Clausal Tableaux for Multimodal Logics of Belief

Abstract

We develop clausal tableau calculi for six multimodal logics variously designed for reasoning about multi-degree belief, reasoning about distributed systems of belief and for reasoning about epistemic states of agents in multi-agent systems. Our tableau calculi are sound, complete, cut-free and have the analytic superformula property, thereby giving decision procedures for all of these logics. We also use our calculi to obtain complexity results for five of these logics. The complexity of the remaining logic was known.