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The even more liberalized δ-rule in free variable Semantic Tableaux

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Computational Logic and Proof Theory (KGC 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 713))

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Abstract

In this paper we have a closer look at one of the rules of the tableau calculus presented in [3], called the δ-rule, and the modification of this rule, that has been proved to be sound and complete in [6], called the δ +-rule, which uses fewer free variables. We show that, an even more liberalized version, the \(\delta ^{ + ^ + }\)-rule, that in addition reduces the number of different Skolem-function symbols that have to be used, is also sound and complete. Examples show the relevance of this modification for building tableau-based theorem provers.

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References

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  4. Reiner Hähnle. Automated Theorem Proving in Multiple-Valued Logics. Oxford University Press, forthcoming, 1993.

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  6. Reiner Hähnle and Peter H. Schmitt. The liberalized δ-rule in free variable semantic tableaux. Journal of Automated Reasoning, to appear, 1993.

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  7. Steve V. Reeves. Semantic tableaux as a framework for automated theorem-proving. Department of Computer Science and Statistics, Queen Mary College, Univ. of London, 1987.

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Authors and Affiliations

  1. Institute for Logic, Complexity and Deduction Systems, University of Karlsruhe, Am Fasanengarten 5, 7500, Karlsruhe, Federal Republic of Germany

    Bernhard Beckert, Reiner Hähnle & Peter H. Schmitt

Authors
  1. Bernhard Beckert
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  2. Reiner Hähnle
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  3. Peter H. Schmitt
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Editor information

Georg Gottlob Alexander Leitsch Daniele Mundici

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© 1993 Springer-Verlag Berlin Heidelberg

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Beckert, B., Hähnle, R., Schmitt, P.H. (1993). The even more liberalized δ-rule in free variable Semantic Tableaux. In: Gottlob, G., Leitsch, A., Mundici, D. (eds) Computational Logic and Proof Theory. KGC 1993. Lecture Notes in Computer Science, vol 713. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022559

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  • DOI: https://doi.org/10.1007/BFb0022559

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57184-1

  • Online ISBN: 978-3-540-47943-7

  • eBook Packages: Springer Book Archive

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