Epistemic Updates on Algebras

Authors

Alexander Kurz, Chapman UniversityFollow
Alessandra Palmigiano, University of Amsterdam

Document Type

Article

Publication Date

2013

Abstract

We develop the mathematical theory of epistemic updates with the tools of duality theory. We focus on the Logic of Epistemic Actions and Knowledge (EAK), introduced by Baltag-Moss-Solecki, without the common knowledge operator. We dually characterize the product update construction of EAK as a certain construction transforming the complex algebras associated with the given model into the complex algebra associated with the updated model. This dual characterization naturally generalizes to much wider classes of algebras, which include, but are not limited to, arbitrary BAOs and arbitrary modal expansions of Heyting algebras (HAOs). As an application of this dual characterization, we axiomatize the intuitionistic analogue of the logic of epistemic knowledge and actions, which we refer to as IEAK, prove soundness and completeness of IEAK w.r.t. both algebraic and relational models, and illustrate how IEAK encodes the reasoning of agents in a concrete epistemic scenario.

Comments

This article was originally published in Logical Methods in Computer Science, volume 9, issue 4, in 2013. DOI: 10.2168/LMCS-9(4:17)2013

Recommended Citation

A. Kurz and A. Palmigiano, “Epistemic Updates on Algebras,” Logical Methods in Computer Science, vol. 9, no. 4, Dec. 2013. DOI: 10.2168/LMCS-9(4:17)2013

Copyright

The authors

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.