From conditional probability to the logic of doxastic actions

We investigate the discrete (finite) case of the Popper-Renyi theory of conditional probability, introducing discrete conditional probabilistic models for (multi-agent) knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (non-negatively introspective) type of “knowledge”, and we analyze its role in games. We completely axiomatize the logic of conditional belief, knowledge and safe belief. We develop a theory of dynamic belief revision over probabilistic models, by introducing “action models” and a notion of update, and showing how various beliefrevisions policies considered in the literature, as well as various forms of communication and other belief-changing events, can be represented in this setting. We give a complete and decidable set of axioms for a qualitative dynamic logic of belief-revising actions over probabilistic models.

• Type: Conference
• Year: 2007
• Where: TARK
• Authors: Alexandru Baltag, Sonja Smets
• Keywords: Conditional Belief, Probabilistic Models, Safe Belief, TARK 2007