Synthese 165 (2):179 - 202 (2008)

Authors
Sonja Smets
University of Amsterdam
Alexandru Baltag
University of Amsterdam
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.
Keywords Belief revision  Conditional belief  Dynamic-epistemic logic  Popper functions
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DOI 10.1007/s11229-008-9369-8
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References found in this work BETA

The Logic of Scientific Discovery.Karl Raimund Popper - 1934 - London, England: Routledge.
The Logic of Scientific Discovery.K. Popper - 1959 - British Journal for the Philosophy of Science 10 (37):55-57.
Theory of Knowledge.Keith Lehrer - 1990 - Westview Press.

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Citations of this work BETA

A Probabilistic Semantics for Counterfactuals. Part B.Hannes Leitgeb - 2012 - Review of Symbolic Logic 5 (1):85-121.

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