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Automatic Combinability of Rewriting-Based Satisfiability Procedures

  • Conference paper
Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4246))

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Abstract

We address the problems of combining satisfiability procedures and consider two combination scenarios: (i) the combination within the class of rewriting-based satisfiability procedures and (ii) the Nelson-Oppen combination of rewriting-based satisfiability procedures and arbitrary satisfiability procedures. In each scenario, we use meta-saturation, which schematizes saturation of the set containing the axioms of a given theory and an arbitrary set of ground literals, to syntactically decide sufficient conditions for the combinability of rewriting-based satisfiability procedures. For (i), we give a sufficient condition for the modular termination of meta-saturation. When meta-saturation for the union of theories halts, it yields a rewriting-based satisfiability procedure for the union. For (ii), we use meta-saturation to prove the stable infiniteness of the component theories and deduction completeness of their rewriting-based satisfiability procedures. These properties are important to establish the correctness of the Nelson-Oppen combination method and to obtain an efficient implementation.

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Author information

Authors and Affiliations

  1. LORIA & INRIA-Lorraine,  

    Hélène Kirchner, Silvio Ranise, Christophe Ringeissen & Duc-Khanh Tran

  2. Università di Milano,  

    Silvio Ranise

Authors
  1. Hélène Kirchner
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  2. Silvio Ranise
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  3. Christophe Ringeissen
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  4. Duc-Khanh Tran
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Editor information

Editors and Affiliations

  1. LIX (CNRS, UMR 7161), École Polytechnique, 91128, Palaiseau, France

    Miki Hermann

  2. University of Manchester, UK

    Andrei Voronkov

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© 2006 Springer-Verlag Berlin Heidelberg

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Kirchner, H., Ranise, S., Ringeissen, C., Tran, DK. (2006). Automatic Combinability of Rewriting-Based Satisfiability Procedures. In: Hermann, M., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2006. Lecture Notes in Computer Science(), vol 4246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11916277_37

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  • DOI: https://doi.org/10.1007/11916277_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-48281-9

  • Online ISBN: 978-3-540-48282-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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