Analytic Tableau Systems for Propositional Bimodal Logics of Knowledge and Belief
نویسنده
چکیده
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 : Kφ → Bφ and C : Bφ → K Bφ. 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
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