Results 261 to 270 of about 117,954 (285)
Some of the next articles are maybe not open access.
Cut-Elimination and Proof Schemata
2015By 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 +3 more
openaire +1 more source
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 +2 more
openaire +1 more source
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 +2 more
openaire +1 more source
CUT ELIMINATION FOR CLASSICAL BILINEAR LOGIC
Fundamenta Informaticae, 1995In 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.
openaire +2 more sources
The modal logic of provability: Cut-elimination
Journal of Philosophical Logic, 1983\textit{D. Leivant} [J. Symb. Logic 46, 531--538 (1981; Zbl 0464.03019)] outlined a cut-elimination procedure for the formulation of the provability logic GL based on the only modal rule \(X,\square X,\square A\to A/\square X\to \square A\). The author and \textit{G. Sambin} [J. Philos.
openaire +2 more sources
Cut-elimination and interpolation for Ω-logic
Archive for Mathematical Logic, 1988Girard's \(\Omega\)-logic is based on the category of well-founded orders, while his \(\beta\)-logic is based on the category of ordinals. Here Girard's (unpublished) results are extended from \(\beta\)-logic to \(\Omega\)-logic.
openaire +2 more sources
A Connection Between Cut Elimination and Normalization
Archive for Mathematical Logic, 2005Summary: Sequent systems for classical and intuitionistic logic and natural deduction systems for these logics are characterized by two important theorems. Sequent systems are characterized by cut-elimination theorems, and natural deduction systems by normalization theorems.
openaire +2 more sources
2010
Our aim is to compare different methods of cut-elimination. For this aim we need logic-free axioms. The original formulation of LK by Gentzen also served the purpose of simulating Hilbert-type calculi and deriving axiom schemata within fixed proof length. Below we show that there exists a polynomial transformation from an LK-proof with arbitrary axioms
Matthias Baaz, Alexander Leitsch
openaire +1 more source
Our aim is to compare different methods of cut-elimination. For this aim we need logic-free axioms. The original formulation of LK by Gentzen also served the purpose of simulating Hilbert-type calculi and deriving axiom schemata within fixed proof length. Below we show that there exists a polynomial transformation from an LK-proof with arbitrary axioms
Matthias Baaz, Alexander Leitsch
openaire +1 more source
Sufficient conditions for cut elimination with complexity analysis
Annals of Pure and Applied Logic, 2007João Rasga
exaly
Interpolants, cut elimination and flow graphs for the propositional calculus
Annals of Pure and Applied Logic, 1997Alessandra Carbone
exaly