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.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Robinson J A. A machine-oriented logic based on the resolution principle.JACM, 1965, 12(1): 23–41.
Chang C L, Lee R C T. Symbolic Logic and Mechanical Theorem Proving. New York: Academic Press, 1973.
Andrews P B. Theorem proving via general matings.JACM, 1981, 28(2): 193–214.
Andrews P B. An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Academic Press Inc., 1986.
Wang Xianhao, Liu Xuhua. Generalized resolution.Chinese Journal of Computers, 1982, 5(2).
Murray N V. Completely nonclausal resolution theorem proving.Artificial Intelligence 1982, 18(1).
Smullyan R M. A unifying principle in quantification theory. InProc. Nat. Acad. Sciences, U.S.A. 1963, 49: 828–832.
Wang Bingshan, Li Zhoujun. Universal abstract consistency class, and univeral unifying principle. Technical Report No.8, CIT, 1995.
Wang Bingshan, Li Zhoujun, Chen Huowang. Universal Refutation Method and Its Soundness and Completeness. Technical Report No.9, CIT, 1995
Author information
Authors and Affiliations
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.
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02946524