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.
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.
Included in
Algebra Commons, Logic and Foundations Commons, Other Computer Engineering Commons, Other Computer Sciences Commons, Other Mathematics Commons
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