In his paper “Generalised Ortho Negation” J. Michael Dunn mentions a claim of mine to the effect that there is no condition on `perp frames’ equivalent to the holding of double negation elimination (from ~~A to infer A). That claim of mine was wrong. In this paper I correct my error and analyse the behaviour of conditions on frames for negations which verify a number of different theses. (Ed Mares has pointed out that there’s some overlap between this paper and his earlier “A Star-Free Semantics for R” (JSL 1995), which I’d read long before writing this one. The particular modelling condition for DNE is still original to me, however.)
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.