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Completeness and CutElimination in the . . .
, 2004
"... In this paper we give a semantic proof of cutelimination for ICTT. ICTT is an intuitionistic formulation of Church's theory of types defined by Miller, Scedrov, Nadathur and Pfenning in the late 1980s. It is the basis for the *prolog programming language. Our approach, extending techniques of ..."
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In this paper we give a semantic proof of cutelimination for ICTT. ICTT is an intuitionistic formulation of Church's theory of types defined by Miller, Scedrov, Nadathur and Pfenning in the late 1980s. It is the basis for the *prolog programming language. Our approach, extending techniques
Confluence of cutelimination procedures for the intuitionistic sequent calculus
 Proc. of the 3rd Conf. on Computability in Europe (CiE’07), volume 4497 of LNCS
, 2007
"... Abstract. We prove confluence of two cutelimination procedures for the implicational fragment of a standard intuitionistic sequent calculus. One of the cutelimination procedures uses global proof transformations while the other consists of local ones. Both of them include permutation of cuts to si ..."
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Cited by 1 (1 self)
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Abstract. We prove confluence of two cutelimination procedures for the implicational fragment of a standard intuitionistic sequent calculus. One of the cutelimination procedures uses global proof transformations while the other consists of local ones. Both of them include permutation of cuts
Cutelimination and redundancyelimination by resolution
 Journal of Symbolic Computation
, 2000
"... A new cutelimination method for Gentzen’s LK is defined. First cutelimination is generalized to the problem of redundancyelimination. Then the elimination of redundancy in LKproofs is performed by a resolution method in the following way: A set of clauses C is assigned to an LKproof ψ and it is ..."
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Cited by 39 (14 self)
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A new cutelimination method for Gentzen’s LK is defined. First cutelimination is generalized to the problem of redundancyelimination. Then the elimination of redundancy in LKproofs is performed by a resolution method in the following way: A set of clauses C is assigned to an LKproof ψ
Fast CutElimination by Projection
"... The transformation of arbitrary proofs in Gentzen’s calculus LK into cutfree proofs is of central importance not only to proof theory itself but also to computer ..."
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The transformation of arbitrary proofs in Gentzen’s calculus LK into cutfree proofs is of central importance not only to proof theory itself but also to computer
On proof mining by cutelimination
"... Abstract. We present cutelimination as a method of proof mining, in the sense that hidden mathematical information can be extracted by eliminating lemmas from proofs. We present reductive methods for cutelimination and the method ceres (cutelimination by resolution). A comparison of ceres with red ..."
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Abstract. We present cutelimination as a method of proof mining, in the sense that hidden mathematical information can be extracted by eliminating lemmas from proofs. We present reductive methods for cutelimination and the method ceres (cutelimination by resolution). A comparison of ceres
SEQUENT CALCULUS, DIALOGUES, AND CUTELIMINATION
"... Abstract. It is wellknown that intuitionistic and classical provability can be characterized by the existence of winning proponent strategies in Lorenzen dialogues. In fact, one can bring the winning proponent strategies more or less into correspondence with sequent calculus proofs. This paper ela ..."
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Cited by 2 (0 self)
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one additionally specifies, for each connective, the attacks and corresponding defenses. Similarly, our left and right rule are parameterized by such specifications. The main result is cutelimination for the system without specification of the actual connectives. Cutelimination for any combination
CutElimination and a PermutationFree Sequent Calculus for Intuitionistic Logic
, 1998
"... We describe a sequent calculus, based on work of Herbelin, of which the cutfree derivations are in 11 correspondence with the normal natural deduction proofs of intuitionistic logic. We present a simple proof of Herbelin's strong cutelimination theorem for the calculus, using the recursive ..."
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Cited by 44 (6 self)
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We describe a sequent calculus, based on work of Herbelin, of which the cutfree derivations are in 11 correspondence with the normal natural deduction proofs of intuitionistic logic. We present a simple proof of Herbelin's strong cutelimination theorem for the calculus, using
Cutelimination for a logic with definitions and induction
 Theoretical Computer Science
, 1997
"... In order to reason about specifications of computations that are given via the proof search or logic programming paradigm one needs to have at least some forms of induction and some principle for reasoning about the ways in which terms are built and the ways in which computations can progress. The l ..."
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Cited by 72 (22 self)
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that this logic has a number of applications. In this paper we prove the cutelimination theorem for F Oλ ∆IN, adapting a technique due to Tait and MartinLöf. This cutelimination proof is technically interesting and significantly extends previous results of this kind. 1
Classical Cutelimination in the πcalculus
"... We study the πcalculus, enriched with pairing, and define a notion of type assignment that uses the type constructor →. We encode the terms of the calculus X into this variant of π, and show that all reduction (cutelimination) and assignable types are preserved. Since X enjoys the CurryHoward iso ..."
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We study the πcalculus, enriched with pairing, and define a notion of type assignment that uses the type constructor →. We encode the terms of the calculus X into this variant of π, and show that all reduction (cutelimination) and assignable types are preserved. Since X enjoys the Curry
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