Results 191 to 200 of about 2,682,535 (254)
Some of the next articles are maybe not open access.
, 2015
We present methods for removing top-level cuts from a sequent calculus or Tait-style proof without significantly increasing the space used for storing the proof. For propositional logic, this requires converting a proof from tree-like to dag-like form, but at most doubles the number of lines in the proof.
S. Buss
semanticscholar +2 more sources
We present methods for removing top-level cuts from a sequent calculus or Tait-style proof without significantly increasing the space used for storing the proof. For propositional logic, this requires converting a proof from tree-like to dag-like form, but at most doubles the number of lines in the proof.
S. Buss
semanticscholar +2 more sources
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
IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2022
A LiNbO3 (LN)/SiO2/Si multilayered structure was recently reported as a new platform for achieving wideband radio frequency (RF) filters. However, the in-band ripples in filters resulting from the spurious Rayleigh mode lead to deteriorated performance ...
Huiping Xu +9 more
semanticscholar +1 more source
A LiNbO3 (LN)/SiO2/Si multilayered structure was recently reported as a new platform for achieving wideband radio frequency (RF) filters. However, the in-band ripples in filters resulting from the spurious Rayleigh mode lead to deteriorated performance ...
Huiping Xu +9 more
semanticscholar +1 more source
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
openaire +1 more source
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
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
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 ...
openaire +1 more source
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.
openaire +1 more source
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.
openaire +1 more source
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
openaire +1 more source
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
openaire +1 more source
International Conference on Theorem Proving with Analytic Tableaux and Related Methods, 2021
R. Goré +2 more
semanticscholar +1 more source
R. Goré +2 more
semanticscholar +1 more source
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.
openaire +1 more source
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.
openaire +1 more source