Since 1993, when Hudelmaier developed an O(n log n)-space decision procedure for propositional Intuitionistic Logic, a lot of work has been done to improve the efficiency of the related proof-search algorithms. In this paper a tableau calculus using the signs T, F and Fc with a new set of rules to treat signed formulas of the kind T((A → B) → C) is provided. The main feature of the calculus is the reduction of both the non-determinism in proof-search and the (...) width of proofs with respect to Hudelmaier's one. These improvements have a significant influence on the performances of the implementation. (shrink)

In this paper we propose a Kripke-style semantics for second order intuitionistic propositional logic and we provide a semantical proof of the disjunction and the explicit definability property. Moreover, we provide a tableau calculus which is sound and complete with respect to such a semantics.

In this paper, we provide non-clausal tableau calculi for the maximum satisfiability problem and its variants. We discuss both basic calculi to characterize the problem and their modifications to reduce the proof size.