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Probabilistic Dynamic Belief Revision

Alexandru Baltag and Sonja Smets
Synthese
Vol. 165, No. 2, Knowledge, Rationality & Action (Nov., 2008), pp. 179-202
Published by: Springer
Stable URL: http://www.jstor.org/stable/40271099
Page Count: 24
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Probabilistic Dynamic Belief Revision
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Abstract

We investigate the discrete (finite) case of the Popper-Renyi theory of conditional probability, introducing discrete conditional probabilistic models for 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". We develop a probabilistic version of this concept ("degree of safety") and we analyze its role in games. We completely axiomatize the logic of conditional belief, knowledge and safe belief over conditional probabilistic models. We develop a theory of probabilistic dynamic belief revision, introducing probabilistic "action models" and proposing a notion of probabilistic update product, that comes together with appropriate reduction laws.

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