro- vide these formal properties—as partly identified by research

in linguistic competence (principles knowledge and acquisition of language)—whose enactment—as investigated in studies on

natural language performance (production and understanding of

texts)—draws cognitively on both bases of (explicit and tacit) knowledge.

also be claimed by cognitive linguistic approaches and

computational models of language understanding, their

main traits may help to illustrate the different positions

of semiotic modeling in fuzzy linguistics.

3.1 Cognitive linguistic strata

Cognitive theory has long identified the complex of lan- guage understanding to be a modular system of subsystems of information processing. The idea of symbolic representation and the computer metaphor of- fered a frame for modeling cognitive processes, for- mally grounded on logical calculi and procedurally

realized in algorithms operating on representational

structures. Following and partly supplementing strata

of semiotic description and analysis of signs, differ- ent levels of modular aggregation of external and in- ternal information have been distinguished in cognitive models of language understanding. These partly

correspond to and partly cut accross the syntacticssemantics-pragmatics distinction in the semiotic relat- edness of signs, the utterance-discourse-corpus levels of performative language processing, and the hierarchy

of morpbo-phonological, syntax-sentencial and lexicosemantic descriptions in traditional models of struc- tural linguistics. In one of the rare ventures on discussing of how

cognitive, i.e. knowledge based information processing

mechanisms may be provided with the knowledge bases

they are meant to operate on, and how these knowledge

structures may be related to observable language data,

BlERWlSCH (1981) sketches a hierarchy of information

processing mechanisms whose representational format

(sets of rewrite rules operating on structured data) al- lows algorithms be formulated and implementations be

found to guarantee their computability. According to

this schema (Fig. 1) and starting with the morphophonological level, an information processing mechanism Mi is postulated which receives utterances as in- put and produces some associated structures as output.

In doing so, however, the mechanism's performance will be determined not only by the external input strings

but also by some internal knowledge of elements and

rules which allow to agglomerate the structures identified. The acquisition and representation of this internal

knowledge is hypothesized as resulting from a process

Mi which also includes a multitude of rudimentary, in- complete, and tentative Mi-kind processes. M% is as- sumed to be a complex information processing mechanism whose inputs are corpora of utterances together

with some environmental information, and whose out- puts will be the grammars underying these utterances. Again, this mechanism's results will not only and completely be determined by the external inputs but also

by some internal structures which are believed to control the human language faculty in a fundamental way

as so-called linguistic universals. These may (or may

not) be assumed to be derivable as results of an in- formation processing mechanism M3 whose input is as comprehensive (or unspecified) as the term Janguages

might allow.

544
Utterance Structure Utterances

Corpus Mi Grammar

Languages —«- Universals Languages -*-

Structures

Grammars

Universals

Figure 1 Figure 2

Schemata of model hierarchy of cognitiv linguistic strata of mechanisms (Bierwisch) as compared to model tiling

of computational semiotic coverage of procedures (Rieger) for the analysis and representation of (abstracted and

observable) language phenomena.

Taking the relation of inclusion for Mi C Mi to hold

also for Mi C M3, and considering Mi, M2, M3 computationally specifyable procedures of language analysing

processes instead of mere metaphors for some (more or

less plausible) mechanisms of the human mind, then

it appears reasonable to consider M3 a collection of

all the processes of methodical analysis, representation,

and comparison of structured sets of utterances from

different languages, including the processes in Mi as a

device that explicidly specifies an utterance's structure

relative to a given grammar, and the processes in M2

as a system that generates a grammar from a corpus of

utterances relative to the given set of universals. This

modeling view allows for the notions of Universals => Grammar Structure to be understood as variables

of theoretical constructs hinged on empirical regularities observed in Languages, Corpus, Utterance respectively. Whereas the latter are external representations,

the former are internal to any SCJP-system and considered external representations only under the competence linguistic approach to cognitive modeling. As

such they are hypothesized to form a hierarchy of lin- guistic—not language—entities which formally specify a class of other linguistic entities (following the double

arrows in Fig. 1). The model theoretical and operational problems in- herent in this setup concern the (non universal and

highly restrictive) representational format which is as- sumed to enable the denotation of universais, grammar and structure, and the essentially top-down, nonrecursive propagation of externally presented but in- ternally processed results of these mechanisms. Thus,

M3 whose performance in identifying universals and

representing them externally depends crucially on the

efficient performance of M2 which is said to employ

these universals as internal procedural constraints in

order to identify syntactic regularities and represent

them externally in a rule based format as grammars.

Grammars, in turn, have to be employed as internal

procedural constraints by Mi if this mechanism's identification processes and the external representation of

their findings is meant to be successful.

Distinguishing between these two kinds of structures

either external or internal to the mechanisms M in- troduced so far, is indicative of the systems theoretical view proposed in semiotic modeling. It easily al- lows to translate these mechanisms as sets of procedures which allow to describe and simulate a living

systems' abilility to process environmental input (external structures) according to procedural constraints

known to the system (internal structures) in order to produce some results of this processing. However, it appears not at all conclusively compelling to assume

that these procedural constraints and the processing

results need to be represented in a rule-based format.

According to an ecologically motivated systems theoretical view, systems enacting these processes under

boundary conditions as determined by their surrounding environments, or their internal structuredness, or both, will have to process certain inputs to produce

specified output structures. But identifying their sta- tus of being at the same time internal and external to the processing system is tantamount to the methodological dilemma which can solely be solved on the

grounds of revising the representational mode and the

formatting constraints which the model construction

has to be decided on to allow.

Following Chomsky these modes have been re- stricted to abstract principles of language competence

by processes [2] whose assumed rule-based determinacy

consequently led to formal representations of these

rules giving rise to the above model hierarchy of dis- crete strata [1]. In trying to relate these strata to observable performative language data structures in or- der to mediate observable language regularities with

theoretical constructs supposedly representing principles underlying these constructs, the methodological

shortcomings of the cognitive linguistic approach are

revealed. It suffers from competence theoretically in- spired idealisations of regularities and theoretical abstractions (like universaJs, grammars, sentences) whose

symbolic notations and formal expressions may be scru- tinized for their syntactic correctness but lack empirically observable and experimentally testable procedures of language representation which are independant from competent speakers' understanding of that

545
language.

3.2 Fuzzy linguistic tiling

Other than cognitive linguistic and competence theoretical mechanisms, we propose cognitive semiotic and

language performative procedures which redefine the

modularity of language understanding as an overlapping covering of computational processes. The classi- cal and coarse three-stage description and modeling of

linguistic regularities will be replaced or rather complemented [11] by a multi-stage covering of semiotic

procedures Mn-i to Mn+k (Fig. 2) which allows for

the definition of more adequate soft categories or in- termediate representations to fit regularities of entities on any level. Their essentially cognitive character will not be borrowed from any predefined strata (and their

puportedly related abstract categories) but is to be derived as a result of their performance, i.e. the ability to transform linearly structured entities (strings) of one

level to multi-dimensional structures of entities (vectors) on another.

This is achieved by analysing the linear or syntagmatic and selective or paradigmatic constraints which

natural language structure imposes on the formation of

(strings of) linguistic entities on whatever level of entity formation. It has been shown and illustrated else- where [15], [9] in some detail, that fuzzy linguistic modeling allows to derive the representational means (e.g. soft categories, continuous gradation, variable granularity, flexible plasticity, dynamic approximation, etc.)

which crisp categories and competence theoretically in- spired idealisations of performative regularities lack. The (numerical) specificity and (procedural) definite- ness of sub-symbolic, distributed formats in entity for- mation appear to provide for higher phenomenological

compatibility and more cognitive adequacy than tra- ditional levels of categorial representation whose symbolic mediation and syntactic correctness could only

formally be scrutinized but not empirically or experimentally be tested [11].

4 Procedural (Re-) Construction

The success of computational language analysis and

generation is based upon adequate structural descriptions of input strings and their semantic interpretations. This was assumed to be made possible by the

correctness of rule based representations of (syntactic

and lexical) knowledge of language and of (referential

and situative) world knowledge on which grammar for- malisms and deductive inferential mechanisms can operate on. Although the essentially static representations of structures in this kind of cognitive modeling of

language processing (based on monotonic logics, symbolic representations, rule-based operations, serial processing, etc.), has produced considerable advances in

formal theory and the consistent development of in- creasingly more complex systems, their idea of repre- senting language entities as essentially crisp categorial

type linguistic entities proves to become increasingly

problematic. As the processing of very large language

corpora (VLLC)7

, has made clear, traditional linguistic

categories do not reduce but increase model complexity when applied to regularities and structures which

quantitative-numerical means may easily identify and

represent. Trying to map such sub-rule regularities and

sub-symbolic structures to inadequate categories will generally result in a large number of borderline cases, variations, and ambiguities which then have to be dealt

with, but could possibly more easily be avoided from

the very start. 4.1 Exploiting constraints

Structural linguistics has given substantial hints8 on how language items come about to be employed in communicative discourse the way they are. They have

identified the fundamental constraints that control the

multi-level combinability and formation of language entities by distinguishing the restrictions on linear ag- gregation of elements (syntagmatics) from restrictions on their selective replacement (paradigmatics). This

distinction allows within any sufficiently large set of

strings of natural language discourse to ascertain syntagmatic regularities of element aggregations on level n whose characteristic patterns form paradigmatic regularities tantamount to their aggregational status on

level n + 1. As has been illustrated above, the dis- tinction of representational levels is tantamount to the

categorial constraints applied when identifying regularities. Fully deterministic if-then rules will result in a

rather coarse three-level hierarchy of categorial description whereas probabilistic or possibilistic dependency

produces a continuous, multi-level covering of distributional representations. Thus, it can be distinguished

sharply between cognitive linguistic and semiotic procedures the computations of the latter transform struc- tured input data according to its immanent regularities to yield new, structural representations emerging

from that computation (as hypothesized by performative linguistics and realized in procedural models of

computationaJ semiotics). The elements of these new

structures are value distributions or vectors of input

entities that depict properties of their structural relat- edness, constituting multi-dimensional (metric) space

structures (semiotic spaces). The elements may also

7The Trier dpa-Corpus for instance comprises the complete textual materials from the so-called basic news real ser- vice of 1990-1993 (720.000 documents) which the Deutschen

Presseagentur (dpa), Hamburg, deserves thanks to have the au- thor provided with for research purposes. After deletion of edit- ing commands the TVier-dpa-Corpus consists of approx. 180 Mio.

(18- 107

) running words (tokens) for which an automatic tagging

and lemmatising tool is under development. It is this corpus which provides the performative data of written language use

for the current (and planned) fuzzy-linguistic projects at the our department.

8 In subscribing to a structuralistic view of natural languages, the distinction of langue-parole and competence-performance in modern linguistics allowes for different levels of language descrip- tion and linguistic analysis. Being able to segment strings of language discourse and to categorize types of linguistic entities, however, is but making analytical use of structural couplings pre- sented by natural language discourse to semiotic systems properly attuned.

546
n- \Fn\) |r„| = |Z»| 100- fa An = m-|Fn _ 1 |) 100 • lC

grams (fact.occurr.) (theor.possib.) percent (act.possib.) percent

iX ox OX ixuu,uuu nn nnn ox i nn nnn

oit SIOil7 OOjUlu QfilX s^ ni ^ 3 10.175 29.791 34,154 25.327 40,174

4 54.470 923.521 5,898 315.425 17^268

5 164.045 28.629.151 0,572 1.688.570 9,715

6 357.632 887.503.681 0,040 5.085.395 7,032

7 634.767 27.512.614.111 0,002 11.086.592 5,725

Size of test-corpus : 3.648.326 (signs) 502.587 (words)

Table 1: Graph-(letter-)combinatorics with (theoretically and faktually) possible and actually occurring types of

n-grams in a subset of the Trier dpa-Korpus

be interpreted as fuzzy sets allowing set theoretical operations be exercised on them that do not require cat- egorial type (crisp) definitions of concept formations.

Computation of letter (morphic) vectors in word space,

derived from n-grams of letters (graphemes) [10] [11] as

well as of word (semic) vectors in semantic space [12]

[13], derived from wordtype correlations of their tokens

in discourse will serve to illustrate the operational flexibility and fine granularity of vector notations [9], [16] to

identify regularities of semiotic meaning constitution in

language performance which traditional linguistic cat- egories fail to represent.

4.2 The word space

The following notations will be used to outline the computational semiotic approach on the morphic level:

n-grams are n-elementary strings of entities. For n >

2 they may be analysed as ordered pairs of adjacent items (letters, graphs, sign-strings, word-strings,

etc.) which are the basis of

abstractions over such items procedurally be determined as soft categorial types (corresponding to characters, graphems, morphems, syllables, words, etc.).

These have been introduced as dispositional dependency structures (DDS) [14] [8] and formally declared

as structured

fuzzy (sub-)sets of multi-dimensional sign inventories

Z

n with n > 1 Xn := {(*, /*„(*»: x G Z

n

) C Z

n x [0, 1] (1)

whose elements' grades of membership are defined by

the membership-function

with Z = {zi, . . . , zm} will yield for each y G Z

n ~ x a

vector

/xn :Zn ->[0,l] (2)

membership-values nn (x) may be computed inductively as the overall tendency of linear chaining of

items in language corpora. For an n-elementary

string x G Z

n be Hn (x) the frequency of x occurring in a corpus. Then, for any

bi-gram x = (y,z) G Z

n ,y G Z

n~ l

, z G Z, the coeffi- cient

Hn (x)

(Hn(v,z1 ),...,nn (y,zm)) T

G Rr (4)

The set of all vectors reflect the morphological struc- ture of the corpus analysed which is the numerically

specified basis for the procedural definition of

soft categories which are defined as a system of fuzzy

sub-sets of observed chaining regularities. They may

be interpreted to represent elastic constraints operating on the language items' chaining tendencies which

structure the corresponding corpus.

The presentation of the development of soft categories

as elastic constraints (operating on different levels) can be simplified by their formal introduction as (n-ary)

fuzzy relations and their corresponding numerical for- mats of transition matrices (of higher orders).

For written German discourse analysed on typesetting level with m discernable types of signs (letters)

and maximum lengths n of strings there are quite a number of theoretically possible (Tab. 1, col. Tn ) crisp

n-ary relations Tn = Z

n

, i.e.

T2 = {(xi.xa)

73 = {(xi,X2 ,X3 )

:ii G Z}

:xi,x2 G Z}

:ii,X2,X3 G Z}

Mn(z) = Hn-1(VY

(3)

Tn -1 = {(Xl, . . . ,In -l) :Xl Xn G Z}

Tn = {(xi,.. .,xn ) :xi,...,x„ G Z}.

Out of these, however, only those have to be computed

which are not only actually possible (col. An ) but

which have indeed been observed to factually occur,

i.e. Fn C F„_i x Z (Tab 1, col. Fn ), i.e. Z =FiC{u :xiGZ}

F2 C{(xi,x2 ) :xi€Fi,x2 eZ}

F3 C {(xi,x2 ,x3 ) :(xi,x2 ) G F2 ,x3 G Z}

Fn -i C{(xi,...,xn _i):(xi,...,x„_ 2 ) G F„_ 2 ,x„_i G Z}

Fn C{(xi,...,xn ) :(xi,...,x„_i) G Fn -i,xn G Z).

The fuzzy relational modeling (Eqns. 3 and 2) shows

that even for higher n only bi-grams have to be traced

547
z

1.000

u

.3342 E.2456

X

.3573 N

.3472

T

.4747 X

.7183

I.2804 X

.2914 T

.5713

R

.2186

A

.2146 A.5609

U

.709J L

.7886

tx

.4694 U

J7J6

U

.2564

T

.2057

N

J 000

M

.1000 G

.1000

Figure 4: Tree representation of procedural soft category Z depicting the hierarchy of graded letter agglomeration

according to decreasing transition tendencies (in 7-grams) of German newspaper texts.

and computed due the (n — l)-ary relations computed

on the previous level of representation. It is this principle of procedural self-similarity of n-ary agglomerative

steps which allows for the trie-like representation [3] of

entities that are labeled (by soft categorial n-relative

letter transitions) and are an outcome of procedural

constraints (over n levels of processing) which produce

a dynamically structured system of fuzzy relations that

depicts the overall transition tendencies of signs. For

the letter Z this structure is given in Fig. 4 illustrating

sub-regularities of morphic word formation.

4.3 The semantic space

Based upon the language entity word, its different

types, and their frequencies of occurrence in natural

language discourse, the fundamental distinction of agglomerative or syntagmatic and selective or paradigmatic relatedness can also be employed to reconstruct a system structure which will serve as base for a procedural model generating tree-like representations of dynamic semantic constraints. As these techniques have

been introduced and elaborated elsewhere [9] [15] [20],

their concise description may suffice here.

The core of the representational formalism can be

characterized as a two-level process of abstractions.

The first (called a-abstraction) on the set of fuzzy

subsets of the vocabulary provides the word-types' us- age regularities or corpus points, the second (called

J-abstraction) on this set of fuzzy subsets of corpus

points provides the corresponding meaning points as a

function of all differences of all usage regularities which

a set of word-types may produce by its word-tokens'

frequencies as observed in pragmatically homogeneous

corpora of natural language texts. The basically descriptive statistics to specify intensities of co-occurring lexical items in texts is centred

around the correlational measure

a(xi,Xj) = T,T=i(hit ~ eit)(hjt - ejt )

(Er=i(^-eit ) 2 Et =i(^-eJt ) 2 )

-1 < a[xi,Xj) < +1

(5)

where en = and e^ = -jj-lt, computed over a

textcorpus K = {kt };t = 1 T having an overall

length L = J2t=i WA < h < L measured by the number of word-tokens per text, and a vocabulary V =

{xn }; n = l,...,i,j,...,N of word-types whose fre- quencies are denoted by Hi = 52t=1 hu; 0 < hu < Hi.

To specify these correlational value distributions'

differences, a measure of similarity (or rather, dissimilarity) is used

8(VuVj) = (^2(a(xi,xn ) -a(xjt xn )) 2

^j ; (6)

0<S(yi , yj ) <2v/S

548
COMPUTE

0.00/1.00

ERFAHR

1.29/.669

DIPLOM

1.67/.341

LEIT

1.53/.546

SUCH

1.78/.346

INDUSTRI

2.05/.222

ELEKTRO

2. 11/. 160

BERUF

2.03/.106

UNTERR

5.60/.060

BITTE

4.06/.042 ORGANIS4.51/.041

WUNSCH

4.88/.028

UNTERN

7.28/.019

STADT

6.57/.014

GEBIET

4.05/.012

VERBAND

5.78/.010

ALLGEM

8.78/.008

ARBEIT

8.33/.006

FAEHIG

1.72/.631

KENN

2.B4/.269

TECHNIK

2.79/.160

SCHULE

2.41/.106

SCHREIB

1.94/.081

STELLE

4.21/.031

PERSON

8.26/.022

AUSGAB

5.87/.017

VERANTW

6.39/.006

VERKEHR

6.75/.005

SYSTEM

2.07/.510

ANBIET

4.47/.01 8

WERB

10.9/.012

BUCH

19.8/.008

Figure 5: DDS-tiee representation of meaning of COMPUTER as assembled for relevant meaning points' distances

(first value) and criterialities (second value) on the basis of the semantic space (S, C) intermediate as computed

from a subcorpus of German newspaper texts (Die Welt, 1964 Berlin Edition).

549
The consecutive application of (Eqns. 7) on input

texts and (Eqns. 9) on the output data of (Eqns. 7)

allows to model the meanings of words as a function of

differences of usage regularities (Fig. 6).

Thus, ctij allows to express pairwise relatedness of

word-types (xi, Xj) G V x V in numerical values ranging

from —1 to +1 by calculating co-occurring word-token

frequencies (Eqn. 5) for pairs of items.

As a fuzzy binary relation, d : V x V -> I can be

conditioned on in G V which yields a crisp mapping

&\xn :V ->C;{yn }=:C (7)

where the tupels ((x„,i,d(n, 1)), . .

. , (xn<N ,d(n,N))}

represent the numerically specified, syntagmatic usage

regularities that have been observed for each word-type

Xi against all other xn G V. a-abstraction over one of

the components in each ordered pair defines

xi (d(i,l),...,d(t,N))=: 1/j GC (8)

Hence, the regularities of usage of any lexical item will be determined by the tupel of its a-values which for all word types can be represented as vector space C.

Figure 6: Fuzzy mapping relations d and 8 between the

structured sets of vocabulary items xn G V, of corpus

points yn G C, and of meaning points zn G 5.

Considering C as representational structure of abstract entities constituted by syntagmatic regularities

of word-token occurrences in pragmaticaliy homogeneous discourse, then the similarities and/or dissimilarities of these entities will capture their corresponding

word-types' paradigmatic regularities calculated by 8

Eqn. 6 serving as second mapping function, As a fuzzy

binary relation, 8 : C x C -> I can be conditioned on

yn G C which again yields a crisp mapping

8 | yn C -> 5; {zn } =: 5 (9)

where the tupels ({yn.iySin,!)),. . . ,(yn, N8{n,N)))

represents the numerically specified paradigmatic

structure that has been derived for each abstract syntagmatic usage regularity j/j against all other yn G C.

The distance values can therefore be abstracted analogous to Eqn. 8, this time, however, over the other of

the components in each ordered pair, thus defining an

element Zj G 5 called meaning point by

yj (S<J) l),...,S(J,N))=:zj eS (10)

Identifying zn G 5 with the numerically specified el- ements of potential paradigms, the set of possible combinations 5x5 may structurally be constrained and

evaluated without (direct or indirect) recourse to any

pre-existent external world. Introducing a EuCLlDian

metric

C:5x5-+/ (11)

the hyperstructure (5, C) or semantic space (SS) is declared constituting the system of meaning points as an

empirically founded and functionally derived representation of a lexically labelled knowledge structure. Weighted numerically as a function of an ele- ment's distance values and its associated node's level and position in the tree, Cr(zi) either is an expression of the head-node's Z{ meaning-dependencies on

the daughter-nodes zn or, inversely, expresses their

meaning-criterialities adding up to an aspect's interpretation determined by that head [15]. To illustrate

the feasibility of the A-operation's generative procedure, the substructure of relevant constraints (related

meaning points) DDS(zi) C (5, Q anchored with the

lexical item Xi, i — COMPUTER is shown in Fig. 4.3.

5 Conclusion

It has been outlined here that the morphic sign or the semantic meaning functions' ranges may be computed and simulated as a result of exactly those (semiotic) procedures by way of which (representational) structures emerge and their (interpreting) actualisation

is produced from observing and analyzing the domain's

possibilistically determined constraints as imposed on

the linear ordering (syntagmatics) and the selective

combination (paradigmatics) of natural language entities (morph-types, word-types) in communicative lan- guage performance. For fuzzy linguistic morhology and

lexical semantics this is tantamount to (re-)present an

entity's semiotic potential (function, meaning] by a

fuzzy distributional pattern of the modelled system's

state rather than a single symbol. The representational

system's dynamic structure modeled by the procedures

outlined is to represent a semiotic cognitive information

processing system's interpretation of its environment.

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1994.

551
Linguistic Geometry: Model Evaluation

Boris Stilman

Department of Computer Science & Engineering

University of Colorado at Denver, Campus Box 109

Denver, CO 80217-3364, USA

bstilman @cse.cudenver.edu

http://www.cudenver.edu/~bstilman/boris.html

Abstract

jfc A Linguistic Geometry introduced in this paper

includes mathematical tools for knowledge representation

and reasoning about multiagent discrete pursuit-evasion

games. These class of games is an adequate mathematical

model for the real world combat operations, particularly, for

the air force and navy problem domains. Linguistic

Geometry relies on the formalization of search heuristics,

which allow one to decompose the game into a hierarchy of

images (subsystems), and thus solve otherwise intractable

problems by reducing the search dramatically. These

hierarchical images extracted in the form of networks of

paths from the expert vision of the problem are formalized

as a hierarchy of formal languages. An example of the

simplified four aircraft pursuit-evasion game is considered.

While the solution of this problem was presented in other

publications in this paper we prove optimality of the

solution. Based on this example we can suggest that for a

certain class of multiagent problems Linguistic Geometry

tools generate optimal solutions.

1 Background

Problems of long and short-range mission simulation,

especially for autonomous navigation, aerospace robot

control, such as unmanned aerial vehicles (UAVs),

aerospace combat operations control, etc., are usually

described mathematically in the form of pursuit-evasion

differential games. An example of such problem is the

problem of real time control of the air combat in which a number of planes (manned or unmanned) equipped with the

so-called countermeasures evade a number of pursuers

equipped with missiles. Another example is the problem

optimal control of UAVs which are in the reconnaissance

flight to locate mobile missile launchers. The actual launch

points are usually detected by the satellite based sensor. The

UAVs use detected launch points to initiate their search,

locate and possibly destroy them. In the real world scenario

the UAV control should be considered together with the air combat when UAVs evade pursuing enemy aircraft. Similar

problems for the development and real time replanning of

the combat scenarios are essential for the Navy and Army

battlefields.

The classic approach based on the conventional theory

This research is supported by Sandia National

Laboratories, Albuquerque, NM, USA.

of Differential Games is insufficient, especially in case of

dynamic, multiagent models (Garcia-Ortiz et al., 1993). It is well known that there exists a small number of differential

games, for which exact analytical solutions are available.

There are a few more for which numerical solutions can be

computed, under rather restrictive conditions, in a reasonable amount of time. It is even worse that each of

these games is one-to-one which is very far from the real world combat scenarios. They are also of the "zero-sum

type" which does not allow a new agent to join the game or

all the agents of both sides to be disengaged. Another

difficulties arise from the requirements of the 3D modeling

and from limitation of the lifetime of the agents.

Following (Rodin, 1988; Shinar, 1990) discrete-event

modeling of complex control systems can be implemented

as a purely interrogative discrete simulation. These

techniques can be based on generating geometrically

meaningful states rather than time increments with due

respect to the timeliness of actions. By discretizing time, a

finite game tree can be obtained. The nodes of the tree represent the states of the game, where the players can

select their controls for a given period of time. It is also

possible to distinguish the respective moves of the two sides

(including simultaneous actions). Thus, the branches of the

tree are the moves in the game space. The pruning of such

tree is the basic task of heuristic search techniques.

Interrogative approach to control problems offers much

faster execution and clearer simulator definition (Lirov et

al., 1988).

In the beginning of 80' s Botvinnik, Stilman, and others

developed one of the most interesting and powerful

heuristic hierarchical models based on semantic networks.

It was successfully applied to scheduling, planning, control,

and computer chess. Application of the developed model to the chess domain was implemented in full as program

PIONEER (Botvinnik, 1984). Similar heuristic model was implemented for power equipment maintenance in a number of computer programs being used for maintenance

scheduling all over the former USSR (Botvinnik et al., 1983; Stilman, 1985, 1993a). The semantic networks were

introduced in (Botvinnik, 1984; Stilman, 1977) in the form

of ideas, plausible discussions, and program

implementations.

2 A Linguistic Geometry: Informal Survey

A formal theory, the Linguistic Geometry - LG

(Stilman, 1992-96), includes the syntactic tools for

552
knowledge representation and reasoning about multiagent

discrete pursuit-evasion games. This approach provides us with an opportunity to transfer formal properties and

constructions from one problem to another and to reuse

tools in a new problem domain. In a sense, it is the

application of the methods of a chess expert to robot control or maintenance scheduling and vice versa. Linguistic Geometry has been developed as a generic

approach to a certain class of complex systems that involves

breaking down a system into dynamic subsystems. We

generate new multi-goal, multi-level system and substitute

it for the original one-goal, one-level system by introducing

intermediate goals and breaking the system down into

subsystems striving to attain these goals.

A set of dynamic subsystems is represented as a hierarchy of formal languages. Various examples of

problems solved employing LG tools have been published

(Stilman, 1992-1996). During the entire history of the

development of LG, we were always concerned about

approximate solutions, almost winning strategies, and how

to measure their accuracy. This was like an axiom: in

general, heuristics do not generate an optimum, and even if they do it is usually hard to prove that this is an optimum.

This paper is devoted to a proof of optimality of the

solution generated by LG algorithms for a class of

multiagent problems. We will show how the heuristic

algorithm generates a solution employing a very small

search tree (Section 8). Then, in Section 9, we will prove

that this solution is optimal.

3 A Class of Problems

A Complex System is the following eight-tuple: < X, P, R

p

, {ON}, v, Sj, S t

, TR>, where

X={xj} is a finite set of points; locations of elements;

P={pj } is a finite set of elements; P = Pj u P2 , Pi * 0, P2 *

0;

Rp(x, y) is a set of binary relations of reachability in X (x

and y e X, p e P);

ON(p)=x, where ON is a partial function of placement from

P into X;

v is a function on P with positive integer values describing

the values of elements. The Complex System searches

the state space that has initial and target states; Sj and S t are the descriptions of the initial and target states

in the language of the first order predicate calculus,

which matches with each relation a certain WellFormed Formula (WFF). Thus, each state from Sj or St

is described by a certain set of WFF of the form

{ON(Pj ) = xk};

TR is a set of operators, TRANSITION(p, x, y), of

transitions of the System from one state to another one. These operators describe the transition in terms of two

lists of WFF (to be removed from and added to the

description of the state), and of WFF of applicability of

the transition. Here, Remove list: ON(p)=x, ON(q)=y;

Add list: ON(p)=y; Applicability list: (ON(p)=x)a

Rp(x,y), where p e Pj and q e P2 or vice versa. The

transitions are carried out with participation of a number of elements p from Pj , P2

. According to the definition of the set P, the elements of

the System are divided into two subsets Pj and P2 . They

might be considered as units moving along the reachable

points. Element p can move from point x to point y if these

points are reachable, i.e., Rp(x, y) holds. The current

location of each element is described by the equation

ON(p)=x. Thus, the description of each state of the System

{ON(pj) = x^} is the set of descriptions of the locations of

elements. The operator TRANSITION(p, x, y) describes the

change of the state of the System caused by the move of the

element p from point x to point y. The element q from point

y must be withdrawn (eliminated) if p and q do not belong

to the same subset (Pj or P2

). The problem of the optimal operation of the System is considered as a search for the optimal sequence of

transitions leading from the initial state of Sj to a target

state of St. To solve this class of problems, we could use formal methods like those in the problem-solving or planning systems (like STRIPS or subsequent). However,

the search would have to be made in a space of a huge

dimension (for nontrivial examples). Thus, in practice, no

solution would be obtained. We devote ourselves to finding a solution of a reformulated problem.

4 A Set of Paths: Language of Trajectories

A trajectory for an element p of P with the beginning at x of X and the end at y of X (x * y) with a length / is the

following formal string of symbols a(\) with points of X as parameters: t 0 = a(x)a(X])...<z(x/), where x/ = y, each

successive point Xj + j is reachable from the previous point

Xp i.e., Rp(xrx i+1 ) holds for i = 0, 1,..., /-I; element p

stands at the point x: ON(p)=x. We denote by tp

(x, y, /) the

set of all trajectories for element p, beginning at x, end at y, and with length /. A shortest trajectory t of t p

(x, y, /) is the trajectory of

the minimum length for the given beginning x, end y, and

element p. A Language of Trajectories Lt H(S) for the Complex

System in a state S is the set of all the trajectories of length

less or equal H. Various properties of this language and

generating grammars were investigated in (Stilman, 1993a).

Examples of distance measurements and trajectory

generation for robotic vehicles are considered in (Stilman,

1993a, 1993c, 1994b).

5 Networks of Paths:

Languages of Trajectory Networks

An example of such network is shown in Fig. 2. The

basic idea behind these networks is as follows. Element p0

should move along the main trajectory a(l)a(2)a(3)a(4)a(5)

to reach the ending point 5 and remove the target (an

opposing element). Naturally, the opposing elements should

try to disturb those motions by controlling the intermediate

553
points of the main trajectory. They should come closer to these points (to the point 4 in Fig. 2) and remove element

p0

after its arrival (at point 4). For this purpose, elements q3

or q2 should move along the trajectories a(6)a(7)a(4) and

a(8)a(9)a(4), respectively, and wait (if necessary) at the

next to last point (7 or 9) for the arrival of element pQ

at point 4. Similarly, element pj of the same side as p0 might

try to disturb the motion of q2 by controlling point 9 along

the trajectory a(13)a(9). It makes sense for the opposing

side to include the trajectory a{\ l)a(12)a(9) of element qj

to prevent this control.

Fig. 2. Network language interpretation.

A trajectory connection of the trajectories tj and t2

l%

the relation C(tj,t2

). It holds if the ending link of the

trajectory tj coincides with an intermediate link of the

trajectory t2

; more precisely, tj is connected with t 2

if among the parameter values P(t2 )={y,y|,...,y/} of

trajectory t 2 there is a value y, = xk

, where

t]=a(x0)a(xj)...a(X]

c ). If tj belongs to a set of trajectories

with the common end-point, then the entire set is said to be

connected with the trajectory t 2

. A formal definition of the Language of Zones (based on the trajectory connection) is given in (Stilman, 1993b,

1993c, 1994a). The Zone corresponding to the trajectory

network in Fig. 2 is represented as follows.

Z=f(p0 ,a(lM2M3)«(4M5),5)f(q3,a(6)a(7)a(4),4)

*(q2, a(8)a(9)a(4), 4) f(Pl , a(13)a(9), 1)

t(q ha(\ l)a(12)a(9), 3) f(p2, a(10)a(12), 1)

A language LZ

H(S) generated by the certain grammar

Gz(Stilman, 1993b, 1993c, 1994a) in a state S of a Complex System is called the Language of Zones.

6 A Complex System of Robotic Vehicles

For the robotic model the set X of the Complex System

(Section 3) represents the operational district, which could

be the area of combat operation, broken into smaller 2D or 3D areas, "points", e.g., in the form of the 2D or 3D grid. P

is the set of robots or autonomous vehicles. It is broken into

two subsets and P2 with opposing interests; Rp(x,y)

represent moving capabilities of various robots for various

problem domains: robot p can move from point x to point y

if Rp(x, y) holds. Analogously, we can represent the rest of

the parameters of the Complex System.

7 2D Model: Problem Statement

Robots with various moving capabilities are shown in Fig. 3. The operational district X is the table 8x8. Robot

W-FIGHTER (White Fighter) standing on h8, can move to any next square (shown by arrows). The other robot BBOMBER (Black Bomber) from h5 can move only straight

ahead, one square at a time, e.g., from h5 to h4, from h4 to h3, etc. Robot B-FIGHTER (Black Fighter) standing on a6, can move to any next square similarly to robot WFIGHTER (shown by arrows). Robot W-BOMBER

standing on c6 is analogous with the robot B-BOMBER; it can move only straight ahead but in reverse direction. Thus,

robot W-FIGHTER on h8 can reach any of the points y e {h7, g7, g8} in on step, i.e., RW-FIGHTER(h8, y) holds,

while W-BOMBER can reach only c8 in one step. Assume

that robots W-FIGHTER and W-BOMBER belong to one

side, while B-FIGHTER and B-BOMBER belong to the

opposing side: W-FIGHTER e P{

, W-BOMBER e Pi, BFIGHTER e P2

, B-BOMBER e P2

. •

*•-#-

-

1

0 abcdefgh

Fig. 3. 2D problem.

Also assume that two more robots, W-TARGET and BTARGET, (unmoving devices or target areas) stand on hi

and c8, respectively. W-TARGET belongs to Pj, while BTARGET e P2

. Each of the BOMBERs can destroy

unmoving TARGET ahead of the course; it also has

powerful weapons capable to destroy opposing FIGHTERs

on the next diagonal squares ahead of the course. For

example W-BOMBER from c6 can destroy opposing

FIGHTERs on b7 and d7. Each of the FIGHTERs is capable to destroy an opposing BOMBER approaching its location, but it is also capable to protect its friendly

BOMBER approaching its prospective location. In the latter case the joint protective power of the combined weapons of

the friendly BOMBER and FIGHTER can protect the

BOMBER from interception. For example, W-FIGHTER

located at d6 can protect W-BOMBER on c6 and c7. The combat considered can be broken into two local

operations. The first operation is as follows: robot BBOMBER should reach point hi to destroy the WTARGET, while W-FIGHTER will try to intercept this

554
motion. The second operation is similar: robot WBOMBER should reach point c8 to destroy the BTARGET, while B -FIGHTER will try to intercept this

motion. After destroying the opposing TARGET the

attacking side is considered a winner of the local operation

and the global battle. The only chance for the opposing side

to avenge is to hit its TARGET on the next time increment

and this way end the battle in a draw. The conditions

considered above give us St, the description of target states of the Complex System. The description of the initial state Sj is obvious and follows from Fig. 3. Assume that motions of the opposing sides alternate

and due to the shortage of resources (which is typical in a

real combat operation) or some other reasons, each side can

not participate in both operations simultaneously. It means

that during the current time interval, in case of White turn,

either W-BOMBER or W-FIGHTER can move. Analogous

condition holds for Black. Of course, it does not mean that

if one side began participating in one of the operations it must complete it. Any time on its turn each side can switch

from one operation to another, e.g., transferring resources

(fuel, weapons, human resources, etc.), and later switch

back.

Both restrictions have been relaxed and completely

eliminated in (Stilman, 1995c, 1995d, 1996b).

It seems that local operations are independent, because

they are located far from each other. Moreover, the

operation of B-BOMBER from h5 looks like

unconditionally winning operation, and, consequently, the

global battle can be easily won by the Black side.

Is there a strategy for the White side to make a draw?

The specific formal question is as follows: Is there an

optimal strategy that provides one of the following?

1. Both BOMBERs hit their targets on subsequent time

increments and stay safe for at least one time

increment.

2. Both BOMBERs are destroyed before they hit their

targets or immediately after that. We answer this question in Sections 8-9. Of course, it can be answered by the direct search employing, for

example, minimax algorithm with alpha-beta cut-offs.

Experiments with the computer programs showed that in order to solve this problem employing conventional

approaches the search tree should include about a million

moves (transitions). Consider how the Hierarchy of

Languages works for the optimal control of this Robotic

System (Fig. 3).

8 2D Model: Search

We generate a string of the Language of Translations

representing it as a conventional search tree (Fig. 5) and

comment on its generation.

First, the Language of Zones in the start state is generated. The targets for attack are determined within the

limited number of steps which is called a horizon. In

general, the value of the horizon is unknown. As a rule, this value can be determined from the experience of solving

specific classes of problems employing Linguistic

Geometry tools. In absence of such experience, first, we

have to consider the value of 1 as a horizon, and solve the

problem within this value. If we still have resources

available, i.e., computer time, memory, etc., we can

increase the horizon by one. After each increase we have to regenerate the entire model. This increase means a new

level of "vigilance" of the model, and, consequently, new

greater need for resources.

Fig. 4. Zones in the initial state. In our case it is easy to show that within the horizons of

1, 2, 3, 4 all the models are "blind" and corresponding

searches do not give a "reasonable" solution. But, again,

after application of each of the consecutive values of the

horizon we will have a solution which can be considered as an approximate solution within the available resources. Thus, let the horizon H of the language Lz(S) is equal to 5,

i.e., the length of main trajectories of all Zones must not

exceed 5 steps. All the Zones generated in the start state are shown in Fig. 4. Zones for the FIGHTERs as attacking

elements are shown in the left diagram, while Zones for

BOMBERs - in the right one. Generation begins with the move 1. c6-c7 in the White

Zone with the target of the highest value and with the

shortest main trajectory. The order of consideration of

Zones and particular trajectories is determined by the

grammar of translations. Next move, 1. ... a6-b7, is in the same Zone along the first negation trajectory. Interception

continues: 2. c7-c8 b7:c8 (Fig. 6, left). Symbol ":" means

the removal of element. Here the grammar cuts this branch

with the value of -1 (as a win of the Black side).

Then, the grammar initiates the backtracking climb.

Each backtracking move is followed by the inspection

procedure, the analysis of the subtree generated in the

process of the earlier search. After the climb up to the

move 1. ... a6-b7, the tree to be analyzed consists of one

branch (of two plies): 2. c7-c8 b7:c8. The inspection

procedure determined that the current minimax value (-1) can be "improved" by the improvement of the exchange on

c8 (in favor of the White side). This can be achieved by

participation of W-FIGHTER from h8, i.e., by generation

and inclusion of the new so-called "control" Zone with

main trajectory from h8 to c8. The set of different Zones

from h8 to c8 (the bundle of Zones) is shown in Fig. 6,

right. The move-ordering procedure picks the subset of

Zones with main trajectories passing g7. These trajectories

partly coincide with the main trajectory of another Zone

attacking the opposing W-BOMBER on h5. The motion

along such trajectories allows to "gain time", i.e., to approach two goals simultaneously.

555
The generation continues: 2. h8-g7 b7:c7. Again, the

procedure of "square rules" cuts the branch, evaluates it as a win of the black side, and the grammar initiates the climb.

Analogously to the previous case, the inspection procedure

determined that the current minimax value (-1) can be

improved by the improvement of the exchange on c7.

Again, this can be achieved by the inclusion of Zone from

h8 to c7. Of course, the best "time-gaining" move in this Zone is 2. h8-g7, but it was already included (as move in the Zone from h8 to c8), and it appeared to be useless. No

other branching at this state is generated.

c7-c8 b7:c8 • -1

c6-c7 a6-b7 Q •

h8-g7 b7:c7

-1

c6-c7 b6:c7

a6-b6

h8-g7

-O -1

b6:c6

g7-f6

0

c6-c7 _b6:c7

h5-h4

--1

f6-e5 b6:c6 0

h4-h3

Q

e5-d6 a Q

b6-b7 „ c6:b7 . O l

c7-c8 m b7:c8

h5-h4 c6-c7 a6-b7

< 9

Q-l

g7-f6 .

b7:c7 ^

g7-f6

a6-b7 Q—c6:b7—W_,1

a6-b6 c6-c7 _ b6:c7

<J • 1

f6-e5 b6:c6 9

h4-h3 f6-e7 o nc

a o

h4-h3 . e5-d6_ n O 0

b6-b7 c6:b7

a6-b5 c6-c7 o

h5-h4 _ c7-c8 O

Fig. 5. Search tree for the robotic system.

The inspection procedure does not find new Zones to improve the current minimax value, and the climb continues

up to the start state. The analysis of the subtree shows that inclusion of Zone from h8 to c8 in the start state can be

useful: the minimax value can be improved. Similarly, the

most promising "time-gaining" move is 1. h8-g7. The Black

side responded 1. ... a6-b6 along the first negation

trajectories a(a6)a(b6)a(c7) (Fig. 4, left). Note, that the

grammar "knows" that in this state trajectory

a(a6)«(b6)a(c7) is active, i.e., B-FIGHTER has enough

time for interception. The following moves are in the same Zone of W-BOMBER: 2. c6-c7 b6:c7. This state is shown

in Fig. 7, left. The "square rule procedure" cuts this branch

and evaluates it as a win of the Black side.

t

0

Fig. 6. States where the control Zone from h8 to c8 was detected

(left) and where it was activated (right).

•

t

0

Fig. 7. States where the control Zone from g7 to c7 was detected

(left) and where it was activated (right).

New climb up to the move 2. ... a6-b6 and execution of

the inspection procedure resulted in the inclusion of the new

control Zone from g7 to c7 in order to improve the

exchange on c7. The set of Zones with different main

trajectories from g7 to c7 is shown in Fig. 7, right. Besides

that, the trajectories from g7 to h4, h3, h2, and hi are shown in the same Fig. 7. These are "potential" intercepting

trajectories. It means that beginning with the second symbol

a(f6),a(g6) or a(h6) these trajectories become intercepting

trajectories (Section 5) in the Zone of B-BOMBER h5.

Speaking informally, from squares f6, g6, and h6 WFIGHTER can intercept B-BOMBER (in case of white

move). The move-ordering procedure picks the subset of

Zones with the main trajectories passing f6. These

trajectories partly coincide with the potential first negation

trajectories. The motion along such trajectories allows to gain time, i.e., to approach two goals simultaneously. Thus,

2. g7-f6. This way proceeding with the search we will

generate the tree that consists of 46 moves.

9 2D Model: PROOF

9. 1 Terminal Sets

Let us prove that the optimal variant of the reduced

search tree shown in Fig. 5 is the optimal solution of this problem. This means that we have to prove that this variant

556
is optimal not only within the reduced search tree but also

within the full search tree, which could be generated as a

result of exhaustive search. (Here and below in this paper

we use bold font to designate various sets.)

The set of goal states for this problem can be broken

into three subsets:

1. Subset W-Win is the set of states where B-BOMBER

is destroyed, and W-BOMBER hit B-TARGET and has

been safe for at least one time increment after that. W-Win = BB-Destroyed n WB-Safe

2. Subset B-Win is the set of states where W-BOMBER

is destroyed, and B-BOMBER hit W-TARGET and has

been safe for at least one time increment after that. B-Win = WB-Destroyed n BB-Safe

3. Subset Draw is the set of states where both BOMBERs

hit their targets on subsequent time increments and

have been safe for at least one time increment or both

BOMBERs are destroyed before this happens. The set of states considered in this definition can be

represented as follows:

Draw = Safe u Destroyed,

where

Destroyed = BB-Destroyed n WB-Destroyed,

Safe = BB-Safe n WB-Safe

A subtree of the full search tree is called optimal if after applying the minimax algorithm on the full tree, the

minimax value of the root node is equal to one of the values

of the terminal nodes of this subtree.

Let A be a set of states. The strategy is called an A

strategy if it is represented by the optimal subtree with the

terminal nodes which represent states from A, only. Thus,

for the W-Win strategy, the corresponding terminal nodes

belong to W-Win only. For the B-Win strategy, the

terminal nodes should belong to B-Win. The Draw

strategy is represented by the optimal subtree with the

terminal nodes from Draw.

To prove that the bold subtree of the search tree shown

in Fig. 5 represents optimal strategy for this problem, and

this strategy gives a draw, we have to prove that it represents a Draw strategy for this problem. This means

that the following Theorem holds:

Theorem

1. The terminal states of the bold subtree belong to the

Draw.

2. The bold subtree is optimal (with respect to the full search tree).

Let us prove statement 1.

9. 2 Terminal Sets Expansion

The terminal states of the bold subtree shown in Fig. 5

belong neither of the subsets considered above despite they

received exact values. Let us expand these state subsets

trying to include the actual terminal states. We shall begin

with the expansion of the set Draw by introducing a new

set DrawExpand. By definition this is the set of states such

that for each of them a Draw strategy exists. Ultimately,

we have to prove that our start state belongs to

DrawExpand.

We will achieve this goal by investigating the structure of this set employing LG tools.

First, we will consider the states where the draw can be

achieved by destroying both BOMBERs (Fig. 8). Let BBIntercept be the set of states where for each of the states there is an optimal strategy for W-FIGHTER to intercept BBOMBER. More formally, if BB-Destroyed is the set of

states where B-BOMBER is destroyed (see definition of the

Draw), then BB-Intercept is the set of states where BBDestroyed strategy exists.

Let WB-Intercept be the set of states where for each

state there is an optimal strategy for B-FIGHTER to intercept the W-BOMBER. More formally, if WBDestroyed is the set of states where W-BOMBER is destroyed (see definition of Draw), then WB-Intercept is the set of states where WB-Destroyed strategy exists.

Intercept

BB-DestroyedjL/ WB-Des/royed

Destroyed

Fig. 8. Expansion of terminal sets Consider the intersection of BB-Intercept and WBIntercept,

Intercept = BB-Intercept n WB-Intercept

i.e., the set of states where the Destroyed strategy exists,

taking into account that

Destroyed = BB-Destroyed n WB-Destroyed.

Obviously, Destroyed <= DrawExpand.

Analogously, we will consider the states where the

draw can be achieved by hitting the TARGETS and saving

both BOMBERs.

Let BB-Protect be the set of states where for each of

the states there is an optimal strategy for B-BOMBER to hit the W-TARGET and stay safe. More formally, if BB-Safe

is the set of states where W-TARGET is hit and BBOMBER is safe (see definition of the Draw), then BBProtect is the set of states where BB-Safe strategy exists.

Let WB-Protect be the set of states where for each

state there is an optimal strategy for W-BOMBER to hit BTARGET and stay safe. More formally, if WB-Safe is the

set of states where B-TARGET is hit and W-BOMBER is safe (see definition of Draw), then WB-Protect is the set of states where WB-Safe strategy exists.

Now, consider the intersection BB-Protect and WBProtect

Protect = BB-Protect n WB-Protect

557
i.e., the set of states where the Safe strategy exists taking

into account that

Safe = BB-Safe n WB-Safe.

Obviously, Protect e DrawExpand. Thus,

Intercept u Protect c DrawExpand.

It should be noted that this is a strict implication. The

existence of the Destroyed strategy for Intercept, the Safe

strategy for Protect, and the Draw strategy for Draw

Expand, and the fact that

Draw = Safe u Destroyed,

does not mean that

DrawExpand = Intercept u Protect.

Basically, we are saying that the expansion of the union of

two sets is not equal to the union of their separate

expansions, i.e., the distribution law does not hold in this case. Indeed, there might be states where the draw can be

achieved by the strategy leading to the states from Safe and

Destroyed simultaneously. This means that at some higher

levels of the subtree representing the optimal strategy we

would not be able to distinguish which kind of draw is being currently pursued, Safe or Destroyed. Consequently,

these states might belong to the direct expansion of the

union

Safe u Destroyed,

which means that

DrawExpand - (Intercept u Protect) * 0.

9. 3 A Structure of Expanded Terminal Sets

Let us describe the structure of the subsets introduced

above employing LG tools. We begin with BB-Intercept.

In our problem the only element that can potentially

intercept and destroy the B-BOMBER is the W-FIGHTER.

Consider the set of all states where W-FIGHTER is in the

Zone of B-BOMBER, and it is the only intercepting

element. First we define the local BB-Interceptg_2

one

- BB-Interceptg_2

one can De described as the set of states of

the following set of Zones, the B-Zone, with one of the

following main trajectories: a(h5)a(h4)a(h3)a(h2)a(hl),

a(h4)a(h3)a(h2)a(hl), a(h3)a(h2)a(hl), c(h2)a(hl).

These Zones are nested in each other. Two subsets of BZone are shown in Fig. 9

0

Fig. 9. The sample Zones describing BB-Intercept and

corresponding gateways.

The multiple locations of W-FIGHTER designate Zone

gateways, the locations through which W-FIGHTER can

enter the Zone employing the shortest path leading from h8.

Once in the Zone (through one of the gateways) in case of

White turn the W-FIGHTER is able to intercept the BBOMBER pursuing it persistently even in the worst case,

i.e., if Black does not skip moves in this Zone. In case of

the Zones considered here the proof of guaranteed

interception is trivial. This follows from the fact that the

trajectory of W-FIGHTER is the 1st negation trajectory

which is by definition of such a length that interception is guaranteed.

We assume that this Zone is considered independently

of the rest of the elements of Complex System which means the interception of B-BOMBER is guaranteed if we

consider the motions within the B-Zone, only. For different

problems and more sophisticated Zones to prove that the

optimal variant of the Zone's skirmish contains interception

of the main element we would have to use theorems on Network Languages (Stilman, 1994). The global BBIntercept is a subset of BB-Interceptg_Zone such that

interception is guaranteed with respect to the entire system.

Consider WB-Intercept. In our problem the only

element that can "potentially" intercept and destroy the WBOMBER is the B-FIGHTER. Consider the set of all states where B-FIGHTER is in the Zone of W-BOMBER, and it is the only intercepting element. First we define the local WBIntercept^Y ^one' ^^"'n^erceP^W-Zone can ^e described

as the of the set the set of states of Zones, the W-Zone, with one of the following main trajectories a(c6)a(c7)a(c8),

fl(c7)fl(c8).

These Zones are nested in each other. This W-Zone is considered independently of the rest of the elements of

Complex System which means the interception of WBOMBER is guaranteed if we consider the motions within

the W-Zone, only. Two subsets of W-Zone are shown in Fig. 10. A subset of Zones shown in Fig. 10 (left) represents

Zones as they are in the initial state. The global WBIntercept is the subset of WB-Intercept^ ^one sucrr>that

i nterception is guaranteed with respect to the entire system.

I I

1 Fig. 10. Sample Zones describing WB-Intercept.

Consider BB-Protect. In our problem the only element

that can "potentially" protect the B-BOMBER, if necessary,

and let it hit the W-TARGET is the B-FIGHTER. But the

B-FIGHTER is involyed in WB-Intercept and cannot leave

it. Thus, the B-BOMBER can accomplish its mission safely

without protection only if it does not need one. This means

that the Zone of B-BOMBER, the B-Zone, should be free

of intercepting elements. Consider the set of all the spates

where the B-BOMBER is alone without any 1st negation

trajectories. This is our local BB-Protectg ^one"

558
The global BB-Protect is the subset of BB-Protectg_

Zone suc^ l ^at Protecti°n i s guaranteed with respect to the

entire system.

Finally, let us consider WB-Protect. In our problem

the only element that can potentially protect W-BOMBER

is the W-FIGHTER. Consider the set of all states where WFIGHTER is in the Zone of W-BOMBER. Three possible

locations, the gateways, are shown in Fig. 12 (left). The

gateways are shown as multiple locations of the WFIGHTER, the locations through which the W-FIGHTER

can enter the Zone employing the shortest path leading from

h8. Once in the Zone (through one of the gateways) the WFIGHTER is able to protect the W-BOMBER from being

intercepted. The set of all the states where W-BOMBER is protected by W-FIGHTER from d6, d7, or d8 is included

into WB-Protectw. Zone. Of course, another way to protect

W-BOMBER is for B-FIGHTER to leave this Zone. One of

such states is shown in Fig. 12 (right). Once leaving the

Zone B-FIGHTER would not have chance to enter it and

intercept the W-BOMBER. All such states are also included

into the WB-Protectw_ Zone. The global WB-Protect is the

subset of WB-Protectw_ Zone such that protection is

guaranteed with respect to the entire system.

BB-Protectg_Zone and BB-InterceptBZone represent

different subsets of states of the same set, the B-Zone.

B-Zone = BB-InterceptB. Zone u BB-ProtectB. Zone

A similar statement is true for the Zone of W-BOMBER,

the W-Zone:

W-Zone =WB-InterceptW Zone u WB-ProtectWZone.

4-

Fig. 12. The sample Zones describing WB-Protect.

9. 4 Terminal States of the Subtree

Now we can evaluate all the terminal states of the bold

subtree (Fig. 5, 13). In particular, the terminal states of the following variants:

1 . h8-g7 a6-b6; 2. g7-f6 b6:c6.

1. h8-g7 a6-b6; 2. g7-f6 h5-h4; 3. f6-e5 b6:c6.

1. h8-g7 h5-h4; 2. g7-f6 a6-b6; 3. f6-e5 b6:c6.

belong to global

Intercept = BB-Intercept n WB-Intercept.

The terminal states of the following variants:

1. h8-g7 a6-b6; 2. g7-f6 h5-h4; 3. f6-e5 h4-h3;

4. e5-d6.

1. h8-g7 h5-h4; 2. g7-f6 a6-b6; 3. f6-e5 h4-h3;

4. e5-d6.

1. h8-g7 h5-h4; 2. g7-f6 h4-h3; 3. f6-e7.

belong to global

Protect = BB-Protect n WB-Protect.

Now we conclude that all the terminal states of the bold

subtree belong to Intercept u Protect c DrawExpand.

Thus, statement 1 . is proved.

full search

tree

Destroyed Safe

Fig. 13. Terminal states of the bold subtree. Let us prove statement 2. of the Theorem that the bold

subtree is optimal (with respect to the full search tree).

9. 5 A Zone Status Change

As we know from the above

B-Zone = BB-InterceptB. Zone u BB-ProtectB. Zone, W-Zone = WB-InterceptW Zone u WB-ProtectWZone.

If we consider Zones independently of the rest of the

elements following definition the expanded terminal sets, every Zone can not switch from one terminal set to another.

For example, if the current state of the B-Zone belongs to BB-Intercept and we continue search following the optimal

branch, the B-Zone will never switch to the state from BBProtect, it will reach BB-Destroyed.

4- —< -0

Fig. 14. Interpretation of B-Zone and W-Zone

and their status change.

The initial state of the B-Zone belongs to BB-ProtectB_

Zone'

f°r tne W-Zone it belongs to WB-InterceptWZone.

In the real search every element can move including the

elements that are currently outside the Zone. This might

559
cause the Zone to switch from one status to another. In

particular, if W-FIGHTER comes to one of the gateways f6,

g6, or h6 the current state of the B-Zone will switch from

the initial BB-ProtectB. Zone (Fig. 14, left) to B B -

Interceptg^one (Fig. 14, right).

If no other elements can interfere and White has

enough time for interception, then the new status cannot be

changed, this state actually belongs to the global BBIntercept. In case of the W-Zone, if the W-FIGHTER

arrives at one of the gateways e6, e7, or e8, this Zone

switches from the initial local WB-Intercept-yy ^one (Fig.

14, left) to the global WB-Protect (Fig. 14, right). This

status is final because there are no elements in the Complex

System to interfere.

9. 6 A Description of Winning Strategies

Now, following the definition of terminal sets we can

give a complete description of possible W-Win, B-Win,

and Draw strategies. Obviously, in reality, only one of

them takes place.

1. W-Win strategy:

W-Win = BB-Destroyed n WB-Safe

The W-Win strategy, if it exists, is to change status of both

W-Zone and B-Zone from the initial, WB-Interceptw_

Zone anc* ^^"^ro* ec^B-Zone' t0 ^e gl orj> al WB-Protect

and BB-Intercept, respectively.

To do that we have to move W-FIGHTER from h8 into

both Zones as fast as possible. The presence of WFIGHTER in these Zones immediately converts their status into WB-Protect and BB-Intercept, respectively, and this status stays permanently in the search tree until Zones

shrink to the states where the W-BOMBER is destroyed,

BB-Destroyed state for the W-Zone, or B-TARGET is hit,

BB-Safe state for the B-Zone.

2. B-Win strategy:

B-Win = WB-Destroyed n BB-Safe

The B-Win strategy, if it exists, is to keep the status of both

W-Zone and B-Zone unchanged as they are in the initial state, WB-Intercept^y ^one anc* ^ B-Zone'

respectively, which means to reach the state where the

status is global, and belongs to WB-Intercept and j$BProtect.

To do that Black has to destroy W-BOMBER and hit the B-TARGET as fast as possible by shrinking these Zones

down to WB-Destroyed and BB-Safe states.

3. Draw strategy:

Draw = Safe u Destroyed

where Destroyed = BB-Destroyed n WB-Destroyed,

Safe = BB-Safe n WB-Safe

Thus, the Draw strategy, if it exists, is to change the status of at least one of the Zones, W-Zone or B-Zone, from the

initial, WB-Intercept^y_Zone and BB-Protectg ^one' to

the global WB-Protect and BB-Intercept, respectively.

To do that we have to move W-FIGHTER from h8 into

both Zones as fast as possible. The presence of WFIGHTER in these Zones immediately converts their status

into WB-Protect and BB-Intercept, respectively, and this status stays permanently in the search tree until Zones

shrink to the states where the W-BOMBER is destroyed,

BB-Destroyed state for the W-Zone, or B-TARGET is hit,

BB-Safe state for the B-Zone.

9. 7 A Strategy at the Start State

Obviously, we do not know in advance which strategy

actually takes place in this problem. Let us consider the

start state for this problem and assume that White follows

W-Win strategy while. Black follows B-Win strategy.

Following W-Win strategy W-FIGHTER should get into

both Zones, the W-Zone and the B-Zone. The distance

from the start state (which belongs to BB-Protectg_Zone) to

the set of states BB-Intercept can be measured as the

length of the shortest trajectory of the W-FIGHTER from

h8 to one of the B-Zone gateways. It is equal to 2 steps.

Analogously, the distance from the start state to the WBProtect is equal to the length of the shortest trajectory of

the W-FIGHTER from h8 to one of the W-Zone gateways.

It is equal to 4 steps. The total is 6. However, the distance

from the initial state to the intersection BB-Intercept n

WB-Protect can be reduced down to 4 steps employing the

time-gaining trajectory through g7 and f6 (Fig. 15, left). Also, this is the only way to approach both sets simultaneously. Thus, following the W-Win strategy WFIGHTER moves along the shortest trajectory passing

through g7: 1. h8-g7. Next, the Black, following the B-Win

strategy, should keep the status of W-Zone and B-Zone

unchanged as it is in the start state, WB-Interceptyy_2;

one and BB-Protectg ^one' resPecli vely- This means that Black

should shrink these Zones by moving either the BFIGHTER from a6 along one of the intercepting trajectories

to intercept the W-BOMBER within W-Zone (Fig. 15,

right) or the B-BOMBER from h5 along the main trajectory

a(h5)a(4)a(h3)a(h2)fl(hl) to hit the W-TARGET within the

B-Zone

Fig. 15. The distance measurement to BB-Intercept n WBProtect from the start state (left) and from the state generated after 1 . h8-g7 a6-b6 (right).

If Black is involved in the W-Zone and responds, e.g.,

1. ... a6-b6, the W-FIGHTER should continue motion along

the same shortest trajectory (Fig. 15, right): 2. g7-f6

following the W-Win strategy.

Alternatively, if Black is involved in the B-Zone and

moves 1. ... h5-h4, the B-Zone shrinks (Fig. 16). The new

set of the shortest time-gaining trajectories from g7 through

560
f6 to both W-Zone and B-Zone is shown in Fig. 16. Thus,

following W-Win strategy the response of the White must

be the same: 2. g7-f6. Consequently, the white moves (in

bold) 1. h8-g7 X-X; 2. g7-f6 are universal, i.e., they must

be included in the optimal subtree, the W-Win strategy.

These moves even do not depend of the black first move, 1

.

... X-X, whatever it is, even if Black follows the B-Win

strategy.

is

Fig. 16. The distance measurement from the state after

1. h8-g7 h5-h4 to BB-Intercept n WB-Protect.

According to this strategy the Black should keep the status of the W-Zone and B-Zone unchanged. Let us investigate

three possible alternatives for the Black response 2. ... Y-Y,

a), b), and c).

a) If Black is involved in the W-Zone on the first and

second moves, i.e., if 1. h8-g7 X-X; 2. g7-f6 Y-Y and

X-X and Y-Y are both in the W-Zone, then WFIGHTER at f6 is immediately getting into B-Zone

while the B-Zone itself is changing its status to BBInterceptg_2 0ne - This happens because of the

alternation of turns: while making the Y-Y move,

Black spends one time increment in the W-Zone that

gives an extra time increment to the White in the BZone, the white turn, and the intercepting trajectories

from f6 become the 1st negation trajectories (Fig. 15,

right) - see Section 5. Thus, if White follows the WWin strategy and Black - the B-Win strategy, we

ended up with the change of the status of one of the

Zones, the B-Zone, and this status will stay unchanged

for the rest of the search which means that both WBOMBER and W-FIGHTER will be eventually

destroyed. The state after 2. ...Y-Y is a terminal state that belongs to global WB-Intercept n BB-Intercept.

Consequently, we actually implemented the Draw

strategy,

Draw = Safe u Destroyed

for the case of

Destroyed = BB-Destroyed n WB-Destroyed.

The corresponding branches are included in the bold

subtree (Fig. 5)

b) If Black is involved in the B-Zone on the first and

second moves, i.e. X-X and Y-Y are 1. ... h5-h4 and 2.

... h4-h3, respectively, then the W-FIGHTER should

move towards W-Zone gateways d6, d7, and d8 along

the most time-gaining trajectory through e7 (Fig. 16):

3. f6-e7. This is the terminal state which belongs to

WB-Protect n BB-Protect, i.e., we changed status the

W-Zone. As in the case a), if White follows the WWin strategy and Black - the B-Win strategy, we end

up with the Draw strategy

Draw = Safe u Destroyed

for the case of

Safe = BB-Safe n WB-Safe.

The corresponding branches are included in the bold

subtree (Fig. 5).

c) If Black is involved in the W-Zone on the first move 1

.

... X-X and switches to B-Zone on the second move 2.

... h5-h4, then W-FIGHTER should continue moving

along the shortest time-gaining trajectory 3. f6-e5.

There are two alternatives.

If Black switches back to the W-Zone, then WFIGHTER at e5 is immediately getting into B-Zone

while the B-Zone itself is changing its status to BBIntercept. The situation in this state is similar to the case a): this is the terminal state which belongs to WB-Intercept n BB-Intercept, i.e., we changed

status the B-Zone. Thus, if White follow the W-Win

strategy and Black follow the B-Win strategy,

again, we end up with the Draw strategy

Draw = Safe u Destroyed

for the case of

Destroyed = BB-Destroyed n WB-Destroyed.

Otherwise, if Black continues in the B-Zone 3. ... h4-

h3, then W-FIGHTER at e5 should immediately get

into the W-Zone through d6 gateway while the WZone itself is changing its status to WB-Protect. The

situation in this state is similar to the case b): this is the terminal state which belongs to WB-Protect n

BB-Protect, i.e., we changed status the W-Zone.

Thus, finally, if White follows the W-Win strategy

and Black follows the B-Win strategy, we end up

with the Draw strategy,

Draw - Safe u Destroyed

for the case of

Safe = BB-Protect n WB-Protect.

In case c) the corresponding branches are included in the bold subtree (Fig. 5).

We proved that the only optimal strategy possible at the

start state is the Draw strategy. The bold subtree is an implementation of this strategy. Thus, statement 2. and

Theorem are proved.

10. Discussion

Theoretical results received employing other

approaches and experiments with programs utilizing these

approaches show that the search tree generated in order to solve the problem considered in Sections 7-9 consists of

more than a MILLION moves with the branching factor

(Nilsson, 1980) around 9. In contrast, the Linguistic

Geometry tools allowed to find the optimal solution

generating the search tree which consists of about 46

moves, with the branching factor 1.5. The low branching

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factor indicates that the algorithm is goal-oriented.

The novelty of this paper is in the proof of optimality

of the solution. It appears that LG tools are able to distinguish and significantly expand the "islands of

potential stability", the sets of states (positions) with

known value in the "ocean of all states of unknown

value" to be searched employing conventional brute force

approach. In our case we expanded the small islands of

terminal states, Destroyed and Safe, into the sets Intercept

and Protect. Moreover, I envision the LG search like an "optimal navigation of the ship" from the start state through the ocean of unknown states to the expanded

islands employing the shortest path. In our problem this was reflected as a motion of the W-FIGHTER towards WZone and B-Zone simultaneously. It is likely that similar

ideas work in all the LG examples. This will be a subject of our further research. If this is the case we can speculate that LG tools allow for a very efficient break of the state space

that drives the search directly to the optimum.

It is easy to predict that the power of the Linguistic

Geometry goes beyond the domain of aerospace games. The

definition of Complex System (see Section 3) is generic

enough to cover a variety of different problem domains.

The core component of this definition is the triple X, P, and

Rp. Thus, looking at the new problem domain we have to

define X, the finite set of points - locations of elements. In different real world problems we can consider X as an

operational district of the underwater or on-surface combat,

or even as a set of orbits. The set of elements P, the mobile

units, can be the set of submarines, tanks, squadrons, or

satellites with various moving capabilities. Indeed, these

capabilities are represented with the binary relations Rp,

which is exactly the place for introduction of the variable

speed, the gravity impact, the engine impulse duration, etc. A dramatic search reduction achieved in the serial and

concurrent games (Stilman, 1994-1996) allowed us to

initiate the development of the prototype of the system for

optimal planning and control of the real world aerospace

combat with participation of air fighters, satellites, and

unmanned aerial vehicles - UAVs. This work is currently

under way at Phillips Lab, Kirtland AFB, NM, USA. Also,

a prototype of the generic Hierarchy of Formal Grammars,

a test-bed of the multiagent architecture for various

applications, is planned to be developed at Sandia National

Laboratories, Albuquerque, NM.

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XXI ISAS'96: CONFERENCE REVIEW

ISAS' 96: Conference Review

prepared by A. Meystel, K. Bellman, D. Filev, J. Goguen, C. Hewitt, C. Joslyn,

L. Kohout, M. Kokar, C. Landauer, I. Muchnik, L. Perlovsky, V. Stefanuk, Y. Yufuk

This Review is based upon reports submitted by the workshop's chairmen. The complete

set of reports for ISAS'96 and ISAS'97 will be combined into a white paper entitled "Semiotics:

Its Significance and Perspective". This will be distributed among the organizations involved in

monitoring and funding the research and educational activities in the US.

1. SYNTACTICS OF INTELLIGENT SYSTEMS:

THE KINDS OF LOGIC AVAILABLE

• The main theme of the Syntactics workshop was how to deal with infinite/complex structures

in modeling systems within the framework of logic.

• The main reason to look at systems from the semiotic perspective is the COMPLEXITY of

both real and artificial systems (cf. the comment by Professor Sebeok on the existence of

infinite number of possible signs generated by a finite number of primitives, e.g., genetics,

immune system.)

• The workshop focused on the available tools. The pervasive question was, how can we

feasibly use these tools?

• We generally concluded that various system engineering techniques combined within a framework of logic lead to significant improvement, by using semiotic tools for handle the

complexity of both real and artificial large-scale systems.

• The following approaches have been discussed:

1. Moshe Vardi stated that in order to establish communication between (or among) agents,

they need common (shared) knowledge. Establishing such a knowledge base within the

logical framework may lead to an infinite number of message exchanges. M.Vardi

proposed two approaches to establish such common knowledge in a finite number of

steps.

2. Wlodek Zadrozny proposed an algebra to represent ten categories of signs in Peirce's

classification. Although, it seems that this algebra should be an infinite one. Zadrozny

showed that it can be finite.

3. Mieczyslaw Kokar showed how to combine many methods from system engineering

within a logical framework to improve system performance. The main point is that the

issues of complexity of logical tools can be remedied by such system engineering tools.

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The question is how far can we go with developing such heterogeneous systems into

autonomous ones.

4. Sergey Petrov analyzed languages that are "poor" in the sense that some deductions in

these languages are not possible. His question was if we can decide whether or not there are finite axiomatization for some languages.

5. Jery Tomasik showed that classical results of Rasiowa and Keisler can be used to

construct models of the world based upon inputs from sensors. Sensors can provide

infinite number of input combinations. Tomasik showed how to address infinity within

the framework of model theory.

6. William Farmer showed how an existing interactive theorem proving system (IMPS)

changes contexts via "theory interpretation." IMPS keeps a base of "little theories"

which are examined by the system for their use in a specific problem.

2. MULTIRESOLUTIONAL CONCEPTS AND METHODOLOGIES

• Multiresolutional approach is a powerful tool of complexity reduction. Introduction of

multiple resolution levels has actually determined the architecture of all existing systems

including architecture of the brain. Multiresolutional methods can be applied to the

following: time, space, descriptions and relations of entities, events, problems and plans.

• Advantages: MR-methods allow us to represent the world at many levels of resolution due to

the power of generalization algorithms. This creates a limitation on analysis from above and

from below. Total complexity of computations can be drastically reduced.

• Engineering methodologies of MR-methods include the following: object oriented

programming, fractals, MR-signal processing, Wavelets, multirate control systems,

multiscale and multigranular representations, and others

• Standards of modules and interfaces can be created based upon properly introducing

definitions for granularity, zone of indistinguishability, scope, scale, and cost-functional of

interest.

• Disadvantages: rigidness of hierarchy seems to be the most pervasive complaint.

Frequently, this complaint is linked with neglect of the overall computational advantages.

However, we should work on developing the trade-off methodologies and analysis of the

existing restrictions. One of the ways to avoid the disadvantages is by adding adaptation

capabilities to MR-systems

Participants of the workshop concentrated on three major themes: MR-representation, MRprocedures, and MR-models.

I. MR-REPRESENTATION IN DIFFERENT DOMAINS

The development of this is based on studying multiple results of practical applications for

examples in various areas.

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Example 1: In all problems of image processing, we deal with a hierarchy of pixels - units of

granularity ("atoms" or indistinguishability zones for the images.) Three levels of a pixel

characterization:

• a component of the pixel (a successor or a "child") which can be determined for the

pixel at the lower resolution level (its "father")

• the level quantitative characterization of the image elementary components (the

diameter of the indistinguishability zone.)

• the description of the inclusion relationships among the pixel and pixel's children.

Example 2: Recognition systems for the handwriting:

• the indistinguishability zones or elementary entities are irregular structures; MRmethod allows for the existence of irregular elements of contour images and models

of trajectories. Example (graphs of interactions within large molecules in

biochemistry)

Example 3. Elementary units of different levels of resolution in various domains:

• atoms in physics

• scale units in cartography

• Lyapunov ball control theory

• radical groups of molecular structures in chemistry

• sub-molecules (amino acids in proteins) in chemistry

• hyper units (monomer proteins in multi-domain proteins) in chemistry

• coalitions of protein reloaded with particular biological functions in biochemistry

• irregular elementary entities (iee) from the low level of resolution are integrated in a

trajectories between iee for higher resolution in handwriting analysis

Example 4. Hidden Markov process in the area of signal processing

1st Level of resolution: elements should be vectors parameters for observed component

of the hidden process and names of its hidden states:

2nd Level - elements of structural parameters of the teams of the first level elements.

Example 5. Complex systems analysis: elementary entity at a level characteristic for the objectoriented analysis.

II. MR-PROCEDURES

1. Analysis at a single level:

• aggregation and decomposition of elements for a single level of resolution

• characterization of their uniqueness

• determining their relationship

2. Analysis of the complete structure of the multiresolutional architecture:

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• a priori design of the multiresolutional architecture which delivers the minimum of

computational complexity to a system

• development of mathematical models for systems belonging to a particular resolution

level

• development of relations among mathematical models of the same system at different

levels of resolution

• switch on and off procedures of the single level analysis

• generalization of results of the single level analysis

• evaluation of correlations of these results with final outcome and designing the final

rules to get the outcome

• changing the current multiresolution structure of analysis and iterating it in a new

form

• solution recognition (global stop rule)

• cooperation with a human assistant

III Mathematical Models of Multiresolutional Systems (MRS)

• generators of hierarchical structures

• hierarchical structure algebra

• dynamic models onto hierarchical structures (new automata theory and)

• Methods of Simulation of MRS

• Mathematical criteria for:

* aggregation - decomposition of assemblies

* abstraction - specialization of features

* generalization - insinuation of features

IV. Efficiency Evaluation for the MRS Approach:

Systematic collection is required of the benefits and shortcomings of MRS used for Intelligent

System Development.

3. FUZZY LOGIC AND THE MECHANISMS OF GENERALIZATION

• The main goal of this workshop is to work toward establishing a link between some methods

and concepts from semiotics and fuzzy logic and system fields.

• Fuzzy logic methodology enriches the logic field with methods for handling linguistic

statements in terms of linguistic variables introduced by Zadeh. Fuzzy logic can also deal

with approximation and incompleteness issues.

• Semiotics, on the other hand, provides methods to deal with the meaning of linguistic and

logic statements, paying attention to their syntax, semantics, and pragmatics.

• Deeper integration of these two approaches with the aim to strengthen their applicability in

design, analysis, and use of Intelligent Systems is required.

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• The following issues are discussed:

1. Granularity, Generalization, and Meaning

• The main goal of semiosis is the interpretation of signs and symbols which can be understood

also as recognition of their meaning. The meaning interpretation unit is a very complicated

one. The meaning of something can be different, depending on the scale which is used for

representation. This makes the notion of granularity a very important one. Levels of

granularity are also referred to as levels of resolution, and they are closely related to

generalization.

• Granularity was introduced into fuzzy sets by Zadeh. In his interpretation, "granulation

involves a decomposition of the whole into parts, and conversely organization involves an

integration of the parts into whole."

• Intelligent systems deal with interpreting information communicated in symbolic form.

Interpretation and meaning depend on context. Any dynamic process considered with all its

details and the details of its interaction with its environment cannot be properly understood

unless the details, which are irrelevant within a particular context, are removed. But, the

information on which such an interpretation could be based will often be incomplete. With

incompleteness, there may be more that one interpretation. Indeed, a large family of

interpretations may be possible, which may conflict. Fuzzy sets, relations and logic can play

an important role here. They allow us, through the theory of potentiality (or virtual plurality),

to deal with the whole family of virtual outcomes and also to measure the degree of conflict

of individual members of some possible family of outcomes produced by the meta-process of

interpretation.

2. The Role of Granulation as and for Generalization in Cognition and Action

• Generalization plays an essential role in the human cognitive and symbolic activities. But, it is equally important in artificial intelligent systems. Generalization works as a filter of

information. During the process of generalization, the relevant pieces of information are included in the final outcome, and the irrelevant ones are excluded. Information to be

included and/or excluded depends on the contexts and information processing goals.

• Architectures of intelligent systems employ the concept of granularity. The examples of

multigranular (multiscale, multiresolutional) systems are known in robotics and

manufacturing (e.g. NIST-RCS.)

• Some advanced intelligent system architectures mimic biological models of the human brain.

Such architectures operate as the coupling of functional hierarchical (or heterarchical) levels

and loops. Each level operates at a different level of generality, abstracting many different

features from the world with which the architecture interacts. Granulation and generalization

are closely interlinked.

• In computer science, the problem of structuring systems is commonly addressed via the

Object-Oriented (00) approach. This is a set of important design techniques for structuring

systems in a hierarchical fashion. There are, however, some conceptual and practical

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problems with 00 programming when dealing with highly dynamic systems. Like data base

entities, objects are usually assumed to be given. This, however, hypothesizes hierarchies,

with no accounting for the dynamic binding of levels of individual objects.

• To deal with this problem we have to examine the essence of inheritance and investigate how

the objects emerge. The phenomenon of object emergence is linked with formation of crisp

and fuzzy classes (generalized groupings). Indeed, we deal with the logical theory of fuzzy

relations, which can be used to expose the inadequacy of currently used logical structure of

crisp (i.e. non-fuzzy objects). Logically, generalization is a process in which relevant

properties (intentional specifications) of objects are grouped. We create new objects —

structures (given as such by extension) by new intentional specification. So 00 approach

can be viewed as a very special case of the pragmatics of groupings, a kind of granulation.

• The issues of granulation in their full generality, however, must be adequately addressed by

employing fuzzy classes, the semantics of which can be provided by many-valued logic

based relations with special meta-properties. The issues of adequate multi-context semantics

that is needed for the Intelligent Systems require this generality. The 00 approach has to be

extended.

3. The Issues of Incompleteness of Information

• In Intelligent Systems we must deal with incompleteness of information. This is the domain

where fuzzy sets can help. The context in which objects operate determines the goals and

meaning of the objects and their generalization hierarchical structure. Without the semiotic

notions, this aspect cannot be satisfactorily handled. We need a synergistic development of

fuzzy and semiotic methodologies. One of the classic notions of semiotics is the triadic

structure of the object, its notation and its interpretation.

• The concept of the semiotic triplet of subdisciplines syntax ~ semantics — pragmatics was

coined by Morris in the late 1930s. That is where the duality Semiotics — Mathematics

comes in. In logical methods of proofs, only the "form," the syntactic composition plays the

role. In the logical theory of models, the primary goal is to interpret syntax in semantic

meta-structures and the pragmatics of emergence of either of these. Here, the fuzzy logic can

play an important role since we have the duality of linguistic descriptors and fuzzy structures

to which these descriptors apply. We also have the duality symbolic vs. numerical that are both addressed by what Zadeh called "the fuzzy logic in wider sense."

• When forming grouping/generalizations/classes on the basis of their properties, one

substantial difficulty appears. One needs to generalize on the basis of relevant properties of

objects that are present as well as on the basis of the relevance of the absence some

properties. This leads to entirely new problems. This problem which is closely connected

with semisets and vagueness is determined by problem of lack of properties and by the

locality of negation. These are closely connected with semisets.

Conclusions

1. There are potential links between fuzzy logic and semiotics that should be further

explored. Granularity is essential to develop any complex system. To deal with granularity in

intelligent systems, the potential of fuzzy logic to approximate should be explored. Fuzzy

relations provide high-level specification language and computational tool to form granules that

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subsume equivalences, similarities, and hierarchies of objects. Semiotic concepts and methods

can deal with naming, contexts, dynamics of symbolic communication, and the pragmatics of

naming and actions.

2. There is sufficient background to conduct further discussion and formulating an action

plan to deal with the topic of fuzzy logic, granulation an generalization. This should be pursued

via internet. The chair of this workshop is willing to mediate further discussion and produce a document summarizing these.

4. INTELLIGENCE OF RECOGNITION

• The question of intelligence of algorithms and neural networks is being answered today

in at least five ways. First, mathematical models are developed for psychological

experimental data on perceptual and behavioral phenomena. Second, mathematical tools are developed for modeling human perceptual functions such as vision. Third, mathematical

models are developed for those functions of intellect, which are associated with the internal

working or mind, such as meaning and consciousness. Fourth, mathematical modeling of

brain organization is used to search the understanding of mind. Fifth, mathematical and

metaphysical analysis of intelligence is being undertaken. This establishes connections

among various mathematical concepts and their relationships to metaphysical concepts of

intelligence. These directions are discussed in the workshop.

• Recognition of objects in images and in temporal sequences of images is one of the most

important recognition paradigms. A lot of information is accumulated about biological vision

systems and a lot of effort has been invested into developing mathematical tools and

engineering applications. Although we are still far from completing a general mathematical

theory of vision, significant progress has been achieved in a number of applications and a number of useful mathematical tools has been developed. One thing is clear. A vision

system is not a homogeneous one, but it combines a large number of diverse subsystems. An

image recognition process is generally separated into several steps or stages, both

mathematically and implemented in hardware. A mathematical and engineering reason for

this is to reduce an overwhelming complexity of the problem.

• Biological systems also are known to process visual information in stages, and many of

our mathematical tools are patterned after biological vision systems. A typical breakdown

includes detection of the region of interest, segmentation of the objects, enhancement, and

recognition of the object class and pose. • The following approaches have been discussed:

1. Professor D. Casasent discusses developing new powerful and efficient tools including

new distortion-invariant filters, biologically-inspired Gabor wavelet filter techniques,

hierarchical processing, new representation methods. Casasent also discusses mathematical

methods of combining (fusing) these tools into a unified vision system. Practically important

problems that still await their solutions include distortion-invariant detection and recognition;

efficiently processing of time-sequential image frames; feature selection; and combining

results from several algorithms, and efficient representation techniques.

2. Nonlinearity of human visual processing was recognized in the last century by scientists

including Helmholtz. He found, for example, that a perceived color of an object depends on

the average color of the visual field. But, nonlinear mathematical methods that are suitable

for modeling vision and perception in general did not exist in the last century. These

methods appeared only recently. Resurgence of neural network research in 1980s was due to

emergence of powerful nonlinear neural paradigms. A neural network field can be viewed as a development of nonlinear mathematical tools suitable for modeling the mind. But, many of

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the currently popular neural network paradigms are limited in the basic type of a non-linear

operation performed by a neuron to a nonlinear transformation applied to a weighted sum of

neuronal input signals. Professor G. Ritter discusses a new morphological type of neural

networks, which explores a different type of nonlinearity at the basic neuronal level. In

morphological neurons, multiplication and addition are replaced with additions and max/min

operations.

3. The concept of morphological neural network has roots in image algebra and in an

alternative hypothesis concerning properties of biological neurons. Hierarchical organization

is another important aspect of intelligent systems. Specific mathematical techniques

addressing hierarchical organization has received appreciable attention in the development of

wavelet transforms. Professor H. Szu combines wavelet and neural network techniques to

develop adaptive wavelet transforms. He discusses organization of human perceptual

systems, the mathematical technique, hardware implementations and applications.

4. The roles of learning vs. a priori knowledge is one of the central and most controversial

problems in the development of intelligent algorithms. While symbolic AI emphasizes

apriority of knowledge acquisition, most pattern recognition and neural network techniques

emphasize adaptivity of intelligent systems. In Prof. Minsky's words, "...theory of

representation was developed independent from theory of learning." Model-based

recognition paradigm has been developed to combine apriority of models with adaptivity of

model parameters. Prof. E. Manolakos discusses model-based joint segmentation and

recognition of objects. He develops this technique in the framework of parameter estimation

of hierarchical mixture densities. The maximum a posteriori (MAP) estimate of the

parameters is computed by the application of a modified version of the Expectation

Maximization algorithm (EM with regularizing constraints applied to multiple level

hierarchies). The approach is flexible. It allows for non-stationary pixel statistics, different

noise models, translation and scale invariant and is well suited for recognition of partially

occluded objects. An unsolved problem that should be addressed in the future is the

development and use of complicated structural models.

5. Most recognition algorithms and neural networks can be viewed as seeking a minimum

value of an appropriate objective function during recognition or learning phases. In which

way is maximization of the goal function related to intelligence? In which way does it lead

to an appropriate generalization from the past to future data? What type of intelligence could

be attributed to different types of goal functions? Professor Golden addresses these questions

by establishing a relationship of the goal function maximization to other mathematical

concepts of intelligence. Specifically, he shows that the goal maximization is equivalent to

an inference procedure on a relational system comprised of the data, event space, and relation

operation. This theory is useful for practical applications, as well as for providing insights in

formulating the sense in which a given recognition or neural network algorithm is making

intelligent inferences. Future research should address establishing relationships between

neural networks and the statistical pattern recognition framework, construction of statistical

tests for testing hypotheses about the parameters of such networks, and statistical goodnessof-fit tests for deciding if a given neural network algorithm best fits a given statistical

environment.

6. Genetic mechanisms have a fundamental similarity with the human Mind in producing

adaptive systems based on a priori structures. This property of genetic mechanisms is used to

develop improved recognition techniques in genetic algorithms (GA) and genetic

programming (GP) techniques. Mr. W. Punch describes recognition techniques based on

genetic mechanisms to find the properties of data that are important for data classification

within large datasets. He combines GA with the K-nearest neighbor (knn) algorithm. The

GA determines weights for each feature based on known examples so as to optimize knnclassification based on a linear combination of features. He also describes an extension of

this work to GP. The combined GP-knn technique optimizes data classification by selecting

linear combinations of features, as well as determines functional relationships among the

features. He also compares the effectiveness of GA and GP for biological problems.

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What can be learned about intelligent recognition architectures from brain studies, and

what type of brain organization is suggested by combining current psychological and

neurophysiological data with mathematical models of neural networks? Prof. D. Levine

discusses the mutual interaction between these fields and the neural models of the prefrontal

function. The prefrontal cortex performs the "executive" function within the brain. It is roughly

divided into three interacting parts: affective guidance of responses, linkage among working

memories, and forming behavioral schemata. Neural models of each part is discussed within a

theoretical framework.

5. INTELLIGENCE OF LEARNING AND EVOLUTION

• What is intelligent about our recognition and learning algorithms, neural networks, and

intelligent system architectures? Which aspects of intelligence we understand and know how

to use in our algorithms and neural networks, and which do we not? Does individual

learning resemble evolution of species, and what are the mechanisms of learning and

evolution? These were the questions posed to a group of distinguished scientists and leaders

in the fields of recognition, intelligent systems, neural networks and learning who attended

this workshop.

• The response was tremendous; the discussion of intelligence in our mathematical models

of intellect seems to be timely. It is a matter of both hot debates and quickly emerging

results. Both aspects of the problem are going to be discussed in the papers presented at the

workshop: questions that are posed and questions that are being answered. Mathematical

definitions and models of various aspects of intelligence are the most fascinating and exciting

developments in the history of science. • The question of intelligence of algorithms and neural networks is being answered today

in at least five ways. First, mathematical models are developed to explain psychological

experimental data on perceptual and behavioral phenomena. Second, mathematical tools are developed to simulate human perceptual functions, such as vision function. Third,

mathematical models are developed for some of the functions of intellect. Functions of

interest are associated with the internal working or mind, such as emergence of meaning and

consciousness. Fourth, mathematical modeling of brain organization is used to search the

understanding of mind. Fifth, mathematical and metaphysical analysis of intelligence is being

undertaken. This establishes connections among various mathematical concepts, and their

relationships to metaphysical concepts of intelligence. • The following directions have been discussed at the workshop:

1. Prof. W. Freeman is concerned with the mechanisms of brains by which they construct

meanings within themselves and representations of meanings by motor actions in order to

communicate meanings to other brains: "A machine can only 'know' the inferences it constructs from the sensory consequences of its own actions into the world." This translates

into the construction of machine intelligence by combining robotics and automata theory, in

the context of operations that are modeled on brain dynamics and implemented by noisestabilized chaotic attractors for pattern generation and recognition. Simulations of animal and

human performance in the laboratory are done by constructing sets of differential equations

to represent cortical dynamics in pattern recognition and solving them with digital

computers, with the emphasis on multisensory convergence in the combining of olfactory,

visual, auditory, and tactile inputs. Future work is now being directed toward controlling

chaotic dynamics by regulating the sensitivity to initial conditions, and also toward solving

the equations with analog hardware, taking advantage of the speed and simplicity.

Thereafter, the self-organizing machines will have increasing control of their own input

through effectors by means of which they can control their sensors, and through internal

575
feedback by which they can regulate the attractor landscapes in their sensory/perceptual

processors for pattern recognition. Prof. W. Freeman calls the prototype of such devices

modeled on animal brains a "meaning machine" that can make representations of its internal

states to its trainer.

2. How do categories and symbolic structures develop? How is it possible to adapt and

learn, while using a priori knowledge? What does constitute a priori knowledge? What are the differences and similarities between real-time adaptation and long-term learning of

categories and complicated symbolic structures? Current research directions in this

important area are represented in three talks in the workshop. Prof. R. Sun introduces a hybrid model for bottom-up skill learning in a situated way. The hybrid model combines

connectionist, symbolic, and reinforcement learning within an integrated architecture. In this

model, agents continuously learn from ongoing experience. Both procedural skills and highlevel knowledge are acquired through interaction with the world. The idea is that learning

can be bottom-up: concepts and generic knowledge can be extracted on-line during

interaction with the world, from low-level knowledge that is acquired through exploring the

world. This idea is different from traditional top-learning learning theories in cognitive

science, in which generic knowledge is given and then compiled into procedural skills

through practice.

3. Prof. L. Goldfarb describes a fundamentally new mathematical model for inductive

learning—the evolving transformation system. Although the model unifies the classical vector

space and symbolic models, it suggests that the latter two classical paradigms are fundamentally inadequate to model inductive learning processes, which Goldfarb believes to

be the central cognitive processes. The model also suggests, a simple formal mechanism

responsible for the emergence of "fuzziness."

4. Dr. L. Perlovsky introduces modeling field theory, a model-based neural network whose

learning is based on fuzzy a priori models. The modeling field theory combines a priori

knowledge with adaptation and with structural learning. He also discusses interrelationships

between various mathematical concepts of learning and their surprisingly close connections

to metaphysical concepts of mind developed by philosophers since Plato and Aristotle.

Future research directions include the development of multi-level hierarchical models of

recognition in the context of recognition-behavior loop.

5. Prof. L. Levitin presents a dynamic model explaining Zipfs Law. Zipfs Law is a remarkable relationship observed in many complex systems of surprisingly different nature,

including population growth and linguistics. For example, in linguistics the frequencies of

the word usage are approximately inversely proportional to their ranks in decreasing

frequency order. Levitin discusses an evolutionary model of emergent classification of

objects into classes corresponding to concepts and denoted by words. The model leads to the

emergence of a hierarchical two-tier structure with "superclasses" - groups of classes with

almost equal populations. This model suggests that both, evolution and learning are based on

a-priori concepts, while creating new concepts (new species and genera) is a relatively rare process. Future research directions include determination of the parameters of the model for

various systems, for example of linguistic models of discourse in various areas and analysis

of the relationships of model parameters and meanings of texts.

6. Does evolution of species resemble the process of individual learning? Is it random or

directed? What is the role of a priori information coded in DNA in determining the direction

of evolution and what mechanisms this process may employ? Prof. M. Lane discusses intergene variations of the minimal energy required for mutations and their roles in directing the

evolution process.

7. What is intelligence? Is it possible to act intelligently without being intelligent? This

question has been amplified in Searle's "Chinese Room" mental experiment. The nature of

intelligence is addressed by Prof. L. Kanal. He discusses which type of intelligence can be

now simulated by machines and what is truly "being intelligent?"

576
6. THEORETICAL ISSUES OF APPLIED SEMIOTICS

• The main theme of the workshop on Theoretical Issues of Applied Semiotics was to

further advance the existing theoretical premises as far applying semiotic methodology is

concerned.

• Logical and philosophical component in the theory of semiotics should incorporate the

relevant results obtained in the areas of mathematical logic since Peirce, as well as the views

of the philosophers of our time. • Application of semiotics is now focused upon a number of large complex ("open")

systems. • The following issues were discussed in detail:

1. In this paper, V. Stefanuk showed an example of, how ideas of semiotic sign expressed in

the form of Frege triangular diagram, including the concept of similarity and

multiresolutional approach, may be merged together to give a complete solution to the

problem of discovery of good representation in a collection of problems, which are born by a famous AI puzzle.

2. Jan C.A. van der Lubbe showed the deduction, induction, and abduction were essentially

the same logical procedures based on the Peircean notion of abduction. The difference

emerges when based upon one (or a few) observations, we abductively construct a predicted

value and the rule, which justifies the inference. In a pattern recognition task, he proposed to

dynamically compare automatic abductive reasoning of the system constantly compare with

the classification given by an export. This will greatly increase classification power.

3. Deborah Vakas Duong described a multi-agent simulation of a sample market of

economics. The simulation showed an emergence of right decision on agent "investment"

(trade or production). It also showed an emergence of a money-like property in this society.

The author stressed that unlike general situation in AI, the social type models exhibit the

emergence of new signs and their change in the process of social activity.

4. Leonid Perlovsky used a thoughtful survey of the greatest thinkers including Aristotle,

Goedel, Turing, Penrose to show the genetics of complexity for a numbers of algorithms or

predicates. Also, Perlovsky showed that the exponential combinatorial phenomena may be

overcome by fuzzy logic and a multilevel artificial brain organization.

5. Mark F. Sulcoski, et. al., showed how various semiotic techniques should be combined

together in a practical, military oriented problem. The authors stressed practical importance

of Q-analyses, which allows representation of numerical relational data in a geometrical

space.

6. Joseph Goguen described a mathematical framework which operates with signs in a programming domain. He showed that to describe the whole complexity of signs

construction and transformation of one science system to another, one needs a model using

the theory of categories. The presentation gave the ground for discussion at the end of the

workshop. Another topic of an interesting discussion in which almost all people present in

the workshop participated was understanding of the intrinsic complexity of signs in

semiotics, their emergence, and their use in practical AI systems.

7. SEMIOTIC ISSUES IN BIOLOGY, CONSTRUCTED SYSTEMS, AND

SEMANTIC FOUNDATIONS OF MATHEMATICS

The following issues were discussed at a group of workshops dedicated to biology, constructed

Systems and semantic foundations:

1. How do we develop systems engineering that can create and use 'specifications' for

its human and artificial components? Alternatives were proposed:

577
• Creating likable systems

• Next stage in notions of human-machine interfaces and human factors is required

2. The software analogy was useful for allowing cognitive science to get beyond strict

American behaviorism. But can we invent better models for brain function that

"manipulating representations" or "processing information?" We could then invent/learn new

mechanisms/analogies for constructed systems.

3. How do we integrate, mesh different representations of the 'same' system?

• New ideas to understand the act of 'translation'

• For combining multiple sources of information/decisions

• Levels of representation

4. In many discussions, there was a strange tone of an incipient vitalism combined with an

impoverished model of animal reasoning capabilities (the worse of both worlds). One way to

examine these prejudices is to examine the concept of "reducibility". We started with the

argument that intentionality is irreducible.

5. Intelligent living systems are emotional, social, and physically grounded. What role do each

of these loosely described qualities play in what we call intelligence?

• Social, negotiated context, meanings, and understanding

• Emotional, caring, instructional, attentive systems

• Physically embodied, situated systems.

How do we represent/model?

6. Phantom limbs, "Neuralmatrix," skill acquisition, e.g. "knowing" how much you know, how

well you know it, irreversible quality of knowing (can 'forget' but one doesn't return to the

same ignorance) challenge present models of what it is to know and how it is represented.

7. We want to improve our models and mathematics with improved semantics. We want to

create "shareable" semantics for combined human and automated systems. How do we need

to alter current formal definitions of semantics?

In all topics above, mathematical issues were also addressed. This is the list of mathematical

issues relevant to the themes of discussion:

• Integration Architecture in Constructed complex systems

• System Engineering (Processes and Artifacts)& Validation

• Better Semantic Models of Systems, Behavior, and Time

• Computational Semiotics

• Treatment of Symbols by Computing Systems "Linguistic" Styles of Processing

• Cooperative Autonomous Systems (not control)

• Models of self and others in context

• Mathematical Methods for Self-Reference, Context and Situation

• Model Integration

• Mathematical Proof, Formality, Deductive Processes.

578
8. SYNERGISM/INTEGRATION

1 . The papers on attributes/classification for elements of fuzzy sets correlated very well with the

paper by Y. Yufik who set forth a classification of neuron sets. Y. Yufik also noted some

phenomena that resulted from or affected the human under stress.

2. P. Kugler's paper was seminal because he identified a major area of research in semiotics that

has been obscured by the heavy attention to models, logic control and computation. This is

because none of the above can be done without measuring the world and for open systems the

major measurement component is the human.

3. S. Vahie/B. Ziegler's and N. Farhat/E. D. M. Hernandez'es papers were very important

because they convey a promise that we may be able to create neural laboratories to establish new

measurement systems.

4. Finally F. Brown's paper on logistics is promising; it demonstrates a computing language

capable of handling massive amounts of information.

5. George Klir is on the path to integrating probabilistic, plausibilistic, and possibilistic into a reasoning integrated system.

6. D. Casasent's paper contained excellent results in the area of images fusion,

7. P. Werbos' paper on neural nets, semiotics and brain-like intelligence presented an issue of the

existing duality: computational vs logic.

8. The triangular representation of triadicity was not used by C. Pierce. He used a prong

r Burch showed that the prong was not reducible. The triangle A can be broken into a dyad < a > and should be avoided to prevent a wrong conclusion.

8. L. Domatova's paper on combining models presented an application of information fusion.

9. OPERATORS MODELING AS A SEMIOTIC PARADIGM

The workshop has addressed the following issues:

1. Methods for designing on-line learning systems for acquiring diagnostic knowledge from

manufacturing systems.

2. Methods for estimation of unmeasurable process variables by using fuzzy models of human

operators.

3. Synthesis of supervised control strategies based on spatial aggregation theory.

4. Computational tools for diagnostic hypothesis generation.

579
The conference ISAS'96 had a several plenary lectures and a tutorial.

The plenary lectures:

• J. Albus, A Roadmap to the Future ofIntelligent Systems

• P. Antsaklis, Hybrid Control of Intelligent Systems

• T. A. Sebeok, Evolution ofSemiosis and the Origin ofLanguages

• L. Zadeh, The Key Role of Information Granularity in Human Intellige,

and the materials of tutorial:

• A. Meystel, Applied Semiotics: Theory, Methodology, Toolbox

will be used for preparation of the White Paper.

580
AUTHOR'S INDEX
I
AUTHOR'S INDEX

A

Agre, Gennady 199

Albus, James S 3,75,151,531

Alexander, Jr., John R 239

Anlide, Cesar 137

Anshakov, Oleg M 87

B

Baev, K.V 499

Baggenstoss, Paul M 124

Balasubramanian, S 225

Barber, K. Suzanne 263

Barnhart, Craig M 175

Bellman, Kirstie L 205,422,567

Brito, A.E 157

Brooks, Bernard G 275

Brown, Frank M 103, 252

Burke, Louis 130

C

Cabrera, S.D 157

Casasent, David 57

Cassandras, Cristos G 173

Chandler, Jerry L.R 211

Chen, Chun-Hung 185, 191

Chikrii, Arkadii A 443

Chikrii, Greta Ts 450

Cotsaftis, Michel 517

D

Dai,Liyi 185, 191

Davidson, Ian 269

DeClaris, N 75

Dmitriev, Victor 333

Dolmatova, Ludmila M 66

Donohue, Karen 185

E

Egbers, Emile 37

Ephremides, Anthony 175

F

Ferregut, Carlos 378

Fetzer, James H 493

Filev, D 565

Finn, Victor K 87, 92

Fogel, David 233

Fogel, Lawrence J 59

Frank, Rob 395

Freeman, Walter J 421, 487

G

George, Mary J 378

Goguen, J 567

Goldfarb, Lev Ill

Golovina, E. Yu 50

Gomide, Fernando 477

Gudwin, Ricardo 477

Gutierrez, Jose M , 378

H

Hewitt, L 567

Ho, Yu-Chi 12

Hofkirchner, Wolfgang 248

Hunt, Ken 391

Hutchison, William R 287

7

Joslyn, C 567

Juliano, Benjoe A 313

K

Kadtke, Kim 349

Kamensky, Victor 130

Kim, Eunjin 31

Klimontovich, Yu. L 14, 364

Kohout, Ladislav J 31, 567

Koshelev, M 383

Kosheleva, O. M 158

Kreinovich, Vladik 145, 378, 383

Kulikowski, Casimir 130

Kuttner, Lars 281

Kuznetsov, S.0 96

L

Lacaze, Alberto 75,117,151,477,523

Landauer, Christopher 44, 205, 422, 567

Lau, T.W.Edward 181

Lefebvre, Vladimir A 455

Lenhart, Suzanne 349

Lewis, David 395

Linkins. Dennis 395

M

Maturana, F 225

McKee, Gerard T 275

Merrell, Floyd 339

Meunier, Jean-Guy 325

Meystel, Alexander M 75,117,1 45,151,

477,505,523,567

Mikheyenkova, M.A 6

583
Modell, Mark 130

Muchnik, Ilya 567

N

Nault, Georges 325

Neves, Jose 137

Niloff, Jonathan 130

Nishina, Hiroyuki 471

Norrie, D.H 225

O

Osegueda, Roberto 378

Oussedik, Sofiane 325

P

Panayiotou, Christos G 173

Pentek, Aron 349

Perlovsky, Leonid 1 295,307,319,332,567

Protopopescu, Vladimir 349

Prueitt, Paul S 407

R

Rialle, Vincent 325

Rieger, Burghard B 331, 541

Ritter, Gerhard X 60

5

Samad, Tariq 511

Schenker, Paul S 275

Schnelmer. Tim 252

Sebeok, Thomas A 354

Skvortsov, Dmitry P 87

Smirnov, Evgueni 137

Souza, Claisse Sieckenius de 461

Starks, S.A 145

Stefanuk, V 567

Stilman, Boris 552

Stoica, Adrian 244

Stopp, Andreas 281

Streit, Roy, L 301

Sussner, Peter 60

T

Tadeusz, Szuba 401

Tarassov, Valery 162

Tasoluk, C 478

Tsoukalas, Lefteri H 434

U

Uhrig, Robert E 434

Ulieru, Mihaela 217

V

Vagin, V.N 50

van der Lubbe, Jan C.A 37

W

Wang, Paul 415

Weiss, Joe 395

Werbos, Paul J 66, 82

Wieselthier, Jeffery E 175

Y

Yucesan, Enver 185

Yufuk, Y 567

Z

Zabezhailo, M.I 100

Zadeh, Lotfi A 26

584
LATE SUBMISSIONS

I
!

f
A Neural Iconizer for

Semiotic Processors

H. John Caulfield

Northeast Photosciences, Inc.

4626 Delina Road

Cornersville, TN 37047

jcaulfield@vallnetcom

Abstract

A PCNN (Pulse Coupled Neural

Network) is shown to meet all of the

necessary needs of a semiotic processor for

mining sensor data Into symbols or icons.

At the same time, the single solution to the

most long-lasting and vexing philosophical

problems in cognitive science. These

analyses lead us to speculate that human

symbolic processes which we designed

computers to emulate (eg. Boole's Laws of

Thought) were almost certainly based on

an earlier human facility-semiotic

processing.

I. Introduction

Semiotic processors deal with

concepts and symbols not numbers.

Humans are inherently symbol makers,

while modern, Turing-equivalent, digital

computers are inherently symbol

manipulators.

Dick's age is twice Jane's. Dick's

age (in years) plus Jane's age (in years) is

36 years. To solve this in a computer, we

say

symbol f Let x symbolize Dick's age,

generation I Let y symbolize Jane's age.

x = 2y

x + y-36

Thus /-"^symbol

manipulation

x = 24^

y = 12,

Symbol

J Thus Dick is 24 years old. Interpretation I Jane is 12 years old.

The total system (symbolization - symbol manipulation - resymbolization)

is semiotic. The symbol manipulation Is not

To date most if not all semiotic

processors have incorporated humans to

symbolize resymbolize. Because that

incorporation is universal, it passes

unnoticed most of the time.

If we are to have fully-seniiotic

processors, we must replace

WORLD SENSOR

SYMBOL

MANIPULATOR

HUMAN

BRAIN

DISPLAY

SYMBOL

HUMAN

BRAIN

HY

WORLD

SYMBOL

SENSOR SYMBOLIZER

SYMBOL

MANIPULATOR

SYMBOLBZK

I. (OPTION 1)

DISPLAY HUMAN

BRAIN

587

The full semiotic processor has no need of

a human brain but allows human optional

monitoring.

My goal here Is to discuss

symbolizers for semiotic processors.

II. SYMBOLIZER REQUIREMENTS

The symbohzer converts sensed

data about the natural and the

technological world and produces from

those data symbols for further

manipulation. It is urgent to understand

tius powerful functionality of the human

brain before we try to build it

Remark l. The number of situations

we may encounter is finite but effectivelyinfinite in the sense that look up tables are

precluded in principle. Typical 2D spatial

patterns contain of the order of a million

bytes per scene. Suppose we have a million

pixels each with 8 bits (128 shades of gray)
dynamic range. The number of possible

scenes is then

N=(12&)10000<*°

This meets any definition of effectivelyinfinite.

Remark 2. The goal of

symbolization is to convert any of the N

scenes to one of M(«N) symbols.

Symbolization is compressive. It involves a

deliberate and irreversible loss of

information to facilitate manipulation. For

instance, Mmay be small enough to permit

look up tables. As a human example,

consider all of the scenes we might label

with the word "dog." That set of scenes is

itself effectively infinite, yet very young,

small humans do it routinely and ineranth/.

Remark 3. There are no God-given

categories in the world. Categories,

up till now, have been human semiotic

creations. The world and the images on

our retinas simply are. Humans group

them. We can make "self-organizing*'

computers to group items according to

human-selected criteria. But if we selected

different criteria, the groups would be

different Consider the figures below.

We may decide to put them in two groups

(a human decision). Does it make sense to

ask how many groups are "really there"?

Two obvious groupings are triangles/circles

and MgfsmalL The latter categories are

valid but fuzzy. Is there a radius

F such that circles with r>r are

big and circles with T<T^ are small?

Who chooses T^ ? But mere are many

other valid groupings, for example, figures

588

with centroids above and below the

centroid of the whole. All of these are

"right" answers in the sense mat they

reduce N=12 figures to M=2 groups. None

is more right than the other.

Remark 4. Utility is one way to

select which symbolization or

categorization to choose. At least for the

immediate future, artificial semiotic

processors will be special purpose

machines. Groupings reflecting our a

priori knowledge of the data and problem

domains will be preferred.

Remark S. Symbols must

emphasize the relevant and ignore the

irrelevant - once we decide what is and is

not relevant If we want to classify the

figures above as big or small, we want to

ignore their shapes.

Remark & Combining Remarks 4

and 5, we seek "robust" symbolization in

some problem-dependent sense.

Ill Philosophy of Symbolization

Semiotics can not avoid philosophy.

As seen from Sec. I, semiotic computers

invade a domain previously forbidden to

"mere" symbol -manipulating computers.

Just analyzing the meaning and

implications of the previous sentence is a

major undertaking.

Consider, for example, the strong

version of Church's thesis (almost

universally believed and neither proved nor

disproved). Roughly, it says this: "Any

physical process can be modeled to

arbitrary accuracy with any digital

computer having sufficient memory." But

all digital computers are just symbol

manipulators. Given an input (data and

instructions which are human concepts not

distinguishable by the computer), there is a

unique output Every computer is

equivalent to a giant look up table.

Symbols (to the computer) do not "mean"

anything. That is the symbols do not refer

to anything other than themselves. 1

means 1. 0 means 0. Nothing in a

computer means anything or is a symbol
for anything. Yet we humans mean things

by our symbols and yet our brains are

computers and subject to computer

manipulation. Where does meaning enter

the world?

In "cognitive science," the question

of symbohzation is itself symbolized by

Searle's story of "The Chinese Room " To

most people outside that field, this story

seems to add nothing to their

understanding. The ultimate problem is

mis: "If computers mean nothing and if die

human brain is a computer, then the human

brain means nothing. But humans do mean

things. So how can these contradictions be

accounted for?** Searle and others seem to

feel mat a true semiotic computer (one that

symbolizes things and associates symbols in

such a way that each "means" the other)

cannot be based on current digital

computers. We humans are somehow more

man "just computers." My reply is

computers can be far more man Searle

envisions "mere computers" to be. Enter

the semiotic computer.

IV. A Spatial Pattern Symbolizer

If the useful grouping Is spatial

patterns (e.g. triangles and circles) or can

be represented that way (e.g. a wavelet

transform of a spoken word displayed as a

2D pattern), then "robustness" may be

taken as the ability to ignore mild

distortions, afffne transformations, and the

like.

If, in addition, we do not want to

train the symbolizer, because we do not

know what patterns it may encounter, then

we want a symbolizer which is contractive,

(M«N) for all possible input patterns.

We have experimented with PCNNs

(Pulse Coupled Neural Networks) as symbolizers. We find that they are

contractive for all inputs and extremely

robust

Invented by Eckhorn in Germany to

emulate the observed behavior of the

neurons in the visual cortex of cats, PCNN

efforts in America have been led by J. -

Johnson at the U.S. Army Missile

Command. A special issue of IEEE

Transactions on Neural Networks edited

by Dr. Johnson will be published in 1998.

For now, however, the best way to learn

more and to use PCNNs is to access the

web page of the author's previous

employer (www.caos.aamu). The code is

down loadable or usable there.

The bask idea is that each input

pixel drives its own neuron. Hie neuron is

a classic integrate-fire-reset oscillator, so

neurons driven by brighter pixels pulse

more frequently. Then we perturb the

situation by allowing each neuron to

influence its neighbors. Regions of moreor-Iess equal brightness begin to

synchronize - beat together. What results

is a complex 3D pattern (2D in space, ID in

time). As we seek information

compression, this seems to carry us in the

wrong direction.

Suppose, however, we integrate that

3D signal over 2D space leaving only a ID

time signal. Experimentally, that time

signal has a periodic strange attractor - a

pattern which more-or-less repeats

indefinitely but never exactly repeats. We

call a single period of that time signal the

"icon** of the input pattern. Million bit

patterns lead to very simple, e.g. 10-

position icons. You can see and create

icons at the previously-noted URL.

Another experimental property of

the icons is that they are quite robust

against mild distortions and afnne

transformations nearly always. Yet there

are sharp boundaries between attractor

basin. Consider our running example of

triangles and squares. We can distort each

into the other, e.g.

^

0> O • •

There is a very sharp dividing line between

the attractor basin to which the "perfect"

triangle belongs and the attractor basin to
which the "perfect77 circle belongs.

Note that the PCNN has attractors

for triangles and circles even though it was

not trained to recognize them. If we want

to recognize triangles and circles, all we

have to do is recognize (name) the

attractors.

In the Jewish/Christian/Muslim

story ofAdam (man) and Eve (woman),

God's first assignment to mem was to

name the animals. In PCNN terms, this

may say much about the origin of language

- a deep, unsolved problem which bears

strongly on the uniqueness of humans.

Suppose our DNA directs the formation of

sight and sound PCNNs. We may come to

recognize the sight of a dog and the sound

of the word "dog " If these two are linked

by Hebbian association, I am willing to

assert that the sight comes to mean the

sound and conversely.

It is true that a computer

contemplating its own digits means

nothing. But a special computer - a set of

PCNNs - interacting with the world can

come to mean things. The system - not just

its CPU - and the world come to "ground"

meanings in reality. Thus yet another

fundamental problem can be solved in

principle. The PCNN may be the missing

link between the subsymbohc neural

networks which we know are the basis for

all brain functions and the symbolic

processes you are using at this moment

The subsymbolic PCNN in interaction with

the world produces a "starting set

7

* of

symbols on the basis of which symbolic

processing arises.

iconizer) for a semiotic processor.

(3) PCNNs offer a sing]

plausible answer to many deep, longstanding philosophical questions.

V. Conclusions

I hope mat I have convinced you

that the following propositions are true,

(1) For events symbolizable

in terms of spatial relationships, a PCNN is

an iconizer which exhibits all of the a priori

desirable features of an iconizer.

(2) Therefore, the PCNN

offers a useful front end (symbolizer, r
Information Needs And Its Impact On Medicine

Thomas Hankins, CNM, CP.

Douglas Frank, B.S., C.C.P.

Thomas Williams, M.D., Ph.D.

Until recently with the exception of the area of research, the

only information that was pertinent to hospitals and practicioners was

"How much do we bill and how much do we get paid". Now the

medical community is quickly finding itself faced with a new threat of

a double edged sword which many are not prepared to take on. That

threat is Managed Care. Managed Care has and is turning the practice

of medicine inside out. How does informational needs find itself smack

in the middle of this battle? Every good general knows that the more

you know about your enemy the better off you are and you never let

your enemy know more about yourself than you know. That's where

the informational needs fit in.

For years practicioners were always busy taking care of their

patients the best way they could and usually having little more

information on the patients than the patients medical record. While

on the other hand the insurance carriers were busy keeping actuarial

tables and different bits of information on large populations of patients.

The insurance companies learned early on that 'Those who control

the information.... control the game".

This paper will explore the tremendous impact information

needs is having not only on the practice of medicine but its survival as

well.

591

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Proceedings of the 1997 International Conference on Intelligent Systems and Semiotics: A

Learning Perspective

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Meystel, A.M.

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Manufacturing Engineering Laboratory, Intelligent Systems Division Div. 823

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This publication is the Proceedings of the International Conference ISAS'97, Intelligent Systems and

Semiotics: A Learning Perspective. The Conference will be held at the National Institute of Standards

and Technology, Gaithersburg, Md. from Sept. 22-25, 1997. The Proceedings include a list of

participants, foreword, and the 83 papers written for presentation at the conference.

The papers are arranged within 20 themes: (I) Plenary Lectures (ll)World Representations, (III) Neural

Networks-Models, (IV)Logical Calculi for Semiosis, (V) Learning, (VI) Multiresolutional Semiosis, (VII)

Ordinal Optimization, (VIII)Architectures, (IX) Evolution, (X)Autonomy, (XI)Likelihood, Mixture, and

Symbols, (XII) Semiotics of Texts and Images, (XIII)Multidisciplinary Applications of Semiotics,

(XlV)Semiotics of Open Systems, (XV) Soft Modeling, (XVI)Games and Reflexion,

(XVII)Computational Approaches in Semiotics, (XVIII) Brain, Mentality, and Meaning, (XlV)Semiotics

in Intelligent Control, (XX) ISAS'96 Previously Unpublished papers

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brain; decision making; information; intelligent control; intelligent sys

learning; manufacturing; open systems; optimization; planning; prag

symbol grounding; syntactics;

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terns; knowledge representation;

matics; semantics; semiotics;

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