On the Modal Logic of Jeffrey Conditionalization

Logica Universalis 12 (3-4):351-374 (2018)

Zalan Gyenis
Jagiellonian University
We continue the investigations initiated in the recent papers where Bayes logics have been introduced to study the general laws of Bayesian belief revision. In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using the Bayes rule. In this paper we take the more general Jeffrey formula as a conditioning device and study the corresponding modal logics that we call Jeffrey logics, focusing mainly on the countable case. The containment relations among these modal logics are determined and it is shown that the logic of Bayes and Jeffrey updating are very close. It is shown that the modal logic of belief revision determined by probabilities on a finite or countably infinite set of elementary propositions is not finitely axiomatizable. The significance of this result is that it clearly indicates that axiomatic approaches to belief revision might be severely limited.
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DOI 10.1007/s11787-018-0205-8
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References found in this work BETA

Scientific Reasoning: The Bayesian Approach.Colin Howson & Peter Urbach - 1989 - British Journal for the Philosophy of Science 48 (1):126-131.
Dynamic Logic for Belief Revision.Johan van Benthem - 2007 - Journal of Applied Non-Classical Logics 17 (2):129-155.
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Logic Prizes Et Cætera.Jean-Yves Beziau - 2018 - Logica Universalis 12 (3-4):271-296.

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