Proofs with Star and Perp

January 2024

Proofs with Star and Perp (to appear in New Directions in Relevant Logics)

In this paper, I show how to incorporate insights from the model-theoretic semantics for negation (insights due the late J. Michael Dunn, among others, in his paper “Star and Perp: Two Treatments of Negation”), into a proof-first understanding of the semantics of negation. I then discuss the how a logical pluralist may understand the underlying accounts of proofs and their significance.

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You are welcome to download and read this document. I especially welcome feedback on it. As it is not yet published in final form, if you want to cite the paper, please check with me first. 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.


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