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Generic Modal Cut Elimination Applied to Conditional Logics [PDF]
Logical Methods in Computer Science, 2011 We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies also to a wide
Dirk Pattinson, Lutz Schröder
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Fast Cut-Elimination using Proof Terms: An Empirical Study [PDF]
Electronic Proceedings in Theoretical Computer Science, 2018 Urban and Bierman introduced a calculus of proof terms for the sequent calculus LK with a strongly normalizing reduction relation. We extend this calculus to simply-typed higher-order logic with inferences for induction and equality, albeit without ...
Gabriel Ebner
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Cut-elimination for the mu-calculus with one variable [PDF]
Electronic Proceedings in Theoretical Computer Science, 2012 We establish syntactic cut-elimination for the one-variable fragment of the modal mu-calculus. Our method is based on a recent cut-elimination technique by Mints that makes use of Buchholz' Omega-rule.
Grigori Mints, Thomas Studer
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Cut elimination for knowledge logic with interaction
Lietuvos Matematikos Rinkinys, 2021 In the article the multimodal logic Tn with central agent interaction axiom is analysed. The Hilbert type calculi is presented, then Gentzen type calculi with cut is derived and the proof of cutelimination theorem is outlined.
Julius Andrikonis +1 more
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Inducing syntactic cut-elimination for indexed nested sequents [PDF]
Logical Methods in Computer Science, 2018 The key to the proof-theoretic study of a logic is a proof calculus with a subformula property. Many different proof formalisms have been introduced (e.g. sequent, nested sequent, labelled sequent formalisms) in order to provide such calculi for the many
Revantha Ramanayake
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, 2020 In this paper we give a terminating cut-elimination procedure for a logic calculus SBL. SBL corresponds to the second order arithmetic Pi^{1}_{2}-Separation and Bar Induction.
Toshiyasu Arai
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Cut Elimination for Extended Sequent Calculi
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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Elimination of Cuts in First-order Finite-valued Logics [PDF]
, 1993 A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established.
Baaz, Matthias +2 more
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Cut-Simulation and Impredicativity [PDF]
Logical Methods in Computer Science, 2009 We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic -- in our case a sequent calculus for classical type ...
Christoph Benzmueller +2 more
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Quick cut-elimination for strictly positive cuts [PDF]
Annals of Pure and Applied Logic, 2011 In this paper we show that the intuitionistic theory for finitely many iterations of strictly positive operators is a conservative extension of the Heyting arithmetic. The proof is inspired by the quick cut-elimination due to G. Mints. This technique is also applied to fragments of Heyting arithmetic.
Toshiyasu Arai
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