# Epistemic Updates on Algebras

@article{Kurz2013EpistemicUO, title={Epistemic Updates on Algebras}, author={Alexander Kurz and Alessandra Palmigiano}, journal={Log. Methods Comput. Sci.}, year={2013}, volume={9} }

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…

## 31 Citations

Probabilistic Epistemic Updates on Algebras

- MathematicsLORI
- 2015

The product update construction of PDEL-models is dually characterized as a certain construction transforming the complex algebras associated with the given model into the complex algebraassociated with the updated model, which justifies the axiomatization of the intuitionistic counterpart ofPDEL.

Dynamic Epistemic Logic Displayed

- PhilosophyLORI
- 2013

A display calculus for the logic of Epistemic Actions and Knowledge EAK of Baltag-Moss-Solecki is introduced, which revives the interest in the global semantics for dynamic epistemic logics pursued among others by Baltag, Cirstea and Sadrzadeh.

Łukasiewicz Public Announcement Logic

- Computer Science, PhilosophyIPMU
- 2016

This work provides a Hilbert-style calculus for the logic of Public Announcements, which is one of the simplest and best-known dynamic epistemic systems in the literature, and shows how to develop a Public Announcement Logic based on finite-valued Łukasiewicz modal logic.

A General Framework for Modal Correspondence in Dynamic Epistemic Logic

- Computer Science, PhilosophyLORI
- 2015

A unified framework for dynamic epistemic logics, which in particular encompasses Public Announcement Logic, Epistemic Action and Preference Upgrade is introduced, which consists of a generic language, in which some of the known reduction axioms are expressible, together with relational and algebraic semantics.

Categories for Dynamic Epistemic Logic

- PhilosophyTARK
- 2017

The primary goal of this paper is to recast the semantics of modal logic, and dynamic epistemic logic (DEL) in particular, in category-theoretic terms. We first review the category of relations and…

Dynamic sequent calculus for the logic of Epistemic Actions and Knowledge

- Computer ScienceTACL
- 2013

A new class of more general sequent calculi is proposed (which the authors call dynamic calculi) that overcome the need of contextual rules and enjoy other benefits, including a natural proof-theoretic semantics.

Algebraic and Proof-Theoretic Foundations of the Logics for Social Behaviour

- Computer Science
- 2018

The results and methodologies developed in this thesis pave the way to the logical modelling of the inner workings of organizations and their dynamics, and of social phenomena such as reputational Matthew effects and bank runs.

A proof-theoretic semantic analysis of dynamic epistemic logic

- Philosophy, Computer ScienceJ. Log. Comput.
- 2016

An analysis of the existing proof systems for dynamic epistemic logic from the viewpoint of proof-theoretic semantics, and a generalisation of Belnap’s cut elimination metatheorem for display calculi and a revised version of the display-style calculus D.EAK are provided.

A general framework for dynamic epistemic logic: towards canonical correspondences

- Computer ScienceJ. Appl. Non Class. Logics
- 2017

This article proposes a general framework for dynamic epistemic logics and adds the global operator to the language, which enables it to define the notions of a canonical MTS and canonicity of a DEL formula for a property of MTSs.

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