On Constructive Cut Admissibility in Deduction Modulo

Richard Bonichon 1 Olivier Hermant 1
1 SPI - Sémantiques, preuves et implantation
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : Deduction Modulo is a theoretical framework that allows the introduction of computational steps in deductive systems. This approach is well suited to automated theorem proving. We describe a proof-search method based upon tableaux for Gentzen’s intuitionistic LJ extended with rewrite rules on propositions and terms . We prove its completeness with respect to Kripke structures. We then give a soundness proof with respect to cut-free LJ modulo. This yields a constructive proof of semantic cut elimination, which we use to characterize the relation between tableaux methods and cut elimination in the intuitionistic case.
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Conference papers
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https://hal.archives-ouvertes.fr/hal-01337639
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Submitted on : Monday, June 27, 2016 - 1:37:02 PM
Last modification on : Thursday, March 21, 2019 - 2:43:13 PM

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Richard Bonichon, Olivier Hermant. On Constructive Cut Admissibility in Deduction Modulo. Types for Proofs and Programs, Apr 2006, Nottingham, United Kingdom. pp.33-47, ⟨10.1007/978-3-540-74464-1_3⟩. ⟨hal-01337639⟩

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