Extending probabilistic dynamic epistemic logic
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.
KeywordsDynamic epistemic logic Modal logic Probability
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- Baltag, A., Moss, L., & Solecki, S. (2003). Logics for epistemic actions: Completeness, decidability, expressivity. Indiana University (Manuscript).Google Scholar
- Baltag, A., & Moss, L. S. (2004). Logics for epistemic programs. Synthese, 139(2, Knowledge, Rationality & Action),165–224.Google Scholar
- Fagin, R., Halpern, J., Moses, Y., & Vardi, M. (1995). Reasoning about knowledge. The MIT Press.Google Scholar
- Gariepy R.F., Ziemer W.P. (1995) Modern real analysis. PWS Publishing Company, BostonGoogle Scholar
- Sack, J. (2007). Logic for update products and steps into the past (Manuscript).Google Scholar
- van Benthem, J., Gerbrandy, J., & Kooi, B. (2006). Dynamic update with probabilities. In W. van der Hoek & M. Wooldridge (Eds.), Proceedings of LOFT’06. LiverpoolGoogle Scholar