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Zenon Modulo: When Achilles Outruns the Tortoise Using Deduction Modulo

  • David Delahaye
  • Damien Doligez
  • Frédéric Gilbert
  • Pierre Halmagrand
  • Olivier Hermant
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8312)

Abstract

We propose an extension of the tableau-based first order automated theorem prover Zenon to deduction modulo. The theory of deduction modulo is an extension of predicate calculus, which allows us to rewrite terms as well as propositions, and which is well suited for proof search in axiomatic theories, as it turns axioms into rewrite rules. We also present a heuristic to perform this latter step automatically, and assess our approach by providing some experimental results obtained on the benchmarks provided by the TPTP library, where this heuristic is able to prove difficult problems in set theory in particular. Finally, we describe an additional backend for Zenon that outputs proof certificates for Dedukti, which is a proof checker based on the λΠ-calculus modulo.

Keywords

Tableaux Deduction Modulo Rewriting Automated Theorem Proving Proof Checking Zenon Dedukti 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • David Delahaye
    • 1
  • Damien Doligez
    • 2
  • Frédéric Gilbert
    • 2
  • Pierre Halmagrand
    • 1
  • Olivier Hermant
    • 3
  1. 1.Cedric/Cnam/InriaParisFrance
  2. 2.InriaParisFrance
  3. 3.CRIMINES ParisTechFontainebleauFrance

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