The modal logic of Bayesian belief revision

Brown, William, Gyenis, Zalán and Rédei, Miklós ORCID: 0000-0001-5298-1443 (2018) The modal logic of Bayesian belief revision. Journal of Philosophical Logic. ISSN 0022-3611

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Abstract

In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using Bayes’ rule. We define a hierarchy of modal logics that capture the logical features of Bayesian belief revision. Elements in the hierarchy are distinguished by the cardinality of the set of elementary propositions on which the agent’s prior is defined. Inclusions among the modal logics in the hierarchy are determined. By linking the modal logics in the hierarchy to the strongest modal companion of Medvedev’s logic of finite problems it is shown that the modal logic of belief revision determined by probabilities on a finite set of elementary propositions is not finitely axiomatizable.

Item Type:	Article
Official URL:	https://link.springer.com/journal/10992
Additional Information:	© 2018 The Authors
Divisions:	Philosophy, Logic and Scientific Method
Subjects:	B Philosophy. Psychology. Religion > BC Logic
Date Deposited:	20 Nov 2018 14:41
Last Modified:	17 Oct 2024 17:15
Projects:	K 115593
Funders:	Hungarian Scientfic Research Found, Hungarian Academy of Sciences
URI:	http://eprints.lse.ac.uk/id/eprint/90632

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