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A Tableau Calculus for Quantifier-Free Set Theoretic Formulae

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Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1397))

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Abstract

Set theory is the common language of mathematics. Therefore, set theory plays an important rôle in many important applications of automated deduction. In this paper, we present an improved tableau calculus for the decidable fragment of set theory called multi-level syllogistic with singleton (MLSS). Furthermore, we describe an extension of our calculus for the bigger fragment consisting of MLSS enriched with free (uninterpreted) function symbols (MLSSF).

This work was carried out while the author stayed at the University of Karlsruhe.

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Author information

Authors and Affiliations

  1. Institute for Logic, Complexity and Deduction Systems, University of Karlsruhe, D-76128, Karlsruhe, Germany

    Bernhard Beckert

  2. Technologiezentrum Darmstadt, Deutsche Telekom AG, D-64307, Darmstadt, Germany

    Ulrike Hartmer

Authors
  1. Bernhard Beckert
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  2. Ulrike Hartmer
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Editor information

Editors and Affiliations

  1. Faculty of Philosophy, Tilburg University, P.O. Box 90153, 5000 LE, Tilburg, The Netherlands

    Harrie de Swart

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Beckert, B., Hartmer, U. (1998). A Tableau Calculus for Quantifier-Free Set Theoretic Formulae. In: de Swart, H. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 1998. Lecture Notes in Computer Science(), vol 1397. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69778-0_16

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  • DOI: https://doi.org/10.1007/3-540-69778-0_16

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  • Print ISBN: 978-3-540-64406-4

  • Online ISBN: 978-3-540-69778-7

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