Gyenis, Zalán and Rédei, Miklós and Brown, William (2017) The modal logic of Bayesian belief revision. [Preprint]

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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. The containment relations among the modal logics in the hierarchy are determined. By linking the modal logics in the hierarchy to Medvedev’s logic of finite problems and to Skvortsov’s logic of infinite 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.

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Item Type:	Preprint
Creators:	Creators Email ORCID Gyenis, Zalán gyz@renyi.hu Rédei, Miklós M.Redei@lse.ac.uk Brown, William williamjosephbrown@gmail.com
Keywords:	Modal logic, Bayesian inference, Bayes learning, Bayes logic, Medvedev frames
Subjects:	Specific Sciences > Mathematics > Logic General Issues > Formal Learning Theory Specific Sciences > Probability/Statistics
Depositing User:	Zalán Gyenis
Date Deposited:	22 Nov 2017 16:25
Last Modified:	22 Nov 2017 16:25
Item ID:	14136
Subjects:	Specific Sciences > Mathematics > Logic General Issues > Formal Learning Theory Specific Sciences > Probability/Statistics
Date:	21 November 2017
URI:	https://philsci-archive.pitt.edu/id/eprint/14136

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• The modal logic of Bayesian belief revision. (deposited 22 Nov 2017 16:25) [Currently Displayed]
  • The modal logic of Bayesian belief revision. (deposited 06 Aug 2018 15:18)

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