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Uniform proofs as a foundation for logic programming
 ANNALS OF PURE AND APPLIED LOGIC
, 1991
"... A prooftheoretic characterization of logical languages that form suitable bases for Prologlike programming languages is provided. This characterization is based on the principle that the declarative meaning of a logic program, provided by provability in a logical system, should coincide with its ..."
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Cited by 425 (124 self)
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A prooftheoretic characterization of logical languages that form suitable bases for Prologlike programming languages is provided. This characterization is based on the principle that the declarative meaning of a logic program, provided by provability in a logical system, should coincide
Logic Programming with Focusing Proofs in Linear Logic
 Journal of Logic and Computation
, 1992
"... The deep symmetry of Linear Logic [18] makes it suitable for providing abstract models of computation, free from implementation details which are, by nature, oriented and non symmetrical. I propose here one such model, in the area of Logic Programming, where the basic computational principle is C ..."
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
CutElimination: Experiments with CERES
, 2005
"... Cutelimination 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 cutelimination method CERES (cutelimination by resolution) works by constructing a set of ..."
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Cited by 16 (12 self)
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Cutelimination 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 cutelimination method CERES (cutelimination by resolution) works by constructing a set
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
Proofnets: The parallel syntax for prooftheory
 Logic and Algebra
, 1996
"... The paper is mainly concerned with the extension of proofnets to additives, for which the best known solution is presented. It proposes two cutelimination procedures, the lazy one being in linear time. The solution is shown to be compatible with quantifiers, and the structural rules of exponential ..."
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Cited by 126 (1 self)
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The paper is mainly concerned with the extension of proofnets to additives, for which the best known solution is presented. It proposes two cutelimination procedures, the lazy one being in linear time. The solution is shown to be compatible with quantifiers, and the structural rules
Cutelimination and proofsearch for biintuitionistic logic using nested sequents
, 2008
"... We propose a new sequent calculus for biintuitionistic logic which sits somewhere between display calculi and traditional sequent calculi by using nested sequents. Our calculus enjoys a simple (purely syntactic) cutelimination proof as do display calculi. But it has an easily derivable variant cal ..."
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Cited by 15 (4 self)
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We propose a new sequent calculus for biintuitionistic logic which sits somewhere between display calculi and traditional sequent calculi by using nested sequents. Our calculus enjoys a simple (purely syntactic) cutelimination proof as do display calculi. But it has an easily derivable variant
Modular cutelimination: Finding proofs or counterexamples
 Proceedings of the 13th International Conference of Logic for Programming AI and Reasoning (LPAR06), LNAI 4246
, 2006
"... Abstract. Modular cutelimination is a particular notion of ”cutelimination in the presence of nonlogical axioms ” that is preserved under the addition of suitable rules. We introduce syntactic necessary and sufficient conditions for modular cutelimination for standard calculi, a wide class of (p ..."
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Cited by 9 (0 self)
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Abstract. Modular cutelimination is a particular notion of ”cutelimination in the presence of nonlogical axioms ” that is preserved under the addition of suitable rules. We introduce syntactic necessary and sufficient conditions for modular cutelimination for standard calculi, a wide class
Methods of CutElimination
 PROJECTION, LECTURE
"... This short report presents the main topics of methods of cutelimination which will be presented in the course at the ESSLLI'99. It gives a short introduction addressing the problem of cutelimination in general. Furthermore we give a brief description of several methods and refer to other pape ..."
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Cited by 13 (11 self)
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This short report presents the main topics of methods of cutelimination which will be presented in the course at the ESSLLI'99. It gives a short introduction addressing the problem of cutelimination in general. Furthermore we give a brief description of several methods and refer to other
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
Results 1  10
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