A Logical Account of Relevance

Abstract

The study of relevance has gained considerable attention recently in areas as diverse as machine learning and knowledge representation. In this paper, we focus on one particular area, namely relevance in the context of logical theories. We are interested in answering questions like: when is a sentence (or theory) relevant to a set of propositions, or, when is one set of propositions relevant to another given some background theory? The answers are given semantically in terms of a logic of belief and syntactically in terms of prime implicates . Furthermore, rather than merely adding yet another set of definitions of relevance to the many that already exist, we also show close connections to two others that were recently proposed, thus pointing to some common ground at least as far as logical relevance is concerned.