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The Disconnection Tableau Calculus

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Abstract

In this paper we give a comprehensive presentation of the disconnection tableau calculus, a proof method for formulas in classical first-order clause logic. The distinguishing property of this calculus is that it uses unification in such a manner that important proof-theoretic advantages of the classical (i.e., Smullyan-style) tableau calculus are preserved, specifically the termination and model generation characteristics for certain formula classes. Additionally, the calculus is well suited for fully automated proof search. The calculus is described in detail with soundness and completeness proofs, and a number of important calculus refinements developed over the past years are presented. Referring to the model-finding abilities of the disconnection calculus, we explain the extraction and representation of models. We also describe the integration of paramodulation-based equality handling. Finally, we give an overview of related methods.

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  1. Institut für Informatik, Technische Universität München, D-85748, Garching, Germany

    Reinhold Letz & Gernot Stenz

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  1. Reinhold Letz
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  2. Gernot Stenz
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Correspondence to Reinhold Letz.

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This work was partially funded by the German Federal Ministry of Education, Science, Research and Technology (BMBF) in the framework of the Verisoft project under grant 01 IS C38. The responsibility for this article lies with the author(s).

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Letz, R., Stenz, G. The Disconnection Tableau Calculus. J Autom Reasoning 38, 79–126 (2007). https://doi.org/10.1007/s10817-006-9048-8

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