Forming a conjoint category (square tables) from constituent categories (squares and tables) has traditionally been modeled by formal set intersection. In this traditional view, in which categories are treated as precisely defined sets, an item is a member of the conjoint category if and only if it is a member of both constituent categories. However, as is now widely believed, many categories should be treated as graded, with members that vary in typicality and boundaries that are inexact. In the present article, it is argued that set intersection is inappropriate for combining graded categories. The authors propose an alternative formal mechanism in which a conjoint category is constructed from constituent categories by forming a joint distribution of values. The proposed model accounts for both membership and typicality of instances in conjoint categories, but only when the constituent categories are independent, or the relation between them is known.
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