Computer Science – Logic in Computer Science
Scientific paper
2006-05-22
Computer Science
Logic in Computer Science
26 pages
Scientific paper
We introduce a proof system for Hajek'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 omega[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 2^O(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 omega[0,1]. Finally, since the size of the reduction tree branches is O(n^3), we can describe a polynomial time verification algorithm for BL unprovability.
Bova Simone
Montagna F.
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