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Combining Superposition and Induction: A Practical Realization

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Frontiers of Combining Systems (FroCoS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8152))

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Abstract

We consider a proof procedure aiming at refuting clause sets containing arithmetic constants (or parameters), interpreted as natural numbers. The superposition calculus is enriched with a loop detection rule encoding a form of mathematical induction on the natural numbers (by “descente infinie”). This calculus and its theoretical properties are described in [2,16]. In the present paper, we focus on more practical aspects. We provide algorithms to apply the loop detection rule in an automatic and efficient way. We describe a research prototype implementing our technique and provide some preliminary experimental results.

This work has been partly funded by the project ASAP of the French Agence Nationale de la Recherche (ANR-09-BLAN-0407-01).

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Authors and Affiliations

  1. University of Grenoble (LIG, CNRS), France

    Abdelkader Kersani & Nicolas Peltier

Authors
  1. Abdelkader Kersani
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  2. Nicolas Peltier
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Editor information

Editors and Affiliations

  1. LORIA, Inria Nancy Grand Est, Université de Lorraine, 615 rue du Jardin Botanique, 54602, Villers-les-Nancy, France

    Pascal Fontaine

  2. LORIA, Inria Nancy Grand Est, 615 rue du Jardin Botanique, 54602, Villers-lès-Nancy, France

    Christophe Ringeissen

  3. School of Computer Science, The University of Manchester, Oxford Rd, Kilburn Building, M13 9PL, Manchester, UK

    Renate A. Schmidt

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Kersani, A., Peltier, N. (2013). Combining Superposition and Induction: A Practical Realization. In: Fontaine, P., Ringeissen, C., Schmidt, R.A. (eds) Frontiers of Combining Systems. FroCoS 2013. Lecture Notes in Computer Science(), vol 8152. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40885-4_2

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  • DOI: https://doi.org/10.1007/978-3-642-40885-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40884-7

  • Online ISBN: 978-3-642-40885-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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