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The modal logic of Bayesian belief revision

Gyenis, Zalán and Rédei, Miklós and Brown, William (2018) 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. 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.

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Item Type: Preprint
Creators:
CreatorsEmailORCID
Gyenis, Zalángyz@renyi.hu
Rédei, MiklósM.Redei@lse.ac.uk
Brown, Williamwilliamjosephbrown@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: 06 Aug 2018 15:18
Last Modified: 06 Aug 2018 15:18
Item ID: 14919
Subjects: Specific Sciences > Mathematics > Logic
General Issues > Formal Learning Theory
Specific Sciences > Probability/Statistics
Date: 6 August 2018
URI: https://philsci-archive.pitt.edu/id/eprint/14919

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