Routley-Meyer Semantics

Routley-Meyer semantics is the model-theoretic framework for relevance logic developed by Richard Routley, Nuel Belnap, and Robert K. Meyer in the 1970s. Unlike the binary accessibility relation of modal logic — which connects possible worlds in pairs — Routley-Meyer semantics employs a ternary accessibility relation: a world a is relevantly accessible from a pair of worlds (b, c) when the information in b and c together is sufficient to determine what holds at a. This three-place relation formalizes the core relevance intuition: implication A → B is valid not merely when B holds wherever A holds, but when the connection between A and B is witnessed by a shared contextual situation. The semantics demonstrates that relevance logic is not merely a syntactic restriction on classical rules but a coherent alternative with its own mathematical geography.\n\n\n\n