The Relevance of Semantic Subtyping

We compare Meyer and Routley’s minimal relevant logic B+ with the recent semanticsbased approach to subtyping introduced by Frisch, Castagna and Benzaken in the definition of a type system with intersection and union. We show that – for the functional core of the system – such notion of subtyping, which is defined in purely set-theoretical terms, coincides with the relevant entailment of the logic B+.