# Finite Jeffrey logic is not finitely axiomatizable

Gyenis, Zalán (2018) Finite Jeffrey logic is not finitely axiomatizable. [Preprint]

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## Abstract

Bayes logics based on Bayes conditionalization as a probability updating mechanism have recently been introduced in [http://philsci-archive.pitt.edu/14136/]. It has been shown that the modal logic of Bayesian belief revision determined by probabilities on a finite set of elementary propositions or on a standard Borel space is not finitely axiomatizable [http://philsci-archive.pitt.edu/14136/]. Apart from Bayes conditionalization there are other methods, extensions of the standard one, of updating a probability measure. One such important method is Jeffrey's conditionalization. In this paper we consider the modal logic $\JL_{<\omega}$ of probability updating based on Jeffrey's conditionalization where the underlying measurable space is finite. By relating this logic to the logic of absolute continuity and to Medvedev's logic of
finite problems, we show that $\JL_{<\omega}$ is not finitely axiomatizable. The result is significant because it indicates that axiomatic approaches to belief revision might be severely limited.

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Item Type: Preprint
Creators:
CreatorsEmailORCID
Gyenis, Zalángyz@renyi.hu
Keywords: Bayesian inference, Bayes learning, Bayes logic, Medvedev frames, Jeffrey conditionalization, Jeffrey logic, Non finite axiomatizability
Subjects: Specific Sciences > Mathematics > Logic
Specific Sciences > Probability/Statistics
Depositing User: Zalán Gyenis
Date Deposited: 11 Jan 2018 18:52
Item ID: 14274
Subjects: Specific Sciences > Mathematics > Logic
Specific Sciences > Probability/Statistics
Date: 10 January 2018
URI: http://philsci-archive.pitt.edu/id/eprint/14274