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On Constructive Cut Admissibility in Deduction Modulo

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Types for Proofs and Programs (TYPES 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4502))

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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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Authors and Affiliations

  1. Université Paris 6 - LIP6,  

    Richard Bonichon & Olivier Hermant

Authors
  1. Richard Bonichon
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  2. Olivier Hermant
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Thorsten Altenkirch Conor McBride

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Bonichon, R., Hermant, O. (2007). On Constructive Cut Admissibility in Deduction Modulo. In: Altenkirch, T., McBride, C. (eds) Types for Proofs and Programs. TYPES 2006. Lecture Notes in Computer Science, vol 4502. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74464-1_3

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  • DOI: https://doi.org/10.1007/978-3-540-74464-1_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74463-4

  • Online ISBN: 978-3-540-74464-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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