Several theories have been proposed regarding how causal relations among features of objects affect how those objects are classified. The assumptions of these theories were tested in 3 experiments that manipulated the causal knowledge associated with novel categories. There were 3 results. The 1st was a multiple cause effect in which a feature’s importance increases with its number of causes. The 2nd was a coherence effect in which good category members are those whose features jointly corroborate the category’s causal knowledge. These 2 effects can be accounted for by assuming that good category members are those likely to be generated by a category’s causal laws. The 3rd result was a primary cause effect, in which primary causes are more important to category membership. This effect can also be explained by a generative account with an additional assumption: that categories often are perceived to have hidden generative causes.

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.

An ongoing goal in the field of categorization has been to determine how objects ’ features provide evidence of membership in one category versus another. Well-known findings include that feature diagnosticity is a function of how often the feature appears in category members versus nonmembers, their perceptual salience, how features are used in support of inferences, and how observable features are related to other observable features. We tested how diagnosticity is affected by causal relations between observable and unobserved features. Consistent with our view of classification as diagnostic reasoning, we found that observable features are more diagnostic to the extent that they are caused by underlying features that define category membership, because the presence of the latter can be (causally) inferred from the former. Implications of these results for current views of conceptual structure and models of categorization are discussed. It is generally accepted that people’s concepts include not only the features and attributes of the entity being represented, but also the ways in which those features are related to one another. For example, we know that hormones can alter a person’s behavior, that chemical structure can affect a substance’s hardness, and that processor

A central question in cognitive research concerns how new properties are generalized to categories. This article introduces a model of how generalizations involve a process of causal inference in which people estimate the likely presence of the new property in individual category exemplars and then the prevalence of the property among all category members. Evidence in favor of this causalbased generalization (CBG) view included effects of an existing feature’s base rate (Experiment 1), the direction of the causal relations (Experiments 2 and 4), the number of those relations (Experiment 3), and the distribution of features among category members (Experiments 4 and 5). The results provided no support for an alternative view that generalizations are promoted by the centrality of the to-be-generalized feature. However, there was evidence that a minority of participants based their judgments on simpler associative reasoning processes. Keywords: Causal-based induction; Generalization; Causal reasoning 1.

Two experiments examined the impact of causal relations between features on categorization by adults and 5-6-year-old children. Participants learned about artificial categories containing instances with two causally related features and two non-causal features. They then selected the most likely category member from a series of novel test pairs. Classification patterns and logistic regression were used to diagnose the presence of independent effects of causal coherence, causal status and relational centrality. Adult classification was driven primarily by coherence when causal links were deterministic (Experiment 1), but showed additional influences of causal status and centrality when links were probabilistic (Experiment 2). Children’s classification was based primarily on causal coherence in both cases. These results suggest that the generative model [Rehder, B. (2003). A causalmodel theory of conceptual representation and categorization. Journal of Experimental Psychology: Learning, Memory, and Cognition, 29, 1141-1159] provides a good account of causal categorization in both children and adults. Children’s Causal Categorization 3 It is well established that causal knowledge plays an important role in adult categorization and