A satisfiability algorithm for multimodal logic with converse

Modal logics as formal languages has many ap-plications in computer science, such as in formal verification, databases, programming languages, knowledge representation. Converse modalities are specially purposed constructors that allow modeling reverse properties, for instance, in temporal logics converse modalities are interpreted as past operators. In this paper, we propose a satisfiability algorithm for the traditional multimodal logic with converse. The algorithm is based on the tree-model property, that is, if a formula is satisfiable, then the algorithm provides a tree model of it, otherwise the algorithm outputs it is not satisfiable. We also implemented it with dynamic data structures in order to improve the execution time. Furthermore, several benchmark experiments are also provided.