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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 28 (10 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 and it is shown that C is always unsatisfiable. A resolution refutation of C then serves as a skeleton of an LKproof ψ ′ with atomic cuts; ψ ′ can be constructed from the resolution proof and ψ by a projection method. In the last step the atomic cuts are eliminated and a cutfree proof is obtained. The complexity of the method is analyzed and it is shown that a nonelementary speedup over Gentzen’s method can be achieved. Finally an application to automated deduction is presented: it is demonstrated how informal proofs (containing pseudocuts) can be transformed into formal ones by the method of redundancyelimination; moreover, the method can even be used to transform incorrect proofs into correct ones. 1.
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 papers ad ..."
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Cited by 9 (8 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 papers added to the course material.
Towards Hilbert's 24th Problem: Combinatorial Proof Invariants
, 2006
"... Proofs Without Syntax [37] introduced polynomialtime checkable combinatorial proofs for classical propositional logic. This sequel approaches Hilbert’s 24 th Problem with combinatorial proofs as abstract invariants for sequent calculus proofs, analogous to homotopy groups as abstract invariants for ..."
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Cited by 3 (0 self)
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Proofs Without Syntax [37] introduced polynomialtime checkable combinatorial proofs for classical propositional logic. This sequel approaches Hilbert’s 24 th Problem with combinatorial proofs as abstract invariants for sequent calculus proofs, analogous to homotopy groups as abstract invariants for topological spaces. The paper lifts a simple, strongly normalising cut elimination from combinatorial proofs to sequent calculus, factorising away the mechanical commutations of structural rules which litter traditional syntactic cut elimination. Sequent calculus fails to be surjective onto combinatorial proofs: the paper extracts a semantically motivated closure of sequent calculus from which there is a surjection, pointing towards an abstract combinatorial refinement of Herbrand’s theorem.
CutElimination by Resolution
 J. Symbolic Computation
, 1999
"... .96> ` \Delta 2 \Gamma 1 ; \Gamma 2 ` \Delta 1 ; \Delta 2 and assume that ! is an LKproof with atomic initial sequents. Then, formally, the set of initial sequents is a set of clauses of the form S : P ( t) ` P ( t) (where P is a predicate symbol and t is a term tuple). Either the left or the ..."
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Cited by 1 (1 self)
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.96> ` \Delta 2 \Gamma 1 ; \Gamma 2 ` \Delta 1 ; \Delta 2 and assume that ! is an LKproof with atomic initial sequents. Then, formally, the set of initial sequents is a set of clauses of the form S : P ( t) ` P ( t) (where P is a predicate symbol and t is a term tuple). Either the left or the right occurrence or none of them is a predecessor of the cut formula A (in ! 1 or in ! 2 ). Thus one of the form `, P ( t) `, ` P ( t) or P ( t) ` P ( t) characterizes the connection of the initial sequent with the