The geometry of non-distributive logics
Author
Restall, G; Paoli, FDate
2005-12-01Source Title
JOURNAL OF SYMBOLIC LOGICPublisher
CAMBRIDGE UNIV PRESSUniversity of Melbourne Author/s
Restall, GregoryAffiliation
Philosophy, Anthropology And Social InquiryMetadata
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Journal ArticleCitations
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.Access Status
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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
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