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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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Authors and Affiliations

  1. Oxford University Computing Laboratory, University of Oxford, Parks Road, Oxford, OX1 3QD, UK

    Alexandru Baltag

  2. GPI, University of Hertfordshire, Hatfield, UK

    Alexandru Baltag

  3. Center for Logic and Philosophy of Science, Vrije Universiteit Brussel, Brussels, Belgium

    Sonja Smets

  4. IEG, University of Oxford, Oxford, UK

    Sonja Smets

Authors
  1. Alexandru Baltag
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  2. Sonja Smets
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Correspondence to Sonja Smets.

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Baltag, A., Smets, S. Probabilistic dynamic belief revision. Synthese 165, 179–202 (2008). https://doi.org/10.1007/s11229-008-9369-8

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  • DOI: https://doi.org/10.1007/s11229-008-9369-8

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