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The liberalized δ-rule in free variable semantic tableaux

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Abstract

In this paper we have a closer look at one of the rules of the tableau calculus presented by Fitting [4], called the δ-rule. We prove that a modification of this rule, called the δ+-rule, which uses fewer free variables, is also sound and complete. We examine the relationship between the δ+-rule and variations of the δ-rule presented by Smullyan [9]. This leads to a second proof of the soundness of the δ+-rule. An example shows the relevance of this modification for building tableau-based theorem provers.

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References

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Authors and Affiliations

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

    Reiner Hähnle & Peter H. Schmitt

Authors
  1. Reiner Hähnle
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  2. Peter H. Schmitt
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Hähnle, R., Schmitt, P.H. The liberalized δ-rule in free variable semantic tableaux. J Autom Reasoning 13, 211–221 (1994). https://doi.org/10.1007/BF00881956

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  • DOI: https://doi.org/10.1007/BF00881956

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