School of Historical and Philosophical Studies - Research Publications

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Start date: 2005 × End date: 2005 × Author: Restall, Gregory ×

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    Multiple conclusions
    RESTALL, GA (King's College Publications, 2005)
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    Minimalists about truth can (and should) be epistemicists, and it helps if they are revision theorists too
    RESTALL, GA ; BEALL, JC ; ARMOUR-GARB, B (Oxford University Press, 2005)
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    Constant domain quantified modal logics without Boolean negation
    RESTALL, 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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    Logical Pluralism
    Beall, JC ; Restall, G (Oxford University PressOxford, 2005-11-24)
    Abstract Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline of philosophy. This book presents and defends what it calls logical pluralism, arguing that the notion of logical consequence does not pin down one deductive consequence relation; it allows for many of them. In particular, the book argues that broadly classical, intuitionistic, and relevant accounts of deductive logic are genuine logical consequence relations; we should not search for one true logic, since there are many. The book's conclusions have profound implications for many linguists as well as for philosophers.
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    The geometry of non-distributive logics
    Restall, 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.