Topics in Relevant Logic: A Semantic Perspective

This paper concerns the interface between relevant logics and recent developments in semantics for hyperintensional operators. In the latter area, the notion of topicality or aboutness has begun to play an explicit modeling role, with classes of models being studied which incorporate representations of topics, and of operations on topics. The idea is to use these topics in the evaluations of formulas including hyperintensional operators in order to explain why classically equivalent formulas may not be intersubstitutable in contexts using those operators—though classically equivalent, if a pair of formulas can be interpreted to concern totally unrelated topics, then we should not be able to substitute one for the other in contexts which are sensitive to topics. Relevant logics, and the central relevance property of Variable Sharing, have been read as concerning something like topics in the past, and recently this angle on relevance has seen renewed interest. In this paper, I’ll develop and motivate a method for representing topics in the matrix models of logics, and apply this method to R and its matrix models (given by De Morgan monoids) to argue that there is a clear semantic perspective on topicality according to which R is topic-sensitive as a logic.