1A GENERAL FRAMEWORK FOR MODELING OF SYNTHESIS- INTEGRATION OF THEORIES OF SYNTHESIS -Hideaki Takeda

Masaharu Yoshioka

Tetsuo Tomiyama

National Institute of Informatics

Hokkaido University

The University of Tokyo

takeda@nii.ac.jp

yoshioka@db-ei.eng.hokudai.ac.jp

tomiyama@race.u-tokyo.ac.jp

1. Overview of synthesis and analysis

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What is Synthesis?
zzz

Examples of Synthesis
 Scientific Discovery
 Design
 Art (Novel, Music)
 …
Synthesis is often explained in comparison with analysis
 Synthesis is defined by using definition of analysis
Characteristics of synthesis process In process of scientific discovery
 Many analysis processes and a few synthesis processes
 Fewer hypotheses are preferred In process of design Many analysis processes and many synthesis processes Many hypotheses are acceptable (or preferred)11. Overview of synthesis and analysis

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Two Viewpoints for Terms “Synthesis” and “Analysis”zFrom the viewpoint of “thinking style”
 Purpose-oriented thought process Synthesis or analysis as the purpose for thinking
 Synthesis-oriented thought processz Process to create or find somethingz ≠ abduction
 Creative process (abduction) involves examining
process (deduction)
 Analysis-oriented thought processz Process to examine somethingz ≠ deduction
 Examining process (deduction) involves hypothesizing
process (abduction)

1. Overview of synthesis and analysis

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Two Viewpoints for Terms “Synthesis” and “Analysis”zDefinitions of terms
 From the logical viewpoint
 Synthesis→ Abduction
 Analysis → Deduction
 From the viewpoint of “style of thinking” or naïve definition
 Synthesis→ Synthesis-oriented thought process Analysis → Analysis-oriented thought processz

How can these types of thought processes explained from the logicalviewpoint Integration of two viewpoints

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2. Logical formalization of synthesis

Synthesis and Analysis in the Logical Framework
Synthesis/Analysis as a rational thought process based ontheories
 Theories: Logical relations between foundations andphenomena A thought process based on theories: reasoning using theories,
i.e., finding foundations to phenomena or finding phenomena
for foundations
 Rationality: Consistency to theories

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2. Logical formalization of synthesis

Reasoning with Knowledge: in ScienceK∪Fd |- Th
Deduction: Find Th from K and Fd
Abduction: Three types
１．Find K and Fd from (a part of) Th
２．Find K from (a part of) Th and Fd
３．Find Fd from (a part of) Th and K
In Scientific Thought process Purpose: Discovery of knowledge
 Abduction is Type 1 or 2
 Find knowledge with generality from observablefacts with individuality
 Many observable facts
 Fewer hypotheses
 Many deduction and fewer abduction
 Deduction is a main processzabduction

FoFoK

Fodeduction

Fo3

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2. Logical formalization of synthesis

Reasoning with Knowledge: in Design

K∪Fd |- Th
Deduction: Find Th from K and Fd
 Abduction: Three types
１．Find K and Fd from (a part of) Th
２．Find K from (a part of) Th and Fd
３．Find Fd from (a part of) Th and K
In Design Purpose: new hypotheses
 Abduction is Type 3
 Find defined facts with individuality from observablefacts with individuality
 More knowledge is better Deduction and abduction are equally used
 Abduction is a more important processzabduction

FdFdFoFoFoFd

FoFddeduction

82. Logical formalization of synthesis

Formalization of Two Types of Thought Processes with Logic
Analysis-oriented Thought Process(1) Observation of phenomena
A phenomenon is observed as observations O.
(2) Extraction of facts
Observed facts Fo are extracted from O.
(3) Formation of hypotheses or selection of axioms
Fo can be used to reason out hypothetical axioms
Kh. In obvious cases, a set of known axioms Ke is
selected instead.
(4) Assuming definition facts
Initial definition facts Fd are assumed. Together
with Ke (or Kh), this will be used to derivetheorems Th. Usually, Fd contain such known facts
as boundary conditions and initial conditions.
(5) Derivation of theorems from axioms
Theorems Th are derived from Ke (or Kh) and Fd
deductively. It may break down the original
problem (i.e., derivation of theorems) into smaller
subproblems (the “divide-and-conquer strategy").
(6) Verification of theorems against facts
The derived theorems Th are tested against theobserved facts Fo to check the explicability of thetheorems. If Th ⊇ Fo, this test is satisfied. Then thetheorems are said to explain the extracted facts andthe choice of Ke (or Kh) was appropriate. If Th =Fo, then Ke is complete. If Th ⊃ Fo, then Th – Fosignifies unobserved facts or undiscovered facts inthe future or past. If Fo – Th ≠ ∅, then unexplained
facts remain.
(7) Verification of theorems against other known
axiomsThe derived theorems Th are again tested against
other known sets of axioms K’. This test verifies if
the theorems are compatible with K’ or at least if
they do not violate K’. If the hypotheses obtained instep (3) pass tests (6) and (7), they become axioms.

Synthesis-oriented Thought Process(1) Describing requirements
Requirements for the synthesis R are described astheorems.
(2) Extraction of requirements of interest
From R, we only focus on interesting facts as Fo.
(3) Selection of axioms
Axiom to be used is selected. Synthesis requires,various viewpoints to be considered. This means thatthe number or cardinality of K tends to be large.
(4) Derivation of solutions from requirements andaxioms
Solutions Fd are derived as facts from K and Fo.
The basic reasoning is abduction logically, but otheralgorithms to arrive at solutions can be also used.
The “divide-and-conquer strategy” might be used,
but since the number (or cardinality) of K could belarger than analysis, trade-off and negotiation among
different solutions are important.
(5) Derivation of theorems from axioms and facts
Theorems Th are derived from K and Fd deductively.
This is the same as in the analysis oriented thoughtprocess. Deduction and the divide-and-conquer
strategy are central.
(6) Verification of theorems against requirements
The derived theorems Th are tested against therequirements of interest Fo to check if the derived
Th subsume the initial requirements Fo; (i.e., Th ⊇Fo). By doing so, we can check if the solutions Fd
are satisfactory.
(7) Verification of theorems against other known
axiomsThe derived theorems are again tested against otherknown sets of axioms K’. This test verifies if Fd(and accordingly Fo) is compatible with not only K
but also K’.

492. Logical formalization of synthesisDifference between Synthesis and Analysis Processeszzzz

Problem Definition AOTP: Observation
 SOTP: Enumeration of requirements
 Arbitrariness of Synthesis
Setting of viewpoints (Selection of axiom)
 AOTP: Fewer axioms are preferred SOTP: More axioms are preferred Arbitrariness and complexity of Synthesis
Roles of abduction and deduction AOTP: abduction in selection of axioms
 SOTP: deduction in development and evaluation
 Complementarity of abduction and deduction
Criteria
 AOTP: hypothesized knowledge
 SOTP: hypothesized facts
 Difficulty of evaluation of synthesis

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3. A Computational Framework of Synthesis

A Computational Framework of Synthesis
zRequirements: 3 Types of multiplicity
 Explicit controls for abductive and deductive reasoning processes A variety of knowledge
 Duality of logical reasoning and model-based reasoningz Integration of logical and model-based reasoning
Reasoning Operation
 Use of multiple viewpoints
Design(Describing Requirements,Process
Derivation of Solution, ..)Knowledge
Model Operation
Design Activities

Operation
MentalWorld(Building, Modification, ..) (Synthesis, Analysis, ..)Multiple Model-Based Reasoning Operation
ObjectObjectdependent
modelsMediaBasedAbstraction

independentmodelInterpretation
Satisfiable
WFF

ObjectCodification
Representation
metamodel

Real
Observation
World Abstraction

Axiom as a whole whichis the target of ontology
engineering enriches

Mw ∪ Gw

M iGw iw

Working Spacefor Design,
Diagnosis, etc.

Thσ
Mw: Model
Gw: General Background Knowledge
Th: Theorem in the Working space

Thought
processmodel(Ex.
Synthesis
OrientedThought
Process
Model)

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Duality of Logical Reasoning and Model-based Reasoning

3. A Computational Framework of Synthesiszz

Model-based reasoning: “Modeling”: Description of objects and their environments from a specificviewpoint Pros: Knowledge adapted to the real world is provided
z Knowledge in synthesis: simplicity is not required, but adaptability to
the real world is required Cons: Closed in their specific viewpoints
 Abductive and deductive reasoning are usually indistinguishable
Integration of logical and model-based reasoning
 Model-based reasoning: Operations within individual viewpoints
 Logical reasoning: Orientation of thought process Relationship among viewpoints

3. A Computational Framework of Synthesis12Knowledge Operations in Designzzz

Activities in design consists of a variety of operations
Knowledge Operations: a category of operations byviewing design activities as operating designers’ knowledge
 Different types of knowledge resource
Knowledge Operations
 1. Knowledge/Information Acquisition
 2. Knowledge/Information Reorganization
Model-based Op.
Logical Op.
 3. Information Confirmation
LogicalModel-based
 4. Conflict Resolution
Reasonin
Reasoning 5. Knowledge/Information Revisiong SystemSystems
 Synthesis and analysis
Ontologies.
 6. Solution Synthesis
Metamodel
 7. Object Analysis
Knowledge Operations as combination and/or selection ofmodel and logical reasoning operations
 7 K-Operations = 7 L-Operations + 8 M-Operations

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3. A Computational Framework of Synthesis

Operations in the Logical Reasoning
Object level (l-1) Deduction of properties of objects from objects
 (l-2) Abduction of objects from properties of objects
Meta level (l-3) Setting of objects
 (l-4) Setting of requirement specifications
 (l-5) Setting of design knowledge (selection of axioms)
 (l-6) Consistency checking of knowledge (axioms)
 (l-7) Operations on the current set of design knowledgezz

Ko

Meta LevelDs

PRAbduction

Ko∪ Ds

PRDeduction

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3. A Computational Framework of Synthesis

Operations in Model-based Reasoningzz

Operations in individual models
 (m-1) Building a model (m-2) Reasoning with the model (m-3) Modification of knowledge
Building Reasoning (m-4) Modification of the model (m-5) Reference of the model
Operations for maintenance of multiple Model based reasoning
system librarymodelsIntroduction
 (m-6) Introduction of model-basedsystems
 (m-7) Selection of model-basedsystems
 (m-8) Maintenance of consistency
Conflictamong different models
Reasoning System

Maintenance

Reference
Modification
Modification

Designer’s
workspace

Selection
Modification
Modification

Reasoning Systemwith Model7

3. A Computational Framework of Synthesis

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Knowledge Operations in Designzzzzzzz(k-1) Knowledge/Information Acquisition
 (m-6) or (m-3)
 (l-7)(k-2) Knowledge/Information Reorganization
 (m-7) or (m-8)
 (l-7)(k-3) Information Confirmation
 (m-5) (l-5)(l-6)(k-4) Conflict Resolution
 (m-8) (l-6)(k-5) Knowledge/Information Revision
 (m-3) or (m-4)
 (l-5)(l-6)(k-6) Solution Synthesis
 (m-7)(m-1)(m-2)
 (l-5)(l-2)(k-7) Object Analysis
 (m-7)(m-1)(m-2)
 (l-5)(l-1)

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4. Conclusion

Conclusionzzz

Synthesis is defined theoretically Synthesis thought process in the logical framework
Synthesis is explained computationally A computational framework for synthesis
3 Types of multiplicity
 Explicit controls for abductive and deductive reasoning processes A variety of knowledge
z Integration of logical and model-based reasoningz Use of multiple viewpoints
Synthesis process is also explained computationally Practical synthesis activities are explained in the computational framework
 Seven knowledge operations each of which is composed of logical and/ormodel-based operations

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