A framework for skill acquisition is proposed that includes two major stages in the development of a cognitive skill: a declarative stage in which facts about the skill domain are interpreted and a procedural stage in which the domain knowledge is directly embodied in procedures for performing the skill. This general framework has been instantiated in the ACT system in which facts are encoded in a propositional network and procedures are encoded as productions. Knowledge compilation is the process by which the skill transits from the declarative stage to the procedural stage. It consists of the subprocesses of composition, which collapses sequences of productions into single productions, and proceduralization, which embeds factual knowledge into productions. Once proceduralized, further learning processes operate on the skill to make the productions more selective in their range of applications. These processes include generalization, discrimination, and strengthening of productions. Comparisons are made to similar concepts from past learning theories. How these learning mechanisms apply to produce the power law speedup in processing time with practice is discussed. It requires at least 100 hours of learning and practice to acquire any significant cognitive skill to a reasonable degree of proficiency. For instance, after 100 hours a student learning to program a computer has achieved only a very modest facility in the skill. Learning one's primary language takes tens of thousands of hours. The psychology of human learning has been very thin in ideas about what happens to skills under the impact of this amount of learning—and for obvious reasons. This article presents a theory about the changes in the nature of a skill over such large time scales and about the basic learning processes that are responsible.

A rational model of human categorization behavior is presented that assumes that categorization reflects the derivation of optimal estimates of the probability of unseen features of objects. A Bayesian analysis is performed of what optimal estimations would be if categories formed a disjoint partitioning of the object space and if features were independently displayed within a category. This Bayesian analysis is placed within an incremental categorization algorithm. The resulting rational model accounts for effects of central tendency of categories, effects of specific instances, learning of linearly nonseparable categories, effects of category labels, extraction of basic level categories, base-rate effects, probability matching in categorization, and trial-by-trial learning functions. Al-though the rational model considers just I level of categorization, it is shown how predictions can be enhanced by considering higher and lower levels. Considering prediction at the lower, individual level allows integration of this rational analysis of categorization with the earlier rational analysis of memory (Anderson & Milson, 1989). Anderson (1990) presented a rational analysis ot 6 human cog-nition. The term rational derives from similar "rational-man" analyses in economics. Rational analyses in other fields are sometimes called adaptationist analyses. Basically, they are ef-forts to explain the behavior in some domain on the assump-tion that the behavior is optimized with respect to some criteria of adaptive importance. This article begins with a general char-acterization ofhow one develops a rational theory of a particu-lar cognitive phenomenon. Then I present the basic theory of categorization developed in Anderson (1990) and review the applications from that book. Since the writing of the book, the theory has been greatly extended and applied to many new phenomena. Most of this article describes these new develop-ments and applications. A Rational Analysis Several theorists have promoted the idea that psychologists might understand human behavior by assuming it is adapted to the environment (e.g., Brunswik, 1956; Campbell, 1974; Gib-

Previously published sets of classification and old-new recognition memory data are reanalyzed within the framework of an exemplar-based generalization model. The key assumption in the model is that, whereas classification decisions are based on the similarity of a probe to exemplars of a target category relative to exemplars of contrast categories, recognition decisions are based on overall summed similarity of a probe to all exemplars. The summed-similarity decision rule is shown to be consistent with a wide variety of recognition memory data obtained in classification learning situations and may provide a unified approach to understanding relations between categorization and recognition. Recently, there has been an upsurge of interest among categorization researchers in exploring relations between classification learning and old-new recognition memory. This interest has been fueled by the exemplar view of category representation, which holds that people base classification decisions on similarity comparisons with stored exemplars (Hintzman, 1986b; Medin & Schaffer, 1978; Nosofsky, 1986).

The relationship between subjects ' identification and categorization learning of integral-dimension stimuli was studied within the framework of an exemplar-based generalization model. The model was used to predict subjects ' learning in six different categorization conditions on the basis of data obtained in a single identification learning condition. A crucial assumption in the model is that because of selective attention to component dimensions, similarity relations may change in systematic ways across different experimental contexts. The theoretical analysis provided evidence that, at least under unspeeded conditions, selective attention may play a critical role in determining the identification-categorization relationship for integral stimuli. Evidence was also provided that similarity among exemplars decreased as a function of identification learning. Various alternative classification models, including prototype, multiple-prototype, average distance, and "value-on-dimensions" models, were unable to account for the results. This article seeks to characterize performance relations between the two fundamental classification paradigms of identification and categorization. Whereas in an identification paradigm people identify stimuli as unique items (a one-to-one

Experiments were conducted in which Ss made classification, recognition, and similarity judgments for 34 schematic faces. A multidimensional scaling (MDS) solution for the faces was derived on the basis of the similarity judgments. This MDS solution was then used in conjunction with an exemplar-similarity model to accurately predict Ss ' classification and recognition judgments. Evidence was provided that Ss allocated attention to the psychological dimensions differentially for classification and recognition. The distribution of attention came close to the ideal-observer distribution for classification, and some tendencies in that direction were observed for recognition. Evidence was also provided for interactive effects of individual exemplar frequencies and similarities on classification and recognition, in accord with the predictions of the exemplar model. Unexpectedly, however, the frequency effects appeared to be larger for classification than for recognition. The purpose of this study was to provide tests of a model for relating perceptual classification performance and oldnew recognition memory. The model under investigation is the context theory of classification proposed by Medin and

Subjects learned to classify perceptual stimuli varying along continuous, separable dimensions into rule-described categories. The categories were designed to contrast the predictions of a selective-attention exemplar model and a simple rule-based model formalizing an economy-ofdescription view. Converging evidence about categorization strategies was obtained by also collecting identification and recognition data and by manipulating strategies via instructions. In free-strategy conditions, the exemplar model generally provided an accurate quantitative account of identification, categorization, and recognition performance, and it allowed for the interrelationship of these paradigms within a unified framework. Analyses of individual subject data also provided some evidence for the use of rules, but in general, the rules seemed to have a great deal in common with exemplar storage processes. Classification and recognition performance for subjects given explicit instructions to use specific rules contrasted dramatically with performance in the free-strategy conditions and could not be predicted by the exemplar model. Markedly different theoretical approaches have been applied to account for the learning and representation of welldefined categories structured according to simple rules and more natural, ill-defined categories (Rosch, 1973; E. E. Smith & Medin, 1981). In the case of well-defined categories, it is generally assumed that people formulate and test hypotheses concerning the "rules " that determine category membership

conducted. Forty years of research has assumed that category learning often involves learning to selectively attend to only those stimulus dimensions useful for classification. We confirmed that participants learned to allocate their attention optimally. We also found that learners tend to fixate all stimulus dimensions early in learning. This result obtained despite evidence that participants were also testing one-dimensional rules during this period. Finally, the restriction of eye movements to only relevant dimensions tended to occur only after errors were largely (or completely) eliminated. We interpret these findings as consistent with multiple-systems theories of learning which maximize information input in order to maximize the number of learning modules involved, and which focus solely on relevant information only after one module has solved the learning problem.

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Several researchers have reported marked differences in the abilities of expert and novice problem-solvers to reliably sort problems according to problem structure. These differences have been attributed to the possession of schematized knowledge structures by experts that are lacking in novices. The aim of the present research was to outline and test a descriptive model of schema acquisition. The model describes the processes involved in deriving schemata from psychologically defined problem instances, and the memory structures resulting from the processes so described. Two experiments were conducted to test the model. In the first, the sufficiency of the processes comprising the model for schema abstraction was tested by requiring subjects to answer questions while reading algebra word-problem (questions that were presumed to enhance one or more hypothetical memory structures), and comparing performance on a problem sorting task following reading. Ability to sort previously read and new problems properly on the basis of problem structure was found to vary reliably with the type of question answered while reading. Questions that facilitated comparison of problems yielded better structure sortin performance than questions that focused attention within problems only. Similar results were obtained in Experiment 2, where subjects were required to match problems to symbolic representations (i.e., algebraic equations). Here subjects who answered questions that were presumed to facilitate schema abstraction according to the model performed as well as experts in matching problems to their symbolic representations.

AMBER is a model of first language acquisition that improves its performance through a process of error recovery, The model is implemented as an adaptive production system that introduces new condition-action rules on the basis of experience. AMaER starts with the ability to say only one word at a time, but adds rules for ordering goals and producing grammatical morphemes, based on comparisons between predicted and observed sentences. The morpheme rules may be overly general and lead to errors of commission; such errors evoke a discrimination process, producing more conservative rules with additional conditions. The system's performance improves gradually, since rules must be relearned many times before they are used. AMBER'S learning mechanisms account for some of the major developments observed in children's early speech.