Abstract

We describe a computational technique for functionalmodeling of physical devices . In this technique, func-tions and behaviors of a given device are derived by re-trieving the structure-behavior-function (SBF) modelof a structurally similar device and revising the re-trieved model to meet the specifications of the givendevice . The SBF model of a device explicitly repre-sents its structure, its functions, and its internal causalbehaviors that specify how its structure delivers itsfunctions. The model of the known device is revisedby model-revision plans, where each plan accommo-dates a specific type of structural difference betweenthe new and the known devices. The model ontologygives rise to a classification of structural differencesand corresponding model-revision plans . The processof model revision is focused by the organization of theknown model . The revised model for the new deviceis stored in memory for potential reuse in future . Wecall this computational process adaptive modeling.

Motivations, Background, and GoalsFunctional models of devices have proved to be quiteuseful for reasoning about a variety of function-relatedtasks . The Functional Representation (FR) scheme[Sembugamoorthy and Chandrasekaran 1986 ; Chan-drasekaran, Goel and Iwasaki 1993], for example, hasbeen extensively used for diagnosis (e.g ., [Sticklenand Chandrasekaran 1989]), redesign (e.g ., [Goes andChandrasekaran 1989]), and, more recently, design ver-ification (e.g ., [Iwasaki and Chandrasekaran 1992)] .Since functional models explicitly represent the func-tions of a device and use the function representationsto organize behavioral knowledge about the device,they help define problem spaces for function-relatedtasks, and provide access to the knowledge relevant forsearching the spaces .But the origin, generation and acquisition of func-

tional device models remain open issues . Not only arethese questions fundamental, but, in addition, their an-swers are likely to impose additional representationalconstraints on the models . The research described hereis motivated by both goals : exploration of the origin,

Adaptive Modeling

Ashok K . GoelCollege of Computing

Georgia Institute of TechnologyAtlanta, Georgia 30332-0280

goel@cc.gatech .edu

generation and acquisition of functional device mod-els, and discovery of additional representational con-straints on the models .The origin of this research lies in our earlier work on

the conceptual phase of functional device design . Thetasks of conceptual (or preliminary) device design and(qualitative) device modeling have an "inverse relation-ship" with each other . The task of device design takesas input a specification of the desired output behav-iors of the device, i .e ., the device functions . It has thegoal of giving as output a specification of the struc-ture of the device that can deliver the desired func-tions . Thus, the task of device design is a function -4structure mapping . The task of device modeling takesas input a specification of the structure of a device .It has the goal of giving as output a specification ofthe output behaviors of the system . Thus, the taskof qualitative device modeling is a structure --+ outputbehavior mapping . Since device functions are a subsetof the output behaviors of the device, it follows thatthe two tasks, though not exact inverses of each other,have an inverse relationships .In our work on the conceptual phase of functional

design, this inverse relationship between device de-sign and device modeling led to us to hypothesize thatknowledge of device models may facilitate the adapta-tion of the designs of known devices to design new de-vices of similar functionality . If the structure -3 outputbehavior map of a device was known, then, we hypoth-esized, this map may enable adaptation of the devicestructure for achieving a different, though similar andrelated, set of device functions . In the Kritik family ofsystems, we have extensively investigated this hypoth-esis [Goes 1991, 1992 ; Goel and Chandrasekaran 1992] .Kritik contains a design case memory, where each casein the memory specifies a structure-behavior-function(SBF) model that explains how the structure of the de-

'The "output behaviors" of a device, in our terminol-ogy, include both the intended and the unintended behav-iors . The "functions" of the device refer to the intendedoutput behaviors . The "internal behaviors" of the device,in this terminology, are the causal processes that result inits output behaviors including the device functions .

Goel 67

vice delivers its functions 2 . The ontology of the SBFmodels gives rise to a classification of functional differ-ences between related devices . Kritik contains skeletalplans for design modification, where each skeletal plancan help to reduce a given type of functional difference .When the function of desired device is specified, Kri-tik retrieves a functionally similar design from its casememory along with its SBF model . Also, it notes thedifferences between function desired of and deliveredby the retrieved design, and instantiates correspond-ing design modification plans . The instantiation of theskeletal plans in the context of the SBF model of theretrieved design leads Kritik to a modified design alongwith its (revised) SBF model . The model of the modi-fied design enables design verification, and the verifieddesign is stored in the design case memory for poten-tial reuse . In this way, Kritik uses qualitative modelsof known devices to generate candidate designs . Wecall this computational process adaptive design .But note that the above process of adaptive design

also generates SBF models for the new device designsby revising the SBF models of the known devices . Inanalogy to the technique of adaptive design, this hasled us to think in terms of an adaptive technique forthe general task of qualitative modeling of physical de-vices . In this technique, given the structural spec-ification of a device, some of the output behaviorsof a device are derived by locally revising the (SBF)model of a structurally similar device . The model isrevised through instantiation and execution of skeletalmodel-revision plans, where each plan accommodatesa specific type of structural difference between the newand the known devices . The ontology of SBF modelsgives rise to a classification of structural differences andmodel-revision plans . The process of model revision isfocused by the organization of the internal causal be-haviors of the SBF model of the known device . Therevised SBF model for the new device is stored in amodel memory for potential reuse in future . We callthis computational process adaptive modeling .The goal of this paper is to describe the technique

of adaptive modeling, We illustrate the technique us-ing a simple example that originates from the Kritiksystem . But while Kritik used the technique of adap-tive design to perform function -> structure mappings,the new technique of adaptive modeling performs theinverse structure -4 function mappings . In the follow-ing discussion of adaptive modeling, we focus on theissues of the content and representation of SBF mod-els of known devices, and the computational processof revising SBF models to derive the functions of new,but similar and closely related, devices .

'The SBF device models are closely related to, but dis-tinct from, the FR scheme . The `B' in SBF models standsfor the internal behaviors of the device that explain howthe behaviors of the structural elements of the device getcomposed into the device functions .

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Hot H2SO4

Cold H2O

Water-Pump

I t Hot H2O

new-pipe 2 n

Figure 1 : The Sulfuric Acid Cooler

An Illustrative Example

Cold H2SO4

Heat-Exchange-Chamber

As an illustrative example, let us consider the task ofqualitatively modeling the Sulfuric Acid Cooler (SAC)schematically depicted in Figure 1 . We are given aspecification of the structure of SAC, where the struc-tural specification includes the specification of the com-ponents comprising the system, and the structural andbehavioral interactions among them . It includes, forexample, the specification that the Sulfuric Acid inSAC is highly acidic, and the pipes through which Sul-furic Acid flows are made of a material that allows onlyhigh-acidity liquids .

Let us suppose that a model memory contains anumber of device designs along with their qualitativedevice models . The technique of adaptive modeling,in general, sets up four subtasks of the qualitative-modeling task : (i) model retrieval, (ii) model revision,(iii) model evaluation, and (iv) model storage . Giventhe structural specification of a device, such as SAC,the first subtask retrieves the design of a structurallysimilar device along with its qualitative model . If thestructure of the retrieved design exactly matches thestructure of the specified device, then the model of theretrieved design directly specifies the functions of thedevice, and the processing is terminated . Else, the sec-ond subtask revises the model of the retrieved designto meet the structural specification of the given de-sign . The third subtask evaluates the revised modelfor internal consistency . If the model-evaluation taskfinds that the revised model is internally inconsistent,then the model can be revised again, or alternatively,another model can be retrieved from memory and re-vised to produce the desired model. The fourth and fi-nal task stores the evaluated model in the design modelmemory for potential reuse in future .

Structure-Behavior-Function ModelsLet us assume that the design model memory containsthe design of a Nitric Acid Cooler (NAC) along with itsSBF model. Let us also assume that the Nitric Acid inNAC has a low acidic content, and the pipes throughwhich Nitric Acid flows in NAC allow only low-acidityliquids . In this section, we briefly describe the contentand representation of SBF device models using NACas an illustrative example .The SBF model of a device explicitly specifies (i) its

structure, (ii) its functions (i .e ., the intended outputbehaviors of the device), and (iii) its internal causalbehaviors . The causal behaviors explain the functionalrole of each structural component of the device, andthe causal processes that compose the functions of thestructural components into the device functions .

StructureThe structure of a device is viewed as constituted ofcomponents, substances, and relations among them .The structure of SAC shown schematically in Figure1, for example, is viewed as composed of Sulfuric Acidand Water, a water-pump, a heat-exchange chamber,and various pipes, where the pipes through which Sul-furic Acid flows are connected in series, etc . The sub-stances can be abstract, e.g ., heat, electrical charge,angular momentum. Substances can flow from onecomponent to another if (and only if) the two compo-nents are connected to each other . SBF device modelsthus are flow models.The structural model in a SBF device model is repre-

sented as a schemata that specifies not only the compo-nents and substances constituting the structure of thedevice but also . the structural and behavioral interac-tions among them . It specifies, for example, that pipe2(in NAC) is included in the heat-exchange-chamber,and allows the flow of a low-acidity substance fromone end to another . The SBF ontology borrows thetaxonomy of primitive device behaviors from Bylan-der 's [1991] work on composing the behaviors of thestructural elements of a device into the behaviors ofthe device . The specification of a structural compo-nent includes its functional abstractions in terms ofthe primitive device behaviors . The component speci-fication also contains pointers to the causal behaviorsin which it plays a role .

FunctionDevice functions are viewed as transformations from aninput behavioral state to an output behavioral state .A function is represented in the form of schema . Theschema for a function specifies the behavioral state ittakes as input and the behavioral state it gives as out-put . It also specifies the internal causal behaviors re-sponsible for the achievement of the function ; thus thefunctions of a device act as indices to its internal be-haviors . In addition, the function schema specifies the

BEGIN BehaviorCoolNitricAcid-2

Behavior

USING-FUNCTIONALLOW NitricAcid ofpipe2{endl,end2,space2)BEHAVIORAL-REQUIREMENTS

state liquid

aciditylowUSING-FUNCTIONALLOW Heat of prpe2(endl,end2,s ace2IN-CONTEXT-STRUCTURAL-RELATIONINCLUDESChamber(endl,end2,end3,end4,spaceI )pipe2(end l,end2,space2)AS-PER-DOMAIN-PRINCIPLEZeroth Law of ThermodynamicsIN-CONTEXT-STRUCTURAL-RELATIONCONTAINSCham . erlendI end2�end3,egd4_4_snarrl 1sub

Water

temperature

tl < TIUNDER-CONDITION-TRANSITIONtransition 1-2 of BehaviorHeatWaterPARAMETER-RELATIONT2-Tl=f(+(Q2-Q 1)) ;Q2-Ql=f(-R) ;2-01=f(-r3

END BehaviorCoolNitricAcid-2

Figure 2 : A Fragment of an Internal Behavior ofthe Nitric Acid Cooler

conditions under which the internal behavior accom-plishes the function including the stimulus from the en-vironment which triggers the internal behavior . Func-tion representation in SBF models builds on Chan-drasekaran's FR scheme [Sembugamoorthy and Chan-drasekaran 1986 ; Chandrasekaran, Goel and Iwasaki1993] . Unlike FR, however, the SBF ontology givesrise to a vocabulary for expressing the semantics ofbehavioral states .

Finally, the SBF model specifies the internal behav-iors of the device . The internal behaviors are causalprocesses that compose the structural and behavioralinteractions between the components and substancesinto the functions of the device . A small fragment ofone internal behavior of NAC is shown in Figure 2 .

Goel 69

Knowledge of an. internal behavior is represented asa directed acyclic graph (DAG) . The nodes in a DAGrepresent the behavioral states of the device and thelinks represent the state transitions . A node (i .e ., abehavioral state) is represented in the form of compo-nent and substance schemas . For example, the sub-stance schema representing state2 in Figure 2 specifiesthe location, property, and parameter of a substance,viz ., it specifies that the location of substance NitricAcid is p2 (where p2 is a point in the device space),and the parameter of property temperature is T1 . Italso specifies that the substance Nitric Acid containsanother substance, heat, which has its own propertiesand parameter values .A state transition in an internal behavior is also

represented as a schema . The slots in the transitionschema act as annotations on the state transitions, andspecify the causes of the transitions . For example, thetransition state2 => state3 in BehaviorCoolNitricAcid-2 specifies that one of the causes of the transition isthe function allow low-acidity liquids of pipe2 . A statetransition may be annotated by the function of somecomponent (e .g ., USING-FUNCTION ALLOW), en-abling conditions such as a specific structural relationbetween some components (e .g ., INCLUDES Cham-ber Pipe2), a domain principle (e.g ., Zeroth Law ofThermodynamics), and qualitative parametric equa-tions (e.g ., TZ - Tl = f(+(Q2 - Qj))) as shown inFigure 2 . Since the device functions act as indices intothe internal behaviors responsible for their accomplish-ment, and since a state transition in an internal behav-iors may index the function of a device component, thisleads to hierarchical organization of the device modelof the form function =::~ behavior =::~ function =* behav-ior . . . Again, SBF models borrows this organizationalscheme from Chandrasekaran's FR scheme.Within a given level of this hierarchy, the inter-

nal behaviors are organized along the flow of specificsubstances . This organization builds on Govindaraj's[1987] work on qualitative approximations of quan-titative device models . Interactions between differ-ent internal behaviors are specified through enablingand disabling pointers . For example, the transitionstate2 =;> state3 in BehaviorCoolNitricAcid-2 specifiesUNDER-CONDITION-TRANSITION transition 1-2of BehaviorHeatWater as an enabling condition asshown in Figure 2 . Thus, one internal behavior mayindex another internal behavior .

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Model Revision ProcessIn this section, we briefly describe the functional archi-tecture and computational process of model revisionin adaptive modeling . The SBF model of a known de-vice (such as NAC) is revised by a family of skeletalmodel-revision plans . The functional architecture ofthe model revisor consists of (i) a plan memory, (ii)a plan selector, (iii) a plan executor, and (iv) a dif-ference orderer . The SBF language described in the

previous section leads to a typology of structural dif-ferences between two devices . The plan memory con-tains a plan for each type of structural difference . Thestored plans are indexed by the types of structural dif-ferences to which they are applicable . Given a spe-cific type of structural difference between the new andthe known devices, the plan selector retrieves the ap-plicable model-revision plan from the plan memory.The plan executor instantiates the retrieved plan inthe context of the structure-behavior model of theknown device, and executes it on the model to pro-duce a structure-behavior model for the new device . Ifthe new and the known devices differ in more thanway, then the difference orderer heuristically ranksthe structural differences by the order of the difficultyof accommodating them, and the plans applicable tomore difficult structural differences are retrieved andexecuted before the plans applicable to less difficultones .A model-revision plan specifies a compiled sequence

of abstract operations . Different plans specify differ-ent sequences of (possibly) different operations . Theabstract operations in the plans are specified in thevocabulary of SBF language such as those enclosed inboxes in Figure 2 (e.g ., sub, prop), or shown in capitalletters (e.g ., USING-FUNCTION, ALLOW) .To illustrate the model-revision process, let us return

to the example of modeling the Sulfuric Acid Cooler(SAC) shown in Figure 1 . Recall that the model-retrieval task resulted in the selection of the modelfor the Nitric Acid Cooler (NAC), where the struc-tures of SAC and NAC differ in that (i) while SACcontains high-acidity Sulfuric Acid, NAC contains low-acidity Nitric Acid, and (ii) while the pipes throughwhich Sulfuric Acid flows in SAC allow high-acidityliquids, the pipes through Nitric Acid flows in NACallow only low-acidity liquids . The first of these twodifferences, Nitric Acid -+ Sulfuric Acid, is an instanceof the substance substitution type of structural differ-ences ; the second, pipe (allow low-acidity substances)-+ pipe (allow high-acidity substances), is an instanceof the component replacement type of structural differ-ences . Since the structures of SAC and NAC differ inmore than way, and, since, in the class of domains ofinterest, revising a component-substance model to ac-commodate the structural difference of component re-placement is in general more difficult than revising it toaccommodate the difference of substance substitution,the difference orderer ranks the two differences betweenthe structures of SAC and NAC so that the model forNAC is first revised for the difference of pipe (allowlow-acidity substances) -+ pipe (allow high-acidity sub-stances), and then for the difference of Nitric Acid -~Sulfuric Acid.

Let us consider the revision of the model for NAC,given the structure difference of pipe (allow low-aciditysubstances) -+ pipe (allow high-acidity substances) be-tween the structures of NAC and SAC . This struc-

tural difference is used as probe into the plan mem-ory to access the model-revision plan for component-replacement . The model-revision plan for component-replacement revises the component-substance modelfor NAC in several steps . First, from the spec-ification of the old pipe (pipe2) in NAC, it de-termines that the pipe2 plays a functional role inBehaviorCoolNitricAcid-2 . Then, it decomposes Be-haviorCoolNitricAcid into three segments : (i) the tran-sition in which the old component (pipe2) plays a func-tional role (in the present example, state2 => state3 inBehaviorCoolNitricAcid shown Figure 2, (ii) the se-quence of state transitions preceding it (not shownhere), and (iii) the sequence of state transitions suc-ceeding it (also not shown here) . Next, the transitionin which the old component (pipe2) plays a role is re-vised by replacing the behavioral abstraction of pipe2(which allows the flow of low-acidity liquids) by thebehavioral abstraction of the new pipe (newpipe2) inSAC (which allows the flow the high-acidity liquids) .Then, the revised transition is composed with the pre-ceding and succeeding segments of the original behav-ior to obtain the revised behavior . Finally, the con-straints introduced by the new component, representedby changes in the values of the variables characterizingthe old and new components (pipe2 and newpipe2),are propagated forward through the newly composedbehavior to obtain the revised internal behavior andfunction . Also, the schema for the function is revisedby associating a pointer with it to the revised internalcausal behavior .

Similarly, the structural difference Nitric AcidSulfuric Acid between the structures of NAC and SACis used to access the model-revision plan for substancesubstitution . The model-revision plan for substancesubstitution further revises the (already revised) inter-nal behaviors and functions in the model for NAC byreplacing the old substance (low-acidity Nitric Acid) bythe new substance (high-acidity Sulfuric Acid) . Thisproduces a SBF model for the Sulfuric Acid Cooler(SAC) . The function schema in the SBF model spec-ifies the function of SAC, and the internal behaviorsspecify in the model specify how the structure of SACresults in the function .

In this section, first we describe current work on theevaluation of the technique of adaptive modeling, andthen we relate the technique to other research on qual-itative models and modeling .

Evaluation

Discussion

In the Kritik series of systems, we have extensivelyevaluated the technique of adaptive design . We brieflysummarize the main lessons from the evaluation of theadaptive-design technique because we expect that thetechnique of adaptive modeling is likely to be con-strained by similar factors . Our analysis of the Kritik

work shows that the technique of adaptive design isuseful whenever (i) the differences between the func-tions of the desired and the known devices are small,(ii) design-modification plans for each specific typeof functional difference between the desired and theknown devices are available, (iii) detailed knowledgeof the internal behaviors of the known devices also isavailable, including knowledge of the causal dependen-cies between the behavioral states and the functionalrole played each component and substance in the statetransitions, and (iv) the structural modifications to theknown design needed to reduce the functional differ-ences can be localized to specific components and/orsubstances . For the class of design problems for whichthe above conditions are met, adaptive design providesa productive and feasible technique for the creation ofnew designs through model-based modification of olddesigns .

Our work on adaptive modeling is of more recentorigin, and only now have we begun to systematicallyevaluate it . In one experiment, we have developed aknowledge system called KA [Goel et al 1996, Peterson,Mahesh and Goel 1994] that acquires qualitative devicemodels from device descriptions in the popular sciencebook "The Way Things Work" [Macaulay 1988] . Twocharacteristics of this book relevant to our discussionare that (i) each device description is accompanied by acutaway diagram that reveals the device structure, and(ii) many devices are described through reference toother devices . For example, the very short text on thecommon fire extinguisher is accompanied by detaileddiagrams of its structure and makes explicit referenceto the common spray can . Macaulay's implicit assump-tion appears to be that given the structure of the fireextinguisher and a qualitative model of how the spraycan works, the reader can easily build a similar quali-tative model of the fire extinguisher . Accordingly, wesupply KA with a complete and detailed SBF model ofthe spray can and a structural specification of the fireextinguisher . We have found that KA can use the tech-nique of adaptive modeling to autonomously acquire aSBF model of the fire extinguisher by adapting themodel of the spray can . This appears to indicate thatthe SBF language is adequate for representing boththe fire extinguisher and the spray can, at least up tothe coarse level of one popular science book . It alsoseems to indicate that the technique of adaptive mod-eling is computationally feasible and actually works forcomplex examples taken from a real book .

In another experiment, we are developing a knowl-edge system called Torque [Griffith et al 1996] thatacquires SBF models of hypothetical devices by adapt-ing SBF models of real devices . Torque seeks to modela verbal protocol collected by Clement [1989] . In thisprotocol, a scientist answers questions about how muchan ordinary spring may stretch when an external forceis applied to it . In the course of constructing answersto questions about the spring, the subject imagines

Goel 7 1

a series of hypothetical devices similar to the ordi-nary spring, for example, a spring with only one coil,and a spring with square coils . He constructs qualita-tive models of the hypothetical devices by revising hismodel for the spring, and uses the constructed modelsto verify his answers to the questions concerning theoriginal spring . Nersessian [1995] has argued that thiskind of constructive modeling is a core process in sci-entific problem solving and theory formation . Torqueuses the technique of adaptive modeling for construct-ing SBF models of the hypothetical devices by adapt-ing the SBF model of the spring .

Related ResearchWehave already indicated the relationship between ourSBF device models and Chandrasekaran's, Bylander 'sand Govindaraj's work on device representation . Inresearch in Cognitive Engineering, Rasmussen [1985]has proposed a hierarchical organization for present-ing device knowledge to human users . Like our SBFmodels, his SBF device models too specify the struc-ture, the behaviors, and the functions at each level inthe hierarchy. In Design research, [Umeda et al 1990]have described similar FBS device models. Like in ourSBF models, in their FBS models behaviors mediatebetween function and structure .One common (and justified) criticism of functional

device models has been that they are not generative .Another common (and, again, justified) criticism hasbeen that the functional representations are undercon-strained . Adaptive modeling is a technique for generat-ing and acquiring one class of functional device modelscalled SBF models . Our earlier work on adaptive de-sign too resulted in the derivation of SBF models ofnew devices through revision of SBF models of knowndevices . Our current work on adaptive modeling ex-tracts and generalizes this technique for generatingSBF device models . As we continue the developmentof this technique, we expect it to lead to additionalrepresentational constraints on SBF models.

Bylander [1991] describes an alternative techniquefor deriving the output behaviors of a device . In hismethod, called consolidation, the behaviors of a givendevice are derived by composing the (primitive) behav-iors of its structural components . The behavior com-position is governed both by the structural relationsamong the components and by general rules of compo-sition . The composition process is driven by iterativeapplication of the compositional rules . This processresults in a specification of potential output behaviorsof the device .The technique of adaptive modeling complements

compositional methods such as consolidation . Com-positional methods appear to be more general becausethey can derive all the potential output behaviors ofthe device . But they are computationally expensive,and may require post processing to determine the ac-tual behaviors of the device from its potential behav-

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iors . The adaptive method appears to be more re-stricted in its applicability . For example, the deriva-tion of the output behaviors of SAC in our exampleis limited to the device functions . This is because ourSBF model of NAC specifies only the functions of thedevice, not all of its output behaviors . Of course, wecould enhance the SBF model of NAC by specifyingmore of its output behaviors . But the method stillwould be limited by the completeness of the enhancedSBF model .Note that the technique of adaptive modeling too

has a compositional aspect . The application of themodel-revision plan of component replacement, for ex-ample, first deletes the functions of the old componentfrom the internal causal behaviors of the SBF model,and then adds the functions of the new component tothem . But this composition in adaptive modeling islocalized both by the organization of the SBF modeland by the model adaptation goals .Our technique of adaptive modeling is also related

to some work on theory revision by analogical trans-fer . Falkenhainer [1989], for example, has integratedthe technique of structure mapping [Gentner 1983] withqualitative process representations [Forbus 1984] forcompleting almost complete theories of novel physicalprocesses by analogy to complete theories of knownprocesses . However, the generality and scalability ofthis kind of analogical transfer remains an open ques-tion . The technique of adaptive modeling is closerto case-based reasoning (e.g� [Kolodner 1993]) whichemphasizes almost complete analogical transfer be-tween similar and related situations instead of highly-selective transfer between distant situations .

AcknowledgementsThis work has been supported by the National ScienceFoundation (research grant IRI-92-10925), the Office ofNaval Research (research contract N00014-92-J-1234),and Northern Telecom (research gift) .

ReferencesT. Bylander . A Theory of Consolidation for Reasoningabout Devices . Man-Machine Studies. Vol. 35, pp . 467-489. 1991B . Chandrasekaran, A . Goel, and Y . Iwasaki . FunctionalRepresentation as Design Rationale . IEEE Computer, 48-56 . January 1993 .J . Clement . Learning via model construction and criti-cism . In Handbook of Creativity : Assessment, Theory andResearch, G. Glover, R . Ronning and C. Reynolds (edi-tors), pp . 341-381, New York : Plenum,B. Falkenhainer . Learning from Physical Analogies : AStudy in Analogy and the Explanation Process . Ph.D .Dissertation, Department of Computer Science, Univer-sity of Illinois at Urbana; 1989.K. Forbus . Qualitative Process Theory . Artificial Intelli-gence, 24:85-168, 1984 .

D . Gentner . Structure-Mapping : A Theoretical Frame-work for Analogy . Cognitive Science, 7(2), 1983 .

A . Goel . A Model-based Approach to Case Adaptation .Proc . Thirteenth Annual Conference of the Cognitive Sci-ence Society, August 1991, pp . 143-148 . Lawrence Erl-baum Associates .

A . Goel . Representation of Design Functions inExperience-Based Design . In Intelligent Computer AidedDesign, pp . 283-308 . D . Brown, M. Waldron and H .Yoshikawa (editors) . North-Holland . 1992 .

A . Goel and B . Chandrasekaran . Functional Representa-tion of Designs and Redesign Problem Solving . In Proc .Eleventh International Joint Conference on Artificial In-telligence, pp . 1388-1394. Morgan Kaufmann Publishers .1989 .

A . Goel and B . Chandrasekaran . Case-Based Design : ATask Analysis . In Artificial Intelligence Approaches to En-gineering Design, Volume II. Innovative Design, pp . 165-184 . Tong and D . Sriram (editors) . Academic Press . 1992 .

A . Goel, K . Mahesh, J . Peterson and K . Eiselt . Multistrat-egy Language Understanding for Device Comprehension .To appear in Proc . 1996 Cognitive Science Conference,San Diego, July 1996, Hillsdale, NJ: Erlbaum .

T . Govindaraj . Qualitative Approximation Methodologyfor Modeling and Simulation of Large Dynamic Systems :Applications to a Marine Power Plant . IEEE Transactionson Systems, Man and Cybernetics. Vol . SMC-17 No . 6, pp .937-955 . 1987 .

T . Griffith, N . Nersessian and A. Goel . The Role ofGeneric Models in Conceptual Change . To appear in Proc .1996 Cognitive Science Conference, San Diego, July 1996,Hillsdale, NJ : Erlbaum .

Y . Iwasaki and B . Chandrasekaran . Design VerificationThrough Function- and Behavior-Oriented Representa-tion : Bridging the Gap Between Function and Behavior .Proc . Second International Conference on AI in Design,Pittsburg, July 1992, pp . 597-616, Boston : Kluwer .J . Kolodner . Case-Based Reasoning. Morgan KaufmannPublishers, San Mateo . 1993 .D . Macaulay . The Way Things Work . Boston : HoughtonMifflin Company, 1988 .N . Nersessian . Should Physicists Preach What They prac-tice? Constructive Modeling in Doing and LearningPhysics . Science and Education, 4:203-226, 1995 .Justin Peterson, Kavi Mahesh, Ashok Goel, and KurtEiselt . KA : Situating Natural Language Processing in De-sign Problem Solving . In Proc . Sixteenth Annual Confer-ence of the Cognitive Science Society, August 1994, At-lanta, Georgia, pp . 711-716, Hillsdale, NJ: Lawrence Erl-baum .J_ Rasmussen . The Role of Hierarchical Knowledge Rep-resentation in Decision Making and System Management .IEEE Trans . Systems, Man and Cybernetics, 15 :234-243,1985 .V . Sembugamoorthy and B . Chandrasekaran . FunctionalRepresentation of Devices and Compilation of Diagnos-tic Problem Solving Systems . In Experience, Memory andReasoning, Kolodner and and Riesbeck (editors), Hills-dale, New Jersey : Lawrence Erlbaum Associates, 1986 .

J . Sticklen and B. Chandrasekaran, et al . (1989) . "Dis-tributed Causal Reasoning ." Knowledge Acquisition 1 :139-162 .Y . Umeda, H . Takeda, T . Tomiyama, and H . Yoshikawa .Function, Behavior and Structure . In Proc . Fifth Interna-tional Conference on Applications of AI in Engineering,Vol . 1, pp :177-193, 1990 .

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