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The Geometry of Non-Distributive Logics

Greg Restall and Francesco Paoli
The Journal of Symbolic Logic
Vol. 70, No. 4 (Dec., 2005), pp. 1108-1126
Stable URL: http://www.jstor.org/stable/27588416
Page Count: 19
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The Geometry of Non-Distributive Logics
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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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