Results 11 to 20 of about 117,954 (285)

Cut-elimination and Redundancy-elimination by Resolution

Journal of Symbolic Computation, 2000
The authors propose a new cut-elimination procedure for classical predicate calculus LK. The basic formulation treats a particular case: \[ \text{if }A,\Gamma\vdash\Delta\text{ is derivable and }A\text{ is valid, then }\Gamma\vdash\Delta\text{ is derivable}.\tag{\(*\)} \] In general a cut like \(\Gamma\vdash B\); \(B,\Gamma\vdash\Delta/\Gamma \vdash ...
Matthias Baaz, Alexander Leitsch
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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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Syntactic cut-elimination for common knowledge

Annals of Pure and Applied Logic, 2009
The logic of common knowledge has been formulated by Alberucci and Jäger in a sequential system with a rule of infinite premises so as to enjoy completeness, from which then follows the cut-elimination theorem indirectly. There are also several variations of the logic formulated in cut-free sequential systems but a syntactical cut-elimination proof has
Kai Brünnler, Thomas Studer
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Tautology Elimination, Cut Elimination, and S5

Logic and Logical Philosophy, 2017
Tautology elimination rule was successfully applied in automated deduction and recently considered in the framework of sequent calculi where it is provably equivalent to cut rule. In this paper we focus on the advantages of proving admissibility of tautology elimination rule instead of cut for sequent calculi.
Indrzejczak, Andrzej
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Novikov's Cut Elimination [PDF]

Logique et Analyse, 2018
This is an exposition of Novikov's cut-elimination procedure for a Hilbert-style formulation of the first-order predicate calculus, which depends on a property of formulas introduced by him, called 'regularity'. A comparison with other methods is outlined.
Luca Bellotti
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Elimination and cut-elimination in multiplicative linear logic

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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Confluence as a Cut Elimination Property

, 2003
The goal of this note is to compare two notions, one coming from the theory of rewrite systems and the other from proof theory: confluence and cut elimination. We show that to each rewrite system on terms, we can associate a logical system: asymmetric deduction modulo this rewrite system and that the confluence property of the rewrite system is ...
Dowek, Gilles
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Cut elimination for the unified logic

Annals of Pure and Applied Logic, 1993
The Unified Logic, \(\text{\textbf{LU}}\), is introduced by \textit{J.-Y. Girard} [ibid. 59, 201-217 (1993; Zbl 0781.03044)]. Its sequent is of the form \(\Gamma;\Gamma'\lvdash \Delta';\Delta\), where the outer zone \(\langle\Gamma,\Delta\rangle\) has the linear logic maintenance, and the inner \(\langle\Gamma',\Delta'\rangle\) the classical one. Among
Vauzeilles, Jacqueline
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Tautology Elimination, Cut Elimination and S4?

Logic and Logical Philosophy
The paper “Tautology elimination, cut elimination, and S5” published in this journal presents a novel method for establishing by proof analysis the admissibility of the rule of tautology elimination for certain sequent calculi. Since tautology elimination will typically imply the admissibility of cut, the method promises a new path to show the ...
Fjellstad, Andreas
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The Role of Quantifier Alternations in Cut Elimination

Notre Dame Journal of Formal Logic, 2003
Extending previous results from the author's master's thesis, subsequently published in the proceedings of CSL 2003, on the complexity of cut elimination for the sequent calculus LK, we discuss the role of quantifier alternations and develop a measure to describe the complexity of cut elimination in terms of quantifier alternations in cut formulas and ...
Gerhardy, Philipp
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