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Universal Variables in Disconnection Tableaux

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2796))

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Abstract

The disconnection calculus since its original conception has been developed into one of the most successful tableau methods ever devised. Still, deductions in the disconnection calculus can suffer from redundancies inherent to the tableau framework. Even though the calculus can decide the Bernays-Schönfinkel class of formulae it is in many cases inferior to combinations of a grounding mechanism with a Davis-Putnam prover system. In this paper we address two enhancements of the disconnection calculus that are intended to reduce some of the redundancies typical for tableau methods. First, we investigate the use of local variables, a syntactically detectable form of universal variables. These variables can be used to relax the ∀-closure condition and introduce partial unification for branch closures. However, the use of such variables has certain ramifications we will also discuss. Then, we examine the extended use of context lemmas during proof search by allowing the use of context lemmas for subsumption of new tableau clauses. We also show limitations to this method. Both techniques described in this paper are being implemented as part of the DCTP disconnection tableau prover.

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Author information

Authors and Affiliations

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

    Reinhold Letz

  2. Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123, Saarbrücken, Germany

    Gernot Stenz

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

  1. Dipartimento di Informatica e Automazione, Università di Roma Tre, via Vasca Navale 79, 00146, Roma, Italia

    Marta Cialdea Mayer

  2. Dipartimento di Informatica e Sistemistica (DIS), Sapienza, University of Rome “Sapienza”, via Ariosto 25, 00185, Roma

    Fiora Pirri

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Letz, R., Stenz, G. (2003). Universal Variables in Disconnection Tableaux. In: Cialdea Mayer, M., Pirri, F. (eds) Automated Reasoning with Analytic Tableaux and Related Methods . TABLEAUX 2003. Lecture Notes in Computer Science(), vol 2796. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45206-5_11

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  • DOI: https://doi.org/10.1007/978-3-540-45206-5_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40787-4

  • Online ISBN: 978-3-540-45206-5

  • eBook Packages: Springer Book Archive

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