Properties of independently axiomatizable bimodal logics
Journal of Symbolic Logic
Modalities for reasoning about knowledge and uncertainties
Partiality, modality, and nonmonotonicity
Single Step Tableaux for Modal Logics
Journal of Automated Reasoning
TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
A Tableau for Multimodal Logics and Some (Un)Decidability Results
TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Complexity of Simple Dependent Bimodal Logics
TABLEAUX '00 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
A tableau calculus with automaton-labelled formulae for regular grammar logics
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
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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驴 驴 B驴 and C : B驴 驴 KB驴. The logics KB-C, KB-5, KB-5C are obtained from KB respectively by deletingthe 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.