INTEGRATION OF ASPECTS IN DESIGN PROCESSESHIDEAKI TAKEDA AND TOYOAKI NISHIDA

Graduate School of Information Science
Nara Institute of Science and Technology
address: 8916-5, Takayama, Ikoma, Nara 630-01, Japan
phone: +81-7437-2-5260
fax: +81-7437-2-5219
E-mail: ftakeda, nishidag@is.aist-nara.ac.jp
Abstract. In this paper, we discuss dynamic integration of multiple aspects, i.e., integration accomplished according to progress of design. It is
not prepared in advance, but created in design processes. Firstly, we introduce our model of design processes that is based on a logical framework.
Secondly, we de ne aspects in the logical framework. An aspect is represented as a tuple of theory and vocabulary in the logical framework. In
particular knowledge in analytical aspects is represented as virtual logicaltheory. Thirdly, we propose integration of aspects by abduction that is another approach than integration of models. Abduction de ned with multiple
aspects integrates aspects by superposition of hypothesis which is identi cation of instantiated entities in hypothesis. It also examines connectivity
of hypotheses by explanatory coherence. Since superposition of hypotheses
and theories used in abduction tell us how aspects are integrated in design,
they can contribute to re-organize aspect knowledge-bases.

1. Introduction
Designers use di erent kinds of aspects when they recognize artifacts. Some
aspects have been developed in traditional engineering

elds and havermtheories like kinematics and electric circuits. Other aspects are more vague
and have not establishedrm theories like cost estimation, and manufac-

turability. Some aspects are numerical, others are symbolic or linguistic.
It is nature of design to take di erent aspects into consideration. Even

Hideaki Takeda and Toyoaki Nishida2

if purpose of design can be described in a single aspect, artifacts in the realworld would receive various kind of e ects which come from not only theoriginal aspect but many di erent aspects. Designers, thus, should consider
various aspects in order to accomplish design successfully.
Traditional design studies emphasize uniqueness of representation of
artifacts and therefore dismiss importance of variety of aspects.
On the other hand, various kind of analysis methods have been developed in the engineering

eld. They emphasize completeness of their meth-ods and representation of artifacts. They ignore aspects behind themselves,
which are important to use these analysis methods in design.
In this paper, we discuss dynamic integration of multiple aspects. Dynamic integration means that integration is accomplished according toprogress of design. It is not prepared in advance, but created in design
processes. Firstly, we introduce our model of design processes that is basedon a logical framework. Secondly, we de ne aspects in the logical framework. In this de nition, knowledge in analytical aspects is represented as
virtual logical theory. Thirdly, we propose integration of aspects by abduction that is another approach than integration of models. Then we show
examples with our prototype system. Finally we conclude the paper.

2. Logical Design Process Modeling
We need a theory about design which isformal, general and descriptive inorder to understand and represent design. And considering to apply it toCAD (Computer-Aided Design) system, it should be also computable sothat computation systems would be drawn from it. There are many designmodels proposed such as Pahl

et al.(1984), Hubka(1988), and Suh(1990),

but they are not sucient for above requirements. For example, Pahl andBeitz's approach is speci c to domains, and Suh's approach is too prescriptive.

et al.,
et al., 1990d) as a descriptive and also computable model.

We have proposed a logical model of design processes (Takeda
1990c) (Takeda

A design process is interpreted as combination of inferences de ned in the

logical framework in this model. In this section, we depict our design processmodel shortly. Details are shown in Ref. (Takeda

et al., 1990d).

et al., 1990c) and (Takeda

2.1. THE LOGICAL FRAMEWORK FOR DESIGNIn 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 todescribe design processes, i.e., required speci cations, design solutions (de-Integration of Aspects in Design Processes

3

sign objects), and knowledge. And we interpret design as logical inference
among them.
It may seem natural to take thedeductive framework to describe design

processes in logic. In this approach, we can formalize design as follows;
where

S [ K ` Ds
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 adopts the \design is deduction" paradigm.
Many works which explain design or design processes in logic are basedon this framework in principle. For example, Treur(1991), and Dietterichet al.(1987) took this approach, and we also took it in Ref. (Takeda et al.,1990a). This \design as deduction" approach may be suitable for routine
design, but it cannot o er a sucient framework for other more

exibleand complicated design. For example, solutions and knowledge are always
incomplete in design, but it requires solid and absolute knowledge andsolutions.
Then we can use the second framework | theabductive 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(1988)
and RESIDUE system(Finger

et al., 1985) stand for this approach for designformalization. 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 of objects themselves. It is moredesirable than knowledge representation in the deductive framework whereknowledge is about how to design. Furthermore solutions the abductive
inference can generate are, by de nition, not de nite solutions but feasible
solutions. Therefore, we adopt the abductive framework as the frameworkof the logical formalization of design.

2.2. THE LOGICAL INFERENCE MODEL FOR DESIGN PROCESSESThe inference model we propose is illustrated in Figure 1. We de ne thedesign process model as a logical inference model.
Here there are two levels in the model, one is the object level and theother is the action level. The object level contains descriptions of design

Ds, knowledge about objects KO , and descriptionsof object properties and behaviors P . P can include required speci cations.

objects (design solution)

The basic design process is interpreted by iteration of abduction anddeduction that evolves design objects and their properties and behaviors,

Hideaki Takeda and Toyoaki Nishida

4

Deduction
Action-Level
Meta-level inference
Conditionsof object level

Object-Level
Circumscription

Ko

Ko

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

P

P

Abduction
Abduction with Ko1

Ds 0 = {}Deduction

Ds

Ds

P 0= R

deduction with Ko1

Abduction with Ko2

P1

Ds 1

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

Ds final

PfinalIteration of abduction
and deduction

Figure 1. The logical design process model Figure 2.

and circumscription is invoked to resolve inconsistency. The action levelcontains knowledge about actions (knowledge about how to design)Ka,and the meta-level inference is performed to proceed design by specifying

Ds, KO ,P . Changing of design objects (Ds) is managed by the multi-world

inferences in the object level and operating directly the contents ofandmechanism based on a type of modal logic. Every state of design objects
in design processes corresponds to a possible world in modal logic so as tomanage multiple solutions and operations to design processes themselves.

2.3. ITERATION OF ABDUCTION AND DEDUCTION AS THE BASIC
PROCESSWe interpret a design process as an evolutionary process, that is, the design
objects are re ned in step-wise manner (see Figure 2). We call each stateof step-wise re nement as adesign state. In each state, the following three

types of descriptions are hold; The

design solution which is denoted by

rst one is descriptions of the current

Ds. It consists of identi ers of design

objects which are components of the current design solution, and properties
and relations which arenecessary to identify the objects. The second one is

P , descriptions of properties and behaviors of the current design solution.
It consists of all kinds of properties and behaviors that the current design
solution has. Required speci cations are included in

P . The third one is

KO , knowledge that is available at the current state. These descriptions
are kept consistent to satisfy the following formula;Ds [ KO ` P:
Given design knowledge KO and the required properties P as the speci-

Integration of Aspects in Design Processes
cations, designers try to

5nd a candidate by abduction, hence, the current

descriptions of the design 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 thegiven speci cations and knowledge. Then again abduction is performed to
evolve the 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 designers either try an alternative solution or modify 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 handthe next process (e.g., manufacturing).

3. Integration of Multiple Aspects

3.1. TELEOLOGICAL INTEGRATION VS. ONTOLOGICAL INTEGRATION
It is important for future CAD systems to keep integration of knowledge.
In order to support design, we have been putting models and knowledge
from various backgrounds in computer. But there are no uni ed methods
to integrate them. Since design is not archived with a single model andvarious 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, both
integrations of models are required.

ontological and teleological

The current approach to integrate multiple aspects is to integrate as-

et al., 1990), STEP, metamodel(Tomiyama et al., 1990). We can summarize this approach as ontological integration of aspects theories, because it aims to establish relapect models, for example, product model(Suzuki

tions among representations of objects, i.e., relations among di erent on-

tologies(Gruber, 1993).
As an approach to model integration, Tomiyama

et al.(1990) proposed

the concept of metamodel 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 modeling physical phenomena, and (3) as atool for describing evolving design objects. Each model in CAD systems isconnected only through metamodel where physical phenomena as concepts
are used to describe objects. They also proposed a metamodel system basedon qualitative physics (Xueet al., 1991). Here qualitative physics plays as

an inter-aspect theory among models.

Hideaki Takeda and Toyoaki Nishida

6

Model integration approach provides basic and common connections
among aspect models, but it is not

all information to integrate aspects.

To design new objects, in particular in creative design, yields new relations among aspects. Creative design does not happen within a single existing aspect, but with a new aspect which is new combination of existing
aspects. New combination means that designers

nd new way to combine

aspects, i.e., new relations among aspects. To design objects creatively is,thus, tond new relations among aspects that have not been recognized

yet. It is another kind of integration of aspects which is guided by designers'
intension. We thus call themteleological integration of aspects.

It is to notice that such relations are notrm ones until design is com-pleted, because they just depend on designers' intension and are never
examined in the real world. They should be examined by experiment andmanufacturing.
For example, suppose that a screw is introduced in a design from structural aspect and a stopper of linear movement from kinematics aspect.
Then a designer decides to use the screw as the stopper. In this case aninter-aspect relation between the kinematics aspect and structural aspectis arisen. The designer is not sure that this relation, i.e., \screw as stopper"
is really true before precise estimation of geometry, but s/he tries to keep it
unless it turn out false. If screw as stopper is a general idea not but a special
case in a special situation, it can possibly be added to ontological relations
between kinematics and structural views. In this paper we formalize thisprocess by abduction with multiple aspects.
Another problem in integration of aspects is that even relations between aspects which are conceptually clear are often dicult to describe
in a formal way, because ontological descriptions would be exhaustive. For
example, interpretation of results of stress analysis is conceptually clear,but it is not easy task to describe relation between stress analysis aspectand some designing aspect, i.e., how it would a ect design processes. For
this problem, we propose a virtual theory to describe relations between
analytical aspects and synthetic aspects. A virtual theory is a logical description of an analytical (non-logical) aspect from a point of view of using
the aspect.

3.2. ASPECTS IN THE LOGICAL FRAMEWORK
In logical design process modeling, we assumed a single theory

Ko as de-signers' knowledge. As we mentioned, it is not a good assumption to deal
with multiple aspects. So we re-de ne theory in logical process modeling.
Instead of assuming a single theory, we here assume a set of theories,
i.e., the theory is divided into separate

aspect theories each of which has

Integration of Aspects in Design Processes7

its own perspective of description.
Perspective of an aspect theory is how to represent phenomena or concepts as propositions in laws or rules. It is de nition of vocabulary for the
aspect. Every aspect has its vocabulary so that any propositions can be
determined whether they are in the aspect or not. Because purpose of aspects is to show a consistent and independent view of the real world, aspect
theories should be consistent and closed for its vocabulary.

(Aspect)
An aspect Ai is a tuple of an aspect theory Ki and vocabulary Vi . The aspect
theory is a set of formulae. An aspect hKi ; Vi i should satisfy the following
conditions;
1. Ki is consistent, and
2. Any atomic formulae in Ki is within Vi .

De nition 1

Furthermore we assume clusters in an aspect theory. Although an aspect
theory can be huge, what is needed in design is not always the whole ofan aspect theory but some part of the aspect theory. We assume that an
aspect theory consists of a set of cluster theories.

(Aspect theory)
An aspect theory Ki is union of cluster theories KCij (j 2 3i ), i.e.,S
Ki = j23 KCij
where 3i is a set of identi ers for cluster theories in aspect theory Ki .

De nition 2

i

We need knowledge to connect di erent aspect theories in order to usethem together. We call it aninter-aspect theory. Since di erent aspect the-ories may represent the same phenomena or concepts di erently, the interaspect theory holds relations among such representations.

De nition 3 (Inter-aspect theory)
An inter-aspect for a set of aspects A is a tuple of inter-aspect theory KI
and vocabulary VI that is union of vocabularies in A, i.e.,
S V
V =

I

i2A i

Then we can de ne a theory for design.

De nition 4 (Background design theory)
The background design theory KB is union of aspect theories Ki and theinter-aspect theory KI , i.e.,
S
KB = i2A Ki [ KI ;where A is a set of aspect identi ers.
We can now de ne an explanatory design theory, i.e., a theory that is needed
to design objects from given requirements.

Hideaki Takeda and Toyoaki Nishida8

De nition 5(Explanatory design theory)

An explanatory design theory KE for the background design theory KB
is union of cluster theories taken from aspect theories in the backgrounddesign theory, i.e.,
S S
KE = i2A j 2E KCij [ KI ;where Ei is selector of aspect theory Ki , which is subset of its cluster theory
indicators, i.e., Ei  3i .
iAn explanatory design theory is de ned as collection of clusters of knowledge selected from knowledge of aspects (see Figure 3).

3.3. VIRTUAL LOGICAL THEORY
Aspects in the engineering

eld are so various in representation scheme andin 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. In
our approach logic is the shared scheme. Every vocabulary in an aspect isde 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. We describe every execution of inference as a formula, i.e, condition as premise and results as conclusion. Sincesuch logical formulae would cover all the situations ultimately, we can say
we could represent an aspect theory as a logical theory.
For example, suppose an analysis system that can calculate the maximum displacement of beam with given force, we can write a formula asfollows;

cantilever(X) ^ form(X,A) ^ vertical force(F) ^ contact with the end(X,F) ^beam bending calculation(X,F,D) ! maximum displacement(X,D)
In the antecedent there are conditions to determine whether this system is applicable and a predicate which is interface to the analysis system. In this example,

beam(X) ^ form(X,A) ^ vertical force(F) ^ con-tact with the end(X,F) are conditions for applying the aspect system, andbeam bending calculation(X,F,D) is the interface term. Here A is a constantassociated to a speci c geometric form. It passes values ofanalysis system, and returns a value of

D as a result.

X and F to the

A virtual logical theory is a set of formulae each of which is combinationof conditions to use analysis systems, and interfaces to them. From point ofview of logical inference, it behaves like ordinal logical theories, and frompoint of view of application systems it acts as interface to other systems.

Integration of Aspects in Design Processes

9

There can be many formulae each of which represents relations between
two aspects in a speci c situation. These formulae can be generated dynamically in design processes when such situations occur, and can be accumulated in a logical theory.

4. Integration of Aspects by Abduction
We have presented our model of design processes that consists of abduction,
deduction, circumscription, meta-level inference, and multi-world mechanism. Abduction is crucial part of 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, meta-level inference provides knowledge for abduction, and multiworld mechanism maintains changing of object descriptions.
Although we have shown function of abduction in design, we have notdiscussed mechanism how abduction should be performed. We discuss themechanism to involve such nature of abduction as an inference in this section.

4.1. RESEARCH ON ABDUCTION
C.S. Peirce introduced abduction as the third kind of reasoning in logic inaddition to deduction and induction.
One of important characters of abduction he argued is that directionof inference in abduction is opposite to that in deduction. For example, hedemonstrated abduction as follows (Peirce, 1935);
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

et al.(1986), andet al.(1985), but their de nitions for abduction are basically similar,

recently, for example Levesque(1989), Poole(1988), Cox
Fingeri.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 that A [ T ` O is hold and that A [ T is consistent. This de ni-tion is logically sound and suitable to represent the character of abduction
mentioned above.
Unfortunately, this de nition of abduction fails to capture another important character of abduction. Abduction is
deduction is merely

ampliative reasoning, while

explicative reasoning. In ampliative inference the con-

Hideaki Takeda and Toyoaki Nishida10

clusion introduces new ideas into our store of knowledge, but it it does notfollow from the premises with necessity (Fann, 1970). In explicative inference the conclusion explicates what is stated in the premises and follows
form the premises necessarily.
Hypotheses generated by the above de nition arede nitely all what

can deduce the given observation with the given theory, and ampliativity
is realized just by enumeration of multiple hypotheses.
Thisclear and de nite abduction is unattractive in design because ofcomplexity and quantity of object structures and knowledge. Since it translates ampliative ability of abduction into enumeration of multiple hypotheses, it would generate an enormous number of hypotheses. We need theother 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. Abduction should
include not only problem solving but also problem formation. Althoughabduction may generate hypotheses by using reasoning like reversed deduction , it does not imply that the whole process of abduction is suchreasoning. The other issue is lack of structures in hypotheses and the background theory. They assume simple and uniform structures that hide crucial
problems in abduction like composition of hypotheses. For the former issue,
we propose abduction as a process which includes

nding theory used indeduction-style inference. For the latter, we use structuralized theory andhypotheses according to aspects.
In the following discussion, a problem given to abduction to solve iscalled anobservation. It represents facts in the target world and it is what

we shouldand explanation for. Knowledge used tond explanation is calledbackground theory. A hypothesis is an idea conjectured by abduction.

4.2. DEFINITION OF ABDUCTION WITH MULTIPLE ASPECTS
Here we provide aobservations

rst-order language L, and explanatory hypotheses

O, and a background theory KB are written in thepredicate language. We can de ne abduction as follows;A,

rst-order(Explanation)
An explanation of an observation O with a background theory KB is hA; K i,
a tuple of an explanatory hypothesis A and an explanatory theory K which
satisfy the following conditions;0 K  KB ,0 K [ A is consistent,
0 K 6j= O ,0 A [ K j= O , and0 there are no E  A [ K that strati es E j= O .
De nition 6

Integration of Aspects in Design Processes

11

A explains an observation O by an exK . In this paper, we restrict both observations and hy-

We can say that a hypothesis
planatory theory

potheses to ground formulae, i.e., no variables are appeared in them. Furthermore observations are given as a set of literals (atomic formulae ornegation of atomic formulae).
The de nition may seem identical to the de nition in Section 4.1, but
an explanation is not a hypothesis but combination of a hypothesis and an
explanatory theory, and the whole background theory is not required to use
in abduction. As we have mentioned, theory used in abduction is a theory
which consists of part of aspect theories (see De nition 5).
Then we should discuss how integrated and creative abduction is realized in this framework. The key idea is that minimalization of hypotheses
and explanation with given constraints. The

rst approach is to minimalize

hypotheses and the second is to minimalize explanations.

4.3. SUPERPOSITION IN HYPOTHESES
According to the structure in explanatory theory, we can divide an explanatory hypothesis as follows;

A = ATH [ AI
ATH is derivative hypothesis that can be derived from the backgroundtheory and the observation. AI is connective hypothesis that integrates
Here,

members of the derivative hypothesis (see Figure 3). A derivative hypothesis

ATH alone can satisfy derivativeness of the observation O, i.e.,
ATH [ KO j= O:

Since 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 anaspect theory. To ensure integration of the hypothesis, we need the connective hypothesis which combines parts of the derivative hypothesis together.
We realize this connective hypothesis as superposition of hypothesis.

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 entities needed to solve the given problem. We
call these entities instantiated entities.
Introduction of new entities should be careful because it changes thedegree of integration of explanation. It is one of important criteria to create
and evaluate hypotheses. Here we assume that there are no constants inthe explanatory theory.
Supposea = ha1 ; :::; ak i a tuple of constants appeared in the observation,i = hi1 ; :::; im i a tuple of instantiated constants appeared in the hypothesis

Hideaki Takeda and Toyoaki Nishida

12

Knowledgecluster

Vocabulary

Aspect theory

Aspect1
derivative
hypothesis

hyopothesis

connective
hypothesis

Aspect2

derivative
hypothesis

Explanatory theory

Observation

Figure 3. Hypothesis and explanatory theory

A, and x = hx1 ; :::; xn i a tuple of variables. 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 elaborate tond a sub- to all variables in A(x) so that A(x) = A (Lloyd, 1984). We canalso represent O as O(y) a where a = fa1 =y1 ; :::; ak =yk g is a substitution.
stitution
Then,

8xA(x) [ K j= O (y) a :O(y) a not as O(y) indicates that
O should be restricted to constants
used in the substitution a . It means that A(x) [ K [ O (y) should be
minimal with respect to each predicate in O. Minimality with respect to a
The fact that the observation is given as

terms which satisfy every predicate inpredicate is that the extension of the predicate (a set of tuples which satisfy the predicate) is minimal (Davis, 1980). The extension of a predicate

O for A(x) [ K [ O(y) should be the same to the extension for O(y) a .
This restriction is realized as a substitution a for A(x), which abductive
procedures with the resolution principle can nd. But A(x)a can have freevariables still. Then these free variables in A(x)a are assigned either toinstantiated constants or to constants in O . Here s stands for a substitution from variables to variables, i for a substitution from variables toinstantiated constants. Then A = A(x)s i a . s represents identi cationinbetween di erent terms, i.e., the way which entities in hypotheses shouldbird(a); fly (a)g as O, andfis alive(x) ^ has(x; y ) ^ wing (y ) ^ is feather (y ) ! bird(x);has(x; y) ^ wing (y) ^ is big (y) ! fly(x)g

be identi ed. For example, suppose f

as

K . If there are no ideas to identify entities, both
A1 = fis alive(a); has(a; b); wing(b); is feather(b); has(a; c);wing(c); is big(c)g andIntegration of Aspects in Design Processes
A2

=

13

fis alive(a); has(a; b); wing (b); is feather (b); is big (b)gcan be hypotheses. The former seems redundant, but both hypotheses areminimal because

A1 6 A2 and A1 6 A2 . The di erence is the way how to

introduce entities in hypotheses.

Minimality of Entities in Explanation

One of criteria to integrate hy-

potheses is minimality of entities. Domain circumscription (McCarthy, 1980)
can be used to achieve minimality of entities in explanations. Domain circumscriptionnds models that have minimal domains to hold given formu-lae. In this caseA(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 feather (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 edwing(x) and bird(x) shouldwing(x) can be uni ed to eachor not. In this case, entities which can satisfy
be di erent, while entities which can satisfy

other. 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 knowledge, we can postulate at least consistency of aspect theories.
Relations among predicates in an aspect are all what are written in the aspect theory. If two proposition have predicates in the same aspect, they are
not allowed to identify unless these predicates are the same. Suppose

K1
K2
K
O

=
=
=
=

where

A

fis alive(x) ^ has(x; y ) ^ wing (y ) ^ is feather(y ) ! bird(x)gfpart(x; y ) ^ lift force device(y ) ! fly (x)g
K 1 [ K2
bird(a) ^ fly(a)K1 and K2 are aspect theories. We can get a hypothesis= fis alive(a); has(a; b); wing (b); is feather (b); part(a; c);lift force device(c)g:

If we assume superposition

fhas(x; y ); part(x; y )g and fwing (x); lift force device(x)g,then the hypothesis isA0=

fis alive(a); has(a; b); part(a; b); wing (b); is feather(b);lift force device(b)g:

It is to notice that such superposition is also a hypothesis, and validityof the superposition is examined by deduction and further abduction fromthe whole or part of the hypothesis

A0 . In particular, part of the hypothesis

which includes identi ed entities is important in further abduction and deduction in order to realize how the superposition is feasible. In this example,
it is fwing(b); is feather(b); lift force device(b)g.

Hideaki Takeda and Toyoaki Nishida

14

4.4. EXPLANATORY COHERENCE
Ng

et al. (1990) proposed explanatory coherence as the primary measure

to evaluate the quality of an explanation. Explanatory coherence computesP

the degree of connectivity of a hypothesis as follows;C=1ij l Ni;j =Nl (l 0 1)=2
l is the total number of the observation, N is the total number ofnodes 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 are elements of the observation.

where

This quantity may be useful to compare tightly connected hypotheses,

but we need more qualitative scale to evaluate coherence of explanations
where connectivity is not so tight, andnding connectivity of explanation

itself is one of purposes of abduction.
Here we introduce anations.

coherent segment of explanation to evaluate expla-

De nition 7 (Partial explanation) When an explanation hA; K i for an
observation O is given, a partial explanation hA(O0 ); K (O0)i for the observation O0  O is de ned as follows;
A(O0 ) and K (O0 ) are both minimal sets of formulae that satisfy A(O0 ) 
A, K (O0 )  K and A(O0 ) [ K (O0 ) j= O0 .
In case of multiple partial explanations, we denote

A(O0 )[i] and K (O0 )[i].

De nition 8 (Direct connection)
Given an explanation hA; K i for O, O1  O and O2  O are directly
connected to each other if and only if (A(O1 ) \ A(O2 )) [ (K (O1 ) \ K (O2 )is non empty. This set is called \direct connection of explanation between
O1 and O2 ".
Direct connection of an explanation corresponds that there exists
speci edni and nj in Ng and Mooney's de nition.

nk for(Indirect connection)
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 otheror there is O3  O that is indirectly connected to both O1 and O2.
De nition 10 (Coherent segment)
Given an explanation hA; K i for O, if every element of O0  O is indirectly
connected to other element in O0 , and any element in O 0O0 is not indirectly
connected to element in O0, hA(O0); K (O0 ); O0 i is a coherent segment of
De nition 9

explanation.

If the number of coherent segments for an explanation is 1, the whole explanation is connected. If the number is more than 1, the explanation includes

Integration of Aspects in Design Processes

15

Figure 4. A snapshot of the design simulatorsome explanations that are not related to each other. Those coherent segments are calculated by tracing dependency of members of hypotheses.

5. Design simulation
We have been developed a prototype system called

design simulator toevaluate our inference model discussed in Section 2 and Section 4. Thissystem has two purposes. One is to show computability of the proposedmodel, and the other is to show adaptability to actual design processes.
Figure 4 is a snapshot of the system. This system is implemented in Lucid/Allegro Common Lisp, CLX (Common Lisp X interface), and X11 on
Decstation/Sparcstation.
We show how abduction can explain designers' processes by using asimple example taken from protocols in design experiments(Takeda

et al.,

1990b). We interpret this design session as an inference by knowledge. We
pick up pieces of protocol (verbal protocol andgures), and represent themas logical formulae. Inference procedures in the system have been describedin Ref. (Takeda

et al., 1990d).

The speci cation is to design ascale. It means to design an object thatcan support and measure given weight (see Figure 5(a)). In this session,ve aspects, i.e., scale aspect, exterior-design aspect, supportmotion aspect, translate-motion aspect, and manufacturing aspect. These

we assume

aspects have rules that are representation of designers' knowledge in thisdesign session.
Designers suggest a structure of typical scales(see Figure 5(b)). Highlighted lines indicate newly added members of the hypothesis. SinceHideaki Takeda and Toyoaki Nishida16(support sc1 w)(measure sc1 w)(weight w)(quantity 100kg w)(move d w sc1)(displacement d)(quantity 5mm d)have not been abduced yet and other 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 the fol-lowing 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))
Application of this rule introduces \(stopper st14)" and \(slide-guidesl11)', and also makes these propositions connect to the segment which
includes \(upper-frame u3)" and \(base-frame b1)". Thus the numberof coherent segments is decreased. Using the exterior-design aspect, they
get a new hypothesis as design descriptions shown in Figure 5(c).
Furthermore they decide to connect the plastic cover and the upper baseby screws. \(connected

dp15 ub17)" is abduced to \(screw z18)(fixed
z18 ub17)(fixed z18 dp15)" by a rule in manufacturing aspect, Thenthey notice these screws can be used as the stopper of the vertical movement. They identify \(screwz18)" and \(stopper st14)". Figure 4 isa 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 5(d). In this hypothesis, highlighted lines are descriptions of the object which should act as both screw and stopper. One problem they shouldsolve next is to develop and examine descriptions of this object.

6. Conclusion
We discussed representation and integration of aspects in design in thispaper. We represent aspect knowledge as virtual logical theory. It enables
to represent multiple aspects in a single framework. Then we discussed
how di erent aspects are related in design. We categorize relationship between aspects in two types. One is ontological integration, and the other isteleological integration. The former is already established relations between
aspects, and it is realized as model integration. The latter is relations which
we wish to establish in design. We described it by abduction.
Abduction is reasoning tond feasible hypotheses from given theory.

In this paper, we characterized abduction as integration of aspect theories.
Our abduction with combination of multiple aspect theories proposes descriptions of objects supported by multiple aspects. Integration of isolated
aspect theories is realized by superposition in hypothesis and evaluated byexplanatory coherence. It is important to generate object descriptions from

Integration of Aspects in Design Processes

(a)

(b)

(c)

17

(d)

Figure 5. Changing of descriptions of design objects
multiple aspects in design, because object descriptions not from a single
aspect but from various aspects are necessary to create new objects in thereal world. In other words, designing itself is integrating of aspects.
When we consider our abduction as knowledge-based system, we could
conclude as follows. Abduction can support designers to achieve dynamic
integration of knowledge. Both explanatory theories and superposed propositions represent dynamic integration of knowledge. A generated explanatory theory is an example of combination of knowledge used in design.
Superposed propositions is also an example how descriptions in di erent
aspects can be related to each other. Accumulation of these informationin successful design processes shows how knowledge is used in design processes. It is useful to re-organize aspect knowledge-bases as well as to create
new relationship among di erent aspect knowledge-bases. Thus cooperationof two types of integration of knowledge could make CAD systems more
exible and more designer-oriented.

Acknowledgement
Part of work in this paper was done when the

rst author was in Norwe-gian Institute of Technology (NTH). The author would like to thank Prof.
yvind Bjrke of NTH for his useful advice and support. The author are
also grateful to Prof. Hiroyuki Yoshikawa and Prof. Tetsuo Tomiyama of
the University of Tokyo.

18

Hideaki Takeda and Toyoaki Nishida

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