Current dynamic-epistemic logics model different types of information change in multi-agent scenarios. We generalize these logics to a probabilistic setting, obtaining a calculus for multi-agent update with three natural slots: prior probability on states, occurrence probabilities in the relevant process taking place, and observation probabilities of events. To match this update mechanism, we present a complete dynamic logic of information change with a probabilistic character. The completeness proof follows a compositional methodology that applies to a much larger class of dynamic-probabilistic (...) logics as well. Finally, we discuss how our basic update rule can be parameterized for different update policies, or learning methods. (shrink)

Current dynamic-epistemic logics model different types of information change in multi-agent scenarios. We generalize these logics to a probabilistic setting, obtaining a calculus for multi-agent update with three natural slots: prior probability on states, occurrence probabilities in the relevant process taking place, and observation probabilities of events. To match this update mechanism, we present a complete dynamic logic of information change with a probabilistic character. The completeness proof follows a compositional methodology that applies to a much larger class of dynamic-probabilistic (...) logics as well. Finally, we discuss how our basic update rule can be parameterized for different update policies, or learning methods. (shrink)

In this paper I combine the dynamic epistemic logic ofGerbrandy (1999) with the probabilistic logic of Fagin and Halpern (1994). The resultis a new probabilistic dynamic epistemic logic, a logic for reasoning aboutprobability, information, and information change that takes higher orderinformation into account. Probabilistic epistemic models are defined, and away to build them for applications is given. Semantics and a proof systemis presented and a number of examples are discussed, including the MontyHall Dilemma.

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. (shrink)