Reasoning with Concepts

A unified treatment of different types of reasoning with concepts, such as category-based induction, nonmonotonic reasoning, analogies, and generics.

Psychologists and philosophers have worked on topics such as category-based induction, nonmonotonic reasoning, analogies, and generics, but these problems have largely been investigated independently. In Reasoning with Concepts, Peter Gaerdenfors and Matias Osta-Velez bring them all together by presenting models built on the theory of conceptual spaces. This theory offers a rich framework for modeling many aspects of the structure of concepts. In particular, it allows the definition of measures for similarity, typicality, diagnosticity, and coherence of concepts, notions long employed informally by psychologists and philosophers.

While probabilistic models exist for some of these notions, no comprehensive formal framework has previously encompassed them all. The proposed measures here, based on distances in conceptual space and prototypes, generate novel testable predictions while unifying previously disparate theoretical territories. Furthermore, the models can be implemented in artificial systems that deal with different forms of reasoning.