Rules of explosion and excluded middle: constructing a unified single-succedent Gentzen-style framework for classical, paradefinite, paraconsistent, and paracomplete logics

DOI10.1007/s10849-024-09416-6MaRDI QIDQ6612000

Norihiro Kamide

Publication date: 27 September 2024

Published in: Journal of Logic, Language and Information (Search for Journal in Brave)

zbMATH Keywords

cut-elimination theoremrule of excluded middlefalsification-aware Gentzen-style sequent calculusrule of explosionsingle-succedent Gentzen-style sequent calculus

Mathematics Subject Classification ID

Mathematical logic and foundations (03-XX) Computer science (68-XX)

Cites Work

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• Proof theory of Nelson's paraconsistent logic: a uniform perspective
• Dual intuitionistic logic and a variety of negations: the logic of scientific research
• On an implication connective of RM
• On interpretation of inconsistent theories
• Classical logic, intuitionistic logic, and the Peirce rule
• A remark on Gentzen's calculus of sequents
• Applications of Kripke models to Heyting-Brouwer logic
• The logic of paradox
• The logic of information structures
• Refutation systems in modal logic
• Dual-intuitionistic logic
• Refutations, proofs, and models in the modal logic K4
• Four-valued paradefinite logics
• Proof theory of paraconsistent quantum logic
• Handbook of philosophical logic. Vol. 6
• Intuitive semantics for first-degree entailments and `coupled trees'
• A formalization of the propositional calculus of H-B logic
• Semantics-based nonmonotonic inference
• A Łukasiewicz-style refutation system for the modal logic S4
• Falsification-aware semantics and sequent calculi for classical logic
• A calculus of antinomics
• On the theory of inconsistent formal systems
• Logic of antinomies
• Falsification, natural deduction and bi-intuitionistic logic
• Natural deduction systems for Nelson's paraconsistent logic and its neighbors
• Constructible falsity and inexact predicates
• On cut elimination in the presence of perice rule
• The Logic of Contradiction
• Natural 3-valued logics—characterization and proof theory
• Refutations in Wansing’s Logic
• A deductive-reductive form of logic: General theory and intuitionistic case
• Normalisation for Some Quite Interesting Many-Valued Logics
• Hybrid Deduction-Refutation Systems for FDE-Based Logics
• A MODAL TRANSLATION FOR DUAL-INTUITIONISTIC LOGIC
• Constructible falsity
• Refutation-aware Gentzen-style calculi for propositional until-free linear-time temporal logic
• Falsification-aware calculi and semantics for normal modal logics including S4 and S5
• Refutation systems: an overview and some applications to philosophical logics

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