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Proof and Model Generation with Disconnection Tableaux

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2001)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2250))

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Abstract

We present the disconnection tableau calculus, which is a free-variable clausal tableau calculus where variables are treatedin a nonrigidmanner. The calculus essentially consists of a single inference rule, the so-called linking rule, which strongly restricts the possible clauses in a tableau. The method can also be viewed as an integration of the linking rule as used in Plaisted’s linking approach into a tableau format. The calculus has the proof-theoretic advantage that, in the case of a satisfiable formula, one can characterise a model of the formula, a property which most of the free-variable tableau calculi lack. In the paper, we present a rigorous completeness proof and give a procedure for extracting a model from a finitely failed branch.

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Authors and Affiliations

  1. Institut für Informatik Technische, Universität München, D-80290, Munich, Germany

    Reinhold Letz & Gernot Stenz

Authors
  1. Reinhold Letz
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  2. Gernot Stenz
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Editors and Affiliations

  1. Department of Software, Technical University of Catalonia, Jordi Girona 1, 08034, Barcelona, Spain

    Robert Nieuwenhuis

  2. Department of Computer Science, University of Manchester, Kilburn Building, Oxford Road, M13 9PL, Manchester, UK

    Andrei Voronkov

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Letz, R., Stenz, G. (2001). Proof and Model Generation with Disconnection Tableaux. In: Nieuwenhuis, R., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2001. Lecture Notes in Computer Science(), vol 2250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45653-8_10

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  • DOI: https://doi.org/10.1007/3-540-45653-8_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42957-9

  • Online ISBN: 978-3-540-45653-7

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