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PROBABILISTIC STABILITY, AGM REVISION OPERATORS AND MAXIMUM ENTROPY

Part of: Foundations of probability theory General logic Artificial intelligence (68Txx) Communication, information

Published online by Cambridge University Press:  21 October 2020

KRZYSZTOF MIERZEWSKI
KRZYSZTOF MIERZEWSKI*
Affiliation:
LOGICAL DYNAMICS LAB, CENTER FOR THE STUDY OF LANGUAGE AND INFORMATION STANFORD UNIVERSITYSTANFORD, CA 94308, USAE-mail: kmierzew@stanford.edu
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Abstract

Several authors have investigated the question of whether canonical logic-based accounts of belief revision, and especially the theory of AGM revision operators, are compatible with the dynamics of Bayesian conditioning. Here we show that Leitgeb’s stability rule for acceptance, which has been offered as a possible solution to the Lottery paradox, allows to bridge AGM revision and Bayesian update: using the stability rule, we prove that AGM revision operators emerge from Bayesian conditioning by an application of the principle of maximum entropy. In situations of information loss, or whenever the agent relies on a qualitative description of her information state—such as a plausibility ranking over hypotheses, or a belief set—the dynamics of AGM belief revision are compatible with Bayesian conditioning; indeed, through the maximum entropy principle, conditioning naturally generates AGM revision operators. This mitigates an impossibility theorem of Lin and Kelly for tracking Bayesian conditioning with AGM revision, and suggests an approach to the compatibility problem that highlights the information loss incurred by acceptance rules in passing from probabilistic to qualitative representations of belief.

Keywords

AGMbelief revisionBayesian conditioningprobabilistic stabilityacceptance rulestrackingmaximum entropy

MSC classification

Primary: 03B42: Logics of knowledge and belief (including belief change)
Secondary: 68T27: Logic in artificial intelligence 60A05: Axioms; other general questions 94A17: Measures of information, entropy
Type
Research Article
Information
The Review of Symbolic Logic , Volume 15 , Issue 3 , September 2022 , pp. 553 - 590
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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