I’m sorry, I truly am.
Back in the period 1990-1992, I wrote a couple of papers on the semantics of relevant logics. I thought they were pretty nifty, and I submitted them to a prestigious journal. They got accepted. The first of these papers is “Simplified Semantics for Relevant Logics (and some of their rivals).”
Unfortunatley, there’s a hole in the middle of this paper. That’s the problem with being a logician, people can sometimes prove you wrong by presenting a counterexample to your claim. That’s the nice thing about playing a game with relatively clear rules. You can figure out what constitutes good play!
Anyway, Tony Roy did a fantastic job of isolating the problem, which exists in not only my paper, but Graham Priest’s text An Introduction to Non-Classical Logic, which followed the simplified semantics rather closely. The problem is serious, for in my semantics for the relevant logic R, it turns out that disjunctive syllogism (the inference from A v B and ~A to B) is valid, and it shouldn’t be.
Tony isolated the problem, and we came up with a fix. The result is the paper “On Permutation in Simplified Semantics.” Please take a look over it before we sent it off to a journal.
Oh, and to the greater philosophical community (or at least, the tiny fraction that has come across this paper) – I’m sorry for deceiving you. I hope this paper helps make up for it.
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.