what is computational cognitive modeling

computational modeling in cognitive psychology computational modeling in cognitive science a manifesto for change theoretical status of computational cognitive modeling
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Introduction to Computational Cognitive Modeling Ron Sun - Instead going straight into dealing with specific approaches, issues, and do- mains of computational cognitive modeling, it would be more appropriate to first take some time to explore a few general questions that lie at the very core of cognitive science and computational cognitive modeling. What is computational cognitive modeling? What exactly can it contribute to cognitive science? What has it contributed thus far? Where is it going? Answering such questions may sound overly defensive to the insiders of com- putational cognitive modeling, and may even seem so to some other cognitive scientists,butthey areverymuchneededinavolumelikethis—becausetheylie attheveryfoundationofthis field. Manyinsiders andoutsidersalikewouldlike totakea balancedandrationallookatthesequestions,withoutindulging inex- cessive cheer-leading, which, as one would expect, happens sometimes amongst computational modeling enthusiasts. However, given the large number of issues involved and the complexity of these issues, only a cursory discussion is possible in this introductory chapter. One may thus view this chapter as a set of pointers to the existing literature, rather than a full-scale discussion. 11 What is Computational Cognitive Modeling? Research in computational cognitive modeling, or simply computational psy- chology,explorestheessenceofcognition(broadlydefined,includingmotivation, emotion, perception, and so on) and various cognitive functionalities through developing detailed, process-based understanding by specifying corresponding computational models (in a broad sense) of representations, mechanisms, and processes. It embodies descriptions of cognition in computer algorithms and programs, based on computer science (Turing 1950). That is, it imputes com- putational processes (in a broad sense) onto cognitive functions, and thereby it produces runnable computational models. Detailed simulations are then con- ductedbasedonthecomputationalmodels(see,e.g.,Newell1990,Rumelhartet al1986,Sun2002). Rightfromthebeginningoftheformalestablishmentofcog- nitive science around late 1970’s, computational modeling has been a mainstay 1 of cognitive science. Ingeneral,models incognitivesciencemayberoughlycategorizedinto com- putational, mathematical, or verbal-conceptual models (see, e.g., Bechtel and Graham1998). Computationalmodels (broadlydefined) presentprocessdetails using algorithmic descriptions. Mathematical models presents relationships be- tween variables using mathematical equations. Verbal-conceptual models de- scribe entities, relations, and processes in rather informal natural languages. Each model, regardless of its genre, might as well be viewed as a theory of whatever phenomena it purports to capture (as argued extensively before by, for example, Newell 1990, Sun 2005). 1 The roots of cognitive science can, of course, be traced back to much earlier times. For example, Newell and Simon’s early work in the 60’s and 70’s has been seminal (see, e.g., Newell and Simon 1976). The work of Miller, Galanter, and Pribram (1960) has also been highly influential. See the chapter by Boden in this volume for a more complete historical perspective (see also Boden 2006). 2Although each of these types of models has its role to play, in this volume, we will be mainly concerned with computational modeling (in a broad sense), including those based on computational cognitive architectures. The reason for this emphasis is that, at least at present, computational modeling (in a broad sense)appearstobethemostpromisingapproachinmanyrespects,anditoffers the flexibility and the expressivepower that no other approachcan match, as it providesavarietyofmodelingtechniquesandmethodologiesandsupportsprac- tical applications of cognitive theories (Pew and Mavor 1998). In this regard, note that mathematical models may be viewed as a subset of computational models, as normally they can readily lead to computational implementations (although some of them may appear sketchy and lack process details). Computational models are mostly process based theories. That is, they are mostly directed at answering the question of how human performance comes about, by what psychological mechanisms, processes, and knowledge structures andinwhatwaysexactly. Inthisregard,notethatitisalsopossibletoformulate theories of the same phenomena through so called “product theories”, which provide an accurate functional account of the phenomena but do not commit to a particular psychological mechanism or process (Vicente and Wang 1998). We may also term product theories blackbox theories or input-output theories. Product theories do not make predictions about processes (even though they may constrain processes). Thus, product theories can be evaluated mainly by product measures. Process theories, in contrast, can be evaluated by using process measures when they are available and relevant (which are, relatively speaking, rare), such as eye movement and duration of pause in serial recall; or by using product measures, such as recall accuracy, recall speed, and so on. Evaluation of process theories using the latter type of measures can only be indirect, because process theories have to generate an output given an input based on the processes postulated by the theories (Vicente and Wang 1998). 3Depending on the amount of process details specified, a computational model may lie somewhere along the continuum from pure product theories to pure process theories. There can be several different senses of “modeling” in this regard, as dis- cussed in Sun and Ling (1998). The match of a model with human cognition may be, for example, qualitative (i.e., nonnumerical and relative), or quanti- tative (i.e., numerical and exact). There may even be looser “matches” based on abstracting general ideas from observations of human behaviors and then developing them into computational models. Although different senses of mod- eling or matching human behaviors have been used, the overall goal remains the same, which is to understand cognition (human cognition in particular) in a detailed (process-oriented) way. This approach of utilizing computational cognitive models for understand- ing human cognition is relatively new. Although earlier precursors might be identified, the major developments of computational cognitive modeling have occurred since the 1960’s. It has since been nurtured by the Annual Confer- ences of the Cognitive Science Society (which began in the late 1970’s), by the International Conferences on Cognitive Modeling (which began in the 1990’s), as well as by the journals of Cognitive Science (which began in the late 1970’s), Cognitive Systems Research (which began in the 1990’s), and so on. From Schank and Abelson (1977) to Minsky (1981), a variety of influen- tial symbolic “cognitive” models were proposed in Artificial Intelligence. They were usually broad and capable of a significant amount of information process- ing. However, they were usually not rigorously matched against human data. Therefore, it was hard to establish cognitive validity of many of these models. Psychologists have also been proposing computational cognitive models, which are usually narrower and more specific. They were usually more rigorously evaluated in relation to human data. An early example is Anderson’s HAM 4(Anderson 1983). Many of such models were inspired by symbolic AI work at that time (Newell and Simon 1976). The resurgenceof neuralnetworkmodels in the 1980’sbroughtanother type of model into prominence in this field (see, e.g., Rumelhart et al 1986, Gross- berg 1982). Instead of symbolic models that rely on a variety of complex data structures that store highly structured pieces of knowledge (such as Schank’s scripts or Minsky’s frames), simple, uniform, and often massively parallel nu- merical computation was used in these neural network models (Rumelhart et al 1986). Many of these models were meant to be rigorous models of human cognitive processes, and they were often evaluated in relation to human data in a quantitative way (but see Massaro 1988). Hybrid models that combine the strengths of neural networks and symbolic models emerged in the early 1990’s (see, e.g., Sun and Bookman 1994). Such models could be used to model a wider variety of cognitive phenomena due to theirmorediverseandthusmoreexpressiverepresentations(butseeRegier2003 regarding constraints on models). They have been used to tackle a broad range of cognitive data, often (though not always) in a rigorous and quantitative way (see, for example, Sun and Bookman 1994, Sun 1994, Anderson and Lebiere 1998, Sun 2002). Foroverviewsofsomecurrentlyexistingsoftware,tools,models,andsystems for computational cognitive modeling, the reader may refer to the following Websites (among others): http://www.cogsci.rpi.edu/rsun/arch.html http://books.nap.edu/openbook.php?isbn=0309060966 http://www.isle.org/symposia/cogarch/archabs.html as well as the following Websites for specific software, cognitive models, or cog- nitive architectures (e.g., Soar, ACT-R, and CLARION): 5http://psych.colorado.edu/oreilly/PDP++/PDP++.html http://www.cogsci.rpi.edu/rsun/clarion.html http://act-r.psy.cmu.edu/ http://sitemaker.umich.edu/soar/home http://www.eecs.umich.edu/kieras/epic.html 2 What is Computational Cognitive Modeling Good for? There are reasons to believe that the goal of understanding the human mind strictly from observations of human behavior is ultimately untenable, except for small and limited task domains. The rise and fall of behaviorism is a case in point. This point may also be argued on the basis of analogy with physical sciences (see Sun, Coward, and Zenzen 2005). The key point is that the pro- cesses and mechanisms of the mind cannot be understood purely on the basis of behavioral experiments, with tests that inevitably amount to probing only relatively superficial features of human behavior, which are further obscured by individual/groupdifferencesandcontextualfactors. Itwouldbeextremelyhard to understandthe human mind in this way, just likeit would be extremely hard to understand a complex computer system purely on the basis of testing its behavior, if we do not have any a priori ideas about the nature, the inner work- ing, and the theoretical underpinnings of that system (Sun 2005). For a simple example, in any experiment involving the human mind, there is a very large number of parameters that could influence the results, and these parameters are either measured or left to chance. Given the large number of parameters, many have to be left to chance. The selection of which parameters to control and which to leave to chance is a decision made by the experimenter. This decision is made on the basis of which parameters the experimenter thinks are 6important. Therefore, clearly, theoreticaldevelopmentneed to go hand-in-hand with experimental tests of human behavior. Giventhecomplexityofthehumanmind,anditsmanifestationinbehavioral flexibility,complexprocess-basedtheories,thatis,computationalmodels(inthe broad sense of the term), are necessary to explicate the intricate details of the human mind. Without such complex process-based theories, experimentation may be blind—leading to the accumulation of a vast amount of data without any apparent purpose or any apparent hope of arriving at a succinct, precise, and meaningful understanding. It is true that even pure experimentalists may often be guided by their intuitive theories in designing experiments and in gen- erating their hypotheses. So, it is reasonable to say that they are in practice not completely blind. However, without detailed theories, most of the details of an intuitive (or verbal-conceptual) theory are left out of consideration, and the intuitive theory may thus be somehow vacuous, or internally inconsistent, or otherwise invalid. These problems of an intuitive theory may not be discovered until a detailed model is developed (Sun, Coward, and Zenzen 2005, Sun 2005). There are many reasons to believe that the key to understanding cognitive processes is often in fine details, which only computational modeling can bring out (Newell 1990, Sun 2005). Computational models provide algorithmic speci- ficity: detailed, exactly specified, and carefully thought-out steps, arranged in preciseandyetflexiblesequences. Therefore,theyprovidebothconceptualclar- ity and precision. As related by Hintzman (1990), “The common strategy of trying to reason backwardfrom behavior to underlying processes (analysis) has drawbacks that become painfully apparent to those who work with simulation models (synthesis). To have one’s hunches about how a simple combination of processes will behave repeatedly dashed by one’s own computer program is a humbling experience that no experimental psychologist should miss” (p.111). One viewpoint concerning the theoretical status of computational modeling 7and simulation is that they, including those based on cognitive architectures, shouldnotbetakenastheory. Asimulation/modelis ageneratorofphenomena anddata. Thus itis atheory-buildingtool. Hintzman (1990)gavea positiveas- sessment of the role of simulation/model in theory building: “a simple working systemthatdisplayssomepropertiesofhumanmemorymaysuggestotherprop- erties that no one ever thought of testing for, may offer novel explanations for known phenomena, and may provide insight into which modifications that next generation of models should include” (p.111). That is, computational models areusefulmediaforthoughtexperimentsandhypothesisgeneration. Inparticu- lar, one may use simulations for exploring various possibilities regarding details ofacognitiveprocess. Thus,asimulation/modelmayserveasatheory-building tool for developing future theories. A related view is that computational mod- eling and simulation are suitable for facilitating the precise instantiation of a pre-existing verbal-conceptual theory (e.g., through exploring various possible details in instantiating the theory) and consequently the careful evaluation of the theory against data. A radically different position (e.g., Newell 1990, Sun 2005) is that every simulation/model provides a theory. It is not the case that a simulation/model is limited to being built on top of an existing theory, being applied for the sake of generating data, being applied for the sake of validating an existing theory, or being applied for the sake of building a future theory. To the contrary, according to this view, a simulation/model is a theory by it- self. In philosophy of science, constructive empiricism (van Fraasen 1980) may make a sensible philosophicalfoundation for computational cognitive modeling, consistent with the view of models as theories (Sun 2005). Computationalmodelsmaybenecessaryforunderstandingasystemascom- plex and as diverse as the human mind. Pure mathematics, developed to de- scribe the physical universe, may not be sufficient for understanding a sys- tem as different and as complex as the human mind (cf. Luce 1995, Coombs 8et al 1970). Compared with scientific theories developed in other disciplines (e.g., in physics), computational cognitive modeling may be mathematically less elegant—but the point is that the human mind itself is likely to be less mathematically elegant compared with the physical universe (see, e.g., Minsky 1985) and therefore an alternative form of theorizing is called for, a form that is more complex, morediverse, and morealgorithmic in nature. Computational cognitive models provide a viable way of specifying complex and detailed theo- ries of cognition. Consequently, they may provide detailed interpretations and insights that no other experimental or theoretical approach can provide. In particular, a cognitive architecture denotes a comprehensive, domain- genericcomputationalcognitivemodel,capturingtheessentialstructures,mech- anisms, and processes of cognition. It is used for a broad, multiple-level, multiple-domain analysis of cognition and behavior (Sun 2004, Sun, Coward, and Zenzen 2005, Sun 2005). It deals with componential processes of cognition in a structurally and mechanistically well defined way (Sun 2004). Its function is to provide an essential framework to facilitate more detailed modeling and understanding of various components and processes of the mind. A cognitive architecture is useful and important because it provides a comprehensive initial framework for further exploration of many different domains and many differ- ent cognitive functionalities. The initial assumptions may be based on either available scientific data (e.g., psychological or biological data), philosophical thoughts and arguments, or ad hoc working hypotheses (including computa- tionally inspired such hypotheses). A cognitive architecture helps to narrow down possibilities, provides scaffolding structures, and embodies fundamental theoreticalpostulates. Notethatthevalueofcognitivearchitectureshasbeenar- gued many times before; see, for example, Newell (1990), Anderson and Lebiere (1998), Sun (2002), Anderson and Lebiere (2003), Sun (2004), Sun, Coward, 92 and Zenzen (2005), Sun (2005), and so on. As we all know, science in general often progresses from understanding to prediction and then to prescription (or control). Computational cognitivemod- eling potentially may contribute to all of these three phases of science. For instance, through process-based simulation, computational modeling may re- veal dynamic aspects of cognition, which may not be revealed otherwise, and allows a detailed look at constituting elements and their interactions on the fly during performance. In turn, such understanding may lead to hypotheses con- cerning hitherto undiscovered or unknown aspects of cognition and may lead to predictions regarding cognition. The ability to make reasonably accurate predictions about cognition can further allow prescriptions or control, for ex- ample, by choosing appropriate environmental conditions for certain tasks, or by choosing appropriate mental types for certain tasks and/or environmental conditions. In sum, the utility and the value of computational cognitive modeling (in- cludingcognitivearchitectures)canbearguedinmanydifferentways(seeNewell 1990, Sun 2002, Anderson and Lebiere 2003, and so on). These models in their totality are clearly more than just simulation tools or programming languages of some sorts. They are theoretically pertinent, because they represent theo- ries in a unique and, I believe, indispensable way. Cognitive architectures, for example, are broad theories of cognition in fact. 2 For information about different existing cognitive architectures, see, for example, http://www.cogsci.rpi.edu/∼rsun/arch.html. See also Sun (2006) for information on three major cognitive architectures. 103 Multiple Levels of Computational Cognitive Modeling Astrategicdecisionthatonehastomakewithrespecttocognitivescienceisthe level(s) of analysis (i.e., level(s) of abstraction) at which one models cognitive agents. Computational cognitive modeling can vary in terms of level of process details and granularity of input and output, and thus may be carried out at multiple levels. Let us look into this issue of multiple levels of computational cognitivemodeling, drawingupon theworkofSun, Coward,andZenzen(2005). We note that traditional theories of multi-level analysis holds that there are variouslevels eachofwhichinvolvesa differentamountofcomputationaldetails (e.g.,Marr1982). InMarr’stheory,first,thereisthecomputational theorylevel, in which one is supposed to determine proper computation to be performed, its goals, and the logic of the strategies by which the computation is to be carried out. Second,thereisthe representation and algorithm level,inwhichoneissup- posed to be concerned with carrying out the computational theory determined at the first level and, in particular, the representation for the input and the output and the algorithm for the transformation from the input to the output. The third level is the hardware implementation level, in which one is supposed tophysicallyrealizetherepresentationandalgorithmsdeterminedatthesecond level. According to Marr, these three levels are only loosely coupled; that is, they are relatively independent. Thus there are usually a wide array of choices ateachlevel, independent ofthe other two. Somephenomena may beexplained at only one or two levels. Marr (1982) emphasized the “critical” importance of formulation at the level of computational theory, that is, the level at which the goalsandpurposesof a cognitiveprocessarespecified andinternalandexternal constraints that make the process possible are worked out and related to each otherandtothegoalsofcomputation. Hisreasonwasthatthenatureofcompu- 11level object of analysis 1 computation 2 algorithms 3 implementations Figure 1: A traditional hierarchy of levels (Marr 1982). level object of analysis type of analysis computational model 1 inter-agent processes social/cultural collections of agents 2 agents psychological individual agents 3 intra-agent processes componential modular construction of agents 4 substrates physiological biological realization of modules Figure 2: Another hierarchy of four levels (Sun, Coward, and Zenzen 2005). tation depended more on the computational problems to be solved than on the way the solutions were to be implemented. In his own words, “an algorithm is likelytobeunderstoodmorereadilybyunderstandingthenatureoftheproblem being solved than by examining the mechanism (and the hardware) in which it is embodied.” Thus, he preferred a top-down approach—from a more abstract level to a more detailed level. See Figure 1 for the three levels. It often appears that Marr’s theory centered too much on the relatively minor differences in computational abstractions (e.g., algorithms, programs, and implementations; see Sun, Coward, and Zenzen 2005, Dayan 2003, Dawson 2002). It also ap- pears that his theory represented an over-simplificationof biologicalreality (for example, ignoring the species-specific or motivation-relevant representations of the environment and the close relationship between low-level implementations andhigh-levelcomputation), and as a resultrepresentedanover-rationalization of cognition. Another variantis Newell and Simon’s three-leveltheory. Newell and Simon 12(1976) proposed the following three levels: (1) The knowledge level, in which why cognitive agents do certain things is explained by appealing to their goals and their knowledge, and by showing rational connections between them. (2) The symbol level, in which the knowledge and goals are encoded by symbolic structures, and the manipulation of these structures implements their connec- tions. (3)Thephysicallevel,inwhichthesymbolstructuresandtheirmanipula- tionsarerealizedinsomephysicalform. Sometimesthisthree-levelorganization wasreferredtoas“theclassicalcognitivearchitecture”(Newell1990). Thepoint being emphasized here was very close to Marr’s view: What is important is the analysisat the knowledgelevel and then at the symbol level, that is, identifying the task and designing symbol structures and symbol manipulation procedures suitableforit. Oncethisanalysis(atthesetwolevels)isworkedout,theanalysis can be implemented in any available physical means. In contrast, according to Sun, Coward, and Zenzen (2005), the differences (borrowed from computer programming) amongst “computation”, algorithms, programs, and hardware realizations, and their variations, as have been the focus in Marr’s (1982) and Newell and Simon’s (1976) level theories, are rel- atively insignificant. This is because, first of all, the differences among them are usually small, fuzzy, and subtle, compared with the differences among the processes to be modeled (that is, the differences among the sociological vs. the psychological vs. the intra-agent, etc.). Second, these different computational constructsareinreality closelytangled(especially in the biologicalworld): One cannot specify algorithms without at least some considerations of possible im- plementations, and what is to be considered “computation” (i.e., what can be computed) relies on algorithms,especially the notion of algorithmiccomplexity, and so on. Therefore, one often has to consider computation, algorithms, and implementation together somehow (especially in relation to cognition). Third, accordingto Sun, Coward,andZenzen(2005),the separationofthese computa- 13tional details failed to produceany major useful insight in relationto cognition, but theoretical baggage. A re-orientation toward a systematic examination of phenomena, instead of tools one uses for modeling them, is thus a step in the right direction. The viewpoint of Sun, Coward, and Zenzen (2005) focused attention on the very phenomena to be studied, on their scopes, scales, degrees of abstractness, and so on. Thus, the differences among levels of analysis can be roughly cast as thedifferencesamongdisciplines,fromthemostmacroscopictothemostmicro- scopic. These levels of analysis include: the sociological level, the psychological level, the componential level, and the physiologicallevel. See Figure 2 for these levels. Different levels of modeling may be established in exact correspondence with different levels of analysis. First of all, there is the sociological level, which includes collective behavior ofagents(Durkheim1895),inter-agentprocesses(Vygotsky1986),sociocultural processes, as well as interaction between agents and their (physical and socio- cultural) environments. Only recently, the field of cognitive science has come to grip with the fact that cognition is, at least in part, a social/cultural process (Lave 1988, Vygotsky 1986, Sun 2006). To ignore the sociocultural process is to ignore a major underlying determinant of individual cognition. The lack of understanding of sociological processes may result in the lack of understanding ofsomemajorstructuresandconstraintsincognition. Thus,anyunderstanding of individual cognition can only be partial and incomplete when sociocultural 3 processes are ignored or downplayed. The next level is the psychological level, which covers individual behaviors, beliefs, knowledge, concepts, and skills (as well as motivation, emotion, percep- tion, and so on). In relation to the sociological level, one can investigate the 3 See Sun (2001, 2006) for a more detailed argument of the relevance of sociocultural pro- cesses to cognition and vice versa. 14relationship of individual beliefs, knowledge, concepts, and skills with those of the society and the culture, and the processes of change of these beliefs, knowl- edge, concepts, and skills, independent of or in relation to those of the society and the culture. At this level, one can examine human behavioral data, and compare them with models and with insights from the sociological level and further details from the lower levels. The third level is the componential level. It is important to note that in computational cognitive modeling, the computational process of an agent is mostly specified in terms of components of the agent, i.e., in terms of intra- agent processes. Thus, at this level, one may specify a cognitive architecture and components therein. In the process of analysis, one specifies essential com- putational processes of each component as well as essential connections among various components. Thus, analysis of capacity (functional analysis) and anal- ysis of components (structural analysis) become one and the same at this level. However, at this level, unlike at the psychological level, work is more along the line of structural analysis than functional analysis (while the psychological level is mostly concerned with functional analysis). At this level, one models cognitive agents in terms of components, with the theoretical language of a particular paradigm, for example, symbolic computation or connectionist net- works, or their combinations (Sun and Bookman 1994). That is, one imputes a computational process onto a cognitive function. Ideas and data from the psychological level—the psychological constraints from above, which bear on the division of components and possible implementations of components, are among the most important considerations. This level may also incorporate biological/physiologicalobservations regarding plausible divisions and their im- plementations; that is, it can incorporate ideas from the next level down—the physiological level, which offers the biological constraints. This level results in cognitive mechanisms, although they are usually computational and thus ab- 15stract, compared with physiological-level specifications of details. Although this level is essentially in terms of intra-agentprocesses, computa- tional models developed therein may also be used to model processes at higher levels,includingtheinteractionatasociologicallevelwheremultipleindividuals areinvolved. This canbe accomplished, for example, by examining interactions of multiple copies of individual agents (Sun 2006). The lowest level of analysis is the physiological level, that is, the biological substrate, or biological implementation, of computation (Dayan 2003). This level is the focus of a range of disciplines including physiology, biology, com- putational neuroscience, cognitive neuroscience, and so on. Although biological substrates are not among our major concerns here, they may nevertheless pro- vide valuableinput as to what kind of computation is likely employedand what a plausible architecture (at a higher level) should be like. The main utility of this level is to facilitate analysis at higher levels, that is, to use low-level in- formation to narrow down, at higher levels, choices in selecting computational architectures and choices in implementing componential computation. Although computational cognitivemodeling is often limited to within a par- ticular level at a time (inter-agent, agent, intra-agent, or substrate), this need not always be the case: Cross-level analysis and modeling could be intellectu- allyhighlyenlightening,andmightbeessentialtotheprogressofcomputational cognitive modeling in the future (Sun, Coward, and Zenzen 2005, Dayan 2003). These levels described above do interact with each other (e.g., constraining each other) and may not be easily isolated and tackled alone. Moreover, their respective territories are often intermingled, without clear-cut boundaries. For instance, the cross-level link between the psychological and the neuro- physiological level has been strongly emphasized in recent years (in the form of cognitive neuroscience; see, e.g., LeDoux 1992, Damasio 1994, Milner and Goodale 1995). For example, Wilson et al. (2000) presented a model of human 16subjects perceiving the orientation of the head of another person. They ac- counted for the empirical findings from psychologicalexperiments with a model based on a population code of neurons in the visual cortex, and thus the un- derlying neural structures were used to explain a psychological phenomenon at a higher level. For another instance of cross-level research, the psychological and the social level may also be crossed in many ways, in order to generatenew insights into social phenomena on the basis of cognitive processes (e.g., Boyer and Ramble 2001,Sun 2006)and, conversely,to generateinsights into cognitive phenomena on the basis of sociocultural processes (e.g., Hutchins 1995, Nisbett et al 2001). In all of these cases, the ability to shift appropriately between levels when needed is a critical part of the work. Beyondcross-levelanalysis,there may be “mixed-level”analysis (Sun, Cow- ard, and Zenzen 2005). The idea of mixed-level analysis may be illustrated by the research at the boundaries of quantum mechanics. In deriving theo- ries, physicists often start working in a purely classical language that ignores quantum probabilities, wave functions, and so forth, and subsequently overlay quantum concepts upon a classical framework (Greene 1999, Coward and Sun 2004). The very same idea applies to mixing cognitive modeling and social simulation as well. One may start with purely social descriptions but then sub- stitute cognitiveprinciples andcognitiveprocess details for simpler descriptions of agents (e.g., Sun and Naveh 2004). Relatedly, there has also been strong interplay between psychological models and neurophysiologicalmodels—for ex- ample, going from psychological descriptions to neurobiological details. Note that Rasmussen (1986) proposed something similar to the view de- scribed above on levels. His hierarchy was a more general framework but had a number of constraining properties (see also Vicente and Wang 1998): (1) All levels deal with the same system, with each level providing a different descrip- tionofthesystem; (2)eachlevelhasitsownterms,concepts,andprinciples; (3) 17the selection of levels may be dependent on the observer’s purpose, knowledge, and interest; (4) the description at any level may serve as constraints on the operation of lower levels, whereas changes at a higher level may be specified by the effects of the lower levels; (5) by moving up the hierarchy, one under- stands more the significance of some process details with regard to the purpose of the system; by moving down the hierarchy, one understands more how the system functions in terms of the process details; (6) there is also a means-ends relationship between levels in a hierarchy. Note also Ohlsson and Jewett’s (1997) and Langley’s (1999) idea of ab- stract cognitive model, which is relevant here as well. To guard against over- interpretationofempiricalevidenceandto avoidtheusually largegapsbetween evidence and full-blown computational models, Ohlsson and Jewett (1997) pro- posed “abstract computational models”, which were relatively abstract models that were designed to test a particular (high level) hypothesis without taking a stand on all the (lower level) details of a cognitive architecture. Similar ideas were also expressed by Langley (1999), who argued that the source of explana- tory power of a model often lay at a higher level of abstraction. Insum,therehavebeenvariousproposalsregardingmultiplelevelsofcompu- tational cognitive modeling. Although details vary, the very notion of multiple levels of cognitive modeling appears to be useful. It can be expected to be of importance for the further development of this field. 4 Success Stories of the Past Therehavebeenquiteafewsuccessstoriesofcomputationalcognitivemodeling, in a practical or a theoretical sense. They include, among many others: • the various models of developmental psychology, including the connec- tionist models of verb past-tense learning and the controversiesstemming 18from such models, • the tutoring systems based on the ACT-R cognitive architecture, • the model of implicit and explicit learning based on the CLARION cog- nitive architecture. For instance, computational models of child developmenthavebeen success- ful in accounting for, and in explaining, fine-grained developmental processes. In terms of widespread impact and associated theoretical interests and contro- versies, computational models of verb past-tense learning may be ranked as being at the top of all computational cognitive models (see, e.g., Rumelhart et al 1986). Theoretically, successful developmentmodels haveclarified a number of ma- jor issues. In developmental psychology, there is the dichotomy contrasting knowledge that the child acquires through interacting with the environment (nurture) with knowledge of phylogenic origin (nature). It was argued that mechanisms of gene expression and brain development did not allow for the de- tailed specification of neural networks in the brain as required by the nativist position. Ithasbeenarguedthatamoreplausibleroleforinnateknowledgeisat the level of architectures and timing of development (see the chapter by Shultz and Sirois in this volume). In this regard,neural network models haveprovided new ways of thinking about innateness. That is, instead of asking whether or notsomething is innate, oneshouldask howevolutionconstrainsthe emergence of a brain function during individual development. This kind of theorizing has benefited from the use of neural networks (as detailed in the chapter by Shultz and Sirois). Developmentalpsychologistshavealsobeendebatingthedistinctionbetween learninganddevelopment. Astaticneuralnetworkcanonlylearnwhatiswithin its representationalpower. Thus, when static neural networks areused, it is as- 19sumed that the ultimate brain network topology has already been developed (even if initial weights are random). However, this assumption implies repre- sentationalinnateness,whichhasbeenarguedtobeimplausible. Analternative is to use neural network models that form their network topology as a result of their experience. Using constructive learning models also resolves the “para- dox of development”: It was argued that if learning was done by proposing and testing hypotheses, it was not possible to learn anything that could not al- ready be represented. This argumentbecomes irrelevantin light of constructive learning models where learning mechanisms that construct representations are separate from the representation of domain-specific knowledge. A constructive model builds representational power that it did not previously possess. Thus, computationalmodeling suggeststhat developmentis functionally distinctfrom learning (as argued in the chapter by Shultz and Sirois). Similarly, as another example, an interpretation of a broad range of skill learning data (including those from the implicit learning literature) was pro- posed based on the CLARION cognitive architecture (see Sun, Slusarz, and Terry 2005 and Sun 2002; see also the chapter by Taatgen and Anderson in this volume concerning cognitive architectures). At a theoretical level, this work explicates the interaction between implicit and explicit cognitive processes in skill learning, in contrast to the tendency of studying each type in isolation. It highlights the interaction between the two types of processes and its various effects on learning (including the so called synergy effects; see Sun 2002). At an empirical level, a model centered on such an interaction constructed based on CLARION was used to account for data in a variety of task domains: process control tasks, artificial grammar learning tasks, serial reaction time tasks, as well as some much more complex task domains (such as Tower of Hanoi and Minefield Navigation). The model was able to explain data in these task do- mains,sheddinglightonsomeapparentlycontradictoryfindings(includingsome 20