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Resolution on Quantified Generalized Clause-sets

Article type: Research Article

Authors: Jin, Jiwei; * | Zhao, Xishun

Affiliations: Institute of Logic and Cognition, Sun Yat-sen University, People’s Republic of China. E-mails: [email protected], [email protected]

Note: [*] Research was partially supported by the NSFC projects under Grant No.60970040 and a MOE project under Grant No. 05JJD72040122.

Keywords: quantified generalized clause-sets, satisfiability, Q-resolution, Horn

DOI: 10.3233/SAT190073

Journal: Journal on Satisfiability, Boolean Modeling and Computation, vol. 7, no. 1, pp. 17-34, 2010

Received 1 July 2009
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Revision received 1 November 2009
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Published: 1 March 2010
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Abstract

This paper is devoted to investigate resolution for quantified generalized clause-sets (QCLS). The soundness and refutation completeness are proved. Then quantified generalized Horn clause-sets are introduced for which a restricted resolution, called quantified positive unit resolution, is proved to be sound and refutationally complete. Moreover, it is shown that the satisfiability for quantified generalized Horn clause-sets is solvable in polynomial time. On the one hand, the work of this paper can be considered as a generalization of resolution for generalized clause-sets (CLS). On the other hand, it also can be considered as a generalization of Q-resolution for quantified boolean CNF formulae (QCNF).

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