Proof theory of Nelson's paraconsistent logic: a uniform perspective

DOI10.1016/j.tcs.2011.11.001zbMath1382.03048OpenAlexW2054776590MaRDI QIDQ764309

Heinrich Wansing, Norihiro Kamide

Publication date: 13 March 2012

Published in: Theoretical Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.tcs.2011.11.001

zbMATH Keywords

cut eliminationnormalizationsequent calculiparaconsistent logicinconsistency-tolerant reasoningnatural deduction systemsNelson's paraconsistent logic N4

Mathematics Subject Classification ID

Cut-elimination and normal-form theorems (03F05) Paraconsistent logics (03B53)

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Uses Software

• Pesca

Cites Work

• Limits for paraconsistent calculi
• A non-deterministic view on non-classical negations
• Dual intuitionistic logic and a variety of negations: the logic of scientific research
• Some useful 16-valued logics: How a computer network should think
• Constructive negations and paraconsistency
• Inconsistency-tolerant description logic. II: A tableau algorithm for \(\mathcal{CALC}^{\mathsf C}\)
• Combining linear-time temporal logic with constructiveness and paraconsistency
• Hyper-contradictions, generalized truth values and logics of truth and falsehood
• A remark on Gentzen's calculus of sequents
• Semantical analyses of propositional systems of Fitch and Nelson
• Intuitionistic logic with strong negation
• Paraconsistent logic programming
• On logics with coimplication
• The value of the four values
• The logic of information structures
• Informational interpretation of substructural propositional logics
• Dual-intuitionistic logic
• Paraconsistent declarative semantics for extended logic programs
• Handbook of philosophical logic. Vol. 6
• Intuitive semantics for first-degree entailments and `coupled trees'
• Display logic
• Partiality and its dual
• A formalization of the propositional calculus of H-B logic
• Reasoning with logical bilattices
• The power of Belnap: sequent systems for \(SIXTEEN_{3 }\)
• Propositional sequence-calculi for inconsistent systems
• On the theory of inconsistent formal systems
• Admissibility of structural rules for contraction-free systems of intuitionistic logic
• Symmetric and dual paraconsistent logics
• Intuitionistic Trilattice Logics
• A Paraconsistent Linear-time Temporal Logic
• SEQUENT CALCULI FOR SOME TRILATTICE LOGICS
• Constructive negation, implication, and co-implication
• Natural deduction systems for Nelson's paraconsistent logic and its neighbors
• Constructible falsity and inexact predicates
• The Logic of Contradiction
• Bilattices and the semantics of logic programming
• Logic Programming with Strong Negation and Inexact Predicates
• Logic programming and negation: A survey
• Sequent calculus in natural deduction style
• Belnap's Four-Valued Logic and De Morgan Lattices
• A note on dual-intuitionistic logic
• The Trilattice of Constructive Truth Values
• Knowledge, Uncertainty and Ignorance in Logic: Bilattices and beyond
• A deductive-reductive form of logic: Intuitionistic S4 modalities
• Characterizing Belnap's Logic via De Morgan's Laws
• A Cut-Free Sequent Calculus for Bi-intuitionistic Logic
• Sixty Years of Stable Models
• A semantical study of constructible falsity
• Constructible falsity
• A natural deduction system for first degree entailment
• Subtractive logic
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