Bridging the Two Plans in the Semantics for Relevant Logic

Abstract

This paper considers how the two plans in the semantics for relevant logic are related to each other. The so-called American plan, classical-style four-valued semantics, is intuitive, but weak. The so-called Australian plan, two-valued frame semantics, is very powerful, but the semantic devices employed need some explanation. Examining R. Routley’s 1984 paper ‘American plan completed, ’ this paper argues that the American plan provides an explanatory and ontological basis for the Australian plan, and that the latter is just a developed form of the former.