The Even More Liberalized delta-Rule in Free Variable Semantic Tableaux
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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