A general tableau method for propositional interval temporal logics: Theory and implementation

In this paper, we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau methods for interval-based ones. We develop a general tableau method for Venema’s CDT logic interpreted over partial orders (BCDT+ for short). It combines features of the classical tableau method for first-order logic with those of explicit tableau methods for modal logics with constraint label management, and it can be easily tailored to most propositional interval temporal logics proposed in the literature. We prove its soundness and completeness, and we show how it has been implemented

Analytic Tableau Systems for Propositional Bimodal Logics of Knowledge and Belief

We give sound and complete analytic tableau systems for the propositional bimodal logics KB , KB C , KB 5 , and KB 5C . These logics have two universal modal operators K and B , where K stands for knowing and B stands for believing. The logic KB is a combination of the modal logic S5 (for K ) and KD45 (for B ) with the interaction axioms I : K ! B and C : B ! K B . The logics KB C , KB 5 , KB 5C are obtained from KB respectively by deleting the axiom C (for KB C ), the axioms 5 (for KB 5 ), and both of the axioms C and 5 (for KB 5C ). As analytic sequent-like tableau systems, our calculi give simple decision procedures for reasoning about both knowledge and belief in the mentioned logics