Results 141 to 150 of about 578,113 (185)
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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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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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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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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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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
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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
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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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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.
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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.
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