Relevance from an epistemic perspective

Abstract

In this paper we study relevance relations in the context of prepositional logical theories and subject matters or topics of interest, which we take to be sets of atomic propositions. In particular, we are interested in answering questions like the following: when is a sentence (or theory) relevant to a subject matter, or, when is a topic relevant to another topic or sentence given some background theory? Relevance is studied from a subjective or epistemic point of view, that is, we try to capture relevance relations from an agent's point of view relative to his or her deductive capabilities. For this purpose, we start out with the definition of regular belief, which covers a wide range of belief models, from the very weak to those closed under classical logical implication. In the paper, we consider one example from each of the extremes, which are called explicit and implicit belief, respectively. We define a notion of prime implicates which applies to all models of regular belief and which has its usual meaning under implicit belief. Prime implicates turn out to be the right primitive from which all definitions of relevance are derived. Among the main technical contributions is a detailed comparison between relevance under implicit belief and three other approaches in the literature. This investigation reveals that all four share a lot of common ground even though some have very different starting points. We also study the complexity of determining relevance relations for implicit as well as explicit belief. While intractability obtains often, but not always, for implicit belief, the analogous problems for explicit belief are almost always tractable.