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Mathematical Structures in Computer Science, 2017
We investigate cut elimination in multi-focused sequent calculi and the impact on the cut elimination proof of design choices in such calculi. The particular design we advocate is illustrated by a multi-focused calculus for full linear logic using an explicitly polarised syntax and incremental focus handling, for which we provide a syntactic cut ...
Taus Brock-Nannestad, Nicolas Guenot
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We investigate cut elimination in multi-focused sequent calculi and the impact on the cut elimination proof of design choices in such calculi. The particular design we advocate is illustrated by a multi-focused calculus for full linear logic using an explicitly polarised syntax and incremental focus handling, for which we provide a syntactic cut ...
Taus Brock-Nannestad, Nicolas Guenot
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Cut elimination for entailment relations
Archive for Mathematical Logic, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Davide Rinaldi, Daniel Misselbeck-Wessel
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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
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Fast cut-elimination by projection
1997The 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
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Cut Elimination for S4C: A Case Study
Studia Logica, 2006The paper contains a cut-elimination proof for a logic of continuous transformations of a topological space, called S4C [cf. \textit{P. Kremer} and \textit{G. Mints}, Ann. Pure Appl. Logic 131, No. 1--3, 133--158 (2005; Zbl 1067.03028)]. It consists of the modal logic S4 enlarged by another modality operator \(\circ\). In the intended models of dynamic
Grigori Mints
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Cut-Elimination: Experiments with CERES
2005Cut-elimination is the most prominent form of proof transformation in logic. The elimination of cuts in formal proofs corresponds to the removal of intermediate statements (lemmas) in mathematical proofs. The cut-elimination method CERES (cut-elimination by resolution) works by constructing a set of clauses from a proof with cuts.
Matthias Baaz +4 more
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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.
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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.
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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.
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