From conditional probability to the logic of doxastic actions

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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.
Alexandru Baltag, Sonja Smets
Added 09 Jun 2010
Updated 09 Jun 2010
Type Conference
Year 2007
Where TARK
Authors Alexandru Baltag, Sonja Smets
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