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Algebraic proofs of cut elimination [PDF]
The Journal of Logic and Algebraic Programming, 2001 Jeremey Avigad. Algebraic Proofs of Cut Elimination.
Jeremy Avigad
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Cut elimination in coalgebraic logics [PDF]
Information and Computation, 2010 We give two generic proofs for cut elimination in propositional modal logics, interpreted over coalgebras. We first investigate semantic coherence conditions between the axiomatisation of a particular logic and its coalgebraic semantics that guarantee that the cut-rule is admissible in the ensuing sequent calculus.
Dirk Pattinson, Lutz Schröder
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Cut Elimination in Multifocused Linear Logic [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 We study cut elimination for a multifocused variant of full linear logic in the sequent calculus. The multifocused normal form of proofs yields problems that do not appear in a standard focused system, related to the constraints in grouping rule ...
Taus Brock-Nannestad, Nicolas Guenot
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Elimination and cut-elimination in multiplicative linear logic [PDF]
CoRR, 2022 We associate to every proof structure in multiplicative linear logic an ideal which represents the logical content of the proof as polynomial equations. We show how cut-elimination in multiplicative proof nets corresponds to instances of the Buchberger algorithm for computing Gröbner bases in elimination theory.
Daniel Murfet, William Troiani
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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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Structural Cut Elimination [PDF]
Proceedings of Tenth Annual IEEE Symposium on Logic in Computer Science, 2000 Presents new proofs of cut elimination for intuitionistic, classical and linear sequent calculi. In all cases, the proofs proceed by three nested structural inductions, avoiding the explicit use of multi-sets and termination measures on sequent derivations.
Frank Pfenning
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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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Quick cut-elimination for strictly positive cuts [PDF]
Annals of Pure and Applied Logic, 2010 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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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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Towards a Semantic Characterization of Cut-Elimination [PDF]
Studia Logica, 2006 An occurrence of the cut rule in a derivation is called reductive if either (i) both cut formulas are the principal formulas of logical rules, or (ii) one of the two cut formulas is a context formula of a rule other than the cut, or (iii) one of the two premises is an identity axiom (of the form \(X\Rightarrow X\)). Reductive cut-elimination for simple
Agata Ciabattoni +2 more
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