Simplification Rules for Intuitionistic Propositional Tableaux

Abstract

The implementation of a logic requires, besides the definition of a calculus and a decision procedure, the development of techniques to reduce the search space. In this article we introduce some simplification rules for Intuitionistic propositional logic that try to replace a formula with an equi-satisfiable “simpler” one with the aim to reduce the search space. Our results are proved via semantical techniques based on Kripke models. We also provide an empirical evaluation of their impact on implementations.