Extending probabilistic dynamic epistemic logic

Synthese 169 (2):241 - 257 (2009)
Abstract
This paper aims to extend in two directions the probabilistic dynamic epistemic logic provided in Kooi’s paper (J Logic Lang Inform 12(4):381–408, 2003) and to relate these extensions to ones made in van Benthem et al. (Proceedings of LOFT’06. Liverpool, 2006). Kooi’s probabilistic dynamic epistemic logic adds to probabilistic epistemic logic sentences that express consequences of public announcements. The paper (van Benthem et al., Proceedings of LOFT’06. Liverpool, 2006) extends (Kooi, J Logic Lang Inform 12(4):381–408, 2003) to using action models, but in both papers, the probabilities are discrete, and are defined on trivial σ -algebras over finite sample spaces. The first extension offered in this paper is to add a previous-time operator to a probabilistic dynamic epistemic logic similar to Kooi’s in (J Logic Lang Inform 12(4):381–408, 2003). The other is to involve non-trivial σ -algebras and continuous probabilities in probabilistic dynamic epistemic logic.
Keywords Dynamic epistemic logic  Modal logic  Probability
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    References found in this work BETA
    Barteld P. Kooi (2003). Probabilistic Dynamic Epistemic Logic. Journal of Logic, Language and Information 12 (4):381-408.
    Joshua Sack (2010). Logic for Update Products and Steps Into the Past. Annals of Pure and Applied Logic 161 (12):1431-1461.
    Joshua Sack (2008). Temporal Languages for Epistemic Programs. Journal of Logic, Language and Information 17 (2):183-216.

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    Citations of this work BETA
    Joshua Sack (2010). Logic for Update Products and Steps Into the Past. Annals of Pure and Applied Logic 161 (12):1431-1461.
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