“Defining Double Negation Elimination,” Logic Journal of the IGPL, 8 (2000) 853–860.
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.)