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 | ||||||||||||
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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 |
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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 |
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Date: | 6 August 2018 | ||||||||||||
URI: | https://philsci-archive.pitt.edu/id/eprint/14919 |
Available Versions of this Item
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The modal logic of Bayesian belief revision. (deposited 22 Nov 2017 16:25)
- The modal logic of Bayesian belief revision. (deposited 06 Aug 2018 15:18) [Currently Displayed]
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