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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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Journal of Philosophical Logic, 1984
Semantic tableau methods are sometimes used in logic courses because they produce derivations of various formulas of first order logic in a straightforward way. The feasibility of these tableau methods depends, however, on the formulas to which they are applied.
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Semantic tableau methods are sometimes used in logic courses because they produce derivations of various formulas of first order logic in a straightforward way. The feasibility of these tableau methods depends, however, on the formulas to which they are applied.
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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
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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
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Cut-Elimination and Proof Schemata
Tbilisi Symposium on Logic, Language, and Computation, 2013By 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.
Tsvetan Dunchev +3 more
semanticscholar +2 more sources
Stratification and cut-elimination
Journal of Symbolic Logic, 1991In 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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Annals of Pure and Applied Logic, 2018
Abstract In this paper we calibrate the strength of the soundness of a set theory KP ω + ( Π 1 -Collection ) with the assumption that ‘there exists an uncountable regular ordinal’ in terms of the existence of ordinals.
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Abstract In this paper we calibrate the strength of the soundness of a set theory KP ω + ( Π 1 -Collection ) with the assumption that ‘there exists an uncountable regular ordinal’ in terms of the existence of ordinals.
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A Formally Verified Cut-Elimination Procedure for Linear Nested Sequents for Tense Logic
International Conference on Theorem Proving with Analytic Tableaux and Related Methods, 2021Caitlin D'Abrera, J. Dawson, R. Goré
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2010
In Chapter 5 we analyzed methods which eliminate cuts by stepwise reduction of cut-complexity. These methods always identify the uppermost logical operator in the cut-formula and either eliminate it directly (grade reduction) or indirectly (rank reduction).
Matthias Baaz, Alexander Leitsch
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In Chapter 5 we analyzed methods which eliminate cuts by stepwise reduction of cut-complexity. These methods always identify the uppermost logical operator in the cut-formula and either eliminate it directly (grade reduction) or indirectly (rank reduction).
Matthias Baaz, Alexander Leitsch
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International Conference on Theorem Proving with Analytic Tableaux and Related Methods, 2021
R. Goré +2 more
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R. Goré +2 more
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2020
In this chapter we first introduce a standard cut-elimination procedure for the first-order logic and the \(\omega \)-logic, by which we see that the tree-height of the resulting cut-free proofs is bounded by a tower of exponential functions. Such a control of the tree-heights in cut-elimination is one of the most important results in ordinal analysis.
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In this chapter we first introduce a standard cut-elimination procedure for the first-order logic and the \(\omega \)-logic, by which we see that the tree-height of the resulting cut-free proofs is bounded by a tower of exponential functions. Such a control of the tree-heights in cut-elimination is one of the most important results in ordinal analysis.
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