The geometry of non-distributive logics

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    Author
    Restall, G; Paoli, F
    Date
    2005-12-01
    Source Title
    JOURNAL OF SYMBOLIC LOGIC
    Publisher
    CAMBRIDGE UNIV PRESS
    University of Melbourne Author/s
    Restall, Gregory
    Affiliation
    Philosophy, Anthropology And Social Inquiry
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    Document Type
    Journal Article
    Citations
    Restall, G. & Paoli, F. (2005). The geometry of non-distributive logics. JOURNAL OF SYMBOLIC LOGIC, 70 (4), pp.1108-1126. https://doi.org/10.2178/jsl/1129642117.
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    URI
    http://hdl.handle.net/11343/25410
    DOI
    10.2178/jsl/1129642117
    Description

    C1 - Journal Articles Refereed
    Abstract
    <jats:title>Abstract</jats:title><jats:p>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.</jats:p>
    Keywords
    Logic; Other

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