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A Tableau Calculus for Combining Non-disjoint Theories

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2381))

Abstract

The Nelson-Oppen combination method combines ground satisfiability checkers for first-order theories satisfying certain conditions into a single ground satisfiability checker for the union theory. The most significant restriction that the combined theories must satisfy, for the Nelson-Oppen combination method to be applicable, is that they must have disjoint signatures. Unfortunately, this is a very serious restriction since many combination problems concern theories over non-disjoint signatures.

In this paper we present a tableau calculus for combining first-order theories over non-disjoint signatures. The calculus generalizes the Nelson-Oppen combination method to formulae with quantifiers and to the union of arbitrary theories over non necessarily disjoint signatures.

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Author information

Authors and Affiliations

  1. Stanford University, USA

    Calogero G. Zarba

  2. University of Catania, Italy

    Calogero G. Zarba

Authors
  1. Calogero G. Zarba
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Editor information

Editors and Affiliations

  1. Abteilung Wisssenbasierte Systeme 184/3, Technische Univesität Wien, Favoritenstr. 9-11, 1040, Vienna, Austria

    Uwe Egly

  2. Institut für Computersprachen AG Theoretische Informatik und Logik 185.2, Technische Universität Wien, Favoritenstr. 9-11, 1040, Vienna, Austria

    Chritian G. Fermüller

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Zarba, C.G. (2002). A Tableau Calculus for Combining Non-disjoint Theories. In: Egly, U., Fermüller, C.G. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2002. Lecture Notes in Computer Science(), vol 2381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45616-3_22

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  • DOI: https://doi.org/10.1007/3-540-45616-3_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43929-5

  • Online ISBN: 978-3-540-45616-2

  • eBook Packages: Springer Book Archive

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