This article presents a theory of categorization that accounts for the effects of causal knowledge that relates the features of categories. According to causal-model theory, people explicitly represent the probabilistic causal mechanisms that link category features and classify objects by evaluating whether they were likely to have been generated by those mechanisms. In 3 experiments, participants were taught causal knowledge that related the features of a novel category. Causal-model theory provided a good quantitative account of the effect of this knowledge on the importance of both individual features and interfeature correlations to classification. By enabling precise model fits and interpretable parameter estimates, causal-model theory helps place the theory-based approach to conceptual representation on equal footing with the well-known similarity-based approaches. For the last several decades, research on the topic of categorization has focused on the problem of learning new categories via examples of category members, that is, from empirical observations. The result has been a host of categorization models that are based on representational ideas such as central prototypes, stored exemplars, and variabilized rules, and on processing principles such as similarity, that have considerable explanatory power and experimental support. More recently, the influence of the prior “theoretical ” knowledge that learners often contribute to their representations of categories has also been a topic of study (Carey,

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An important element of learning from examples is the extraction of patterns and regularities from data. This paper investigates the structure of patterns in data defined over discrete features, i.e. features with two or more qualitatively distinct values. Any such pattern can be algebraically decomposed into a spectrum of component patterns, each of which is a simpler or more atomic ‘‘regularity.’ ’ Each component regularity involves a certain number of features, referred to as its degree. Regularities of lower degree represent simpler or more coarse patterns in the original pattern, while regularities of higher degree represent finer or more idiosyncratic patterns. The full spectral breakdown of a pattern into component regularities of minimal degree, referred to as its power series, expresses the original pattern in terms of the regular rules or patterns it obeys, amounting to a kind of ‘‘theory’ ’ of the pattern. The number of regularities at various degrees necessary to represent the pattern is tabulated in its power spectrum, which expresses how much of a pattern’s structure can be explained by regularities of various levels of complexity. A weighted mean of the pattern’s spectral power gives a useful numeric summary of its overall complexity, called its algebraic complexity. The basic theory of algebraic decomposition is extended in several ways, including algebraic accounts of the typicality of individual objects within concepts, and estimation of the power series from noisy data. Finally some relations between these algebraic quantities and empirical data are discussed.

Words, kinds and causal powers: A theory theory perspective on early naming and categorization. For some twenty-five years, the prevailing theories of categorization in philosophy have invoked the idea of “kinds ” (Putnam, 1975; Kripke, 1972). When we look at how adults use words to refer to categories of things we find that they only rarely categorize objects on the basis of their common properties. Instead, adults seem to categorize objects together when they believe that they belong to the same “kind”; that is, that they share some common, abstract “essence.” Psychological investigations of adults have largely confirmed these philosophical intuitions, adults do seem to group objects together based on “kinds ” rather than properties (Murphy &

Theories typically emphasize affordances or intentions as the primary determinant of an object’s perceived function. The HIPE theory assumes that people integrate both into causal models that produce functional attributions. In these models, an object’s physical structure and an agent’s action specify an affordance jointly, constituting the immediate causes of a perceived function. The object’s design history and an agent’s goal in using it constitute distant causes. When specified fully, the immediate causes are sufficient for determining the perceived function—distant causes have no effect (the causal proximity principle). When the immediate causes are ambiguous or unknown, distant causes produce inferences about the immediate causes, thereby affecting functional attributions indirectly (the causal updating principle). Seven experiments supported HIPE’s predictions. Function is a central construct in cognitive science and cognitive neuroscience. Cognitive psychologists have shown that the categorization of an artifact depends not only on its physical properties, but also on its function (e.g., Barton & Komatsu, 1989; Keil,

A theory of categorization is presented in which knowledge of causal relationships between category features is represented as a Bayesian network. Referred to as causal-model theory, this theory predicts that objects are classified as category members to the extent they are likely to have been produced by a category s causal model. On this view, people have models of the world that lead them to expect a certain distribution of features in category members (e.g., correlations between feature pairs that are directly connected by causal relationships), and consider exemplars good category members when they manifest those expectations. These expectations include sensitivity to higher-order feature interactions that emerge from the asymmetries inherent in causal relationships.

One central function of categories is to allow people to infer the presence of features that cannot be directly observed.

We report 4 studies which show that there are systematic quantitative patterns in the way we reason with uncertainty during causal and counterfactual inference.