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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 path ..."
Abstract

Cited by 40 (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 the recursive path ordering theorem of Dershowitz.
Strong Normalization Proofs for Cut Elimination in Gentzen's Sequent Calculi
 Banach Center Publication
, 1999
"... We define an equivalent variant LK sp of the Gentzen sequent calculus LK. In LK sp weakenings or contractions can be performed in parallel. This modification allows us to interpret a symmetrical system of mix elimination rules by a finite rewriting system; the termination of this rewriting system ..."
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Cited by 4 (0 self)
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We define an equivalent variant LK sp of the Gentzen sequent calculus LK. In LK sp weakenings or contractions can be performed in parallel. This modification allows us to interpret a symmetrical system of mix elimination rules by a finite rewriting system; the termination of this rewriting system can be machine checked. We give also a selfcontained strong normalization proof by structural induction. We give another strong normalization proof by a strictly monotone subrecursive interpretation; this interpretation gives subrecursive bounds for the length of derivations. We give a strong normalization proof by applying orthogonal term rewriting results for a confluent restriction of the mix elimination system .