Two Manuscripts, One by Routley, One by Meyer: The Origins of the Routley-Meyer Semantics for Relevance Logics

Abstract

A ternary relation is often used nowadays to interpret an implication connective of a logic, a practice that became dominant in the semantics of relevance logics.  This paper examines two early manuscripts --- one by Routley, another by Meyer --- in which they were developing set-theoretic semantics for various relevance logics.  A standard presentation of a ternary relational semantics for, let us say, the logic of relevant implication R is quite illuminating, yet the invention of this semantics was fraught with false starts.  Meyer's manuscript, in which he builds on some ideas from Routley's manuscript, essentially contains a relational semantics for which R^{ot} is sound and complete.