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Defining Double Negation Elimination

By Greg Restall

Abstract

In his paper \Generalised Ortho Negation" [2] J. Michael Dunn mentions a claim of mine to the eect that there is no condition on `perp frames' equivalent to the holding of double negation elimination A ` A. That claim is wrong. In this paper I correct my error and analyse the behaviour of conditions on frames for negations which verify a number of dierent theses. 1 1 Compatibility Frames Dunn's work on general models for negation has been a signicant advance in our understanding of negation in non-classical logics [1, 2]. These models generalise Kripke models for intuitionistic logic and Routley{Meyer models for relevant implication. I will recount the essential details of these models for negation here before we look at the behaviour of inference patterns such as double negation elimination. Denition 1.1 A frame is a triple hP; C; vi consisting of a set P of points, and two binary relations C and v on P such that v is a partial order on P . That is, v is reexive, transit..

Year: 2001
OAI identifier: oai:CiteSeerX.psu:10.1.1.31.5994
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