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The liberalized δ-rule in free variable semantic tableaux

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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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Hähnle, R., Schmitt, P.H. The liberalized δ-rule in free variable semantic tableaux. J Autom Reasoning 13, 211–221 (1994).

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Key words

  • Mechanical theorem proving
  • tableau calculus