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Sequent Calculi for Branching Time Temporal Logics of Knowledge and Belief
Volume 18, Issue 1 (2007), pp. 103–114
Jūratė Sakalauskaitė  

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https://doi.org/10.15388/Informatica.2007.166
Pub. online: 1 January 2007      Type: Research Article     

Received
1 April 2006
Published
1 January 2007

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.

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Keywords
temporal logics of knowledge and belief branching time sequent calculus restricted cut rule

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INFORMATICA

  • Online ISSN: 1822-8844
  • Print ISSN: 0868-4952
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