Journal of Symbolic Logic 70 (4):1108 - 1126 (2005)

Authors
Greg Restall
University of Melbourne
Francesco Paoli
Universita di Cagliari
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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DOI 10.2178/jsl/1129642117
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References found in this work BETA

Display Logic.Nuel D. Belnap - 1982 - Journal of Philosophical Logic 11 (4):375-417.
The Structure of Multiplicatives.Vincent Danos & Laurent Regnier - 1989 - Archive for Mathematical Logic 28 (3):181-203.
Lattice Theory.Garrett Birkhoff - 1940 - Journal of Symbolic Logic 5 (4):155-157.
Paraconsistent Quantum Logics.Maria Luisa Dalla Chiara & Roberto Giuntini - 1989 - Foundations of Physics 19 (7):891-904.

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Citations of this work BETA

Proof Theory of Paraconsistent Quantum Logic.Norihiro Kamide - 2018 - Journal of Philosophical Logic 47 (2):301-324.
Lattice Logic as a Fragment of (2-Sorted) Residuated Modal Logic.Chrysafis Hartonas - 2019 - Journal of Applied Non-Classical Logics 29 (2):152-170.

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