Towards Multi-aspect Design Support Systems
Hideaki Takeda
February, 24, 1994

Contents
1 Introduction

12 Intelligent CAD

3

3 Logical Design Process Modeling11

4 Aspects and Inter-aspect Relationship

17

2.1
2.2
2.3

3.1
3.2

4.1

4.2
4.3

Research on intelligent CAD : : : : : : : : : : : : : : : : : : : : : : : : : :Requirement for Intelligent CAD : : : : : : : : : : : : : : : : : : : : : : :The Foundations of Intelligent CAD : : : : : : : : : : : : : : : : : : : : : :2.3.1 Design Theory : : : : : : : : : : : : : : : : : : : : : : : : : : : : :2.3.2 Theory of Design Processes : : : : : : : : : : : : : : : : : : : : : :2.3.3 Theory of Design Objects : : : : : : : : : : : : : : : : : : : : : : :The Logical Framework for Design : : : : : : : : : : : : : : : : : : : : : :The Logical Inference Model for Design Processes : : : : : : : : : : : : : :3.2.1 Iteration of Abduction and Deduction as the Basic Process : : : : :3.2.2 Circumscription for Resolution of Inconsistency : : : : : : : : : : :3.2.3 Meta Level Inference for Actions : : : : : : : : : : : : : : : : : : :3.2.4 Multi-worlds for Representation of Changing : : : : : : : : : : : : :Aspect in the Logical Framework : : : : : : : : : : : : : : : : : : : : : : :4.1.1 Aspect Theory as Virtual Logical Theory : : : : : : : : : : : : : : :4.1.2 Structure in Theory : : : : : : : : : : : : : : : : : : : : : : : : : : :Function-Behavior-Structure : : : : : : : : : : : : : : : : : : : : : : : : : :4.2.1 Function-Behavior-Structure Diagram : : : : : : : : : : : : : : : : :4.2.2 Design with FBS : : : : : : : : : : : : : : : : : : : : : : : : : : : :Inter-aspect Relationship : : : : : : : : : : : : : : : : : : : : : : : : : : : :5 Abduction for Design
5.1

5.2

Characters of Abduction in Design : : : : : : : : : : : : : : : : : : : : : :5.1.1 Abduction in Computer Science : : : : : : : : : : : : : : : : : : : :5.1.2 Explanation = Hypothesis + Theory : : : : : : : : : : : : : : : : :5.1.3 Integration of Explanations : : : : : : : : : : : : : : : : : : : : : :5.1.4 Creation of New Ideas : : : : : : : : : : : : : : : : : : : : : : : : :5.1.5 Abduction as Problem Formation : : : : : : : : : : : : : : : : : : :Formalization of Abduction as a Knowledge-based Inference : : : : : : : :5.2.1 Superposition in Hypotheses : : : : : : : : : : : : : : : : : : : : : :
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CONTENTS

ii
5.2.2
5.2.3

Explanatory Coherence : : : : : : : : : : : : : : : : : : : : : : : : : 30
Information for Next Inferences : : : : : : : : : : : : : : : : : : : : 31

6 Design Simulation
6.1

6.2

Design Simulator : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :6.1.1 The Architecture : : : : : : : : : : : : : : : : : : : : : : : : : : : :6.1.2 The Action-level : : : : : : : : : : : : : : : : : : : : : : : : : : : :6.1.3 The Object-level : : : : : : : : : : : : : : : : : : : : : : : : : : : :6.1.4 Multi-World Management System : : : : : : : : : : : : : : : : : : :Examples : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :6.2.1 Example 1 | Tracking of Design Processes | : : : : : : : : : : : :6.2.2 Example 2 | Design with Multi-aspects | : : : : : : : : : : : : :6.2.3 Example 3 | Connection to Analysis | : : : : : : : : : : : : : : :

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7 Summary45

Acknowledgement

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References

49

Appendix A

55

Appendix B

61

List of Figures
2.1
2.2
2.3

Research issues for intelligent CAD : : : : : : : : : : : : : : : : : : : : : :Design process in the ideal knowledge in GDT : : : : : : : : : : : : : : : :Design process in the real knowledge in GDT : : : : : : : : : : : : : : : :

4
7
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3.1
3.2

The logical design process model : : : : : : : : : : : : : : : : : : : : : : : 12
Iteration of abduction and deduction : : : : : : : : : : : : : : : : : : : : : 14

4.1

Explanatory theory : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 20

5.1

Hypothesis and explanatory theory: : : : : : : : : : : : : : : : : : : : : :28

6.1 The architecture of the design simulator : : : : : : : : : : : : : : : : : : :6.2 Inference in the design simulator : : : : : : : : : : : : : : : : : : : : : : : :6.3 The examples of protocol data : : : : : : : : : : : : : : : : : : : : : : : : :6.4 Changing of Ds and P : : : : : : : : : : : : : : : : : : : : : : : : : : : : :6.5 The generated worlds : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :6.6 A snapshot of the design simulator : : : : : : : : : : : : : : : : : : : : : :6.7 Changing of descriptions of design objects : : : : : : : : : : : : : : : : : :6.8 A simple mass-dumper-spring system : : : : : : : : : : : : : : : : : : : : :6.9 Behavior of displacement : : : : : : : : : : : : : : : : : : : : : : : : : : : :6.10 Behavior of acceleration : : : : : : : : : : : : : : : : : : : : : : : : : : : :

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iii

Chapter 1
Introduction
Recently CAD systems are largely used in industries, and there is no doubt that CAD
systems contribute toward increasing design quality and decreasing designers' routine work
like drafting. Although current CAD systems, in which geometric modeling is centered,have been developed rapidly and used widely, the next generation CAD systems, which
can support designers from the beginning of design, remain obscure in their concept andrealization.
In this research, we discuss how to support designers' various activities by computer.
The next generation CAD systems should not remain a set of convenient tools like a drawing system, an analyzing system and so on, but a friendly partner that solves problems
together with designers as well as provides its computational capability.
We emphasize two issues that we should solve. One is understanding designers' thinking, and the other is understanding variety of representation of objects. Although there
are many systems, methods, and tools that can solve some identi ed problems, the relations among these problems are unknown. It is needed to realize CAD systems tocooperate designers in all design stages to connect such isolated problems.
In this report, we rst discuss what is required for the next generation CAD systems
in Chapter 2. We also show some research domains related to this, and identify researchissues to solve. In those issues, we focus on integration of multiple aspects in this report.
We introduce our logical design process model which is base of our discussion in Chapter
3. Then we discuss aspects and inter-aspect relationship in Chapter 4. We identify
structure of aspects and relationship among aspects. In Chapter 5, we discuss abduction
as integration of aspects. Then we show how cooperation can be done with synthesis andanalysis with multi-aspects.

1

2

CHAPTER 1. INTRODUCTION

Chapter 2Intelligent CAD
2.1 Research on intelligent CAD

The concept of so-called \intelligent CAD" has risen from both AI and design research
eld. From AI eld, \design" is an attractive research issue because design is one of themost complicated but yet not-solved human activities. In early works, they preferred thewords\automated design" rather than \computer-aided-design", but soon they realized it
was not so easy to \automate" design activities because design activities includes various
thinking processes, and then they have attacked smaller problems which design includes.
That is, AI research would not provide something which would replace human designers,
but some useful systems which could solve problems that designers would want to solvein their design.
We can nd two streams in design research eld, that is, geometric CAD based researchand design theory or methodology based research. Geometric CAD research is confronting
a turning point. There are few research issues left in geometric CAD and they are trying toextend CAD to support not only drawing but also earlier stages of design, e.g., conceptual
design. That is, they want to make CAD more intelligent.
On the other hand there exist some design theories that explain or formalize design
with various ways. Researchers have developed their theories independently from CAD
research. Therefore, they have seldom taken care of \computability", and it makes themdicult to apply their theories directly to developing CAD.
But now CAD researchers and \design theorists" agree that the common target is\intelligent CAD".
Now as a mixture of these trends, many works have done which concern this problems(1)(2)(3)(4)(5and various problems are pointed out as problems in design.

2.2 Requirement for Intelligent CAD
Here I use the word \design" in a wide sense. That is, \design" does not mean merely\creating some artifacts", but including various activities such as analysis, optimization,
searching database, documentation, etc, to accomplish creation of artifacts.
Here we want to discuss \COMPUTER-AIDED DESIGN" in the above sense, notconvention meaning of \CAD".
3

CHAPTER 2. INTELLIGENT CAD

4

CAD approach
2. IICAD
Design study approach

12. Feature

Convetional CAD

4. DPM
5. FHT
3. DT

13. CS

1. CICAD

11. KB
10. AI-DS

6. IVM

8. IQQ

9.FBS
7. QRDAI approach

1. CICAD: Concept of Intelligent CAD
2. IICAD: Implementation of Intelligent CAD
3. DT: Design Theory
4. DPM: Design Process Modeling
5. FHT: Formalization of Human Thinking in design
6. IVM: Integration of Various Models
7. QRD: Qualitative Reasoning in Design
8. IQQ: Integration of Qualitative and Quantitative reasoning
9. FBS: Function, Behavior, and Structure
10. AI-DS: AI Design Systems
11. KB: Knowledge Base
12. Feature: Feature, feature-based systems
13. CS: Constraint Solving

Figure 2.1: Research issues for intelligent CAD

2.2. REQUIREMENT FOR INTELLIGENT CAD

5

There are mainly three ways to use computers in design now1 , that is, current CAD (geometric CAD) systems, CAE (computer-aided engineering), and expert systems (knowledgebased systems) in design.
In this meaning, current CAD (geometric CAD) systems deal apparently very smallpart of design. It is valid only in drawing. Other approach to use computer in design
is so-called CAE (computer-aided engineering). In this case, it emphasizes analyzing
phase in design, ignoring other activities. The last approach is utilization of expert
systems technology in design. There are some successful results in routine design, but its
application is restricted to clearly prede ned problems.
So far, we can make requirements for a future CAD system. A future CAD system
must be a \design-centered system". that is, the center of the system is neither drawing,
nor analysis nor a certain problem solving, but designing itself. It should support fromthe beginning of design to the end of design with various aspects of designing. Ant it
also should be a highly interactive system. Attempts of expert systems show us thatdesign activities include many processes incapable to computers. Design is so exible andlimitless as a whole that we never get perfect description of design. It means the system
must be always open to designers.
More detailed requirements for a future CAD system can be described as follows(7); The system should be integrated;{ integration of subsystems,{ integration of design models based on an integrated model,{ integration of design processes which means computerization of even very earlystages, and as its results,{ integration of design knowledge.
 The system should be intelligent;{ intelligent problem solving,{ intelligent support of designer,{ intelligent interface.
 The system should be interactive.
To achieve these requirements is not so easy. Of course one reason is a purely implementational one, that is, such a system will be a big and complicated and need many state-of-art
computer techniques like knowledge engineering, geometric modeling, user interface management etc.
But a more fundamental reason is that we cannot capture the whole problem, i.e.,
design in a formal manner yet.
Apparently we need to know more about design and design objects, and also we needto know more about knowledge.
1

Furthermore we may include database utilization in design.

CHAPTER 2. INTELLIGENT CAD

6

The above requirements imply that the behavior of intelligent CAD should be in thesame level of designers' behavior. Suppose if the system return a bare gure like \3.0"
as a result of design or analysis. It forces a user n(designer) to interpret its meaning by
her/himself. It cannot be intelligent nor interactive for the user, and also it cannot be
integrated as a system because it cannot deal the gure any more. But if it knows thatthe gure is the length of a certain shaft and that the user is determining the shape of the
shaft, it can response him more understandably and deal the gure in the system more
properly.
It turns out that intelligent CAD should have knowledge about design and design
objects. Intelligent CAD should be built as a knowledge-based or \knowledge-navigated"system.
Here we can divide the problem into three, which are di erent in perspective. Thatis(7);

Theory of design If we do not know what design is, we are obliged to use ad hoc

approaches to build a CAD system. It might be powerful in a particular eld, but
not in general. If we want to build a CAD system applicable to wider elds, weshould know the nature of design to design a fundamental architecture of the CAD
system.
Theory of design is necessary; to clarify what design is, to formalize design process, and to formalize design knowledge.

Theory of design objects Although representation of objects is perhaps most developed area in CAD studies, yet there exist issues to be further studied; for example,

 how to represent ambiguous or rough descriptions
 how to integrate various models

Theory of knowledge Above two theories are expected to reveal the nature of design
processes and design objects and tell us what is knowledge of design processes anddesign objects. But another problem is how to deal these types of knowledge in thesystem.

2.3 The Foundations of Intelligent CAD
2.3.1 Design Theory
Design theory is not a new concept. Some researchers in Europe, especially in Germany
have developed some \design theories" (8) (9) (10). But these theories do not seriously
concern the nature of design but how to improve actual design. And they are in manycases dependent of researchers' experience. Therefore they seem to be useful for designers,
but understandable only for designers.

2.3. THE FOUNDATIONS OF INTELLIGENT CAD

7

On the other hand, Yoshikawa (the Univ. of Tokyo) have proposed another \design
theory" which is called as \general design theory"(11) (12) (13). It is based on topology
in mathematics and roughly speaking, it starts with setting three axioms and de ning
design as a mapping from attribute space to function space. It derives some importantconcept such as \metamodel" and \evolutionary design process model" which lead morepractical discussion.
Although Yoshikawa's theory is not completed and theoretically there are much room todevelop it, it provides a good framework and some important concept needed to construct
intelligent CAD.

Design as Mapping

Function Space

Attribute Space

Figure 2.2: Design process in the ideal knowledge in GDT2.3.2 Theory of Design Processes
We can identify two subproblems in the eld where design theory is expected to cover.
One is the problems about design processes and the other is one about design objects.
While the latter is closely related to physical problems, the former is related to cognitive
problems.
Takeda et al. proposed a logical framework for design processes (14)(15)(16). In it
they de ned design and a design process in terms of logic and explained how a design
process is formed under given knowledge. This contributes to construct a general structureof intelligent CAD systems, for example, it clari es what kind of inferences should be
prepared (a strategy of integration of inference systems) and when they are used in design
processes (a strategy of integration of inference execution).

2.3.3 Theory of Design Objects
Various models (models of artifacts) are used for design and analysis. Human designers
can model a single object from various points of view. That is, they can get some di erent
models from it and use them. But the important point is that they still regard thesemodels as representation of the same object. So they can transfer new information they
get in a model to another. It is not easy for computers to deal such \multi-viewed" object
description. We have to re-think about what \modeling" means.

CHAPTER 2. INTELLIGENT CAD

8Design as a Stepwise
Refinement Process

Function Spacein terms of
Physical Phenomena

Attribute Space
Measured by
Physical Rules

Metamodel Space(Physical Phenomenon Space)
as Physical Features

Figure 2.3: Design process in the real knowledge in GDT

2.3. THE FOUNDATIONS OF INTELLIGENT CAD

9\Metamodel" derived from General Design theory is one candidate to solve this problem(17). Every modeling is dependent on some physical laws (or physical views). To say more
precisely, every model has a background theory to describe objects, and such backgroundtheory is formalization of physical phenomena (i.e., physical law).
Since metamodel is described in physical phenomenon space, we can get speci ed
descriptions (a model) from metamodel descriptions by specifying physical phenomenon
without losing information about relations between the model and the metamodel.

10

CHAPTER 2. INTELLIGENT CAD

Chapter 3
Logical Design Process Modeling
3.1 The Logical Framework for Design
In order to describe design processes in the logical framework, we should clarify what
we should represent in logic. Although many factors are complexly related to design,
we use three factors which are prerequisite to describe design processes. These factors
are required speci cations, design solutions (design objects), and knowledge. And weinterpret design as logical inference among them.
It may seem natural to take the deductive framework to describe design processes inlogic. In this approach, we can formalize design as follows;S[ K ` Ds

where S , K , and Ds are sets of formulae that denote required speci cations, knowledge used in design, and design solutions, respectively. Here solutions are derived from
speci cations and knowledge as the results of deduction. In short, this approach adoptsthe \design is deduction" paradigm.
Many works which explain design or design processes in logic are based on this framework in principle. For example, Treur(18), and Dietterich and Ullman(19) took thisapproach, and we also took it in Ref. (14).
This \design as deduction" approach may be suitable for routine design, but it cannoto er a sucient framework for other more exible and complicated design. Althoughsolutions and knowledge are always incomplete in design, it requires solid and absoluteknowledge and solutions.
Then we can use the second framework | the abductive framework. In this case,speci cations can be derived from design solutions and knowledge.
Ds[ K ` S:

Here design is abduction with knowledge and speci cations.
Coyne(20) and RESIDUE system(21) stand for this approach for design formalization.
Knowledge represented in this framework is knowledge about objects themselves, i.e.,knowledge about object properties and behaviors, because formulae in this framework
should be prepared to deduce properties and behaviors of objects from descriptions ofobjects themselves. It is more desirable than knowledge representation in the deductive
framework where knowledge is about how to design.
11

CHAPTER 3. LOGICAL DESIGN PROCESS MODELING

12

Meta Level Inference

Deduction

Ka

C

O

Ka: Knowledge on actions
Conditionsof object level

Object Level Inference
Circumscription

Ko

Operations to object level(deduction, abduction,
circumscription, etc)

Deduction

Ds

P

Abduction
Ds: Descirptions of objects
P: Descriptions of properties and behaviors of objects
Ko: Knowledge on objects

Figure 3.1: The logical design process model
Furthermore solutions the abductive inference can generate are, by de nition, notde nite solutions but feasible solutions.
Therefore, we adopt the abductive framework as the framework of the logical formalization of design.

3.2 The Logical Inference Model for Design Processes
The inference model we propose is illustrated in Figure 3.1. We de ne the design processmodel as a logical inference model.
Here there are two levels in the model, one is the object level and the other is theaction level. The object level contains descriptions of design objects (design solution) Ds,
knowledge about objects K o, and descriptions of object properties and behaviors P . P
can include required speci cations.
The basic design process is interpreted by iteration of abduction and deduction thatevolve design objects and their properties and behaviors, and circumscription is invoked
to resolve inconsistency.
The action level contains knowledge about actions (knowledge about how to design)
Ka, and the meta-level inference is performed to proceed design by specifying inferencesin the object level and operating directly the contents of Ds, K o, and P .
Changing of design objects (Ds) is managed by the multi-world mechanism based ona type of modal logic. Every state of design objects in design processes corresponds to apossible world in modal logic so as to manage multiple solutions and operations to design3.2. THE LOGICAL INFERENCE MODEL FOR DESIGN PROCESSES

13

processes themselves.

3.2.1 Iteration of Abduction and Deduction as the Basic
Process
We regard a design process as an evolutionary process, that is, the design objects arere ned in step-wise manner. We call each state of step-wise re nement as a design state.
In each state, the following three types of descriptions hold; The rst one is descriptionsof the current design solution which is denoted by Ds. It consists of identi ers of design
objects which are components of the current design solution, and properties and relations
which are necessary to identify the objects. The second one is descriptions of properties
and behaviors of the current design solution, P . It consists of all kinds of properties andbehaviors that the current design solution has. Required speci cations are included in P .
The third one is knowledge that is available at the current state, K o. These descriptions
are kept consistent to satisfy the following formula;Ds[ K o ` P:

Given design knowledge K o and the required properties P as the speci cations, thedesigner tries to nd a candidate by abduction, hence, the current descriptions of thedesign objects are formed. Then deduction is performed to obtain all the properties of
the current solution with respect to the current available knowledge. It is performed (i) to
see what properties the solution has and (ii) to see whether the solution does not contradict
with the given speci cations and knowledge. Then again abduction is performed to evolvethe solution more | new descriptions for the next state are formed. If the solution does
not satisfy the speci cations or can not evolve any more, the designer either tries analternative solution or modi es the design knowledge and the speci cations.
This iteration of abduction and deduction continues until the descriptions of the objects
become fully detailed ones that are suitable to hand the next process (e.g., manufacturing)or reach a situation where no more evolutions are possible.

3.2.2 Circumscription for Resolution of Inconsistency
Inconsistency in design has not only negative e ects in design but also positive ones.
Most cases of inconsistency in design does not mean that knowledge has wrong information essentially, but that knowledge is used in a wrong manner. Knowledge is usedbeyond situations where it is expected to be used. But it is not impossible to describe
all applicable situations in advance, because it is the nature of knowledge in design thatboundary of applicability is vague.
Here we assume that inconsistency comes from such incompleteness of the knowledge
description. Then resolution of inconsistency is to nd implicit descriptions of knowledge
which restrict applicability of knowledge. One solution to accomplish this process iscircumscription(22)(23).
Circumscription is a type of commonsense reasoning and has been developed to deal
with exceptions. In circumscription, exceptions for given contexts can be determined by

CHAPTER 3. LOGICAL DESIGN PROCESS MODELING

14

Deduction

Ko

Ds

P

Abduction
Abduction with Ko1

Ds 0 = {}P 0= R

deduction with Ko1

Abduction with Ko2

P1

Ds 1

Ds final

PfinalFigure 3.2: Iteration of abduction and deduction

3.2. THE LOGICAL INFERENCE MODEL FOR DESIGN PROCESSES

15

minimizing logical extensions of the predicates which represent abnormality with keeping
the whole context consistent.
Here abnormality is the implicit description of each piece of knowledge.
When abduction is performed with the modi ed knowledge by circumscription, we
can obtain di erent results from before. Thus use of circumscription not only solves
inconsistency but also helps design to proceed more by modifying knowledge.

3.2.3 Meta Level Inference for Actions
We de ned the basic design process as iteration of abduction and deduction on descriptionsof objects, knowledge about objects, and descriptions of object properties and behaviors.
We also introduced circumscription to resolve inconsistency.
Although they explain what the designer can do with given knowledge and speci cations, they can not deal with change of knowledge or speci cations because such actions
require change of axioms or theorems of the logical system and therefore it is out of alogic system.
In order to solve this problem, we introduce a meta-level inference architecture. Metallevel inference architectures for reasoning are suggested by many researchers. For example,
Weyhrauch(24) proposed FOL which is a meta-level reasoning system based on rst-orderlogic. Usually the relation between axioms and theorems in the object-level logical systemcorresponds to the atomic formula in the meta-level logical system. In our approach, what
the meta-level system treats as its atomic formula is the relation among descriptions ofobjects, available knowledge about objects, and descriptions of object properties andbehaviors in the object-level system. We can represent this as follows;Ds[ K o `LO P , `LM design(Ds; K o; P ):where `LO and `LM denote derivativeness in the object-level system and in the metalevel system respectively.
The current condition of the three elements in the object level systems is constantly
reported to the meta-level system, and the results of inference in the meta-level system
are re ected to the object-level system. The re ection is the change of the condition of
the object level system, i.e., either speci cation of the next inference or modi cation of
the contents of the three elements in the object-level system.
Knowledge about how to design can be described as formula in the meta-level system.
For example, a rule \if you are designing a certain object g , you should use knowledge
base Kg " can be described as follows;(

design Ds; K; P

) ^ g 2 Ds ! design (Ds; K [ Kg ; P )0

We can thus describe knowledge like design rules and design procedures in this level.

3.2.4 Multi-worlds for Representation of Changing
Each element of the object level system (descriptions of objects, available knowledge about
objects, and descriptions of object properties and behaviors) is changed dynamically by

16

CHAPTER 3. LOGICAL DESIGN PROCESS MODELING

either the object-level inference or the meta-level inference. We introduce the multi-world
mechanism based on modal logic to manage this changing.
Since a designer accumulates her or his decisions as the design solution in step-wise
re nement processes, it is crucial to distinguish what is already determined from what
is not determined yet. It is suitable to represent such situations by partial semantics.
Therefore we can use data logic to represent them. Data logic(25)(26) is intuitively aversion of modal logic based on partial semantics. There are three truth values, i.e., t, f,
and u. The third value can be interpreted as undecided . Among these values, a partialorder w is de ned where t w u and f w u are hold. In this logic, we can access the otherpossible worlds from a certain possible world, if the value of every proportion in the worldis not lower than that in the original world with respect to partial-order w. This meansthat the next world is more determined one than the current world. The truth value u isthus expected to fall into either t or f at last.
Since changing of descriptions of object properties and behaviors (logically it means a
set of derivable formulae) is monotonic, we can use possible worlds and accessibility torepresent design states and their relations.
In this formalization, if a designer obtains two new di erent object descriptions froma single solution, two possible worlds are created as descendants of the current possible
world. Revision and retraction of the design solution means backtracking to the desirable
world (the latest world which does not contradict with the new object descriptions) andcreating a new world as its descendant.

Chapter 4
Aspects and Inter-aspect
Relationship
Designers have some di erent kinds of aspects when they recognize artifacts. Some aspects
have been developed in traditional engineering elds and have rm theories like kinematics
and electric circuits. Other aspects are more vague and have not established rm theories
like cost estimation, manufacturability. Some aspects are numerical, others are symbolicor linguistic.
It is nature of design to take some di erent aspects into consideration. Even if purposeof design (function) can be described in an aspect, artifacts in real world should receive
various kind of e ects which are included not only in the original aspect but in many
di erent aspects.
Traditional design studies dismiss the importance of aspects and emphasize uniquenessof representation of artifacts. On the other hand, various kind of analysis methods havebeen developed in the engineering eld. But they emphasize completeness of their methods
and representation of artifacts. They ignore aspects behind their analysis methods, which
are important to use these analysis methods in design.
We discuss multiple aspects in design in two way, i.e., syntactically and semantically.
As the former approach, We regard an aspect theory as a logical theory, and we discuss
how to represent various aspects in a single framework, and how to cooperate aspects, inparticular to combine design and analysis methods. As the latter approach, we regard an
aspect theory as F-B-S (Function{Behavior-Structure) diagram, and discuss how design
is represented in it.

4.1 Aspect in the Logical Framework
Firstly, we discuss syntax of aspect, i.e., give de nition of an aspect in logical framework.
Secondly we discuss semantics of aspect, i.e., we de ne aspect as a tuple of function,
behavior, and structure.
17

CHAPTER 4. ASPECTS AND INTER-ASPECT RELATIONSHIP

18

4.1.1 Aspect Theory as Virtual Logical Theory
Aspects in the engineering eld are so various in representation scheme and in reasoning
style that it is impossible to provide a single representation scheme with a single reasoning
style that covers all the aspects.
Instead of a representation scheme covering for all the aspects, we assume a representation scheme that can be accessed from all the aspects. We employ logic for the sharedscheme. Every vocabulary in an aspect is de ned in the logical framework. But it is
impossible in general to represent whole of an aspect theory as a logical theory, because
reasoning in some aspects is beyond logical reasoning. In such cases, we describe every
execution of inference as a formula, i.e, condition as premise and results as conclusion.
Since such logical formulae would cover all the situations ultimately, we can say we could
represent an aspect theory as a virtual logical theory.
Generated formulae can be so enormous and every formula contains so detailed information that it seems dicult to deal with these formulae. But case based reasoning
provides the way how to deal with huge case bases, and inductive reasoning can help tomake them concise.
For example, an analysis system can calculate the maximum displacement of the beamwith given force, we can write a formula as follows;( ) ^^beem X( ) ^ contact with the end(X; F )beem bendig calculation(X; F; D ) ! maximum displacement(X; D )vertical f orce F

In antecedent there are conditions to determine whether this system is applicableand a predicate which is interface to the analysis system. In this example, beem(X ) ^vertical f orce(F ) ^ contact with the end(X; F ) are conditions for applying the aspect
system, and beem bendig calculation(X; F; D ) is the interface term. It passes values of
X and F to the analysis, and returns a value of D as a result.
A virtual logical theory is a set of formulae which are combination of conditions to use
analysis systems, and interfaces to them.
From point of view of logical inference, it behaves like ordinal logical theories, and frompoint of view of application systems it acts as interface between users and other systems.

4.1.2 Structure in Theory
In logical design process modeling, we assumed a single theory Ko as designers' knowledge.
As we mentioned, it is not a good assumption to deal with multiple aspects. So we rede ne theory in logical process modeling.
When designers design even a single object, they usually use various kinds of knowledge
which come from some di erent aspects. They can manage to combine and use such kindsof knowledge which sometimes seem to be inconsistent to each other. It is important for
design to deal with such variety of knowledge.
Instead of assuming a single background theory, we here assume a set of backgroundtheories, i.e., the background theory is divided into separate aspect theories each of which
has its own perspective of description. The perspective of an aspect theory is how torepresent phenomena or concepts as propositions in laws or rules. It is de nition of
vocabulary for the aspect.

4.2. FUNCTION-BEHAVIOR-STRUCTURE

19

Furthermore we assume clusters of knowledge in an aspect theory. We often use somepart of an aspect theory instead of the whole aspect theory. A cluster of knowledge is aunit to handle aspect theories. An aspect theory consists of a set of clusters.
We can de ne aspect theories as follows;

De nition 1 Aspect.

An aspect Ai consists of vocabulary Vi , an aspect theory Ki, and clustering of knowledgeji = fkci g. The aspect theory is a set ofSformulae written with the vocabulary, anddivided into knowledge clusters, i.e., K Ci = j 3C kcji where 3 is a set of identi ers forknowledge clusters.
KC

2

We need knowledge to connect di erent aspect theories in order to use them together.
We call it an inter-aspect theory. Since di erent aspect theories may represent the same
phenomena or concepts di erently, the inter-aspect theory holds relations among such
representations. Then we can de ne the background theory.

De nition 2 Background theory.

The background theory K0 is union of aspect theories Ki and the inter-aspect theory KI ,
i.e.,
U =

K

[

i 3

i [ KI ;K

2

where 3 is a set of aspect identi ers.
Then an explanatory theory can be de ned as collection of clusters of knowledge toexplain the given observation (see Figure 4.1).

De nition 3 Explanatory theory.

An explanatory theory K for the background theory K0 is union of knowledge clusters
taken from aspect theories in the background theory.

4.2 Function-Behavior-Structure
The ultimate purpose of design is to create artifacts to achieve given functions, i.e., toobtain structural descriptions from functional descriptions. But usually it is not directly
done but through intermediate descriptions. Behavior is often used as intermediate descriptions between function and structure. In this section, we model an aspect theory byanalyzing meaning of its contents such as function, behavior, and structure.

4.2.1 Function-Behavior-Structure Diagram
Each aspect has de nitions of elements which are dealt with in it. And there are a set of
attributes of elements and relations among elements, which can be measured and operated
in it.
Then we can represent structure of objects by attributes and relations. Some of attributes and relations of objects are not constant, and thus we call structure at a moment

CHAPTER 4. ASPECTS AND INTER-ASPECT RELATIONSHIP

20
Aspect theory1

Aspect1

Knowledgecluster
Background theory1

Vocabulary1
Aspect theory2

Aspect2

Background theory2
Inter-aspect
theoryVocabulary2
Aspect theory3

Aspect3

Vocabulary3

Figure 4.1: Explanatory theory

state of structure. Changing of structure is recognized as behavior of objects. It does notmean that all sorts of changing in structure are recognized as behavior. But a given setof behaviors in the aspect enables to recognize some sorts of changing. Some behaviors
concerns changing of only attributes, others concern changing of attributes and relations
too.
Relationship between structure and behavior is determined by phenomena which the
aspect concerns, In particular physical phenomenon are explicitly written as physicallaws. Some of phenomena in other elds are also written as laws or rules, for example,
economical laws.
Although selecting a set of behavior is arbitrary, de nitions of structure and behavior
can be strict and de nite. On the contrary de nition of function is more vulnerable,
because it is deeply related to recognition of value by human, that is, related to somesubjective a airs. Here we de ne function as interpretation of behavior. Practically it isde ned as a set or a network of behaviors. Subjectivity is implicitly expressed in selectionof behaviors.
In logical de nition, vocabulary of aspects are divided into three, i.e., vocabulary for
function, behavior, and structures. Aspect theory consists of descriptions of de nitionsof elements of function, behavior, and structures, and descriptions of function-behavior,
behavior-structure relationship.

4.2.2 Design with FBS
In this section we will explain how design is achieved with FBS diagram in terms of logic.
We represent an aspect FBS system Ax as a proposition F B SAx (f; b; s) and logicalformulae KAx as de nition of F BSAx (f; b; s). Here lower case term f ; b; s::: represent a
set of variable terms, and upper case term F; B; S::: represent a set of constant terms.
If you specify a tuple hF; B; S i each of which are constants, the logic system can

4.3. INTER-ASPECT RELATIONSHIP
determine either

21

Ax ` F BSAx (F; B; S )KorAx 6` F BSAx (F; B; S ):K

Ax (F; B ; S ) stands for complete description of an object, while F BSAx (f; b; s)
indicates all objects that aspect Ax can represent.
If you want to get descriptions of function and behavior from descriptions of structure
like diagnosis and analysis, it is represented as follows;
F BS

K

Ax ` F BSAx (f; b; S )As a result of proof, you will get values for variable f and b. In FBS diagram, sincebehaviour is de ned by structure and function is de ned by behavior, this process is notdicult.
In pure conceptual design, required speci cations are given as function. It seems
reasonable to assume
KAx ` F BSAx (F; b; s):
But it must beK

Ax ` F B SAx ([F jf ]; b; s):Here [Ajb] represents a part of this term is matched to constant A and the other matched
to variable b. In this formula, constant F stands for required speci cations and variable
f for derived function or unexpected functions.
In general, speci cations do not consist of only functions, but mixture of function,
behavior, and structure, that is,K

Ax ` F BSAx ([F jf ]; [B jb]; [S js]):

Here F , B , and S stands for required function, behavior, and structure respectively, andf , b, and s stands for derived function, behavior, and structure respectively.

4.3 Inter-aspect RelationshipWe have been putting models and knowledge from various backgrounds in computer inorder to support design. But there are no uni ed methods to integrate them. Since design
is not archived with a single model, but various perspectives should be taken into account,integration of various models and knowledge is crucial to realize future CAD systems.
Furthermore future CAD systems should have not only ability of exchanging information in various models to each other, but also ability of guiding use of various models.
That is, static and dynamic integration of models are required.
Methodology to exchange information among models tends to deal with objects andaspects ontologically, while integrated use of models in design tends to deal with objects
and aspects teleologically. If every relation among models be clear enough, there would
be no reason to be teleological. Since we could not expect such a situation in design,designers assume relations under their purpose. Then such relations are very vulnerable

22

CHAPTER 4. ASPECTS AND INTER-ASPECT RELATIONSHIP

and should be examined by experiment and manufacturing. But if it turns out that they
are true and useful relations, then they can be included into ontological knowledge.
The easiest way to use di erent aspects in the same time is to provide translation
between di erent two aspects. For example, translation between B-reps and CSG representation in geometric modeling and translation between geometric modeling aspect andFEM modeling aspect are well investigated. It may works well among a few aspects, but
one-to-one correspondence would be exponential if the number of aspects is increased.
As an approach to model integration, Tomiyama et al.(27) proposed the concept ofmetamodel for a new modeling framework for design objects. The metamodel is used as(1) as a central modeling mechanism to integrate models, (2) as a mechanism for modelingphysical phenomena, and (3) as a tool for describing evolving design objects. Each modelin CAD systems is connected only through metamodel where physical phenomena as
concepts are used to describe objects. They also proposed a metamodel system basedon qualitative physics(28). Here qualitative physics plays an inter-aspect theory amongmodels. It represents physical phenomenon as a model instead of representing every detailof aspect models. It de nes conceptual relations between metamodel and aspect models.
If two aspects represent one physical phenomena by their own ways, they share the same
concept in metamodel. That is, two terms in the two aspects are related via metamodel.
The bene t of this approach is that physical phenomenon as mediator are so generalthat it is expected to be easy to connect new aspects. The disadvantage is that de ned
relations are so conceptual that it does not imply precise relations like numerical relations.
We showed the way of integration of synthetical method and analytical method byvirtual logical theory. We will show an example for it in Section 6.2.3. We do not use
qualitative physics but just symbolic representation for object as metamodel.
The metamodel based on qualitative physics can provide basic and common connections among aspect models, but it is not appropriate to represent and describe integration
generated in design processes. Integration of aspects di ers in every design, and furthermore it is also the goal of design because objects should be represented as integrationof aspects. We discuss abduction as a method for dynamic integration of aspects in
Chapter 5.
Thus corporation of two types of integration of knowledge could make CAD systems
more exible and more designer-oriented.

Chapter 5
Abduction for Design
5.1 Characters of Abduction in Design
We have presented our model of design processes that consists of abduction, deduction, circumscription, meta-level inference, and multi-world mechanism. Abduction is crucial partof this model, because it should represent synthesis in design. Abduction generates object
descriptions as a hypothesis, while other types of reasoning assist this process. Deduction examines validity of the object descriptions proposed by abduction, circumscription
maintains knowledge used in abduction and deduction by resolving inconsistency, metalevel inference provides knowledge for abduction, and multi-world mechanism represents
evolution of the object descriptions.
Although we have shown the function of abduction in design, we have not discussed
mechanism how abduction should be performed. We discuss nature of abduction in designin this section, and then discuss the mechanism to involve such nature of abduction as aninference in the next section.

5.1.1 Abduction in Computer Science
C.S. Peirce introduced abduction as the third kind of reasoning in logic in addition to
deduction and induction.
One of important characters of abduction he argued is that direction of inference inabduction is opposite to that in deduction. For example, he demonstrated abduction as
follows(29);The surprising fact C is observed,
But if A were true, C would be a matter of course;
Hence, there is reason to suspect that A is true.
Many logical formalizations for abductive reasoning have been proposed recently (forexample, (30) (31) (32)(21)), but their de nitions for abduction are basically similar, i.e., abduction for an observation O with a theory T is to nd a hypothesis A which consists of (ground instances of)possible hypotheses and satis es both A [ T ` O and A [ T is consistent. This de nition
is logically sound and suitable to represent the character of abduction mentioned above.
23

24

CHAPTER 5. ABDUCTION FOR DESIGN

Unfortunately, this de nition of abduction fails to capture another important characterof abduction. Abduction is ampliative reasoning, while deduction is merely explicative
reasoning. In ampliative inference the conclusion introduces new ideas into our store ofknowledge, but it it does not follow from the premises with necessity(33). In explicative
inference the conclusion explicates what is stated in the premises and follows form thepremises necessarily.
Hypotheses generated by the above de nition are de nitely all what can deduce thegiven observation with the given theory, and ampliativity is realized just by enumerationof multiple hypotheses.
This clear and de nite abduction is unattractive in design because of complexity andquantity of object structures and knowledge. Since it translates ampliative ability of abduction into enumeration of multiple hypotheses, it would generate an enormous numberof hypotheses. We need the other way to interpret ampliative ability of abduction.
The problem lies in the following two issues. One issue is that they put abduction
into a traditional problem solving scheme. It should include not only problem solving but
also problem formation to some extent. Although abduction may generate hypotheses
by using reasoning like reversed deduction , it does not imply that the whole process of
abduction is such reasoning. The other issue is lack of structures in hypotheses andthe background theory. They assume simple and uniform structures that hide crucial
problems in abduction like composition of hypotheses.
In the following discussion, a problem given to abduction to solve is called an observation. It represents facts in the target world and it is what we should nd explanation for.
Knowledge which is used to nd explanation is call a background theory. A hypothesis is
an idea conjectured by abduction.
Then we will discuss what kind of characters are needed for abduction in design.

5.1.2 Explanation = Hypothesis + Theory
When a set of facts is given as an observation, abduction is to make hypotheses that
explain the given facts with a background theory. It is important to show not only
proposed hypotheses but also how the background theory is used to explain the facts.
One of the requirements that the proposed hypotheses should satisfy is to show that they
can deduce the given facts. In this deduction, at least the background theory that is usedin abduction should be included in the axiom.
But there are no reasons that the background theory used in abduction is identical to
the whole background theory that exists before abduction. It is natural to assume thatthe background theory used in abduction can be extracted from the whole backgroundtheory. We call this used background theory an explanatory theory. Then abduction is
to make a hypothesis and an explanatory theory of which combination can explain thegiven facts.
The content of explanatory theories need not be created newly. To create new rules orlaws is another abduction problem in a higher level. An explanatory theory consists offormulae that are selected from the existing background theory.

5.1. CHARACTERS OF ABDUCTION IN DESIGN

25

5.1.3 Integration of Explanations
As we mentioned, the rst requirement for hypotheses is to derive the observation withthe background theory. But it is not sucient to restrict generation and selection of
hypotheses, and some criteria are proposed as methods, for example, speci city(34) andcreditability (35).
In this paper, we use integration of explanations for criteria for generating and selecting
explanations, It means how parts of explanation are integrated together as an explanation,and this criteria is thus to ensure that an explanation is valid to explain observation asa whole. Integration of explanations has two meanings; One is coherence of explanations
that is integration of the way how they explain the observation. It represents plausibilityof hypotheses as explanation. We will discuss this problem in Section 5.2.2. The otheris integration of hypotheses that is how parts of a hypothesis are integrated together.
It represents plausibility of hypotheses themselves. It is related to the problem how
abduction can yield new ideas. We clarify it in the next subsection.

5.1.4 Creation of New Ideas
Creation of new ideas in abduction can be realized as new combinations of propositions inhypotheses. Even if every proposition in a hypothesis is well-known, combination of these
propositions can express a new idea if it is a new and meaningful combination. Therefore,
it is crucial for abduction to provide meaningful combinations in a hypothesis.
In order to obtain meaningful combinations, members of a hypothesis should be related
to each other. A set of irrelevant propositions does not carry any new ideas as a hypothesis.
Integration of hypotheses to yield new ideas is therefore to conglomerate propositions
which are able to carry new ideas.
In design, an important relationship among propositions is sharing of entities. Combination of propositions in a hypothesis is more important in design if they share entities,
because it forms a description of an object.
Integration of hypotheses in design is, so far, to form conglomerate of information
around entities. More propositions share entities in a hypothesis, more integrated it is tobe able to carry new ideas.
This problems is signi cant when an explanation needs new entities. Since each proposition in a hypothesis is proposed as explanation of some propositions in the observation,
it can have its own new entities if the explanation requires entities which are di erent
from entities in the observation.
If di erent propositions in the hypothesis can share such newly required entities, we canobtain a more integrated hypothesis. It means to identify entities which are introduced
independently and therefore have di erent properties. We call identi cation of di erent
entities superposition . It is a fusion of di erent concepts and such fusion can produce
a new concept. In abduction this process is performed in order to obtain integrated
hypotheses. We will discuss how to realize it in Section 5.2.1.

26

CHAPTER 5. ABDUCTION FOR DESIGN

5.1.5 Abduction as Problem Formation
Abduction can work not only to solve problems but also to generate information to de ne
problems.
Since design consists of a lot of ill-de ned problems, it is dicult in design to de nespace for solution and domain of knowledge (heuristics) for each problem in advance. In
such domains, abduction can serve to de ne space for solution and extent of knowledge
to solve the problem preliminarily.
As we have shown in the design process model, abduction in design is used iteratively
and develops hypotheses gradually. Each abduction stops its inference by using somecriteria, and generates hypotheses and explanatory theories gathered from the backgroundtheory. Since each hypothesis is not so de nite, it does not indicate that the hypothesis
is a solution exactly, but that there would exist a solution around the hypothesis. Thus
we can use it as preliminary de nition of space for solution. An explanatory theory also
indicates preliminary de nition of knowledge. Because the explanatory theory is collectedjust to explain the observation, it is not all information we can solve the problem. But atleast it is related and maybe needed to solve the problem. It serves, therefore, the rst
de nition of extent of knowledge.
After we obtain preliminary de nitions of space for solution and extent of knowledge,
we can use more de nite methods like deduction.
Furthermore characters of abduction we have explained can generate other information
to de ne problems. We will discuss how these types of information can be used in aknowledge-based inference in Section 5.2.3.

5.2 Formalization of Abduction as a Knowledge-basedInference
We have discussed general characters of abduction in design in the previous section. In thissection we focus on how to realize abduction in the current knowledge-based framework.
Here we provide a rst-order language L, and explanatory hypotheses, observations,and background theory are written in the rst-order predicate language. We can de ne
abduction as follows;
As we mentioned in Chapter 4, instead of assuming a single background theory, we
here assume a set of aspect theories. Furthermore we assume clusters of knowledge in an
aspect theory.
We de ned aspect theories as follows;

De nition 4 Aspect.

An aspect Ai consists of vocabulary Vi , an aspect theory Ki , and clustering of knowledgejKCi = fkci g. The aspect theory is a set of formulae written with the vocabulary, andSdivided into knowledge clusters, i.e., K Ci = j 3C kcji where 3 is a set of identi ers forknowledge clusters.
2

De nition 4 Explanation.

An explanation of an observation O with a background theory K0 is hA; K i, a tuple ofan explanatory hypothesis A and an explanatory theory K which satisfy the following
conditions;5.2. FORMALIZATION OF ABDUCTION AS A KNOWLEDGE-BASED INFERENCE27
 K  K0 ,
 K [ A is consistent,
 K 6j= O , A [ K j= O , and there are no E  A [ K that strati es E j= O .
We can say that a hypothesis A explains an observation O by an explanatory theory. In this paper, we restrict both observations and hypotheses to ground formulae, i.e.,
no variables are appeared in them. Furthermore observations are given as a set of literals(atomic formulae or negation of atomic formulae).
This de nition may seem identical to the de nition in Section 5.1.1, but an explanation
is not a hypothesis but combination of a hypothesis and an explanatory theory, and thewhole background theory is not required to use in abduction. But we have not de ned
how an explanatory theory is taken from the background theory, and what an explanatory
hypothesis consists of.
Under this de nition, we then de ne structures of a background theory and hypotheses
to realize integration of explanation.
K

5.2.1 Superposition in Hypotheses
As we discussed in Section 4.1.2, theory in design is not a single one, but consists ofserveral aspect theories which is needed for the current design task.
Then we can also divide an explanatory hypothesis as follows;A= ATH [ AI

Here, ATH is the derivative hypothesis that can be derived from the background theSory and the observation. ATH is a set of formulae with vocabulary V0 = i 3 Vi . AI isthe connective hypothesis that integrates members of the derivative hypothesis (see Figure 5.1). A derivative hypothesis AT H alone can satisfy derivativeness of the observation
O , i.e.,2

T H [ K0 j= O:

ASince the hypothesis is generated from combination of di erent aspect theories, it may
be merely a set of hypotheses each of which is generated from an aspect theory. To ensure
integration of the hypothesis, we need the connective hypothesis which combines parts ofthe derivative hypothesis together. We realize this connective hypothesis as superpositionof entities.

CHAPTER 5. ABDUCTION FOR DESIGN

28

Knowledgecluster

Vocabulary

Aspect theory

Aspect1
derivative
hypothesis

hyopothesis

connective
hypothesis

Aspect2

derivative
hypothesis

Explanatory theory

Observation

Figure 5.1: Hypothesis and explanatory theory

5.2.1.1 Instantiation of Entities
An observation is a description about entities, and a hypothesis is another description
about entities appeared in the observation. But in synthesis one should consider not only
entities presented in the observation, but also other entities needed to solve the given
problem. We can call these entities instantiated entities.
Introduction of new entities should be careful because it changes the degree of integration of explanation. It is one of important criteria to create and evaluate hypotheses.
Suppose a = ha1 ; :::; ai i a tuple of constants appeared in the observation, i = hi1 ; :::; ij ia tuple of instantiated constants appeared in the hypothesis A, and x = hx1 ; :::; xi i a tupleof variables.
Suppose that there are no constants in the explanatory theory.
We can get A(x) by substituting each constant in A, A(x) itself can explain the observation too, i.e.,

8xA(x) [ K j= O:
Since we need hypotheses of ground formulae, we nd a substitution  to all variablesin A(x) so that A(x) = A(36).
We can also represent O as O (y) a where a = fa1 =y1 ; :::; ai =yi g is a substitution. Then

8xA(x) [ K j= 8yO(y):Since the observation is given as O (y) a not as O (y), terms which satisfy every predicate
in O should be restricted to constants used in the substitution a . It means that A(x) [K [ O should be minimal with respect to each predicate in O . Minimality with respect
to a predicate is that the extension of the predicate (a set of tuples which satisfy thepredicate) is minimal(37). The extension of a predicate in O for A(x) [ K [ O shouldbe the same to the extension for O . This restriction can nd a substitution a for A(x).
Abductive procedures with the resolution principle can nd this substitution. But still
A(x)a can have free variables. Then these free variables in A(x)a are assigned either
to instantiated constants or to constants in O . Here s stands for a substitution from

5.2. FORMALIZATION OF ABDUCTION AS A KNOWLEDGE-BASED INFERENCE29
variables to variables, i for a substitution from variables to instantiated constants. Then
A = A(x)s i a . s represents identi cation between di erent terms, i.e., the way which
entities in hypotheses should be identi ed.
For example, supposef( ) ^ has(x; y ) ^ wing (y ) ^ is f eather (y ) ! bird(x);has(x; y ) ^ wing (y ) ^ is big (y ) ! f ly (x)gis alive x

as K and fbird(a); f ly (a)g as O . If there are no ideas to identify entities, both
= fis alive(a); has(a; b); wing (b); is f eather (b); has(a; c); wing (c); is big (c)gA1

and= fis alive(a); has(a; b); wing (b); is f eather (b); is big (b)gA2

can be hypotheses. The former seems redundant, but both hypotheses are minimal
because A1 6 A2 and A1 6 A2 . The di erence is the way how to introduce entities inhypotheses.

5.2.1.2 Minimality of Entities in Explanation
One of criteria to integrate hypotheses is minimality of entities. Domain circumscription(23) can be used to achieve minimality of entities in explanations. Domain circumscriptionnds models that have minimal domains to hold given formulae. In this case A(x)a ^K ^ O (a) is a formula to circumscribe. But using domain circumscription without any
restrictions will make undesirable results. For the above example, we can get

fis alive(a); has(a; a); wing (a); is f eather (a); is big (a)g
as a hypothesis with domain circumscription. This hypothesis seems unnatural, because we have knowledge about what kind of entities can be uni ed or not. In this case,entities which can satisfy wing (x) and bird(x) should be di erent, while entities which
can satisfy wing (x) can be uni ed to each other1 .
Superposition is identi cation between entities, but it is speci ed by two propositions
which have entities to be identi ed.
Although it is impossible to describe all possible uni able entity relations in knowledge2 ,we can postulate at least consistency of aspect theories. Relations among predicates inan aspect are all what are written in the aspect theory. If two proposition have predicatesin the same aspect, they are not allowed to identify unless these predicates are the same.
SupposeK1= fis alive(x) ^ has(x; y ) ^ wing (y ) ^ is f eather(y ) ! bird(x)g

K2= fpart(x; y ) ^ lif t f orce device(y ) ! f ly (x)g

1 It is not a matter of course. If there are more than two entities which satisfy the same

predicate, each of such predicates can be related to di erent entities.
2 It is the frame problem to enumerate all combinations among predicates (38).

CHAPTER 5. ABDUCTION FOR DESIGN30
K= K1 [ K2O= bird(a) ^ f ly (a)where K1 and K2 are aspect theories. We can get a hypothesisA= fis alive(a); has(a; b); wing (b); is f eather(b); part(a; c); lif t f orce device(c)g:

If we assume superposition fhas(x; y ); part(x; y )g and fwing (x); lif t f orce device(x)g.
Then the hypothesis is0A= fis alive(a); has(a; b); part(a; b); wing (b); is f eather (b); lif t f orce device(b)g:

Notice such superposition is also a hypothesis, and validity of the superposition is
examined by deduction and further abduction from the whole or part of the hypothesis
A . In particular, part of the hypothesis which includes identi ed entities is important infurther abduction and deduction in order to realize how the superposition is feasible. In
this example, it is fwing (b); is f eather (b); lif t f orce device(b)g.
05.2.2 Explanatory Coherence
Ng and Mooney(39) proposed explanatory coherence as the primary measure to evaluate
the quality of an explanation. Explanatory coherence computes the degree of connectivityof a hypothesis as follows;

X

C

=

1ij lNi;j

( 0 1)=2

Nl lwhere l is the total number of the observation, N is the total number of nodes in the
proof graph, and Ni;j is the number of distinct nodes nk in the proof graph such that
there is a sequence of directed edges from nk to ni and also nk to nj where ni and nj areelements of the observation.
This quantity may be useful to compare some tightly connected hypotheses, but weneed a more qualitative scale to evaluate coherence of explanations where connectivity is
not so tight, and nding connectivity of explanation itself is one of purposes of abduction.
Here we introduce a coherent segment of explanation to evaluate explanations.

De nition 5 When an explanation hA; K i for an observation O is given, a partial explanation hA(O ); K (O )i for the observation O  O is de ned as follows;
A(O ) and K (O ) are both minimal sets of formulae that satisfy A(O )  A, K (O )  K
and A(O ) [ K (O ) j= O .
0

0

0

0

0

0

0

0

0

0

In case of multiple partial explanations, we denote A(O )[i] and K (O )[i].
00De nition 6 Given an explanation ShA; K i for O, O1  O andS O2  O are directly

connected to each other if and only if i;j (A(O1 )[i] \ A(O2 )[j ]) [ i;j (K (O1 )[i] \ K (O2 )[j ])is non empty. This set is called \direct connection of explanation between O1 and O2 ".

5.2. FORMALIZATION OF ABDUCTION AS A KNOWLEDGE-BASED INFERENCE31
Direct connection of an explanation corresponds there exists nk for speci ed ni and nj in
Ng and Mooney's de nition.

De nition 7 Given an explanation hA; K i for O, O1  O and O2  O are indirectly

connected to each other if O1 and O2 are directly connected to each other or there isO3  O that is indirectly connected to both O1 and O2 .

De nition 8 Given an explanation hA; K i for O, if every element of O  O is indirectly
0connected to other element in O , and any element in O 0 O is not indirectly connected
to element in O , hA(O ); K (O ); O i is a coherent segment of explanation.
0

0

0

0

0

0

If the number of coherent segments for an explanation is 1, the whole explanation isconnected. If the number is more than 1, the explanation includes some explanations
that are not related to each other. This coherent segments are calculated by tracing
dependency of members of hypotheses.

5.2.3 Information for Next Inferences
Abduction can generate useful results for next inferences.
As discussed, an explanation consists of not only a hypothesis but also an explanatory
theory. Furthermore we can obtain superposition of propositions to identify entities, andcoherent segments of the explanation.
These types of information are used by two di erent ways, i.e., for successive inference
steps, and for inferences to solve similar problems.
Explanatory theories and explanatory coherence are useful for successive inferences.
An explanatory theory is a primary theory for deduction that is used to con rm the
hypothesis proposed by abduction, i.e., deduction should use at least this theory. And it
is also a reference theory for the next abduction. Clusters of knowledge in an explanatory
theory are most plausible candidate theories for the next abduction.
Explanatory coherence helps us to determine the extent of next problems. If there aresome coherence segments, it seems reasonable to divide the current problem. Even if there
is only one coherent segment, we can form sub problems by direct or indirect connections
among members in the observation and the hypothesis.
Explanatory theories and superposition of propositions are useful to solve similar problems. The sets of clusters that are used in abduction are examples of adherence among
knowledge. And superposition of propositions is also examples of connections amongpredicates in di erent aspect theories. By gathering such information, we can develop theinter-aspect theory, or add more descriptions in meta-level knowledge (see Section 3.2.3).

32

CHAPTER 5. ABDUCTION FOR DESIGN

Chapter 6
Design Simulation
6.1 Design Simulator
We implemented a prototype of the design simulator that realizes the inferences discussed
in Section 3. We call it design simulator because it is designed to track the design processes
performed by designers. The purpose of this system is to show the proposed model iscomputable as well as suitable to represent design processes.
This system is implemented in Allegro Common Lisp, CLX (Common Lisp X interface),and X11 on Sparcstations.

6.1.1 The Architecture
The design simulator consists of three main parts; i.e., the action level inference system,
the object level inference system, and the multi-world management system (see Figure6.1). The object level inference furthermore consists of workspace Ds, P , and K o, andthree inference subsystems, i.e., deduction, abduction and circumscription subsystems.
Design Simulator
Multi-world
Management
SystemAction-level Inference System
Knowledge-baseon actions

changeof worlds

operations

conditions

justifications

ATMS

Object-level Inference System
abduction
deduction
justifications
circumscription
workspace
Ds

P

Ko

Knolwedge-baseon objects

aspects

Figure 6.1: The architecture of the design simulator
The system invokes the action level inference and the object level inference mutually.
33

34

CHAPTER 6. DESIGN SIMULATION

Every time it executes the action level inference and gets the results, it asks the user tochoose one among the results which are a list of operations to the object level. It executes
then the object level inference according to the user's choice. Again it goes back to theaction level and repeats this process until there are nothing to infer. It also invokes themulti-world mechanism when a new design state is required (see Figure 6.2).

6.1.2 The Action-level
The action-level inference system works as the meta-level to the object-level inference
system. The inference on this level is currently performed by a rule-based deductive
system. Knowledge used on this level is about how to design, for example, knowledge
about selecting a knowledge base and scheduling inferences according to the condition of
the object level. Results of inference in this level is a single or a sequence of operations
on the object level.

6.1.3 The Object-level
Abduction, deduction, and circumscription are provided so as to change the current stateof Ds, P , and K o in the object level. Workspace Ds contains the current descriptions ofobjects, P the current descriptions of object properties and behaviors, and K o the current
available knowledge.
Ko is a set of Horn clause formulae, while P and Ds are a set of literals, i.e.,, atomic
formula or its negation. Inference on the object level modi es the contents of Ds, P ,or K o and sometimes causes contradictions, which are reported to the action-level as acondition of the object level.

The Abductive Inference There are some studies in which the abductive inferencewith Horn clauses is realized by using the resolution principle(21)(31). The basic idea isthat we can obtain a subset of Horn clause database that is used to infer whether the given
formula is derivable from the database by the resolution principle. Suppose G is a single
or a set of atomic formula, A is a set of formulae which represent possible hypotheses,and K is a set of formulae which represent knowledge. We can nd A  A and K  K
which satisfy A [ K ` G. This A is the result of abduction.
This algorithm may generate many solutions which include trivial ones (e.g., G itself).
We choose only maximal solutions with respect to the relation deeper in order to eliminate
these solutions. Here a set of formulae A1 is deeper than A2 i A1 [ K ` A2 and A1 6 A2 .

Circumscription The circumscription system is implemented using the algorithm pro-

posed by Nakagawa and Mori(40) that is an algorithm for computing circumscription(22)on clausal forms. Their basic idea is to use the technique of program transformation suchas unfolding when eliminating variable predicates and abnormal predicates.

6.2. EXAMPLES

35

6.1.4 Multi-World Management System
The multi-world management system keeps design states and their relations as data dependency cooperated with ATMS system(41). The idea of multi-worlds with ATMS isshown by Morris and Nado(42). Here we can operate the multi-worlds by logical formulaewith modal operators 2 (necessity) and 3 (possibility).

Multi-world Operation
Changing of
the current world
Multi-world comparison

Action Level InferenceKa

Deduction

C

O

User

Knowledge-baseon actions

Object Level Inference Deduction
Circumscription

aspects

Ko

Knolwedge-baseon objects

Ds

P

Abduction

Figure 6.2: Inference in the design simulator

6.2 Examples
6.2.1 Example 1 | Tracking of Design Processes |We demonstrate how this system works with a set of formulae which we extracted from theprotocol data(43). Figure 6.3 shows the original protocol data. We interpret this design
session as an inference by knowledge. We pick up pieces of protocol (verbal protocol andgures), and represent them as logical formulae. Inference procedures in the system has
been described in Ref. (44).
This is the rst part of the design of which the task is \to design a scale". Figure
6.4 shows how Ds (descriptions of objects) and P (descriptions of object properties andbehaviors) change during the inference. In this gure, a bold formula denotes a newly
added one, and an italic formula indicates a contradiction.
World 1 (Figure 6.4(a)) is the beginning of a session where there are only the required
speci cations in them. Then the action level inference prepares available knowledge. After
abduction and deduction are executed three times we can obtain World 5 (Figure 6.4(b)).
This state corresponds to protocol 8 in Figure 6.3. Then, the formula which represent
protocol 11 and 12 are introduced into K o. This makes an inconsistency situation (World
6, Figure 6.4(c)). It is because protocol 11 and 12 are contradictory sentences to protocol

CHAPTER 6. DESIGN SIMULATION

36(1) What mechanism does a standard scale use?
(2) It measures the weight like this (Figure A).
(3) You use the spring to pull, but you can use it oppositely.
(4) If we use it to push, it is like this (Figure B).
(5) If we can use a rack and pinion (Figure C), we can measure the weightbecause the displacement is in proportion to the weight.
(6) Do you know any other way to support the weight?
(7) No, only spring.
(8) Anyway, we think the indicator first.
(9) As a conclusion, what we want is something to measure the displacement(x in Figure A).
(10) It is better to make it easy to see.
(11) Since it translates 5mm of the displacement
to 100kg weight, the displacement per 1kg is 0.05mm.
(12) It is impossible to realize it with this (Figure C).
(13) If we don't mind the accuracy, it is possible by using many gears.
(14) Indicators in scales we can buy are upturned.
(15) Then, we have to use helical gears, but scales we can buy must use
simpler mechanism.
...
foot
foot
fig. Ax

fig. B

fig. C

Figure 6.3: The examples of protocol data
5. Circumscription modi es the formula which represents protocol 5, and it makes us
abandon the current solution. The we obtain another solution (World 9, Figure 6.4(d)).
Finally we obtain Ds and P shown as Figure 6.4(d). Figure 6.5 shows all the worlds
generated during this session. The path from the world 19 to world 21 does not appearedin the protocol data, but the system can generate such possible design processes. The
di erence between World 18 and World 21 is whether the spring is used for compression
or expansion.

6.2.2 Example 2 | Design with Multi-aspects |In this example, we assume multi-aspects in designers' knowledge. The example is takenfrom the same series of design experiments to Example 1, but the experiment done bydi erent subjects.
In this session, we assume ve aspects, i.e., scale aspect, exterior-design aspect, supportmotion aspect, translate-motion aspect, and manufacturing aspect. These aspects haverules that are representation of designers' knowledge in this design session.
The speci cation is to design a scale. It means to design an object that can supportand measure given weight (see Figure 6.7(a)).
Then designers suggest a structure of typical scales(see Figure 6.7(b)). Revered lines
are newly added members of the hypothesis.
Since \(support sc1 w)(measure sc1 w)(weight w)(quantity 100kg w)(move dw sc1) (displacement d)(quantity 5mm d)" have not been abduced yet and other6.2. EXAMPLES

37

Ds

P

displacement(5mm)weight(100kg)
translate(sc1 100kg 5mm)
scale(sc1)displacement(5mm)weight(100kg)
translate(sc1 100kg 5mm)
scale(sc1)(a) World 1

displacement(5mm)weight(100kg)
translate(sc1 100kg 5mm)
indicator(i8)has(sc1 i8)
spring(sp9)has(sc1 sp9)
push(sc1 sp9)

displacement(5mm) scale(sc1)
support(sc1 100kg)
weight(100kg)
translate(sc1 100kg 5mm)
indicator(i8)can-measure(sc1 100kg)
has(sc1 i8)
spring(sp9)has(sc1 sp9)
push(sc1 sp9)(b) World 5

displacement(5mm)weight(100kg)
indicator(i8)has(sc1 i8)
spring(sp9)has(sc1 sp9)
push(sc1 sp9)
is-in-prop(sc1 100kg 5mm)

displacement(5mm) scale(sc1)weight(100kg)
support(sc1 100kg)
indicator(i8)can-measure(sc1 100kg)
has(sc1 i8)translate(sc1 100kg 5
spring(sp9)¬translate(sc1 100kg 5mm)
has(sc1 sp9)mm)
push(sc1 sp9)
is-in-prop(sc1 100kg 5mm)

displacement(5mm)weight(100kg)
indicator(i8)has(sc1 i8)
spring(sp9)has(sc1 sp9)
push(sc1 sp9)
is-in-prop(sc1 100kg 5mm)
many-gears(mg12)
has(i8 mg12)(c) World 6
displacement(5mm) scale(sc1)weight(100kg)
support(sc1 100kg)
indicator(i8)can-measure(sc1 100kg)
has(sc1 i8)translate(sc1 100kg 5mm)
spring(sp9)¬ is-upward(i8)has(sc1 sp9)
push(sc1 sp9)
is-in-prop(sc1 100kg 5mm)
many-gears(mg12)
has(i8 mg12)(d) World 9

displacement(5mm)weight(100kg)
indicator(i13)has(sc1 i13)
spring(sp18)
has(sc1 sp18)
push(sc1 sp18)
many-gears(i17)has(i13 i17)
helical-gear(hg16)
has(i13 hg16)
rack&pinion(rp20)
has(sc1 rp20)

displacement(5mm) scale(sc1)weight(100kg)
support(sc1 100kg)
can-measure(sc1 100kg)
indicator(i13)has(sc1 i13)translate(sc1 100kg 5mm)
spring(sp18)
is-upward(i13)¬ is-easy-mechanism(i13)has(sc1 sp18)
is-easy-to-see(i13)push(sc1 sp18)
is-in-prop(sc1 100kg 5mm)
many-gears(i17)has(i13 i17)
helical-gear(hg16)
has(i13 hg16)
rack&pinion(rp20)
has(sc1 rp20)(e) World18

Figure 6.4: Changing of Ds and P

CHAPTER 6. DESIGN SIMULATION

38

W1
W2
W3

W12

W4

W13

W5

W14

W15

W8

W9

W16

W19

W10

W11

W17

W20

: a possible world
W18n: a world where contradiction is found

W21

W6

W
n
W
n
W
n
W
n
W
n

W7

: a world where circumscription is performed: a world where specifications are not satisfiedW:a possible path which was not appearedmin the protocol data

Figure 6.5: The generated worlds

6.2. EXAMPLES

39

members of the hypothesis are connected to each other at this moment, there are eight
coherent segments. Then they abduce \(support sc1 w)"and get a hypothesis using thefollowing rule;(support *s *w) <(upper-frame *u)(has *s *u)(base-frame *b)(has *s *b)(slide-guide *sl)(connected *sl *u)(connected *sl *b)(pickup *pk)(has *pk *sc)(stopper *st)(connected *st *u)(connected *st *b))This rule introduce \(stopper st14)" and \(slide-guide sl11)', and also make these
propositions connect to the segment which includes \(upper-frame u3)" and \(base-frameb1)". Thus the number of coherent segments is decreased. Using the exterior-design aspect, they get a new hypothesis as design descriptions shown in Figure 6.7(c).
Furthermore they decide to connect the plastic cover and the upper base by screws.
\(connected dp15 ub17)" is abduced to \(screw z18)(fixed z18 ub17)(fixed z18dp15)" by a rule in manufacturing aspect, Then they notice these screws can be used as the
stopper of the vertical movement. They identify \(screw z18)" and \(stopper st14)".
Figure 6.6 is a snapshot of the design simulator when superposition of propositions is
asked to users. Using some other rules, they can get a hypothesis shown in Figure 6.7(d).
In this hypothesis, revered lines are descriptions of the entity which should play two rolesin this design. One problem they should solve next is to develop and examine descriptionsof this entity.

6.2.3 Example 3 | Connection to Analysis |In the session of scale design, the designers adopted a spring system to translate weight
into displacement and wire-spring-pulley mechanism to indicate displacement.
When we interpret aspect of mechanical dynamics, we can extract models of mechanicaldynamics from descriptions of the scale. Then we can simulate behavior of the scale.
We consider the spring system to translate weight into displacement, we just use threeelement in the aspect, i.e., mass, spring, and dumper. upper-frame and a human-body
are material particles, springs are a spring and a dumper. The properties of material
particle, spring, and dumper are mass, spring rate, and dumping rate respectively.
We can extract a system structure and some properties of elements in the model using
knowledge base about mechanical dynamics parts from the current descriptions of design
objects.
In order to simulate motions, we should ll other properties of elements and add initialand boundary conditions which are not speci ed in the previous design session.
In this example, there are no descriptions for dumping rate and no clear initial conditions. Firstly we assume 1,000 [Ns/m] for the dumping rate here. We assume initialconditions as follows; The system is an equilibrium state before putting mass M
And we assume that the lower-frame is xed and a mass of M is put on the upper-frame
without force. It means that force from outside is constant M , and velocity is 0 at t = 0,
The initial situation is as follows;40

Figure 6.6: A snapshot of the design simulator

CHAPTER 6. DESIGN SIMULATION

6.2. EXAMPLES

(a)

41

(b)

(c)

Figure 6.7: Changing of descriptions of design objects(d)CHAPTER 6. DESIGN SIMULATION

42

m

k

d
(a)

Figure 6.8: A simple mass-dumper-spring system(upper-frame uf) (lower-frame lf) (spring sp) (body bd) (fixed uf sp)(fixed lf sp) (spring-rate sp 196000) (damping-rate sp 5000)(weight bd 100) (axis sp z) (ground lf) (movable uf z)
Weight of the upper-frame is calculated from its shape, dimension, and density. Shapeand dimension are dealt with geometric aspect in which sizes and shapes are explicitly
dealt with. It is the results of the current design, and can be supplied by the design system.
Furthermore we added the following proposition to determine the initial situation.

(fixed bd uf)(force bd 981 z)
The rst proposition means that the human body is xed to the upper frame, and thesecond that it receives z-axis force of 981 [N].
Then we introduce knowledge about mechanical-dynamic aspect. In this aspect unit
is de ned, which shows what is a member of the aspects, and relations like xed between
units, properties like mass-of, spring-rate, dumping-rate for units. For example, mass-unit
consists of one solid object or some xed solid objects and has mass, axis and force aspropertyIn this aspect, we have a simple model which consists of a mass, a dumper, a spring,and ground shown ( gure 6.2.3).
In this case, the human body and the upper frame form the mass in the simple model,
and the lower frame is eliminated by regarding as a part of ground.
Then we can get the following results.

(SIMPLE-MD-SYSTEM ((UF BD) (SP) Z))(K-OF-MD-SYSTEM ((UF BD) (SP) Z) 196000)(D-OF-MD-SYSTEM ((UF BD) (SP) Z) 5000)(M-OF-MD-SYSTEM ((UF BD) (SP) Z) 101.25)(F-OF-MD-SYSTEM ((UF BD) (SP) Z) 981)
The rst proposition means that a simple mass-spring-dumper system can consist of theupper frame and the human body as a mass unit, spring as a spring and dumper unit.
In the initial situation, z coordinate of the upper frame is 0, and its derivation is also0.

6.2. EXAMPLES

43

0.006
*x) * sin(36.41619568313407 * x + 0.9749664071663291) + 0.005005102040816327)

0.005

0.004

0.003

0.002

0.001

0
0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Figure 6.9: Behavior of displacement(cord uf z 0)
(derv uf z 0)
The formula corresponding this model is a simple as follows;mx

00+ dx + kx = F
0

Since solution of this formula is well known, we can solve it for x with the initialcondition (see 7).
Using these formulae, we can get the solution as follows;(BEHAVIOR-OF-DISPLACEMENT-OF-MD-SYSTEM((UF BD) (SP) Z)(+ (* -0.006047124104574503 (EXP (* -1 24.691358024691358 X))(SIN (+ (* 36.41619568313407 X) 0.9749664071663291))) 981/196000))x= 00:00605 exp(024:7t) sin(36:4 2 t + 0:975) + 981=196000

Then we can trace the behavior of this value. Figure 6.9 shows behavior of displacement.
The behavior of acceleration is shown as Figure 6.10.

CHAPTER 6. DESIGN SIMULATION

44

10* 24.691358024691358 * x) * cos (36.41619568313407 * x + 0.9749664071663291))
8

6

4

2

0

-2

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Figure 6.10: Behavior of acceleration(BEHAVIOR-OF-ACCELERATION-OF-MD-SYSTEM((UF BD) (SP) Z)(- (* -0.006047124104574503(- (SQR 24.691358024691358) (SQR 36.41619568313407))(EXP (* -1 24.691358024691358 X))(SIN (+ (* 36.41619568313407 X) 0.9749664071663291)))(* 2 -0.006047124104574503 24.691358024691358 36.41619568313407(EXP (* -1 24.691358024691358 X))(COS (+ (* 36.41619568313407 X) 0.9749664071663291)))))x= 00:00605 2 (24:72 0 36:42 ) 2 exp(024:7t) sin(36:4t + 0:975)
02 2 (00:00605) 2 24:7 2 36:4 2 exp(024:7t) cos(36:4t + 0:975)
From this behaviors, we can pick up some important features.

 The maximum of positive displacement from the equilibrium position is about 0.6
mm. It means that clearance between the upper frame and the lower frame should
be more than 0.6 mm (usually it should be multiplied by safety factor).
 The minimum of acceleration is about -2.58. It tells us how tension of measurement
wire should have.
These features, then, are used to modify the current design object.
We can analyze the behavior of the wire which is connected to pulleys, gears, and aspring.

Chapter 7
Summary
In this report, we discussed what is a design process and how we can support design bycomputer. Firstly, we de ned design in a logical framework and modeled a design process
as a logical inference. We adopted not only classical logical inference but also non-classicallogical inferences such as abduction, circumscription, and meta-level inference. Thus adesign process is represented formally by the logical framework.
Then we discussed aspects in design. Designers use various aspects even in a single
design. Variety of aspects is essential, that is, to involve various aspects is necessary fordesign because any artifacts in the real world can not be represented by a single aspect.
We showed two approach to represent aspects. One is an aspect as virtual logical theory,and the other is an aspect as F-B-S(Function-Behavior-Structure) diagram. Furthermore
we discussed how di erent aspects are related in design. One is ontological relationship,
and the other is teleological relationship. The former is relationship already establishedbetween aspects, and it is described as a set of relations between attributes in aspects. The
latter is relationship which we wish to establish in design. We described it by abduction.
Abduction is reasoning to nd feasible hypotheses from given theory. In this report,
we characterized abduction as integration of aspect theories. Abduction with mixtureof some aspect theories proposes hypotheses as results. But most parts of a hypothesis
describe objects from a single aspect because each aspect theory is isolated in the theory.
By pasting such single-aspect descriptions on an object, we can create a real object which
has multiple aspects. This is another way to achieve integration of aspects. In otherwords, designing itself is integrating of aspects.
Finally, we built a system called design simulator to examine how our discussion canbe achieved in a computer system and what our theory can solve. Three examples areshown.
In this report, we emphasized theoretical approach to build future CAD systems. Furthermore we concentrated to design processes but design objects. Thus, our researchalone is not enough to realize future CAD systems, but theory of objects and practicalknowledge of design are needed to cooperated with it. Since theory of design processes
is a backbone to integrate such theory and knowledge, we hope that this research will
accelerate realization of new-generation CAD systems.

45

46

CHAPTER 7. SUMMARY

Acknowledgement
The author would like to thank Prof. yvind Bjrke for his useful advice and support.
The author would also like to thank Prof. Kesheng Wang for his kind advice and useful
discussion with him, and Dr.ing students in Production Engineering for their kind advice
in research and also in living in Norway.
The author are also grateful to Prof. Hiroyuki Yoshikawa and Prof. Tetsuo Tomiyamaof the University of Tokyo. The help provided by all former colleagues is gratefully
acknowledged.

47

48

ACKNOWLEDGEMENT

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Appendix A: Related Work toIntelligent CAD
Now there are many and various works about \AI in design"or \AI in engineering",andrelationship between design research and AI research is not so simple nowadays. Here I
focus on \Intelligent CAD", which has been my research target, and show some related
works.

1. Concept of intelligent CAD As mentioned above, the concept of intelligent CAD
comes from various backgrounds. So we need general discussion of the concept ofintelligent CAD. For example,

 What is needed as the function of intelligent CAD?
 How should intelligent CAD work?
 What is needed to realize intelligent CAD?
 How would intelligent CAD look like?
 ...
Veth and his group (CWI, Holland) presented some discussions about intelligent CAD
and showed its framework (45) (46) (47). They characterized design as knowledge
processing and proposed a framework of \III CAD" in which some AI techniques areembodied.
Closely related to above, Tomiyama et al. (The Univ. of Tokyo) also showed theconcept of intelligent CAD systems (7).
From AI eld, Smithers et al. (48) showed their wide-ranged \AI in design research
programme" and an architecture about AI-based design support system.
Forbus(49) also proposed the concept \intelligent computer-aided engineering" inwhich qualitative reasoning play an important role.
State-of-art: Many people seem to agree that intelligent CAD will not be achieved as
simple extension of conventional CAD nor application of AI. We need a new concept
for intelligent CAD, but it is still a matter in dispute.

2. Implementation of intelligent CAD There are few reports about implementationof intelligent CAD system. For example, Xue et al. (The Univ. of Tokyo) presented a
prototype of intelligent CAD(28). It is an implementation of some theoretical results
55

56

APPENDIX A.
(matamodel theory and logical formalization of design processes) shows that suchtheories can contribute realization of intelligent CAD. But it is not a system which
can be used by actual design activities.

3. Design theory Design theory is not a new concept. Some researchers in Europe,

especially in Germany have developed some \design theories" (8) (9) (10). But these
theories do not seriously concern the nature of design but how to improve actual
design. And they are deeply dependent of researchers' experience. Therefore they
seem to be useful for designers, but understandable only for designers.
On the other hand, Yoshikawa (the Univ. of Tokyo) have proposed another \design
theory" which is called as \general design theory"(11) (12) (13). It is based on topology in mathematics and roughly speaking, it starts with setting three axioms andde ning design as a mapping from attribute space to function space. It derives some
important concept such as \metamodel" and \evolutionary design process model"
which lead more practical discussion.
Suh have proposed \axiomatic" design theory(50)(51). Here there are some axioms
of design which drive design. But his theory is prescriptive one, that is, his axioms
describe not the nature of design but how to obtain a good design, and they are
given a priori.
State-of-art: Although Yoshikawa's theory is not completed and theoretically there
are much room to develop it, it provides a good framework and some importantconcept needed to construct intelligent CAD.

4. Design process modeling We can identify two subproblems in the eld where de-sign theory is expected to cover. One is the problems about design processes andthe other is one about design objects. While the latter is closely related to physicalproblems, the former is related to cognitive problems.

Takeda et al. proposed a logical framework for design processes (14) (15)(16). It
explains how a design process is formed in terms of logic. He also shows morecognitive nature of design processes using protocol analysis(43).
Ullman investigates design processes and proposes a design process model called\TEA model" in which ten operators are de ned to operate design objects and otherinformation (52) (53) (54).
Goel and Pirolli views design processes as problem solving and showed tasks andow of information in design(55).
State-of-art: Di erent ideas come from Di erent elds. But it may be natural because
design is so complicated that we can take various ways to view it. Discussions here
is related to information processing to some extent so it is expected to be a bridge
between design theory and system oriented issues (the concept of intelligent CAD
and AI design systems).

5. Formalization of human thinking in design Basically it belongs to AI eld, buteven for AI researchers formalization of thinking in \design" is a challenging issue
which can yield new idea in AI elds. There are many topics abut this issue;

57

 analogy
 learning case-based reasoning abduction
 hypothesis reasoning abstraction ...
State-of-art: It is a hot topic for AI eld. Many people are interested in this issue andsome propose new ideas. Each of them seem to be useful for some parts of design,
but we will need some strategy to apply these ideas to CAD.

6. Integration of various models Following four issues can be categorized as \the de-sign object issue". In design various models (models of artifacts) are used for design
and analysis. Human designers can view a single object from various points of view.
That is, they can get some di erent models from it and use them. But the important
point is that they still regard these models as representation of a single object. So
they can transfer new information they get in a model to another. It is not easy
for computers to deal this \multi-view" concept. We have to re-think about what\modeling" means.

\Metamodel" derived from General Design theory is one candidate (17). Everymodeling is dependent on some physical laws (or physical view). Since metamodel is
described in physical phenomenon space, we can get speci ed descriptions (a model)
from matamodel descriptions by specifying physical phenomenon without losing information about relations between the model and the metamodel.
In AI elds, this problem is conceived as \ontology" on knowledge representation(56).
Their concern is how to connect di erent knowledge representations which have different kinds of ontology.
There are many results how to connect two models; e.g., translation between FEM
model and solid model.

7. Qualitative reasoning in design One of the important issues in design object rep-resentation is \qualitative" modeling and reasoning. Designers often think theirdesign problems qualitatively, i.e, they represent and analyze their objects qualitatively. But researchers in design study have not been much interested in suchqualitative thinking.

In AI eld, \qualitative reasoning" is becoming an important subject. Qualitative
reasoning in AI have proposed as a solution of naive physics. It is not physics
described with di erentials but physics which people have before formalizing withdi erentials. (We can predict the orbit of ball which is thrown). Roughly speaking,in qualitative reasoning, variables are represented as some discrete values divided by\landmarks". For example, there are three values +, 0, 0 if we use \0" as landmark.
There are many di erent types of qualitative reasoning in AI (for example, (57),(58)).

APPENDIX A.

58

Qualitative can play a crucial role in intelligent CAD(49). Various works have done
to apply qualitative reasoning to design eld. Some uses qualitative reasoning todesign, but most uses it to analyze behavior of objects.

8. Integration of qualitative and quantitative reasoning The problem using qualitative reasoning is that only using qualitative reasoning is not sucient for design.
Cooperation with quantitative reasoning is needed.

It is not so easy to accomplish this without ad hoc technique. There are some works(59) ((60)), but still there need more investigation.

9. Function, behavior, and structure The terms \function", \behavior" and \struc-ture" are commonly used in very domain, but the meaning of these words are notclear. Although many people agree that design starts with \functional" descriptions
as required speci cations, it is hard to nd the de nition of function.
There are few works concerning this issue directly (61). Gero(62) also shows functionbehavior-structure model in the context of design.
But many works are related to this issue.
There are many descriptions about function in \traditional" design theories or methodologies. But these descriptions are not universal and not applicable to other domains.

Some people try to de ne \function" in terms of qualitative reasoning (59) (55).
Although behavior is clearly de ned in qualitative reasoning, at the current state,
their approach is not so successful.
Many people realizes that function is another important keyword to connect engineering and AI eld, and many works will be done from various viewpoints.

10. AI design systems There are some works about \innovative" design systems using

AI technique. Following research are proposals of design systems using qualitative
reasoning.

PROMPT(63) showed a way how to change models if necessary. it provide multiple
models and modi cation operators, and if it nds it is impossible to deal a problem
in a model, change models by using an appropriate modi cation operators.
In 1stPRINCIPLE(64), the system analyzes a set of equations which describe themodel qualitatively and tries to nd optimized values. if it does not match speci cations, it divides a region of the object into two parts and gets a new set of equations,and then repeats the optimization process to nd the solution.
Furthermore Dyer et al. propose EDISON system for \design invention system"(65).
Here objects are represented by \device topology" and behavior by processes on
device topology. The system try to make a structure which satis es given function
by using stored object database.

11. Knowledge base So-called expert systems have made and used knowledge base ad

hoc. It is the reason that early expert systems met with success and also the reason
they are getting trouble to apply more practical or larger problems now. Knowledge base itself is an important problem. We need knowledge base independent

59
from application programs. There are many works how to organize such knowledge
base. One direction is to investigate the nature of knowledge in a domain (for example, MacCallum(66)). Another direction is to make large scale knowledge base (forexample, CYC project(67)(68)).

12. Feature, feature-based systems Features derivable from the geometry are called\form feature", for example hole is one of the form features.

De nition of features has a wide variety, because features are de ned from various
perspectives, e.g., designer, manufacturer, process planner ... Feature is expected to
be a bridge between geometric representation and symbolic representation and many
researchers are interested in it (for example, (69)(70)). The current main streams
are \feature extraction" and \design with feature".

13. Constraint solving Another bridge between geometric representation and symbolic

representation is constraint solving. As constraints are described as symbolic representation, it is expected to cooperate with knowledge systems or AI systems. It isalso related geometric reasoning (for example, (71)).

60

APPENDIX A.

Appendix B: An Analytical Solution
for the Di erential Equation
The formula corresponding this model is a simple as follows;00

nmx+ dx + kx = F
0It is easily translated into more general formula as follows;x00+ 2bx + !0 (x 0 x0 ) = 0
0

!0
b
x0

=
=
=

q
k=m

2

d= m
F =m!0The solution of its formula is as follows;
x

=

!

=

q

ae

0

bt sin(!t + ) + x

0

2 0 b2!0With initial conditions xjt=0 = 0 and x jt=0 = 0,0a= tan 1 (!=b)= 0x0 = sin 
061