TOWARDS A MATHEMATICAL THEORY OF ANALOGY

Abstract

This paper presents a mathematical theory of analogy, which should be a basis in developing analogical reasoning by a computer. The analogy is a partial identity between two sets of facts. In order to compare several analogies, we introduce an ordering of analogies, and we define two types of optimal analogies, maximal analogies and greatest ones. We show a condition under which the greatest analogy exists, and also present a top-down procedure to find the maximal analogies.