- School of Historical and Philosophical Studies - Research Publications
School of Historical and Philosophical Studies - Research Publications
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ItemTruth values and proof theoryRestall, G (Springer Science and Business Media LLC, 2009-07-01)
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ItemOn Permutation in Simplified SemanticsRestall, G ; Roy, T (SPRINGER, 2009-06)
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ItemConstant domain quantified modal logics without Boolean negationRESTALL, GA (Victoria University of Wellington, 2005)This paper provides a sound and complete axiomatisation for constant domain modal logics without Boolean negation. This is a simpler case of the difficult problem of providing a sound and complete axiomatisation for constant-domain quantified relevant logics, which can be seen as a kind of modal logic with a twoplace modal operator, the relevant conditional. The completeness proof is adapted from a proof for classical modal predicate logic (I follow James Garson’s presentation of the completeness proof quite closely [10]), but with an important twist, to do with the absence of Boolean negation.
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ItemMODAL MODELS FOR BRADWARDINE'S THEORY OF TRUTHRestall, G (CAMBRIDGE UNIV PRESS, 2008-08)
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ItemNo Preview AvailableOne way to face factsRestall, G (BLACKWELL PUBL LTD, 2004-07)
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ItemNo Preview AvailableCarnap's tolerance, meaning, and logical pluralismRESTALL, GA ( 2002)
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ItemNo Preview AvailableJust What Is Full-Blooded Platonism?†RESTALL, G (Oxford University Press (OUP), 2003-02-01)
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ItemNo Preview AvailableRelevant restricted quantificationBeall, JC ; Brady, RT ; Hazen, AP ; Priest, G ; Restall, G (SPRINGER, 2006-12)
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ItemNo Preview AvailableThe geometry of non-distributive logicsRestall, G ; Paoli, F (CAMBRIDGE UNIV PRESS, 2005-12)Abstract In this paper we introduce a new natural deduction system for the logic of lattices, and a number of extensions of lattice logic with different negation connectives. We provide the class of natural deduction proofs with both a standard inductive definition and a global graph-theoretical criterion for correctness, and we show how normalisation in this system corresponds to cut elimination in the sequent calculus for lattice logic. This natural deduction system is inspired both by Shoesmith and Smiley's multiple conclusion systems for classical logic and Girard's proofnets for linear logic.