Conditionalization and total knowledge

Journal of Applied Non-Classical Logics 18 (2-3):247-266 (2008)
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Abstract

This paper employs epistemic logic to investigate the philosophical foundations of Bayesian updating in belief revision. By Bayesian updating, we understand the tenet that an agent's degrees of belief—assumed to be encoded as a probability distribution—should be revised by conditionalization on the agent's total knowledge up to that time. A familiar argument, based on the construction of a diachronic Dutch book, purports to show that Bayesian updating is the only rational belief-revision policy. We investigate the conditions under which the premises of this argument might be satisfied. Specifically, we consider the case of an artificial agent whose language (of thought) features a modal operator TK, where TK ψ has the interpretation “My total knowledge is ψ”. We show that every proposition of the form TK ψis epistemically categorical: it determines, for every proposition φ in the agent's language, whether the agent knows that φ. We argue that, for certain artificial agents employing such a language, the diachronic Dutch book argument for Bayesian updating is on firm ground.

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References found in this work

Probability and the Art of Judgment.Richard C. Jeffrey - 1992 - New York: Cambridge University Press.
Conditionalization and observation.Paul Teller - 1973 - Synthese 26 (2):218-258.

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