Semantics of Analogies from a Logical Perspective

Abstract

A number of different approaches to model analogies and analogical reasoning in AI have been proposed, applying different knowledge representation and mapping strategies. Nevertheless, analogies still seem to be hard to grasp from a formal perspective, with no known treatment in the literature of, in particular, their formal semantics, though the empirical treatments involving human subjects are abundant. In this paper we present a framework that allows to analyze the syntax and the semantics of analogies in a universal logic-based setting without committing ourselves to a specific type of logic. We show that the syntactic process of analogy-making by finding a generalization can be given a sensible interpretation on the semantic level based on the theory of institutions. We then apply these ideas by considering a framework of analogy-making that is based on classical first-order logic.