typed feature structures and design space exploration

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Typed feature structures and design space exploration

R. WOODBURY,1 A. BURROW,2 S. DATTA,1 and T-W. CHANG1

1School of Architecture, Landscape Architecture and Urban Design, University of Adelaide, SA 5005, Australia2Department of Computer Science, University of Adelaide, SA 5005, Australia

(Received June 23, 1998; Final Revision March 31, 1999; Accepted April 1, 1999!

Abstract

Design space explorers are computer programs that play on an exploration metaphor to support design. They assist

designers in creating alternative designs by structuring the process of design creation in a space of alternatives. Sub-

sidiary metaphors relevant to design space explorers are generation, navigation, and reuse. This paper introduces, in

two sketches, typed feature structures as a formal system in which a design space explorer and its knowledge level

might be implemented. First, informal and abstract properties of typed feature structures suffice to build a sketch of the

behavior of a design space explorer. Second, using an example based on single-fronted cottages ~a common Australian

housing type!, we outline the typed feature structure machinery most relevant to design space exploration.

Keywords: Exploration; Generation; Navigation; Reuse; Design Spaces

1. INTRODUCTION

In studying the phenomenon of design, we use models ~met-

aphors! to envision mechanisms by which computers might

support design. One such mechanism is variously called

search, exploration, discovery ~and other terms!under anyname it is a guided movement through a space of possibil-

ities. Design space explorers are computer media that en-

gage designers in exploration. With them, designers explore

possibilities. This encompasses discovering new designs,

as well as recalling, comparing, and adapting existing de-

signs. In creating design space explorers we represent the

possibilities in the form of symbol structures called states

and seek efficient representations for these states and al-

gorithms over them. We represent spaces of possibilities

as a relation over states and seek definitions of the space-

generating relation, which are relevant to the exploration

metaphor and lend themselves to tractable computations.

A pervasive notion within the exploration metaphor isgoal-directness, which arguably can be traced to the origins

of the exploration metaphor in cognitive accounts of human

rationality. In essence, goals exist independently of the de-

signs that realize them and the process of exploration is

guided by a set of goals that itself may be transformed within

the exploration process. Computing with goals requires their

representation. Because goals may change throughout an ex-

ploration process, design states record the goals toward which

they aim and the artefacts that ~partially! realize those goals.

Another notion is that of nondeterminismthe goal doesnot of itself determine the decisions enacting the explora-

tion. An external agent, often the user, must resolve the in-

determinacy in seeking the goal. In design space explorers,

each decision is expressed in the transformation of one de-

sign state to another. A design space is implicitly defined by

a set of initial design states and a set of state transforming

operators. A design space explorer assists a user to unfold

this compact and implicational description into an explicit

space of recorded possibilities. This exploration history is

necessarily a subset of the complete design space. Design

space explorers provide a mixed initiative environment where

the user and computer play complementary roles.A user ex-

periences the design space explorer inter alia through re-

solving exploration nondeterminism. Support for this role

is therefore critical to the external qualities of a design space

explorer. The careful presentation of alternatives avoids over-

whelming a user, and assists a user to perceive coherent

movements in the design space. Visualization of the design

space and its place in the exploration history provides a con-

text for the presentation of alternatives. A sound organiza-

tion of alternatives manages information and introduces a

perceptible rationale.

Reprint requests to: R. Woodbury, School of Architecture, LandscapeArchitecture and Urban Design, University of Adelaide SA 5005, Austra-lia. Phone: 618-8303-4588; Fax: 618-8303-4377; E-mail:[email protected]

Artificial Intelligence for Engineering Design, Analysis and Manufacturing ~1999!, 13, 287302. Printed in the USA.Copyright 1999 Cambridge University Press 0890-0604099 $12.50

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The experience from extant spatial grammar based tools

is that a necessary modification to their formalisms and thus

their interpreters is a mechanism to control the availability

of transformations so that construction occurs in coherent

phases. The representation of operators should reflect this

need to structure and organize these alternatives. The set of

transformations available at each design state is the primi-

tive relation describing exploration nondeterminism. How-ever, there are natural structures in this relation that should

be exploited. Alternatives may be mutually exclusive, in-

terdependent, or independent. Without a structuring princi-

ple for operators, these properties will be evident only in

the pattern of discovered alternatives and distributed across

the design space. With a structuring principle for operators

these properties may be expressed in the presentation of al-

ternatives, their grouping, and the ordering of these groups.

In their action of tracing out design spaces, explorers leave

in their trail a record of work, effectively a case-base in the

terms of case-based design. Organizing, accessing, and re-

using this resource of past work is a chief challenge for de-

sign space explorers.A final aspect of the mixed-initiative dialogue between

user and explorer is the genesis and development of opera-

tors. When designer action is interpreted as design space

exploration it is widely recognized that the set of design

moves used are typically developed in the context of de-

sign ~Archea, 1987!. A design space explorer should there-

fore support the discovery and application of new operators

within and between design sessions and design projects.

A design space explorer is then a device that represents

goals, operators, and design possibilities. It organizes these

states into spaces, provides ways of accessing states and ap-

plying operators to extend the explored space, provides ways

of reusing states in the already explored space, and sup-ports the invention of new operators. A designer interacts

with an explorer through states, spaces, operators, and pre-

sentation of their interactions. Systems that can be de-

scribed as design space explorers have at least the

functionality of recognizing how operators apply in a state,

and in most cases can, in some sense, autonomously act upon

such recognition. The design space explorer is an active par-

ticipant in a mixed initiative environment based on the ex-

ploratory unfolding of design spaces.

This paper presents typed feature structures, a formal sys-

tem in which a design space explorer might be realized.

Typed feature structures make the presumption, common but

by no means universal in the design literature, that the en-

tities of interest ~Newsome et al., 1989; March, 1995! can

be structured into a composition of objects and features. Thus

representations such as shapes ~Stiny, 1980! in which a def-

inite representation comprises an indefinite set of parts would

seem, at first glance, to be excluded from the typed feature

structures game.1

A deep understanding of typed feature structures requires

an appreciation of its formal mechanics, which, at least in

the first authors experience, takes fair effort to acquire. In

this paper we approach typed feature structures through two

sketches, one of their behavior as a representation for a de-

sign space explorer and the other of their underlying formal

mechanics and our extensions to them. Carpenter provides

a more complete description of typed feature structures, in-cluding many proofs for those readers wishing to tackle the

formalism in full gory detail.

2. TYPED FEATURE STRUCTURES AS A

REPRESENTATION

As a first approximation, consider a system made out of three

sets of components: types T, structures F, and descriptions

D, put into a representation scheme with a building design

domain as shown in Figure 1. The types comprising Tstand

for expressed knowledge of the domain of interest, in this

case a building design. Structures from Frepresent models

of particular designs, in this case, buildings and0or their com-ponents, either physical or conceptual. Structures from F

are expressed in terms of the information expressed in T.

Descriptions from D are utterances in a formal textual lan-

guage and stand for themselves in the representation scheme,

but correspond symbolically and inter alia to sets of struc-

tures from F. The essential act of generation corresponds to

the discovery of models of buildings that are simulta-

neously compatible with a description and the knowledge

from the domain of interestin typed feature structure ter-

minology generation is the computation of structures com-

patible with a given set of types and a given description. All

of this is ordinary in the realm of current knowledge-based

system theory and can be found, in many variations, in theliterature. In the sequel we describe aspects that typed fea-

ture structures provide to a design space explorer. For now,

as much as possible, we eschew the abstract symbolic terms

of type, structure, and description, relying instead on their

domain counterparts, namely, knowledge, model, and de-

scription.

We use as an example, a house type, common in Austra-

lia, known as a single-fronted cottage, an example of which

is shown in Figure 2. Single-fronted cottages are simple

1See Section 5. Fig. 1. Abstract elements of a typed feature structurerepresentation scheme.

288 R. Woodbury et al.


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houses, comprising a single-loaded hallway, rooms off of

the hallway, and a collection of spaces at the end of the hall-

way. The rooms along the hallway are typically generic in

function and can be used as bedrooms, lounges, dining

spaces, studies, etc. The hallway and its adjacent rooms are

typically housed under a single roof, which is either a gable

or a hip. The collection of rooms at the end of the hallway is

typically configured as a skillion ~space under a shed roof

addition! or historically as separate structures ~typically a

kitchen and toilet!. A porch along the front of the cottage

completes the typical picture. Single-fronted cottages are a

historic housing type, filling a niche of small, mostly inex-

pensive housing. Latterly, many have been upgraded withparticular attention being given to elaborations of the skil-

lion addition, usually into a combination family room, din-

ing room, and kitchen. New houses in the single-fronted

genre are still being constructed in inner suburban areas.

2.1. Structures are both intensional and partial

Intensionality in a representation scheme means that two

symbol structures can be identical in all aspects yet remain

distinct. In an intensional representation, the actual identity

of two structures must be explicitly called out, for example,

by a declaration that two compatible structures are, in fact,

one and the same. From a domain point of view, we wish to

be able to distinguish between models that differ only by

the fact of their separate existences. As shown in Figure 3,

in our example realm of single-fronted cottages, the three

rooms of the room row can be identical in all aspects, yet

remain distinct.

Partialness means that a structure need not contain all in-

formation that might be inferred about it from its associated

types. In effect, a partial representationA stands for all more

complete representations that contain at least the informa-

tion in A. Appealing to a domain perspective, a model may

contain less information than we can infer from our knowl-

edge of it. Figure 4 shows that a model of a single-fronted

cottage with its dining room in the room row can exist with-

out holding any other information on single-fronted cottages.

Partialness and intensionality swim together. We can know

very little of two structures, except that they are differentor

that they are exactly the same structure. In terms of cot-

tages, we may know that the dining room is or is not the

third room in the row. Conversely, within a computation, a

given structure is not necessarily the same as another that

contains consistent information, but might be made so at

some future point in the computation. For example, Fig-

ure 5 shows that two separate cottage models may at some

point become a single composite model, containing all in-

formation from both. In this figure and in all figures dem-

onstrating information inclusion, we depart from the normal

convention in artificial intelligence of drawing specializa-

tion relations with the most general concepts at the top. We

do this for two reasons: ~1! to cohere with the intuition that

a structure containing more information than another is some-

how greater than the other, and ~2! the typed feature struc-

tures literature follows this convention.

2.2. Partialness is in the eye of the beholder

Whether a structure is partial or not depends on the content

of its associated types. In domain terms a model might be

partial against one set of knowledge but complete with re-

spect to a subset of the knowledge. For example, if knowl-

edge of single-fronted cottages is limited to their spatial

Fig. 2. A typical single-fronted cottage.

Fig. 3. Rooms 1, 2, and 3 can be identical in all aspects yet remain dis-

tinct.

Fig. 4. That the dining room is located in Room 3 of the room row is all

that is known in this structure, even though the available knowledge of

single-fronted cottages would allow more to be inferred.

Typed feature structures and design space exploration 289


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organization, as might be the case for an urban geographer,

a complete model of a cottage would assign functions to

physical spaces. Such a model would be partial with re-

spect to a larger set of knowledge, containing, for example,

knowledge of how to construct single-fronted cottages.

In terms of design space explorers, partialness in a model

indicates that more exploration is possible from that model.

Conversely, adding new knowledge opens up new explora-

tion possibilities for previously completed models.

In the domain of single-fronted cottages, Figure 6 shows

that a cottage about which we know only the location of the

dining room is consistent with several alternatives for the

placement of other rooms. If our knowledge of the building

type consists of only spatial organization, a model is com-

plete once we have allocated all functions to specific rooms.2

2In this example and those that follow in this section, partialness wouldappear to be based on the subset relation, that is, a partial model is a subsetof a set and the set is the ultimate complete model. With the introductionof the actual typed feature structure mechanism in Section 3 it becomesclear that partialness as a concept has more richness.

Fig. 5. Two cottage models that are consistent yet incomplete can be joined into a single cottage model containing the information

from both models.

Fig. 6. A partial model of a single-fronted cottage that is consistent with multiple complete models.



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2.3. A generative system without rules

Recall that our formal system comprises three sets: types T,

structures F, and descriptions D, with elements ofD stand-

ing for subsets of F. Further, imagine, first that there is a

relation of satisfaction M linking the structures from Fthat

are consistent with a given description; second, that there is

an efficient procedure P for computing M; and third, that a

type from Titself has a corresponding description in D. Thenthe same procedure that generates structures consistent with

a description can generate structures consistent with the set

of types. In effect, the type hierarchy itself becomes what

Carlson describes as a design space description mechanism~Carlson, 1994!. In domain terms, from knowledge we can

infer designs.

2.4. An exploration system

Much has been made in the literature on the distinction be-

tween search and exploration systems, on the basis of the

ability to consider changing goals within a computationalprocess. The distinction disappears when goals are held in

the same structures as other models in a system, and this is

the case with most extant generative formalisms. The present

mechanism is no different. The set of types need not remain

fixed. Different sets of types define different sets of com-

plete structures. Though we do not discuss how a particular

knowledge level representation that would include, inter alia,

goals and design representations, might be expressed with

the typed feature structures mechanism, like all knowledge,

goals are expressed as types, which like all knowledge, can

be changed.

2.5. Monotonic generation

The fact of partial structures provides, in itself, a notion of

what might comprise generation, namely, the alternative

completions of partial structures into more specific partial

structures and finally to complete structures. This amounts

to a claim that the generating procedure P must act incre-

mentally, that is, it must progressively generate more and

more complete structures as it works through its input de-

scription. P thus stands as the design space generator in this

schemeby its action it traces out a derivation relation from

state to state. Under such a regime, generation is monotonic

with respect to the structures it creates. In other words, if a

fact is known in a model, it remains known in all models

that can be created from that model. It is well-known that

monotonicity is a double-edged sword. While it enables

search strategies based on branch-and-cut, it restricts the set

of allowable operators and possible derivation sequences.

Appealing to our example domain, Figure 7 shows that a

partial model of a single-fronted cottage is consistent with

multiple models, partial and complete, and these models are

related by the action of the procedure that generates one

from the other. In this example, we are clearly recovering

part of the subset relation over the set of rooms in the single-

fronted cottagein the structures we have in mind, mono-

tonic generation is more complex.

2.6. Design spaces are structured by subsumption

Monotonic generation implies that the derivation relation is

a subsumption relation, that is, a model B derived from a

model A contains strictly more information than A. With

respect to single-fronted cottages, each model in the chainin Figure 8 contains strictly more information than its

predecessor.

Derivation defines only a subset of the full subsumption

relation. If we presume an efficient way of comparing struc-

tures from F for their information specificity, that is, for

their relative position in the subsumption relation, then the

full subsumption relation for a set of discovered structures

can be recovered in the process of generation ~Fig. 9!. Fur-

ther, if structures are thought of as themselves comprising

structures this subsumption relation can be recovered for all

the parts of a structure.

Having access to the full subsumption relation in a de-

sign space enables forms of exploration richer than branch-

and-backtrackusual in generative systems. The branch aspect

of generation remains largely unchanged. Backtracking be-

comes more rich, in that the derivation relation along which

backtracking typically takes place is replaced by the full sub-

sumption relationfrom a given state, it is possible to move

to less specific designs that have previously been discov-

ered and to less specific designs for parts, irrespective of

the process by which the designs were generated.

Fig. 7. From a partial model of a single-fronted cottage can be generated

a graph of consistent partial and complete models.



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Last, the ability to find the appropriate place for a givenmodel in a subsumption relation opens the door to the non-

monotonic operator of information removal. Removing in-

formation from a model results in a less-specific model,

which has its own place in the subsumption relation. Thus,

it is possible to move to less specific designs that have not

been previously discovered, though at the cost of losing the

cut part of branch-and-cut search strategies, if the infor-

mation removal operator is included in the generation pro-

cedure.

2.7. Reuse is intrinsic

The aspirations of design space exploration trade heavily

on an ability to reuse information already discovered, for

example, to find and adapt for the present single-fronted de-

sign that clever island-feature kitchen design someone in

your firm did in the Darwin office sometime in the last

2 years.

Together, partialness and the subsumption ordering over

structures provide a seductive view on the reuse of de-

signs, the required actions for which are retrieval and ad-

aptation. Recall that a structure is a partial specification of

an object, that it is consistent with all objects that containat least the information specified in it, and that structures

exist in a subsumption ordering. It follows that any struc-

ture effectively indexes those structures more specific than

it in the subsumption orderingthe same mechanism by

which designs are represented can be used for retrieval. Once

retrieved, the design space explorer operations ~monotonic

generation, enriched backtracking, and informationremoval!

are available to adapt the design to a new context.

In their support of reuse, typed feature structures would

appear to do some of the duties of a case-based design sys-

tem, for which the required mechanisms are representation,

indexing, retrieval, and adaptation. In the typed feature struc-

tures view, both cases and their indexes are indistinguish-able from a structure, case retrieval indistinguishable from

navigation in a subsumption relation of designs, and case

adaptation indistinguishable from design space explora-

Fig. 8. In a derivation chain of partial single-fronted cottages, each suc-

cessive cottage model contains at least the information contained in its

predecessor.

Fig. 9. The derivation relation is a subset of the full subsumption order over models.



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tion. We believe it worthwhile to draw two distinctions be-

tween cases and the mechanics of typed feature structures

for reuse. First, much of the work in case-based reasoning

is motivated by, or at least plays to, a reproduction of hu-

man reasoning processes. Thus, designs for case-based rea-

soning systems appeal to features such as cognitive closeness

of match in retrieval and a specialized adaptation process.

In contrast, the retrieval and adaptation mechanisms sug-gested by typed feature structures are structured first by ef-

ficient computations in the mechanism and second by an

appeal to elegance in humancomputer interaction marked

by reluctance to introduce new mechanisms. Second, much

of the work in case-based reasoning is situated within weakly

structured symbol systems and therefore requires different

and typically more complex strategies for retrieval and ad-

aptation than does the typed feature structures mechanism,

defined as it is over a strongly structured and ordered uni-

verse. For these two reasons, we believe that casting our

reuse mechanism as case-based reasoning could generate

more heat than light. Nonetheless, below we sketch some

relations between typed feature structures reuse and case-based reasoning.

Structures as cases provide a feature that is commonly

used in case-based systems. By its place in the derivation

relation, a structure provides sets of generation steps by

which a case has been created from scratch, as does, for

example, JULIA ~Hinrichs, 1992!. To this, structures, by their

place in the larger subsumption relation, provide alternative

sets of generation steps by which a case might be created

from scratch.

If cases are structures, then case adaptation is the normal

process of design generation, namely, the combined action

of a monotonic generating procedure, backward movement

in the subsumption relation and removal of content.If we consider a case index as a structure, then indexes,

like structures, have their own place in the subsumption

relation of structures. More specific structures are in-

stances of the case; less specific structures are a form of

partial match of the case. This view on cases corresponds to

the two kinds of matches that Flemming describes for cases

in the SEED system ~Flemming, 1994!. Given the availabil-

ity of the subsumption relation over structures and their parts,

the index vocabulary problem described by Kolodner ~1993,

Chap. 6! would appear to disappearthe index vocabulary

is the full vocabulary from which structures are constructed

and indexes are implicit in the subsumption ordering.

We end this discussion of cases with a disclaimer. Typed

feature structures are seductive as formal devices for case

representation, retrieval, and adaptation. We have yet to dis-

cover if their siren call leads us to founder on some rugged

coast or signals a clear, concise, and new approach.

2.8. Summary

In the light of the above seven features, to the system sketch

in Figure 1 can be added two principal relations correspond-

ing to computational paths among its symbolic components

as shown in Figure 10.

The generating procedure P ~called p-resolution! that cap-

tures a relation from descriptions to structures M:D r F

acts as the main exploration mechanism in the system.

Access to the subsumption relation S : Fr F for struc-

tures and their parts provides a design space structure that

includes the derivation relation as a subpart. Case indexing

and retrieval are essentially search in the subsumption re-

lation. An episode of design space exploration would em-

ploy both P and movement in the subsumption relation.

Several computation paths would appear to be excludedfrom the family of computations available in this scheme.

Types especially seem to be estranged. Later we will show

that a description can call out a type, thus bringing types

back into the fold. Most other paths have corresponding well-

formed relations, but these are subsidiary in design space

exploration and we will only explain the ones on which our

principal paths depend.

3. THE MECHANICS OF TYPED FEATURE

STRUCTURES

The term feature structures denotes a class of record-like

data structures that comprise sets of attribute-value pairs

called features and values, respectively. Feature structures

arose in the areas of computational linguistics and logic

programming and have natural analogues in terminologi-

cal knowledge representationtheir provenance, which is

beyond the scope of this paper, is summarized by Carpen-

ter ~1992!. Here we sketch a particular formalization typed

feature structures as developed in Carpenter ~1992! that

admits a variety of efficient algorithms over these data struc-

tures. Carpenter was motivated by the expression of par-

Fig. 10. Principal computation paths in typed feature structures.



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tial information, so that the absence of a feature in a feature

structure is not taken to imply its absence in an object that

the feature structure might represent.

As a computational system feature structures comprise

four elements: a type hierarchy, a set or sets of feature struc-

tures, a description language, and a set of algorithms over

these. On the first three of these elements are posed condi-

tions that collectively admit the robustness and efficiencyof the algorithms in the fourth component. In the present

context, the type system, feature structures, and utterances

in the description language correspond to the types, struc-

tures, and descriptions of the abstract system described in

the previous section.

We proceed with an informal specification of the princi-

pal algorithms over feature structures as a way of motivat-

ing the necessarily detailed presentation of the type system,

feature structure syntax, and description language. For now,

we take feature structures to be objects comprising parts,

without further specifying what sorts of things these ob-

jects and parts are.

The first algorithm computes if two feature structures Aand B are in a subsumption relation A vB, that is, ifA sub-

sumes B. Informally, subsumption is a relation of informa-

tion specificity: If A subsumes B, then B contains at least

the information contained in A. If two feature structures mu-

tually subsume each other, they are called alphabetic vari-

ants. Subsumption modulo alphabetic variance is a partial

order, under it features structures and thus information may

or may not be ordered, but if ordered display the formal

properties of reflexivity, antisymmetry, and transitivity. In

the design space exploration game, subsumption orders the

design space and the case retrieval process.

The second algorithm, p-resolution, computes the satis-

faction relation from descriptions to feature structures. Fora given description, the algorithm computes a set of consis-

tent feature structures. Satisfaction is monotonic: If a fea-

ture structure satisfies a description, than every feature

structure it subsumes also satisfies the description. Satisfac-

tion is an approximate explanation of p resolution: Later

we explain how and why the p-resolution algorithm com-

putes only the most general satisfiers. In design space ex-

ploration p-resolution is the principal generation process.

A third algorithm, unification, computes a feature struc-

ture satisfying both of two given feature structures. Such a

feature structure is the minimal feature structure subsumed

by both of the given feature structures. Unification is a par-

tial function from F Fr F, where Fis the set of all fea-

ture structures. Unification plays no direct role in design

space exploration; rather, it is an integral component of

p-resolution where it generates consistent structures, and is

used to decide whether two pieces of information are

consistent.

Subsumption and p-resolution are the fundamental fea-

ture structure algorithms for a design space explorer. The

feature structure mechanism, which we now describe, is, in-

ter alia, structured to admit efficient instances of these al-

gorithms. Describing feature structures relies on types and

feature structure descriptions rely on feature structures, so

we specify the parts in the following order: types, feature

structures, and descriptions.

3.1. Types

The finite set of types is organized into a structure accord-

ing to information specificity. We say that type s subsumes

type t ~and write s v t! if type t contains strictly more

information than type s. Type s is said to be a supertype oft; t a subtype ofs. Beyond the partial order properties im-

plied by the type subsumption relation ~which is not the same

relation as the feature structure subsumption relation!, a fea-

ture structure type hierarchy is required to have two addi-

tional properties. First, for any set of types there is at most

one type that is directly subsumed by all types in the set. A

set of types with a common subtype is said to be bounded or

consistent. This condition on the type hierarchy amounts to

saying that there must be a unique most general subtype forany consistent set of types in the hierarchy. Second, there

must be a most general type ~conventionally called Bottom

and written ! at which all types meet. This condition is

implied by the first if the sets of consistent types includes

the empty set. Together with the partial order conditions of

transitivity, antisymmetry, and reflexivity, these conditions

create what is called a bounded complete partial order~BCPO!.

A tree is an example of a bounded complete partial order,

and a tree-structured inheritance relation ~so-called single

inheritance! is therefore admissible as a type hierarchy. More

complex relations are as well, including so-called multiple

inheritance schemes, providing that the inheritance relationremains a BCPO.

With types are associated features, drawn from a finite

set Feat of features. The function Intro : Featr Type de-fines for every feature a unique most general type at which

that feature is introduced into the type hierarchy. All sub-

types of Intro ~ f! contain f and f is said to be appropriate

for Intro ~ f! and its successor subtypes. Subtype feature in-

clusion and being a complete function in Feat implies thatany feature that is multiply inherited from two or more su-

pertypes is, in fact, the same feature; thus some typical am-

biguities of multiple inheritance do not arise. The partial

function Approp : Feat Type r Type gives a type re-striction on the values of a particular feature: Approp ~ f, t!is the most general type that a value of feature f in type t

can have. On Approp are placed the conditions of upward

closure mentioned above and that feature values can only

become more specific in subtypes, that is, if for two types s

and t, Approp ~ f, s! is defined and s v t, then Approp ~ f, t!

is also defined and Approp ~ f, s! v Approp ~ f, t!.

When we discuss descriptions in Section 3.3 below, we

will add a function associating a description with each type

in a type hierarchy. These descriptions serve as type



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constraintsthey specify further structure in well-formed

instances of a type.

In summary, types are bounded complete partial orders

and impose a strict feature introduction and appropriate-

ness regime on the set of features used. Constraints on types

in the form of descriptions associated with types are dis-

cussed in Section 3.3 below.

3.2. Feature structures

Feature structures are a frame-like representation compris-

ing a set of nodes, each of which is labelled by type infor-

mation, all of which are connected by directed arcs denoting

features and one of which is designated as a root node. Fea-

ture structures have a formal definition ~Carpenter, 1992,

p. 36!, but their essential features can be demonstrated ei-

ther as a graph diagram ~which, despite superficial resem-

blance is neither a Hasse diagram nor a DAG! or in attribute-

value matrix ~AVM! notation, as shown for a fragment of

an abstract boundary solid representation in Figure 11. In

essence, a feature structure comprises:

a set of nodes Q; a root node Sq, a distinguished member of Q;

a total node typing function u : Qr Type that for eachnode assigns a type from Type; a partial feature value function d : FeatQr Q that

assigns a node to features held by nodes in Q.

Feature structures themselves rely on the existence of a

set of types, but these need not be ordered into an inheri-

tance hierarchy until the subsumption and unification con-

ditions over feature structures are considered. In a feature

structure a path, a list of features, identifies a node relative

Fig. 11. Graph diagram and attribute-value matrix

notation for a feature structure.



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to the root node. A node A at the end of a path can itself be

considered as the root node of a feature structure whose nodes

comprise the set of nodes reachable by paths from A. Fea-

ture structures can structure share and be cyclic. The for-

mer, also known as path equation, means that different paths

can pick out the same node; the latter that a path from A can

have A as its value ~thus the transitive closure of the feature

value function is not a partial order!.The relation between feature structures and types does

not follow the common notions of type and instance from

object-oriented programming. Feature structures may exist

which are are consistent with a type but contain additional

information or not well-formed instances of any known type.

3.3. Descriptions

Descriptions are a textual notation for denoting sets of fea-

ture structures. As such they can be specified as a linear

sequence of symbols, which greatly assists their processing

with computers. A given description is satisfied by a set of

feature structures, which is empty if the description is

unsatisfiable.

The description language for feature structures ~Carpen-

ter, 1992, p. 52! is terse and is given over the collection

Type of types and Feat of features as the least set suchthat:

a type is a description; for formal purposes, the absurd type, Top, is a descrip-

tion;

a path comprising features followed by a description isa description;

two paths equated form a description;

two paths disequated form a description; and descriptions may be combined with the logical opera-

tors and and or.

A choice of precedence rules is required over the opera-

tors and these may be notationally circumvented by the in-

troduction of parentheses.

Descriptions serve to call out specific feature structures.

Every feature structure can be picked out by some descrip-

tion that includes no disjunctions. For every description there

is a, possibly empty, set of feature structures that satisfy the

description. Of these there is a subset called out by the func-

tion that comprises pairwise incomparable feature struc-

tures and whose members collectively subsume all feature

structures satisfying the description.

Descriptions also play the role of type constraints. A total

function Cons: Type r Desc maps types to descriptions,

establishing for each type a constraint expressed as a de-

scription. In addition to its own constraint, a type suffers

the constraints inherited from each of its supertypes, namely,

Cons*~t! svt

Cons~s!.

Any feature structure that satisfies a type t must satisfy

the recursive constraint given by Cons*~t!.

With a sketch of the form of feature structures, we now

proceed to the principal relations and algorithms over them.

3.4. Subsumption

Subsumption determines if one feature structure general-izes another and is written A vB if feature structure A sub-

sumes ~or generalizes! feature structure B. Carpenter ~1992,

p. 40! motivates subsumption by the interpretation of fea-

ture structures as representing partial information, that is,

what is known about an object at some stage of a computa-

tion, not as a necessarily complete description of an object.

Thus, determining if a feature structure is more specific than

another can be taken as determining if its represented ob-

ject is more specific than the represented object of the other

feature structure. Such is clearly a sensible motivation in

our context, where we are habitually concerned with incom-

plete designs. We carry this interpretation a step further and

consider that to a feature structure information can be addedto make it an alphabetic variant of any feature structure that

it subsumes. Subsumption is formally described as a mor-

phism, a mapping from the node set of one feature structure

to another in which all of the shared paths and all of the

types at the ends of paths remain consistent. Algorithmi-

cally, subsumption can be decided in time linear to the size

of the subsuming feature structure.

Mutual subsumption A vB and B vA defines the equiv-

alence relation of alphabetic variants written A ; B. Each

element of a set of alphabetic variants carries the same in-

formation as any other in the set. Because feature structures

are intensional, alphabetic variants are distinct objects.

Though it is possible to construct a language free of alpha-betic variance @abstract feature structures ~Carpenter, 1992,

p. 43!#, we take a feature structure to stand for its equiva-

lence class and discipline the construction of feature struc-

tures to ensure disjoint node sets. This is equivalent to

working in the quotient set ~or factor space! of feature struc-

tures modulo alphabetic variance.

3.5. Satisfiability

Descriptions serve to call out feature structures through the

satisfaction relation. Satisfaction is monotonic: If a feature

structure satisfies a description ~Carpenter, 1992, p. 55!, then

so too does every feature structure which it subsumes. There-

fore, a description may be interpreted as a reference to its

most general satisfiers and thus be treated as a name for a

possibly empty set of pairwise incomparable feature struc-

tures. If a description is disjunction free, the named set will

either be empty or contain only mutual alphabetic variants.

Given the set of all disjunction free descriptions NonDisj-

Desc, there is a surjection MGSat : NonDisjDescrF. Forthe set of descriptions Desc, sets of pairwise incomparablefeature structures are identified by the function MGSats :



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Desc r 2F. Satisfaction : Fr Desc is defined in ref-erence to descriptions ~Carpenter, 1992, p. 53!. Informally,

a feature structure satisfies a type if the type subsumesthe feature structure;

no feature structure satisfies top; a feature structures satisfies a path comprising features

followed by a description if the node at the correspond-

ing path in the feature structure satisfies the description;

a feature structure satisfies two equated paths if bothcorresponding paths in the feature structure pick out

the same node;

a feature structure satisfies two disequated paths if thecorresponding paths in the feature structure do not pick

out the same node and are marked as disequated;

a feature structure satisifies the conjunction of two de-scriptions if it satisfies both of the conjuncts; and

a feature structure satisifies the disjunction of two de-scriptions if it satisfies one of the disjuncts.

3.6. Describability

Satisfiable disjunction free descriptions and feature struc-

tures are interchangeable entities. By the satisfaction re-

lation described above, any satisfiable disjunction free

description corresponds to an equivalence class of mutually

alphabetic variant featurestructures. In addition, any feature

structure corresponds to a disjunction free description.

Formally, corresponding to any feature structure F F

there is a nondisjunctive description Desc ~F! such that F;

MGSat~Desc ~F!!.

The significance of describability is twofold. First, fea-

ture structures can be used directly to specify constraints in

types and queries, suggesting a programming-by-exampleform of interaction with a design space explorer. Second,

feature structures can be converted to a textual form.

3.7. Unification

Given two feature structures, A and B, unification, written

A t B, produces a third feature structure C subsumed by

both A and B if such a feature structure can exist, otherwise

unification fails. Feature structure unification produces the

most general feature structure that contains all of the infor-

mation in its two arguments. Unification is interesting, as it

provides a disciplined way to combine information or to add

information to a structure. In a design context, the result of

a feature structure unification can be taken as a new, more

complete object that is consistent with the objects repre-

sented by the argument feature structures. Unification cre-

ates a set of equivalence classes of nodes by following paths

in the two argument feature structures, A and B. Each node

in A and B begins in a singleton equivalence class, except

for the root nodes whose equivalence classes are merged by

default. Equivalence classes are merged through the feature

value function: Where a feature is shared by nodes in an

equivalence class, the equivalence classes containing the

nodes on the shared features are merged. There exists a lin-

ear time unification algorithm for unification, though in prac-

tice, a near linear algorithm is typically used.

3.8. p-resolution

The p-resolution algorithm maps descriptions into sets offeature structures that satisfy them, taking into account a

type hierarchy, including the recursive t ype constraints de-

fined within it.

Given a query description D, p-resolution is the search

across a sequence of feature structures P0 v P1 v P2 v

. . . v Pk. The initial feature structure in each sequence is a

most general satisfier of the query description. The se-

quence represents the inclusion of type information in the

form of constraintseach element extends its predecessor

by unification with a type constraint. Because most general

satisfiers may occur as collections and unification may fail,

the search for resolved feature structures involves a collec-

tion of sequences.With these relations sketched, Figure 12 adds to the dia-

gram of the principal computation paths in featurestructures

the relations satisfiability, describability, and unification. Be-

cause a type is a primitive description, we also note that sDesc ifsType. Since each type hasa constraint expressed

as a description, we add Cons~u !. Because the root node Sq of

any feature structure has a type, every feature structure calls

out a type u~ Sq! Type. Finally, inheritance orders types.

4. AN EXAMPLESINGLE-FRONTED

COTTAGES

We conclude this paper with an example of types, feature

structures, and descriptions that together denote a corpus of

single-fronted cottages. We include only the physical spaces

identified by name and labels denoting functional use. Both

the expression of a knowledge level representation for a de-

sign space explorer and the consideration of geometric in-

formation are left for a future paper. The language used for

the example is ALE ~Carpenter & Penn, 1997!, which im-

plements typed feature structures in a Prolog environment.

4.1. Type hierarchy

Immediately above the type bottom are three types, corre-

sponding to buildings, briefs, and massings. The models cor-

responding to the type building can be thought of as designs

for buildings, those corresponding to the type brief as ar-

chitectural briefs, and those corresponding to the type mass-

ing as volumes that together compose an overall building

mass. All of these types are abstract, serving to refine the

type bottom and do not introduce any features. We shall

see later how such abstract types can be used in constraint

expressions.



12/16

Massings can recursively contain other massings. The type

massing has a sequence of subtypes massing1, mass-

ing2 . . . in which massingn v massingn1 . Each typemassingn introduces a feature MASS_ELn, which denotes

a submassing ofmassingn. Thus, a feature structure of type

massingn is a representation of a massing of nj submass-

ings, where j 0.

The type brief has a single subtype house at which fea-

tures corresponding to functions are introduced. These fea-

tures carry only functional information, in contrast to the

the features introduced in sfc ~single-fronted cottage!. These

features, corresponding to a porch, hall, row of rooms, and

skillion, denote the particular spatial organization of single-

fronted cottages without making commitment to actual ad-

jacencies or dimensions. Type sfc inherits from both building

and massing4. The type sfc_house inherits features from

both sfc and house. Section 4.2 below describes how the

diverse features relating to function, abstract form, and mass-

ing are related through type constraints.

Figure 13 diagrams these types, showing inheritance, fea-

ture introductionIntro~ f!, and appropriatenessApprop~ f,t!

conditions. Following Carpenter ~1992! and order theorists

such as Davey and Priestley ~1994!, and contrary to stan-

dard practice in artificial intelligence we draw type hierar-

chies with the most general type bottom at the bottom of

the diagram. We do this because type subsumption ex-

presses an information ordering in which s is less than or

equal to t in information content ifs v t.

4.2. Type constraints

Associated with the types above are constraints, Figure 16

shows the types having nonempty constraint sets: house,

sfc, and sfc_house. As is normal in most languages, effi-

ciencies can often be realized through macroexpressions,

and descriptions are no exception. Before explaining the con-

straints, we introduce a bit of notation about constraint mac-

ros. A constraint macro comprises a parameterized head and

a body. The head acts as a name, the body is a description

that substitutes for the name, and the parameters in the head

are substituted into their indicated place in the body. Forexample, the three-argument macro mdq ~mutual dise-

quate! in Figure 14 disequates the node at feature A with

those at features B and C and issues a call @ mdq~B,C! to

the two-argument macro mdq/2.3

Thus, the macro call @ mdq~sleeping, lounge,kitchen! with head mdq, actual parameters sleeping,

3Note the use of the Prolog convention of giving the arity of a macrowhen a parameter list is not given.

Fig. 12. Augmented computation paths in typed feature structures.



13/16

lounge, and kitchen results in a pairwise inequation

of the functions sleeping, lounge, and kitchen.

The constraints of type massingn simply pairwise dise-

quate the n massing elements inside a massing. This pre-

vents massings from being structure-sharedarchitecturally,

a thoroughly Victorian restriction appropriate with the single-

fronted cottage type.

The constraints of type house pairwise inequate the fea-

tures that compose house. This prevents their ever being

structure-shared in any feature structure consistent with

house.

Type sfc structure-shares the four submassing elements

and the abstract spatial features that compose a single-

fronted cottage. Thus porch, hall, room_row, and

skillion become new names for the elements, mass_el1,

mass_el2, mass_el3, and mass_el4. The reason for this

simple sharing of feature values ~and thus names! is that it

sets the scene for a generic definition of the in/2 macro,

Fig. 13. The type hierarchy for the single-fronted cottage example.

Fig. 14. Definition for mdqmutual disequate.

Fig. 15. Definitions for in1 and in2.

Fig. 16. Type constraints for the single-fronted cottage example. The

share macro shares the nodes at the end of the two given paths. The innmacro constrains the second argument to be structure-shared with one of

the first n massing elements of the first argument.



14/16

which operates over the mass_eln features irrespective of

their other names as architectural elements or functions.

All so far is deterministicthe descriptions in house and

sfc contain no disjunctions, and so have but a single most

general satisfier under p-resolution. The alternatives are all

generated in type sfc_house, in which alternative assign-

ments of functions to spaces are made in four disjuncts as

follows. In all alternatives, the sleeping area is confined tothe first two rooms of the room row.

1. Thedining andthe loungefunctions arebothin theroom

row. The kitchen and bathroom are in the skillion.

2. The dining function is in the room row. The kitchen,

lounge, and bathroom are in the skillion.

3. The lounge function is in the room row. The kitchen,

dining, and bathroom are in the skillion.

4. The kitchen, dining, lounge, and bathroom are in the

skillion.

The macro inn, n 1 makes these assignments of func-

tional spaces into physical spaces by either calling inn1or by structure sharing the functional space with the nth con-

tained massing element of the physical space. Macro in1

simply structure shares the functional space with the first

contained massing element of the physical space. Figure 15

gives the code for in1 and in2the definitions for inn

follow by induction.

Fig. 17. The 32 single-fronted cottage plans produced by the example-type hierarchy. By convention, the layout of the drawings

corresponds to typical abstract layouts for single-fronted cottagesno geometry is included in this example.



15/16

4.3. Feature structures for single-fronted cottages

The type hierarchy and its associated type constraints pro-

vide the entire specification required for generating alter-

native mappings of function into the form of single-fronted

cottages. Given a query comprising only the type sfc_house,

the p-resolution algorithm generates the set of pairwise in-

comparable, most general resolved feature structures con-

sistent with the type hierarchy and its constraints. These areshown in Figure 17.

We return now to the seven behaviors that typed feature

structures lend to a generative design system to interpret

these in the light of the given example.

Intensionality. Each of the feature structures is inten-

sional in standing for a particular representation of a

single-fronted cottage.

Partialness. Any feature structure is partial in that it may

not give all that could be known about the cottage it

represents. Another way of saying this is that there may

be resolved feature structures subsumed by a featurestructure picked out by p-resolution as a most general

resolved feature structure. Figure 19 gives an example

in which feature structure #5 in Figure 17, which has

only two rooms in the room row, in effect stands for

feature structures that have three, four, or more rooms

in the room row.

Adding new knowledge. By extending the type hierar-

chy, say by including massing5, additional resolved fea-

ture structures become possible.

No rules. The type hierarchy itself plays the roles usu-

ally reserved for rules in a generative system. The dis-

juncts in the constraint expressions create choice points

in the derivation graph.

Monotonic generation. We do not discuss the internal

action of the p-resolution algorithm here,4 so we can-

not peek inside its operation to show that each of its

steps is strictly monotonic. However, monotonicity can

be demonstrated indirectly by showing that, for exam-

ple, mgsat~house! v mgsat~sfc-house!.

Subsumption. The 32 most general resolved feature struc-

tures of the query sfc-house form an antechain in

the subsumption relation of feature structures under the

given type hierarchy. Subsuming these feature struc-

tures are the incremental steps of the p-resolution al-

gorithm. Subsumed by these structures are the resolved,

but not most general, feature structures admitted by the

type hierarchy.

Reuse. Consider the first feature structure in Figure 18.

It subsumes only cottages #28 and #31 of Figure 17.

The feature structure for cottage #28 is included in the

figure.

5. SUMMARY

Typed feature structures are a model for design space ex-

ploration in which both the action of exploration and the

structure of a design space are given a sound theoretical

basis. As a representation of designs, typed feature struc-

tures provide well-founded support for an object-and-

relations view of representation and within that view support

intensionality, partialness, structure sharing, and cyclic-

ity. In this paper we have demonstrated that typed feature

structures can tersely express and solve simple, apparently

finite-domain, generation of alternative mappings of func-

tion into form in the building domain. It remains to be

shown how more complex domain structures, such as the4See Burrow and Woodbury ~1998!.

Fig. 18. A feature structure ~a) used as a query to retrieve feature struc-

tures #28 and #31 shown as ~b) from Figure 17.



16/16

SEED5 Knowledge Level can be supported. The problems

posed by geometry also remain. To foreshadow a solution,

consider that well-founded type inference in typed feature

structures requires at least unique joins in a type hierarchy,

and that many operations over point sets, such as union

and intersection, generate structures with stronger formal

properties than this required minimum. Both of these is-

sues, the expression of a knowledge level, and the han-

dling of geometric information, are topics for future papers.

ACKNOWLEDGMENTS

The authors acknowledge the support given by the Australian Re-

search Council Large Grants Scheme; The Department of Indus-

try, Science and Tourism Major Grant Scheme; the Australian

Postgraduate Award Scheme; The Commonwealth of AustraliaOverseas Postgraduate Research Scholarship Scheme; The Key

Centre for the Social Applications of Geographic Information Sys-

tems; andThe University ofAdelaide School of Architecture, Land-

scape Architecture, and Urban Design.

REFERENCES

Akin, O., Aygen, Z., Change, T.-W., Chien, S.-F., Choi, B., Donia, M.,Fenves, S. J., Flemming, U., Garrett, J. H., Gomez, N., Kiliccote, H.,Rivard, H., Sen, R., Snyder, J., Tsai, W.-J., Woodbury, R., & Zhang, Y.~1997!. SEED: A Software Environment to support the Early phases ofbuilding Design. The International Journal of Design Computing. http:00www.arch.usyd.edu.au0kcdc0journal0index.html.

Archea, J. ~1987!. Puzzle-making: What architects do when no one is look-ing. In Computability of Design, Principles of Computer-Aided De-sign, ~Kalay, Y., Ed.!, Chap. 2, pp. 3752. John-Wiley & Sons, NewYork.

Burrow, A., & Woodbury, R. ~1998!. Pi-resolution in design space explo-ration. Technical Report, Department of Architecture, Universityof Adelaide. http:00www.arch.adelaide.edu.au 0;rw0publications 0progress.html.

Carlson, C. ~1994!. Design space description formalisms. Proc. Formal Design Methods for CAD, pp. 121131. North-Holland, Amsterdam.

Carpenter, B. ~1992!. The logic of typed feature structures with applica-tions to unification grammars, logic programs and constraint resolu-

tion. Cambridge University Press, New York.Carpenter, B., & Penn, G. ~1997!. The attribute logic engine users guide.

Computational Linguistics Program, Philosophy Department, Carne-gie Mellon University, Pittsburgh, PA.

Davey, B., & Priestley, H. ~1994!. Introduction to lattices and order. Cam-bridge Mathematical Textbooks. Cambridge University Press, Cam-bridge, UK.

Fenves, S., Rivard, H., Gomez, N., & Chiou, S.-C. ~1995!. Conceptual

structural design in SEED. ASCE Journal of Architectural Engineer-ing 1(4), 179186.

Flemming, U. ~1994!. Case-based design in the SEED system. Automationin Construction 3, 123133.

Flemming, U., & Woodbury, R.F. ~1995!. Software Environment to sup-port Early phases in building Design SEED: Overview. ASCE Journalof Architectural Engineering 1(4), 147152.

Hinrichs, T.R. ~1992!. Problem solving in open worlds: A case study indesign. Erlbaum Associates, Hillsdale, NJ.

Kolodner, J. ~1993!. Case-based reasoning. Morgan Kaufmann Publish-ers, Inc., San Mateo, CA.

March, L. ~1995!. The smallest interesting world? Environment and Plan-ning B: Planning and Design 23 (1), 133142.

Newsome, S., Spillers,W., & Finger, S. ~1989!.Design Theory 88. Springer,New York.

Stiny, G. ~1980!. Introduction to shape and shape grammars. Environmentand Planning B: Planning and Design 7(3), 343352.

Woodbury, R., Fenves, S., Flemming, U., Coyne, R., Chang, T.-W., Chiou,S.-C.,& Gomez,N. ~1994!. SEED-Config requirements analysis. http:00seed.edrc.cmu.edu 0SC0requirements-new0SC-req-new.book.html.

Dr. Robert Woodbury holds a B.Arch from Carleton Uni-

versity and an M.S. and Ph.D. from Carnegie Mellon Uni-

versity. He is presently an Associate Professor ~Reader! at

The University of Adelaide in Australia. His main research

focus is on generative design systems. His work is distinc-

tive in its emphasis on implementation within the research

process, without which results in this area can neither be

falsified nor forcefully demonstrated. He is the author of

over 100 technical papers.

Andrew Burrow is a Ph.D. candidate at the University of

Adelaide in the Department of Computer Science and School

of Architecture, Landscape Architecture and Urban Design.

He holds a Bachelor of Engineering ~Chemical! and a Bach-

elor of Science ~Mathematical and Computer Science! with

Honors from the University of Adelaide. His research inter-

ests include: design applications of typed feature struc-

tures, knowledge visualization, and order theory.

Sambit Datta holds a Dip.Arch from the School of Archi-

tecture, CEPT, India, and an M.Arch from the National Uni-

versity of Singapore. He is presently a doctoral student in

the School of Architecture, Landscape Architecture and Ur-ban Design at the University of Adelaide. His current re-

search is on developing interaction techniques for design

representations.

Mr. Teng-Wen Chang holds a B.Arch. from Tunghai Uni-

versity in Taiwan, an M.Arch. from The University of Penn-

sylvania, and an M.S. from Carnegie Mellon University. He

is presently a Ph.D. student at The University of Adelaide

in Australia. His main research focus is on representing geo-

metric information in generative design systems.

5~Woodbury et al., 1994; Flemming & Woodbury, 1995; Akin et al.,1997!.

Fig. 19. A most general resolved feature structure with respect to a

p-resolution query may subsume other, more specific, resolved feature

structures.


typed feature structures and design space exploration

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