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December 2005 The geometry of non-distributive logics
Francesco Paoli, Greg Restall
J. Symbolic Logic 70(4): 1108-1126 (December 2005). DOI: 10.2178/jsl/1129642117

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.

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Francesco Paoli. Greg Restall. "The geometry of non-distributive logics." J. Symbolic Logic 70 (4) 1108 - 1126, December 2005. https://doi.org/10.2178/jsl/1129642117

Information

Published: December 2005
First available in Project Euclid: 18 October 2005

zbMATH: 1100.03049
MathSciNet: MR2194239
Digital Object Identifier: 10.2178/jsl/1129642117

Rights: Copyright © 2005 Association for Symbolic Logic

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Vol.70 • No. 4 • December 2005
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