Theory of linear and integer programming
Theory of linear and integer programming
Satisfiability in many-valued sentential logic is NP-complete
Theoretical Computer Science
Introduction to Algorithms
Uniform Description of Calculi for All t-Norm Logics
ISMVL '04 Proceedings of the 34th International Symposium on Multiple-Valued Logic
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We introduce a proof system for Hájek's logic BL based on a relational hypersequents framework. We prove that the rules of our logical calculus, called RHBL, are sound and invertible with respect to any valuation of BL into a suitable algebra, called (ω)[0,1]. Refining the notion of reduction tree that arises naturally from RHBL, we obtain a decision algorithm for BL provability whose running time upper bound is 2O(n), where n is the number of connectives of the input formula. Moreover, if a formula is unprovable, we exploit the constructiveness of a polynomial time algorithm for leaves validity for providing a procedure to build countermodels in (ω)[0, 1]. Finally, since the size of the reduction tree branches is O(n3), we can describe a polynomial time verification algorithm for BL unprovability.