Journal of Symbolic Logic 70 (4):1108 - 1126 (2005)
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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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DOI | 10.2178/jsl/1129642117 |
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References found in this work BETA
Algebraic Methods in Philosophical Logic.J. Michael Dunn & Gary M. Hardegree - 2005 - Studia Logica 79 (2):305-306.
The Structure of Multiplicatives.Vincent Danos & Laurent Regnier - 1989 - Archive for Mathematical Logic 28 (3):181-203.
Paraconsistent Quantum Logics.Maria Luisa Dalla Chiara & Roberto Giuntini - 1989 - Foundations of Physics 19 (7):891-904.
View all 7 references / Add more references
Citations of this work BETA
Proof Theory of Paraconsistent Quantum Logic.Norihiro Kamide - 2018 - Journal of Philosophical Logic 47 (2):301-324.
Lattice Logic, Bilattice Logic and Paraconsistent Quantum Logic: a Unified Framework Based on Monosequent Systems.Norihiro Kamide - 2021 - Journal of Philosophical Logic 50 (4):781-811.
Weak Disharmony: Some Lessons for Proof-Theoretic Semantics.Bogdan Dicher - 2016 - Review of Symbolic Logic (3):1-20.
Lattice Logic as a Fragment of (2-Sorted) Residuated Modal Logic.Chrysafis Hartonas - 2019 - Journal of Applied Non-Classical Logics 29 (2):152-170.
View all 10 citations / Add more citations
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