Results 251 to 260 of about 772,601 (287)

Cut-Elimination: Syntax and Semantics

Studia Logica, 2014
This article concerns the cut-elimination by resolution (CERES) method for first-order logic [\textit{M. Baaz} et al., Lect. Notes Comput. Sci. 3452, 481--495 (2005; Zbl 1108.03305)]. Compared with reductive cut-elimination (e.g.\ Gentzen-/Schütte-/Tait-style) which can be viewed as sequences of local reductions, CERES operates globally on LK-proofs ...
Matthias Baaz, Alexander Leitsch
openaire   +1 more source

Cut Elimination in the Presence of Axioms

Bulletin of Symbolic Logic, 1998
AbstractA way is found to add axioms to sequent calculi that maintains the eliminability of cut, through the representation of axioms as rules of inference of a suitable form. By this method, the structural analysis of proofs is extended from pure logic to free-variable theories, covering all classical theories, and a wide class of constructive ...
Sara Negri, Jan von Plato
openaire   +2 more sources

Cut-elimination for ω1

Annals of Pure and Applied Logic, 2018
arXiv admin note: text overlap with arXiv:1508 ...
openaire   +1 more source

Stratification and cut-elimination

Journal of Symbolic Logic, 1991
In this paper, we show the normalization of proofs of NF (Quine's New Foundations; see [15]) minus extensionality. This system, called SF (Stratified Foundations) differs in many respects from the associated system of simple type theory. It is written in a first order language and not in a multi-sorted one, and the formulas need not be stratifiable ...
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Towards a clausal analysis of cut-elimination

Journal of Symbolic Computation, 2006
In this paper we show that a large class of cut-elimination methods can be analysed by clause terms representing sets of characteristic clauses extractable from the original proof.
Matthias Baaz, Alexander Leitsch
exaly   +2 more sources

Cut elimination for entailment relations

Archive for Mathematical Logic, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Davide Rinaldi, Daniel Misselbeck-Wessel
openaire   +2 more sources

Fast cut-elimination by projection

1997
The methods of this paper can be applied as well to intuitionistic proof systems like Natural Deduction. It is obvious that the application of extended reductions similar to projections will result in a loss of confluence; on the other hand, confluence is of doubtful value if the complexity of cut-elimination is the main concern.
Matthias Baaz, Alexander Leitsch
openaire   +1 more source

Cut-Elimination and Proof Schemata

2015
By Gentzen's famous Hauptsatz the cut-elimination theorem every proof in sequent calculus for first-order logic with cuts can be transformed into a cut-free proof; cut-free proofs are analytic and consist entirely of syntactic material of the end-sequent the proven theorem.
Cvetan Dunchev, Alexander Leitsch, Mikheil Rukhaia, Daniel Weller 0001   +3 more
openaire   +1 more source

The cut-elimination theorem

2021
AbstractAll the rules of the sequent calculus have the property that all the formulas that are present in the premises also occur in the conclusion. There is only one exception, the cut rule. In this chapter, it is shown using double induction that every theorem provable in Gentzen’s sequent calculi using the cut rule can also be proved without.
Paolo Mancosu, Sergio Galvan, Richard Zach   +2 more
openaire   +1 more source

CUT ELIMINATION FOR CLASSICAL BILINEAR LOGIC

Fundamenta Informaticae, 1995
In this paper a cut elimination theorem is proved for classical non-commutative linear logic without exponentials, presented as a dual Schütte style deductive system. The notion of equality between deductions is sketched and they are interpreted as relations, in the spirit of the formulas as types paradigm.
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