A Routley-Meyer affixing style semantics for logics containing Aristotle's thesis (Q1263574)

Aristotle's thesis is the schema \(\sim (A\to \sim A)\); Boethius' is (A\(\to B)\to \sim (A\to \sim B)\). These are important in connexive logic. Here they are added to the family of relevance logics, beginning with Routley \& Meyer's basic system \(\underset \tilde{} B\) and reaching through the Anderson \& Belnap systems, \(\underset \tilde{} E\), \(\underset \tilde{} R\), etc. These systems so extended are simply inconsistent. Nevertheless, a model theoretic semantics may be defined for them, and the systems proved to be sound and complete with respect to that semantics. This the author does using a variation on the Routley-Meyer affixing style of semantics for relevance logics. (The variation introduced here is less ad hoc than others previously proposed for these extended logics.)