Journal of Symbolic Logic 70 (4):1108 - 1126 (2005)
| Authors |
|
| 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
|
| Keywords | No keywords specified (fix it) |
| Categories | (categorize this paper) |
| DOI | 10.2178/jsl/1129642117 |
| Options |
Mark as duplicate
Export citation
Request removal from index
|
Download options
PhilArchive copy
Upload a copy of this paper Check publisher's policy Papers currently archived: 70,307
External links
- From the Publisher via CrossRef (no proxy)
- citeseerx.ist.psu.edu
(no proxy) - consequently.org (no proxy)
- projecteuclid.org (no proxy)
- journals.cambridge.org (no proxy)
- jstor.org (no proxy)
- cambridge.org (no proxy)
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
- Sign in / register and customize your OpenURL resolver..
- Configure custom resolver
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
Similar books and articles
Sequent Calculus in Natural Deduction Style.Sara Negri & Jan von Plato - 2001 - Journal of Symbolic Logic 66 (4):1803-1816.
Algebraic Logic for Classical Conjunction and Disjunction.J. M. Font & V. Verdú - 1993 - Studia Logica 52 (1):181.
Algebraic Logic for Classical Conjunction and Disjunction.Josep M. Font & Ventura Verdú - 1991 - Studia Logica 50 (3-4):391 - 419.
Abelian Logic and the Logics of Pointed Lattice-Ordered Varieties.Francesco Paoli, Matthew Spinks & Robert Veroff - 2008 - Logica Universalis 2 (2):209-233.
Natural Deduction for First-Order Hybrid Logic.Torben BraÜner - 2005 - Journal of Logic, Language and Information 14 (2):173-198.
A Double Deduction System for Quantum Logic Based on Natural Deduction.Yannis Delmas-Rigoutsos - 1997 - Journal of Philosophical Logic 26 (1):57-67.
The Deduction Rule and Linear and Near-Linear Proof Simulations.Maria Luisa Bonet & Samuel R. Buss - 1993 - Journal of Symbolic Logic 58 (2):688-709.
Analytics
Added to PP index
2009-01-28
Total views
85 ( #137,073 of 2,507,700 )
Recent downloads (6 months)
2 ( #277,114 of 2,507,700 )
2009-01-28
Total views
85 ( #137,073 of 2,507,700 )
Recent downloads (6 months)
2 ( #277,114 of 2,507,700 )
How can I increase my downloads?
Downloads
