Results 1 to 10 of about 4,006 (251)
Cut Elimination for Extended Sequent Calculi [PDF]
Bulletin of the Section of Logic, 2023 We present a syntactical cut-elimination proof for an extended sequent calculus covering the classical modal logics in the \(\mathsf{K}\), \(\mathsf{D}\), \(\mathsf{T}\), \(\mathsf{K4}\), \(\mathsf{D4}\) and \(\mathsf{S4}\) spectrum.
Simone Martini +2 more
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Completeness and cut-elimination theorems for trilattice logics
Annals of Pure and Applied Logic, 2011 The paper deals with Gentzen-type formulations of logics (see [\textit{S. P. Odintsov}, Stud. Log. 91, No.~3, 407--428 (2009; Zbl 1170.03014)]), related to the trilattice \(\mathit{SIXTEEN}_3\) (see [\textit{Y. Shramko} and \textit{H. Wansing}, J. Philos. Log. 34, No.~2, 121--153 (2005; Zbl 1094.03012)]). The authors present a sequent calculus \(L_{16}\
Norihiro Kamide, Heinrich Wansing
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Cut-elimination and Normalization Theorems for Connexive Logics over Wansing’s C
Bulletin of the Section of LogicGentzen-style sequent calculi and Gentzen-style natural deduction systems are introduced for a family (C-family) of connexive logics over Wansing’s basic constructive connexive logic C.
Norihiro Kamide
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One-Sided Sequent Systems for Nonassociative Bilinear Logic: Cut Elimination and Complexity
Bulletin of the Section of Logic, 2021 Bilinear Logic of Lambek amounts to Noncommutative MALL of Abrusci. Lambek proves the cut–elimination theorem for a one-sided (in fact, left-sided) sequent system for this logic.
Paweł Płaczek
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Logical Methods in Computer Science, 2013 We consider cut-elimination in the sequent calculus for classical first-order logic. It is well known that this system, in its most general form, is neither confluent nor strongly normalizing.
Stefan Hetzl, Lutz Straßburger
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On intuitionistic branching tense logic with weak induction
Lietuvos Matematikos Rinkinys, 1998 In the paper, the first-order branching tense logic calculus is given: LB J with the weak induction, that is to say with the axiom (A ∧ A O ☐ A) ⊃ ☐ A instead of the induction axiom (A ∧ ☐ (A ⊃ O A)) ⊃ ☐ A.
Romas Alonderis
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A sequent calculus for a semi-associative law [PDF]
Logical Methods in Computer Science, 2019 We introduce a sequent calculus with a simple restriction of Lambek's product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a semi-associative law ...
Noam Zeilberger
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On Constructive Connectives and Systems [PDF]
Logical Methods in Computer Science, 2010 Canonical inference rules and canonical systems are defined in the framework of non-strict single-conclusion sequent systems, in which the succeedents of sequents can be empty.
Arnon Avron, Ori Lahav
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Normalisation Control in Deep Inference via Atomic Flows [PDF]
Logical Methods in Computer Science, 2008 We introduce `atomic flows': they are graphs obtained from derivations by tracing atom occurrences and forgetting the logical structure. We study simple manipulations of atomic flows that correspond to complex reductions on derivations. This allows us to
Alessio Guglielmi, Tom Gundersen
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A proof of cut-elimination theorem in simple type-theory
Journal of the Mathematical Society of Japan, 1967 exaly +3 more sources