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Universal abstract consistency class and universal refutation

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Abstract

Refutation methods based on the resolution principle are generally applied to a (finite) set of sentences, which must have a series of pre-transformations (prenex normalization, Skolemization and conjunction normalization) before starting the refutation. In this paper, the authors first generalize the concept to abstract consistency class to the most general form—universal abstract consistency class, and prove its universal unifying principle. Then, based on theR-refutation, a universal refutation method is proposed and its soundness and completeness are proved by means of the universal unifying principle. This method can be applied directly to any finite set of wffs without preprocessing the wffs at all so that the refutation procedure is more natural.

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Additional information

This work was partially supported by “863” Hi-Tech Development Program and NNSF of China.

WANG Bingshan is a Professor. His research interest is theoretical computer science.

LI Zhoujun is an Associate Professor in National University of Defense Technology, and a Member of European Association for Theoretical Computer Science. His research interests include concurrency theory and logic in computer science.

CHEN Huowang is a Professor, a Member fo Chinese Academy of Sciences His research interests include software engineering and artificial intelligence.

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Wang, B., Li, Z. & Chen, H. Universal abstract consistency class and universal refutation. J. Comput. Sci. & Technol. 14, 165–172 (1999). https://doi.org/10.1007/BF02946524

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  • DOI: https://doi.org/10.1007/BF02946524

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