A Prelim
liminary Formaliz
lization of Knowledge for Synthesis

Hideaki Takeda
Graduate School of Information Science
Nara Institute of Science and Technology
Akira Tsumaya"Modeling of Synthesis" Project
The University of Tokyo

1. Introduction
In this paper, we investigate how synthesis process should be and propose a preliminary
result of logical formalization of synthesis process.
Since we often mention analysis and synthesis together, we tend to assume thatsynthesis process have somewhat similar nature that analysis process has. But it is notgood assumption because aims of synthesis and analysis are quite different. They aredifferent in their aims so that knowledge for them should have different characteristics.
The aim of analysis is to clarify characteristics of objects. Clarifying objects is to explain
different objects in the same manner. In order to apply different objects as much as
possible, characteristics should be universal and minimum It implies that requirement
for knowledge for analysis is also universal and minimum.
On the other hand, the aim of synthesis is to create objects having necessary
characteristics. In this case, characteristics is not required as universal and minimum
characteristics, rather it should not be. In order to capture human desire for objects,
characteristics should be as rich as possible. Then requirement for knowledge forsynthesis is not universal and minimum rather individual and various.
The last statement indicates that attitude of the traditional logical approach is not
appropriate because it tries to capture our world with minimum and universal axioms.
We are not going to deny logical approach, but we emphasize that we need new ways tosatisfy the above requirements. We have already propose how synthesis can be captured
in a logical framework[1]. It is still based on logical theory, but we introduce multiple
theories in a logical framework. The heart of our formalization is that synthesis is not
applying logical theories but to extend and compose logical theories enough to represent
human desire to create new artifacts. In this paper, we extend our formalization to beable to explain dynamic nature of synthesis, i.e., synthesis process.
2. The three features of designing artifacts
In the previous section, we mentioned that synthesis is related to represent our desire
to create new artifact. Then what is necessary to create “new” artifacts? Whatconditions are required to agree that “it is new”?
We propose three features to ensure “newness” for artifacts. One is physicality, which isensure artifacts to exist in the world. It is no matter necessary for all existing artifacts
that are not new. But it is better for designers to understand physicality because they
can use relations between physical characteristics to realize their intention. Knowledge
for synthesis should include knowledge for analysis in this sense. But it is not all aboutknowledge for synthesis. Knowledge for analysis tends to be minimum and universal,
while knowledge for synthesis needs much variety to represent requirements for
artifacts. It is the key issue for synthesis to provide not minimum but enoughknowledge for given requirement.
The second feature is unlikeness, which means that there are no other artifacts. There
are two problems in unlikeness. The first one is which set of artifacts we should take
into consideration to assure unlikeness. Should we compare designing artifacts with allartifacts in the world? What we can do at most is to collect artifacts that we have design
or encounter or learn. We say such artifacts as design experience. Anyway it isimportant to define a set of artifacts to compare. The second problem is how to compare
designing artifacts with others. It is difficult to compare the designing artifacts withsome design experience because every design experience is so different in whichsituation we encountered it that representation can be different from designing artifacts.
It is the problem about ontological integration.
The third feature is desireness. Even if physicality ensures that the designing artifact
can exist on our world and unlikeness ensures that it has no similar artifacts, it is notenough reason to realize it in our world. For example, there are no reason to create an
artifact which is much more complicated to an existing artifact which has the samefunctions. We need criteria to ensure that is has reason to create a new artifacts. It isvery difficult feature because many reasons come from society and they are implicit
requirements. We can point out an example for it, i.e., “minimally”. To make something
minimize is a good reason to create a new artifacts. To make user operations minimize isa good reason to design a new consumer product.

Abduction

K È DsDs1

nDeduction
P1

Abduction with K3
Deduction with K2

Abduction

Ko È D

PDs2

Abduction with K3

PDs3
P3

Deduction
Ds:Design Solution
P: Properties and Behavior of Design Solution
Ko: Knowledge on Objects
Fig. 1: A Logical Framework of design process

P2

DsfinalPfinalFig 2: Iteration of abduction anddeduction

3. Requirement for formaliz
lization of synthesis process
In this section, we verify our formalization of design process[2][3] in the light of theabove three features of synthesis process.
The primary formula in our formalization is the following one(see Figure 1).
Ds ∪ Ko |= P
Here Ds is a set of logical formula that represents description of design objects. P is a setof logical formula that represents description of properties of design objects. Ko is alogical formula that represents knowledge on object. This formula means that
description of design objects and knowledge on object imply description of properties ofdesign objects. To keep this formula is to keep physicality condition.
Ideal design process is defined as process inferring from knowledge on object and part ofproperties of design objects as design requirement to description of design objects. It is
not deduction process but abduction process[4]. Furthermore design requirements andavailable design knowledge cannot be determined in advance but be defined during
design in real design process. So real design process is defined as process repeating
abduction and deduction (see Figure 2). Description of properties of design object

inferred by deduction from description of design objects and knowledge can help furtherdecision of design requirements. Description of design objects inferred by abduction
from description of properties of design objects and knowledge can suggest what kind ofknowledge is needed to infer more.
This formalization can explain design process in a computational way and also match
actual design processes[5]. But the formalization has three unsolved issues. One isevaluation of design solutions. Abduction process can theoretically infer many solutions
without any order1. We need some scheme to compare them. This problem corresponds
to desireness condition. Other problem is how to provide knowledge. We assume thatknowledge is provided a priori The other problem that is more fundamental one is how
to provide representation of description of design object, properties of design objects,
and knowledge. The second and third problems correspond to unlikeness condition, i.e.,
what ontology and knowledge we should take into consideration.
4. The first atte
ttempt to formalizlize synthesis process
We model synthesis process as intended integration process of design experiences. The
basic idea is that designers evolve their designing artifacts by using their designexperiences as ontology and knowledge for the designing artifacts. We extend ourformalization of design process to capture this process. It consist of three sub processes
as follows (see Figure 3):(1) Collecting of design experiences(2) Forming a model to represent a set of design experiences(3) Minimizing an element that we want to make it new.
(1) Collecting of design experiences
The first issue is how to represent design experiences. What we consider artifacts
during design process means not only to remember an artifacts itself, e.g., to enumerate
its attributes, but to remember or imagine what purpose it has and why it comes to havesuch attributes. In other word, we can imagine its design process. So we model design
experience as a quartet of Ds, Ko, P, and O, i.e., design object, knowledge on objects,properties of design object, and ontology to represent three formulae. We represent a setof design experiences asSome logical methods of evaluation of abduction have been proposed. For example, tominimize propositoins in hypothesis (solution) or links from hypothesis toobservation[6]. But there are no reason why we should do such a way.

1

O3
Ko3 È D3 P3

O1
Ko1 È D1 P1
O2
Ko2 È D2 P2O
Ko1' È D1' P1'

Ko2' È D2' P2'

Ko2' È D2' P2'(Ko1ÈKo2È ... ÈKon) È Ds?

P?

Figure 3: Integration of Design Experiences
de1=(Ds1, Ko1, P1, O1), … den=(Dsn, Kon, Pn, On)
Dsk∪Kok |= Pk, Dsk∈Ok、Kok∈Ok、Pk∈Ok (1≦k≦n)(2) Forming a model to represent a set of design experiences
Although we can collect a set of design experiences, there are based on different
ontologies so that we should integrate design experiences.
It is to find a subsitition of predicates from all O1，O2，…On to a single ontology.
O= O1φ ∪ O2φ ∪ ... ∪ Onφ,de1’= (Ds1’, Ko1’, P1’, O1’)=de1φ=(Ds1φ, Ko1φ, P1φ, O1φ)、…
den’= (Dsn’, Kon’, Pn’, On’)=denφ=(Dsnφ, Konφ, Pnφ, Onφ)
Ko' = Ko1φ∪... ∪Konφ
The new ontology O is a base to represent a new solution.
(3) Minimizing an element that we want to make it new.
For example, to find a simplest solution is to minimize Ds, i.e., to find Ds where|Ds|<|Dsk’| (1≦k≦n). To find minimum knowledge means to find O where Ko’ issmallest.

5. Conclusion
We show the first step of logical formalization of synthesis process. It is a new approach
to formalize synthesis process in a logical framework because it can explain how we canobtain knowledge which is often missing point when discussing logical framworks. But
there are many unsolved problems, i.g., we could not show how to achieve desireness.
We are planning how this formalization can work in actual design processes by testing
it in protocol analysis.
References[1] T. Tomiyama, T. Murakami, T. Washio, A. Kubota, H. Takeda, T. Kiriyama, Y.
Umeda, and M. Yoshioka. The modeling of synthesis -from the viewpoint of design
knowledge. In WDK 25, Proceedings of the 11th International Conference onEngineering Design in Tampere 199, volume 3, pp. 97-100, Tampere, Finland, 1997.
Laboratory of Machine Design, Tampere University of Technology.
[2] H. Takeda, P. Veerkamp, T. Tomiyama, and H. Yoshikawa. Modeling designprocesses. AI Magazine, Vol. 11, No. 4, pp. 37-48, 1990.
[3] H. Takeda, T. Tomiyama, and H. Yoshikawa. A logical and computerable framework
for reasoning in design. In D.L. Taylor and L.A. Stauffer, editors, Design Theory andMethodology - DTM '92 -, pp. 167-174. The American Society of MechanicalEngineers (ASME), 1992.
[4] C.S. Peirce. Collected Papers of Charles Sanders Peirce, volume 5. Harvard U
niversity Press, Cambridge, MA, 1935.
[5] H. Takeda, S. Hamada, T. Tomiyama, and H. Yoshikawa. A cognitive approach of theanalysis of design processes. In Design Theory and Methodology - DTM '90 -, pp.
153-160. The American Society of Mechanical Engineers (ASME), 1990.
[6] H.T. Ng and R.J. Mooney. On the role of coherence in abductive explanation. In
Proceedings of AAAI-90, pp. 337-342, 1990.