Sequent Calculi for Branching Time Temporal Logics of Knowledge and Belief

Authors:
Jūratė Sakalauskaitė
Affiliations:
Institute of Mathematics and Informatics, Akademijos 4, 08663 Vilnius, Lithuania, e-mail: jurates@ktl.mii.lt
Venue:
Informatica
Year:
2007

Citing 5
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A guide to completeness and complexity for modal logics of knowledge and belief

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Modal and temporal logics

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Reasoning about knowledge

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Complete Axiomatizations for Reasoning about Knowledge and Time

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Sequent Calculi for Temporal Logics of Common Knowledge and Belief

Informatica

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Abstract

In this paper we consider branching time temporal logics of knowledge and belief. These logics involve the discrete time linear temporal logic operators “next” and “until” with the branching temporal logic operator “on all paths”. The latter operator is interpreted with respect to a version of the bundle semantics. In addition the temporal logic of knowledge (belief) contains an indexed set of unary modal operators “agent i knows” (“agent i believes”) and it contains the modality of common knowledge (belief). For these logics we present sequent calculi with a restricted cut rule. Thus, we get proof systems where proof-search becomes decidable. The soundness and completeness for these calculi are proved.