Constant Domain Quantified Modal Logics without Boolean Negation

September 2005

“Constant Domain Quantified Modal Logics without Boolean Negation,” Australasian Journal of Logic, 3 (2005), 45-62. Available online at the AJL.

The paper examines what its title says. Constant domain modal frames seem to be the natural semantics for quantified relevant logics and their cousins. Kit Fine has shown us that things are not that simple, as the natural proof theory is not complete for the natural semantics. In this paper I explore the somewhat simpler case of one-place modal operators. The natural proofs work, but there are a few surprises, such as the need to use intuitionistic implication and its dual, subtraction, in the completeness proof. This paper is dedicated to the memory of Richard Sylvan, who contributed so much to the study of the semantics of relevant logics and their neighbours.

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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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