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Probabilistic Epistemic Updates on Algebras

Probabilistic Epistemic Updates on Algebras The present article contributes to the development of the mathematical theory of epistemic updates using the tools of duality theory. Here, we focus on Probabilistic Dynamic Epistemic Logic (PDEL). We dually characterize the product update construction of PDEL-models as a certain construction transforming the complex algebras associated with the given model into the complex algebra associated with the updated model. Thanks to this construction, an interpretation of the language of PDEL can be defined on algebraic models based on Heyting algebras. This justifies our proposal for the axiomatization of the intuitionistic counterpart of PDEL. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

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References (43)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2019 ACM
ISSN
1529-3785
eISSN
1557-945X
DOI
10.1145/3341725
Publisher site
See Article on Publisher Site

Abstract

The present article contributes to the development of the mathematical theory of epistemic updates using the tools of duality theory. Here, we focus on Probabilistic Dynamic Epistemic Logic (PDEL). We dually characterize the product update construction of PDEL-models as a certain construction transforming the complex algebras associated with the given model into the complex algebra associated with the updated model. Thanks to this construction, an interpretation of the language of PDEL can be defined on algebraic models based on Heyting algebras. This justifies our proposal for the axiomatization of the intuitionistic counterpart of PDEL.

Journal

ACM Transactions on Computational Logic (TOCL)Association for Computing Machinery

Published: Aug 21, 2019

Keywords: Intuitionistic probabilistic dynamic epistemic logic

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