A Tableau Calculus for Dummett Logic Based on Increasing the Formulas Equivalent to the True and the Replacement Rule

In this paper we present a multiple premise tableau calculus for propositional Dummett Logic. The aim is to improve the efficiency of the known decision procedures. The investigation is related to the possibility of reducing the size of the deduction by the replacement rule and rules that introduce formulas equivalent to the logical constant True. In this way we want to bound the application of the multiple premise rule, which is the main source of inefficiency, and improve the practical performances of the decision procedure. The timings of a prolog implementation are provided.