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STANDARD BAYES LOGIC IS NOT FINITELY AXIOMATIZABLE

Published online by Cambridge University Press:  22 March 2019

ZALÁN GYENIS*
Affiliation:
Department of Logic, Institute of Philosophy, Jagiellonian University and Department of Logic, Eötvös loránd University
*Corresponding
*DEPARTMENT OF LOGIC INSTITUTE OF PHILOSOPHY JAGIELLONIAN UNIVERSITY KRAKÓW, POLAND and DEPARTMENT OF LOGIC EÖTVÖS LORÁND UNIVERSITY BUDAPEST, HUNGARY E-mail: zalan.gyenis@gmail.com

Abstract

In the article [2] a hierarchy of modal logics has 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 the modal logics of Medvedev frames 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 article 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.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2019 

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