Categorization generated by extended prototypes—An axiomatic approach

We suggest a model of categorization based on prototypes. A set of entities, identified with some finite dimensional Euclidian space, is partitioned into a finite number of categories. Such a categorization is said to be generated by extended prototypes if there is a set of distinguished entities, one for each category, such that the categorization is determined by proximity to these prototypical entities. The prototypes are called extended since they are described by points in a higher dimensional space than the entities. Sufficient conditions for a categorization to be generated by extended prototypes are provided. These conditions are also necessary if the prototypes are in general position.