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On the modal logic of Jeffrey conditionalization

Gyenis, Zalán (2018) On the modal logic of Jeffrey conditionalization. [Preprint]


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We continue the investigations initiated in the recent papers \cite{BGyR,GyBLst} where Bayes logics have been introduced to study the general laws of Bayesian belief revision. In Bayesian belief revision a Bayesian agent revises (updates) 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 {\em 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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Item Type: Preprint
Gyenis, Zalá
Keywords: Modal logic, Bayesian inference, Bayes learning, Bayes logic, Jeffrey learning, Jeffrey conditionalization
Subjects: Specific Sciences > Mathematics > Logic
General Issues > Formal Learning Theory
Depositing User: Zalán Gyenis
Date Deposited: 06 May 2018 15:34
Last Modified: 06 May 2018 15:34
Item ID: 14646
Subjects: Specific Sciences > Mathematics > Logic
General Issues > Formal Learning Theory
Date: 27 March 2018

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