From: AAAI Technical Report FS-94-03. Compilation copyright © 1994, AAAI (www.aaai.org). All rights reserved. UnderstandingControl at the KnowledgeLevel B. Chandrasekaran Laboratoryfor AI Research TheOhioState University Columbus, OH43210 Email: chandra@cis.ohio-state.edu Abstract the food is in the kitchen. That the cat would naturally go to the kitchen under these conditions seems reasonable to the host and presumablyto the guest. Whenpeople talk this way,they are not asserting that the neural stuff of the cat is somekind of a logical inference machineworkingon Predicate Calculus expressions. It is simplya useful wayof setting up a model of agents and using the model for explaining their behavior.Theattributions of the goal and knowledgecan be changedon the basis of further empirical evidence, but the revised modelwouldstill be in the same language of goals and knowledge. The Knowledge Level still needs a representation, but this is a representationthat is not posited in the agent, but onein whichoutsiders talk about the agent. Newellthoughtthat logic wasan appropriaterepresentation for this purpose, leaving openthe possibility of other languages also being appropriate in somecircumstances. Newell used the phrase "Symbol Level," to refer to the representational languages actually used to implementartificial decision agents (or explain the implementation of natural agents). Logic-based languages, Lisp and FORTRAN, neural net descriptions, and even Brook’ssubsumptionarchitectures are all possible Symbol-Levelimplementationsfor a given KnowledgeLevel specification of an agent. Whatis it that unifies the control task in all its manifestations,fromthe thermostat to the operator of a nuclear power plant? At the same time, how do weexplain the variety of the solutions that wesee for the task? I propose a KnowledgeLevel analysis of the task whichleads to a task-structure for control. Differencesin availability of knowledge,the degree of compilation in the knowledgeto mapfrom observationsto actions, andpropertiesrequired of the solutions together determinethe differencesin the solution architectures. I end by discussing a numberof heuristics that arise out of the Knowledge Level analysis that can help in the designof systemsto control the physical world. WhatIs the Knowledge Level? By nowmost of us in AI knowabout the KnowledgeLevel proposal of Newell[Newell, 81]. It is a wayof explainingandpredicting the behavior of a decision-making agent without committingoneself to a description of the mechanismsof implementation.The idea is to attribute to the agenta goal or set of goals and knowledgewhich together would explain its behavior,assuming that the agentis abstractly a rational agent, i.e., onethat wouldapplyan item of relevant knowledgeto the achievementof a goal. Imaginethe following conversation betweena guest anda host at a houseparty: G: Whydoes your cat keepgoing into the kitchen again andagain? H: Oh,it thinksthat the foodbowlis still in the kitchen. It doesn’t knowI just movedit to the porch. Thehost attributes to the cat the goalof satisfying its hunger, and explains its behavior by positing a (mistaken) piece of knowledgethat TheControlProblem at the Knowledge Level Consider the following devices and control agents: the thermostat, the speed regulator for an engine, an animalcontrolling its bodyduring somemotion, the operator of a nuclear power plant, the president and his economicadvisors duringthe task of policy formulationto control inflation and unemployment, and a major corporation planningto control its rapid loss of market share. All these systemsare engagedin a 19 "control" task, but seemto use rather different control techniques and architectures. Is this similarity in high-leveldescriptionjust a consequenceof an informaluse of wordsin our natural language,or is it an indication of someimportant structural similarity that can haveuseful technical consequences7Formulatingthe control problemat the Knowledge Level can help us to see what makesthese problemssimilar, and, at the sametime, to explain the widely divergent implementations of the systemsthat I listed. Fig. 1 is a brief descriptionof the control problemat the Knowledge Level. Control Agent C, System to be controlled S, state vector s, goal state G, defined as a wff of predicates over components of s, Observations O, Action repertoire A, The Task:. Synthesize action sequence from A such that S reaches G, subject to various performance constraints (time, error, cost, robustness, stability, etc.) wouldgenerate the intendedbehavior given the model. ¯ Commonsubtasks: Build a model of S using O (The general version of the problem is abductive explanation: from perception to scientific theory formation are examplesof this.) The task might involve prediction as a subtask. ,, Create a proposed plan to move S to G (The general version of the problem is oneof synthesis of plans.) - Predict behavior of S under plan using model (In general, simulation to analysis maybe invoked.) , Modify plan Fig. 2. Thetask-structureof control In fact, control in this sense indudes a good part of the general problem of intelligence. Fig. 1. Thecontrol task at the Knowledge Level In order to see howdifferent control tasks differ in their nature, thus permitting different types of solutions, we need to posit a task structure [Chandrasekaran, et al, 1992]for it. Thetask structure is a decomposition of the task into a set of subtasks, and is oneplausible way to accomplishthe goals specified in the task description. Fig. 2 describesa task structure for control. Basically, the task involves two important sub_m__ sks: usingO, modelS andgeneratea control responsebasedon the model.Bothof these tasks could use as their subtask a prediction component.Typically, the modelingtask would use prediction to generate consequencesof the hypothesizedmodeland checkagainst reality to verify the hypothesis. The planning component woulduse prediction to check whetherthe plan 2O Everycontrol system neednot do each of the tasks in Fig. 2 explicitly. It is hardto build effective control systemswhichdo not use some sort of observationto sensethe environment,or whichdo not makethe generationof the control signal or policy depend on the observation. Manycontrol systemscan be interpreted as performingthese tasks implicitly. Theprediction subtask mayactually be skipped altogether in certain domains. Thevariety of solutionsto the control problem arises from the different assumptionsand reqniremeatsunderwhichdifferent types of solutions are adoptedfor the subtasks, resulting in different propertiesfor the control solution as a whole. As I mentioned,at one extreme, the subtasks maybe doneimplicitly, or in a limited waythat they only workundercertain conditions. At the other extreme, they mayalso be done with explicit problem solving by multiple agents searching in complexproblem spaces. Andof coursethere are solutions of varyingcomplexity in between. The Thermostat, the Physician and the Neural Net Controller Considera thermostat (C in Fig. 1) For this system,S is the room,s consistsof a single state variable, the roomtemperature,G, the goal state of S, is the desired temperaturerange, Ois the sensing of the temperature by the bimetallic strip, andAconsistsof actionsto turn on andoff the furnace,the air-conditioner,the fan, etc. The modelingsubtask is solved by directly measuringthe variable implicated in the goal predicate. The model of the environment is simplythe valueof the single state variable, the temperature,andthat in turn is a direct function of the curvatureof the bimetallicstrip. Thecurvature of the strip also directly determineswhenthe furnace will be turned on and off. Thus the control generation subtask is solvedin the thermostatby using a direct relation betweenthe modelvalue and the action. Thetwo subtasks, and the task as a whole, are thus implementedby a direct mappingbetween the observationandthe action. Becauseof the extremesimplicity of the way the subtasks are solved, the prediction task, whichis normallya subtask of the modelingand planningrusks, is skippedin the thermostat. Thecontrol architecture of the thermostatis economical and analysis of its behavioris tractable. Butthere is also a price to pay for this simplicity. Supposethe measurementof temperature by the bimetallicstrip is off by 5 reg. The control system will systematically malfunction. A similar problem can be imagined for the control generation component.Alarger control system consisting of a humanproblem solver (or an automateddiagnostic system) the loop maybe able to diagnose the problem and adjust the control behavior. This approach increasesthe robustnessof the architecture, but at the cost of increased complexity of the modelingsubtask. Nowconsider the task facing a physician(C): controlling a patient’s body (S). Various symptoms and diagnostic data constitute the set O. Thetherapeutic options available constitute the set A. Thegoal state is specifiedby a set of predicates over importantbodyparameters,such as the temperature,liver function, heart rate, etc. Considerthe model-making subtask. This is the familiar diagnostic task. In someinstances this problemcan be quite complex, involving abductiveexplanationbuilding, prediction, and so on. This processis modeledas problemspace search. The task of generating therapies is usually not as complex,but could involve plan 21 instantiation andprediction,againtasks that are best modeledas search in problemspaces. Whycan’t the two subtasks, modeling and planning, be handled by the direct mapping techniquesthat seemto be so successful in the case of the thermostat?Tostart off, the number of state variables in the modelis quite large, and the relation betweenobservations and the modelvariables is not as direct in this domain. It is practically impossibleto so instrumentthe bodythat every relevant variable in the model can be observeddirectly. Withrespect to planning, the complexityof a control systemthat mapsdirectly from symptomsto therapies somesort of a huge table look-up - wouldbe quite large. It is muchmore advantageousto mapthe observations to equivalence classes the diagnostic categories - and then index the planningactions to these equivalenceclasses. But doing all of this takes the physician far awayflom the strategies appropriate for the thermostat. As a point intermediate in the spectrumbetweenthe thermostat, whichis a kind of reflex control system, and the physician, whois a deliberative search-basedproblemsolver, consider control systems based on PDP-like (or other types of) neural networks.O providesthe inputs to the neural net, and the output of the net should be composedfrom the elements of the set A. Neural networks can be thought of as systemsthat select, by usingparallel techniques, a path to oneof the output nodesthat is appropriate for the given input. Theactivity of even multiply layered NN’scan still be modeledas a selection of suchpathsin parallel in a hierarchy of pre-enumeratedand organizedsearch spaces. Thiskindofconnection finding in a limited space ofpossibilities iswhythese networks are also often called associative. During a cycle of itsactivity, thenetfinds a connection between actual observations andappropriate actions. This behavior needs to be contrasted with a modelof deliberationsuchas Soar [Laird, et al, 1987] in whichthe essence of deliberation is that traversing a problemspace and establishing connections betweenproblemspaces are themselves subject to open-endedadditional problem solvingat run time. Thethree modelsthat we have considered so far - the thermostat,neural net controllers, and deliberative problemsearch controllers - can be comparedalong different dimensionsas follows. Speed Robustness tradition that different from the one that is prevalent in AI - and attempts to understand biological control. Myownresearch has been motivatedby trying to understand someof the pmgmaticsof humanreasoning in prediction, causal understandingand real-time control. I have catalogued - and I will be discussing in the rest of the paper- a set of heuristics that I characterize as sourcesof powerthat biological control systems use. These ideas can also be usedin the designof practical control systems, i.e., they are not intendedjust as explanationsof biological control behavior. I do not intend themto be an exhaustivelist, but as examples of heuristics that maybe obtainedby studyingthe phenomenon of control at an abstract level. Theseheuristics do not dependon what implementation approaches are used in the actual design - be they symbolic, connectionist networksor fuzzysets. tractability" Reflex fast low easy NN’s medium medium medium Delib. potentially low slow engines high*’ *: tractability of analysis **: dependingon availability of knowledge Table1: Tradeoff between different kinds of control systemsalongdifferent dimensions Byrobustness in Table 1 I meanthe range of conditions under which the control system would perform correctly. The thermostat is unable to handle the situation wherethe assumptionabout the relation betweenthe curvature of the strip and the temperaturewasincorrect. Given a particular body of knowledge, deliberation can in principle use the deductive closure of the knowledgebase in determining the control action, whilethe other twotypes of control systemsin the Table use only knowledgewithin a fixed length of connectionchaining. Of course, any specific implementationof problem space search may not use the full powerof deductive closure, or the deductive closure of the knowledgeavailable maybe unable in principle to handle a given newsituation. The control systems in Table 1 are simply three samplesin a large set of possibilities, but selected becauseof their prominence in biological control models. The reflex and the NN models more commonly used in the discussion of animal behavior and humanmotor control behavior, while deliberation is generally restricted to humancontrol behaviorwhereproblem solving plays a major role. Engineeringof control systemsdoesnot needto be restricted to these three families. Otherchoices can be made in the spaceof possibilities, reflecting different degreesof search and compilation. Integrating Modules of Different Types Wehaveidentified a specmma of controllers: at one end ate fast-acting controllers, but with very circumscribedability to link up observations andactions; and at the other, slowdeliberative controllers whichsearch in problem spaces in an open-endedway. Biological control makesuse of several controllers fromdifferent places in the spectrum.Howthe controllers are organizedso as to makethe best use of themis expressedas Heuristic 1. Heuristic 1. Layer the modulessuch that the faster, less robust modulesare at the lowerlevels, and slower, morerobust modelsare on top of them, overriding or augmentingthe control providedby the lowerlevel ones. This is illustrated in Fig. 3. Deliberation I :_ A e ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ::iN~!i!i::ii::i::i::iiiiiiiiiiiiii i~iiii!iiiiiiiiiiiiiiiiiiii!iiiiiiiiiiii!iiii!iiii Ide Sources of Power I havebeen involved, over the last several years, in the construction of AI-basedprocess control systemsand also in research on causal understandingof devices. I havealso followed the major trends in both control systemstheory - muchof whichcarried on in a mathematical Thethree modules aboveare biologically motivated. Engineering systems donot needto beresb’ietedto thesethreelayerspredsely. Fig. 3. Layeringof modules 22 Manycontrol systemsin engineeringalready followthis heuristic. For example,process engineering systemshave a primarycontrol layer that directly activates certain importantcontrols based on the value of somecarefully chosen sensors. In nuclear powerplants, the primary coolingis activated instantly as soonas certain temperaturesexceedpreset thresholds. In addition, there are often additional controllers that perform morecomplexcontrol actions, someof them to augmentthe control actions of the lower level modules. Whenhumansare in the loop, they mayintervene to override the lower level control actions as well. In general, emergencyconditions(say in controlling a pressure cookeror driving a car) will be handledby the lower level modules.In the case of driving a car, makinghypothesesabout the intentions of other drivers or predicting the consequencesof a route changewouldrequire the involvement of higher-level modulesperformingmorecomplex problemsolving. In addition to overriding their controls as appropriate, the higher level modelscan influence the lower level modulesin another way. They can decomposethe control task and pass on to the lowermodulescontrol goals at a lowerlevel of abstraction that the lower-levelmodulescan achieve morereadily. For example,the deliberative controller for robot control maytake the control goal of "boilingwater"(say, the robot is executing an order to makecoffee) and decomposeit into control goals of "reachingthe stove" and "turn the dials on (or off)". Thesecontrol goals can be achieved by motor control programsby using the more compiledtechniques similar to those in neural andreflex controls. Real-time control Thenext set of heuristics are importantfor the design of real-time control systems and are basedon ideas discussedin [Chandrasekaran, et al, 1991]. Control with a guaranteeof real-time performanceis impossible. Physical systemshave, for all practical purposes, an unboundeddescriptive complexity. Anyset of measurements can only conveylimited informationabout the system to be controlled. This meansthat the best modelthat anyintelligence can build at any lime maybe incompletefor the purposeof action generation. No action generation scheme 23 can be guaranteedto achieve the goal within a given time limit, whateverthe time limit. On the other hand, there exist control schemesfor whichthe moretime there is to achieve the actions, the higherthe likelihoodthat actions can be synthesizedto achievethe control goals. All of this leads to the conclusionthat in the control of physical systems,the time required to assure that a control action will achieve the goal is unbounded. The discussion in the previous paragraph leads to twodesiderata for anyaction generation schemefor real-time control. Desiderata: ¯ 1. For as large a range of goals andsituations as possible, actions needto be generated rapidly and with a high likelihood of success. That is, wewouldlike as muchof the controlas possibleto be reactive. ¯ 2. Someprovision needs to be madefor whatto do whenthe actions fail to meetthe goals in the time available, as will inevitably happensooneror later. Desideratum1 leads to the kind of modulesat the lowerlevels of the layering in Fig. 3. The following Heuristics 3 and 4 say more about howthe modulesshould be designed. Heuristic2. Designsensor systemssuch that the systemto be controlled can be modeledas rapidlyas possible. As direct a mappingas possible should be madefromsensor values to internal states that are related to importantgoals (especiallythreats to importantgoals). Techniques in the spirit of reflex or associative controls could be useful here. In fact, any technique whoseknowledge can be characterizedas "compiled,"in the sense described in [Chandrasekaran,1991], wouldbe appropriate.However, there is a natural limit to howmanyof the situations can be covered in this waywithoutan undueproliferation of sensors. So only the most common and important situations can be coveredthis way. Heuristic 3. Designaction primitives such that mappingfrom models to actions can be madeas rapidly as possible. Action primitives need to be designed such that they haveas direct a relation as possibleto achieving or maintaining the more important goals. Acorrespondinglimit here is the proliferation of primitiveactions. Let us discuss Heuristics 2 and 3 in the context of someexamples. In driving a car, the design of sensor andaction systemshas evolved over time to help infer the most dangerous states of the modelor the most commonly occurringstates as quicklyas possible, andto help take immediateaction. If the car has to be pulled over immediatelybecausethe engine is getting too hot - and if this is a vital control action - install a sensor that recognizesthis state directly. Onthe other hand, we cannot havea sensorfor everyinternal state of interest. For example, there is no direct sensor for a wornpiston ring. That condition has to be inferred through a diagnostic reasoning chain, using symptomsand other observations. Similaxly, as soon as somedangerousstate is detected, the control action is to stop the car. Applyingthe brake is the relevant action here, and cars are designedsuchthat this is available as an action primitive.Again,there are limits on the numberof action primitives that can be provided. For example, the control action of increasing traction does not havea direct control action associatedwith it. Aplan has to be set in motioninvolving a numberof other control actions. Desideratum 2 leads to the followingheuristic. Heuristic 4. Real-control control requires a frameworkfor goal-abandonmentand substitution. This requires as muchpre-compilationof goalsandtheir priority relations as possible. Aswechive a car andnote that the weatheris getting bad, weoften decide that the original goal of getting to the destination by a certain time is unlikely to be achieved.Or, in the control of a nuclearpowerplant, the operator’sattempts to achieve the goal of producingmaximumpower in the presence of somehardware failure might not be bearing frniL In these cases, the original goal is abandoned andsubstituted by a less attractive but moreachievable goal. Thedriver of the car substitutes the goal of getting to the destination an hourlater. The power plant operator abandons the goal of powerproduction, and instead pursues the goal of radiation containment. Howdoes the controller pick the newgoal? It could spendits time reasoningabout whatgoals to substitute at the least cost, or it couldspend the time trying to achieve the newgoal, whatever it mightbe. In manyimportant real-time control problemsreplacementgoals and their priorities can be pre-compiled.In the nuclear industry, for example,a prioritized goal struttare called the safety function hierarchy is madeavailable in advanceto the operators. If the operator cannot maintain safe powerproduction and decides to abandonthe production goal, the hierarchy gives him the appropriate newgoal. Weacquire over time, as weinteract with the world, a numberof such goal priority relations. In our everydaybehavior,these relations help us to navigate the physical worldin close to real time almost always. Weoccasionally have to stop and think about which goalsto substitute,but not often. Qualitative reasoning in prediction Thelast set of heuristics that I will discuss pertain to the problemof prediction. Prediction, as I discussed earfier, is a common subtask in control. Evenif a controller is well-equipped with a detailed quantitative modelof the environment,the input to the prediction task maybe only qualitative t. Of course, the modelitself maybe partly or whollyqualitative as well. de Kleer, Forbus and Knipers have all proposed elements of a representational vocabularyfor qualitative reasoningand associated semantics for the terms in it (see [Forbus,1988]for a reviewof the ideas). Theheuristics that I discuss belowcan be viewedas elements of the pragmaticsof qnalitative reasoningfor prediction. Whateverframeworkfor qualitative reasoning one adopts, there will necessarilybe ambiguities in the prediction dueto lack of completeinformarion. The ambiguities can proliferate exponentially. Howdo humansfare in their control of the physicalworld,in spite of the fact that qnalitarive reasoningis a veritable fountain of ambiguities? I have outlined someof the ways in ’ I amusing the word"qualitative" in the sense of a symbolthat stands for a range of actual values, such as "increasing," "decreasing," or "Large." It is a formof approximatereasoning. Theliterature on qualitative physics uses the wordin this sense. This sense of "qualitative" shouldbe distinguishedfromits use to stand for "symbolic" reasoning as opposedto numerical calculation. Thelatter sense has no connotation of approximation. 24 whichwe do this in [Chandrasekaran, 1992]. The following simple examplecan be used to illustrate the waysin whichwemanage. Supposewewant to predict the consequences of throwinga ball on a wall. Byusing qualitative physical equations (or just commonsense physical knowledge),wecan derive a behavior tree with ever-inerea~ing ambiguities. On the other hand, consider howhumanreasoning mightproceed. 1. If nothing muchdependson it, we just predict the fLrSt coupleof bouncesandthen simplysay, "it will go onuntil it stops." 2. If there is something valuableon the floor that the bouncingball mighthit, wedon’t agonizeover whetherthe ball will hit it or not. Wesimplypick out this possibility as one that impactsa "Protect valuables" goal, and remove the valuable object (or decide against bouncing the ball). 3. Wemaybounce the ball a couple of timesslowlyto get a senseof the its elasticity, and use this informationto prune someof the ambiguitiesaway.Thekey idea here is that weuse physical interaction as a wayof making choicesin the tree of future states. 4. Wemight have bounced the ball before in the same room, and might knowf~m experience that a significantpossibilityis that it will roll underthe bed. Thenexttime the ball is bounced,this possibility can be predictedwithout going through the complexbehavior tree. Further, using another such experience-based compilation, wecan identify the ball getting crushed between the bed and the wall. This possibility is generatedin two steps of predictive reasoning. 5. Supposethat there is a switchon the wall that controls somedevice, and that weunderstand howthe device works. Usingthe idea in 2 above,wenote that the ball mighthit the switch and turn it on and off. Thenbecausewe havea functional understandingof the device that the switchcontrols, wewill be able to make rapid predictions about what wouldhappento the device. In somecases, we might even be able to makeprecise predictions by using available quantitative models of the device. The qualitative reasoningidentifies the impacton the switchof the deviceas a possibility, which then makesit possible for us to deploy additional analytic resources on the prediction problemin a highly focusedway. 25 Theabovefist is representativeof whatI mean by the pragmatics of qualitative reasoning, which are the ways in which we manage to control the physical worldwell enough,in spite of the qualitativenessinherentin our reasoning. In fact, weexploit qualitativenessto reducethe complexityof prediction (as in point 5 above). Thelist aboveleads to the followingheuristics. Heuristic 5. Qualitative reasoningis rarely carried out for morethan a very small number of steps. Heuristic 6. Ambiguitiescan often be resolved in favor of nodes that correspond to "interesting" possibilities. Typically,interestingnessis definedby threats to or supports for variousgoals of the agent. Additionalreasoningor other formsof verification maybe used to check the occurrenceof these states. Or actions mightsimplybe takento avoidor exploit these states. Heuristic7. Direct interaction with the physical world can be used to reducethe ambiguities so that further steps in predictioncan be made. Heuristic 7 is consistent with the proposalsof the situated action paradigmin AI andcognitive science. Heuristic 8. The possibility that an action maylead to an importantstate of interest can be compiledfrom a previous reasoning experience or stored froma previous interaction with the world. This enables the states to be hypothesized without the agent havingto navigate the behavior tree generated fromthe moredetailed physical model. Heuristic 9. Prediction often has to jump levels of abstractionin behaviorandstate representation, since goals of interest occur at many differentlevels of abstraction. Compiledcausal packagesthat relate states and behaviorsat different levels of abstraction are the focus of the workon FunctionalRepresentations, whichis a theory of howdevices achieve their functionality as a result of the functionsof the components andthe structure of the device. Researchon howto use this kind of representation for focused simulation and prediction is reviewedin [Chandrasekaran, 1994]. Concluding Remarks Thereader will note that, as promisedby the use of the term "Knowledge Level" in the title, I haveavoidedall discussionon specific representational formalisms. I have not gotten in- volvedin the debates on fuzzy versus probabflistic representations,linear control versus nonlinear control, discrete versus continuouscontrol and so on. All of these issues and technologies,hnportantas they are, still pertain to the SymbolLevel of control systems. The Knowledge Level discussion enabled us to get someidea both about what unifies the task of control, andabout the reasonsfor the vast differences in actual control systemdesignstrategies. Thesedifferencesare dueto the different consmuntson the various substasks and different types of knowledgethat are available. We can see an evolution in intelligence fromreflex controls whichfix the connection betweenobservations and actions through progressively decreasing rigidity of connectionbetweenobservations and actions, culminatingin individual or social deliberative behaviorwhichprovides the most open-endedwayof relating observatious and actions. I also discusseda number of biologically motivatedheuristics for the design of systemsfor controlling the physical world and illustrated the relevance of these heuristics by lookingat someexamples. References [Chandrasekaran, 1991] B. Chandrasekaran, "Modelsvs rules, deepversus compiled,content versus form: Somedistinctions in knowledge systems research," IEEEExpert, 6, 2, April 1991,75-79. [Chandrasekaran, et al, 1991] B. Chandrasekaran, R. Bhamagarand D. D. Sharma," Real-time disturbance control," Communications of the ACM,August 1991, Vol. 34, # 8, 33-47. [Chandrasekaran,1992] "QPis morethan SPQR and Dynamicalsystems theory: Response to Sacks and Doyle," ComputationalIntelligence, 8(2), 1992,216-222. [Chandrasekaran, et al, 1992] B. Chandrasekaran, Todd Johnson, Jack W. Smith, "Task Structure Analysis for Knowledge Modeling," Communications of the ACM,33-9, Sep, 1992,124-136. [Forbus, 1988]Forbus,K. D., 1988,Qualitative Physics: Past, Present and Future, in Exploring Artificial Intelligence, H. Shrobe, ed., San Mateo, CA, MorganKauffman,239-96. Acknowledgments This research was supported partly by a grant from The OhioState University Office of Research and College of Engineeringfor interdisciplinary researchon intelligent control, and partly by ARPA,contract F30602-93-C-0243, monitoredby USAF RomeLaboratories. I thank the participantsin the interdisciplinaryresearch groupmeetingsfor useful discussions. [Laird, et al, 1987] Laird, J.E., Newell, A. & Rosenbloom,P.S. SOAR:An architecture for generalintelligence. Artificial Intelligence,33, (1987),1-64. [Newell, 1981] Newell, A. The Knowledge Level. A/ Magazine, Summer(1981), 1-19. 26