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A Gentle Non-disjoint Combination of Satisfiability Procedures

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Automated Reasoning (IJCAR 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8562))

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Abstract

A satisfiability problem is often expressed in a combination of theories, and a natural approach consists in solving the problem by combining the satisfiability procedures available for the component theories. This is the purpose of the combination method introduced by Nelson and Oppen. However, in its initial presentation, the Nelson-Oppen combination method requires the theories to be signature-disjoint and stably infinite (to guarantee the existence of an infinite model). The notion of gentle theory has been introduced in the last few years as one solution to go beyond the restriction of stable infiniteness, but in the case of disjoint theories. In this paper, we adapt the notion of gentle theory to the non-disjoint combination of theories sharing only unary predicates (plus constants and the equality). Like in the disjoint case, combining two theories, one of them being gentle, requires some minor assumptions on the other one. We show that major classes of theories, i.e. Löwenheim and Bernays-Schönfinkel-Ramsey, satisfy the appropriate notion of gentleness introduced for this particular non-disjoint combination framework.

This work has been partially supported by the project ANR-13-IS02-0001-01 of the Agence Nationale de la Recherche, by the European Union Seventh Framework Programme under grant agreement no. 295261 (MEALS), and by the STIC AmSud MISMT

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Author information

Authors and Affiliations

  1. Universidad de Buenos Aires, Argentina

    Paula Chocron

  2. INRIA, Université de Lorraine & LORIA, Nancy, France

    Pascal Fontaine

  3. INRIA & LORIA, Nancy, France

    Paula Chocron & Christophe Ringeissen

Authors
  1. Paula Chocron
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  2. Pascal Fontaine
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  3. Christophe Ringeissen
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Editor information

Editors and Affiliations

  1. CNRS,, New York University &amp, USA

    Stéphane Demri

  2. Department of Computer Science, University of New Mexico, 87131-0001, Albuquerque, NM, USA

    Deepak Kapur

  3. Max Planck Institute for Informatics, Campus E1 4, 66123, Saarbrücken, Germany

    Christoph Weidenbach

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Chocron, P., Fontaine, P., Ringeissen, C. (2014). A Gentle Non-disjoint Combination of Satisfiability Procedures. In: Demri, S., Kapur, D., Weidenbach, C. (eds) Automated Reasoning. IJCAR 2014. Lecture Notes in Computer Science(), vol 8562. Springer, Cham. https://doi.org/10.1007/978-3-319-08587-6_9

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  • DOI: https://doi.org/10.1007/978-3-319-08587-6_9

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08586-9

  • Online ISBN: 978-3-319-08587-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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