“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.
I’m Greg Restall, and this is my personal website. I teach philosophy and logic as Professor of Philosophy at the University of Melbourne. ¶ From August 2021, I will be the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews. ¶ Start at the home page of this site—a compendium of recent additions around here—and go from there to learn more about who I am and what I do. ¶ This is my personal site on the web. Nothing here is in any way endorsed by the University of Melbourne.