On Permutation in Simplified Semantics

November 2009

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 → ((AB) → B) and permutation (A → (BC)) → (B → (AC)). 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.

 download pdf

You are welcome to download and read this document. I welcome feedback on it. Please check the final published version if you wish to cite it. Thanks.


I’m Greg Restall, and this is my personal website. I am the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews, and the Director of the Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology I like thinking about – and helping other people think about – logic and philosophy and the many different ways they can inform each other.


To receive updates from this site, subscribe to the RSS feed in your feed reader. Alternatively, follow me at  @consequently@hcommons.social, where most updates are posted.


This site is powered by Netlify, GitHub, Hugo, Bootstrap, and coffee.   ¶   © 1992– Greg Restall.