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Standard Bayes logic is not finitely axiomatizable

Gyenis, Zalán (2018) Standard Bayes logic is not finitely axiomatizable. [Preprint]

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Abstract

In the paper [http://philsci-archive.pitt.edu/14136] a hierarchy of modal logics have been defined to capture the logical features of Bayesian belief revision. Elements in that hierarchy were distinguished by the cardinality of the set of elementary propositions. By linking the modal logics in the hierarchy to Medvedev's logic of (in)finite problems it has been shown that the modal logic of Bayesian belief revision determined by probabilities on a finite set of elementary propositions is not finitely axiomatizable. However, the infinite case remained open. In this paper we prove that the modal logic of Bayesian belief revision determined by standard Borel spaces (these cover probability spaces that occur in most of the applications) is also not finitely axiomatizable.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Gyenis, Zalángyz@renyi.hu
Keywords: Modal logic, Bayesian inference, Bayes learning, Bayes logic, Medvedev frames, Non finite axiomatizability
Subjects: Specific Sciences > Mathematics > Logic
Specific Sciences > Probability/Statistics
Depositing User: Zalán Gyenis
Date Deposited: 11 Jan 2018 18:52
Last Modified: 11 Jan 2018 18:52
Item ID: 14273
Subjects: Specific Sciences > Mathematics > Logic
Specific Sciences > Probability/Statistics
Date: 6 January 2018
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/14273

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