Shepard has argued that a universal law should govern generalization across different domains of perception and cognition, as well as across organisms from different species or even different planets. Starting with some basic assumptions about natural kinds, he derived an exponential decay function as the form of the universal generalization gradient, which accords strikingly well with a wide range of empirical data. However, his original formulation applied only to the ideal case of generalization from a single encountered stimulus to a (...) single novel stimulus, and for stimuli that can be represented as points in a continuous metric psychological space. Here we recast Shepard's theory in a more general Bayesian framework and show how this naturally extends his approach to the more realistic situation of generalizing from multiple consequential stimuli with arbitrary representational structure. Our framework also subsumes a version of Tversky's set-theoretic model of similarity, which is conventionally thought of as the primary alternative to Shepard's continuous metric space model of similarity and generalization. This unification allows us not only to draw deep parallels between the set-theoretic and spatial approaches, but also to significantly advance the explanatory power of set-theoretic models. Key Words: additive clustering; Bayesian inference; categorization; concept learning; contrast model; features; generalization; psychological space; similarity. (shrink)

Six experiments explored the hypothesis that the members of categories which are considered most prototypical are those with most attributes in common with other members of the category and least attributes in common with other categories. In probabilistic terms, the hypothesis is that prototypicality is a function of the total cue validity of the attributes of items. In Experiments 1 and 3, subjects listed attributes for members of semantic categories which had been previously rated for degree of prototypicality. High positive (...) correlations were obtained between those ratings and the extent of distribution of an item's attributes among the other items of the category. In Experiments 2 and 4, subjects listed superordinates of category members and listed attributes of members of contrasting categories. Negative correlations were obtained between prototypicality and superordinates other than the category in question and between prototypicality and an item's possession of attributes possessed by members of contrasting categories. Experiments 5 and 6 used artificial categories and showed that family resemblance within categories and lack of overlap of elements with contrasting categories were correlated with ease of learning, reaction time in identifying an item after learning, and rating of prototypicality of an item. It is argued that family resemblance offers an alternative to criterial features in defining categories. (shrink)