Making Sense of Relevant Semantics (draft)

Abstract: Involving as it does impossible worlds and the like, the Routley-Meyer worlds semantics for relevant logic has seemed unmo-tivated to some. I set a version of relevant semantics in a context to make sense of its different elements. Suppose a view which makes room for structured properties — or related entities which combine in arbitrary ways to form structured ones. Then it may seem natural to say entailment supervenes upon the structures, so that P entails Q just when part of the condition for being p is being q. If P stands in this relation to Q, a result is that there is no possible world where P but not Q, so that P classically entails Q. But the conditions are not equivalent. For all possible worlds, but not all properties, are maximal and consistent. I suggest that relevant semantics is naturally seen as modeling entailment grounded in property structure and makes sense insofar as it reflects this fundamental and intuitive notion.