Greg Restall and Tony Roy “On Permutation in Simplified Semantics,” Journal of Philosophical Logic, 38:3 (2009) 333–341.
This note explains an error in Restall’s ‘Simplified Semantics for Relevant Logics (and some of their rivals)’ (Journal of Philosophical Logic 1993) concerning the modelling conditions for the axioms of assertion A → ((A → B) → B) and permutation (A → (B → C)) → (B → (A → C)). We show that the modelling conditions for assertion and permutation proposed in ‘Simplified Semantics’ overgenerate. In fact, they overgenerate so badly that the proposed semantics for the relevant logic R validate the rule of disjunctive syllogism. The semantics provides for no models of R in which the “base point” is inconsistent.
In this note, we explain this result, diagnose the mistake in ‘Simplified Semantics’ and propose a correction.