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The importance of categorical reasoning in human cognition is well-established in psychology and cognitive science, and one of the most important functions of categorization is to facilitate prediction. This paper provides a model of optimal categorization. In the beginning of each period a subject observes a two-dimensional object in one dimension and wants to predict the object's value in the other dimension. The subject partitions the space of objects into categories. She has a data base of objects that were observed in both dimensions in the past. The subject determines what category the new object belongs to on the basis of observation of its first dimension.
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