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|Title:||Epistemic Updates on Algebras|
|Authors:||Kurz, Alexander A.|
Palmigiano, Alessandra A.
|Publisher:||International Federation of Computational Logic|
|Citation:||Logical Methods in Computer Science, 2013, 9 (4), 17|
|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. © A. Kurz and A. Palmigiano.|
|Rights:||Copyright © the authors, 2013. This is an Open Access article distributed under the terms of the Creative Commons Attribution No Derivatives License ( http://creativecommons.org/licenses/by-nd/2.0/ ) which permits use and distribution in any medium, provided the original work is properly cited and no modifications or adaptations are made.|
|Appears in Collections:||Published Articles, College of Science and Engineering|
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