A Tableau Calculus for Propositional Intuitionistic Logic with a Refined Treatment of Nested Implications

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.