Annals of Pure and Applied Logic 165 (4):963-995 (2014)

Abstract
In the present paper, we start studying epistemic updates using the standard toolkit of duality theory. We focus on public announcements, which are the simplest epistemic actions, and hence on Public Announcement Logic without the common knowledge operator. As is well known, the epistemic action of publicly announcing a given proposition is semantically represented as a transformation of the model encoding the current epistemic setup of the given agents; the given current model being replaced with its submodel relativized to the announced proposition. We dually characterize the associated submodel-injection map as a certain pseudo-quotient map between the complex algebras respectively associated with the given model and with its relativized submodel. As is well known, these complex algebras are complete atomic BAOs . The dual characterization we provide naturally generalizes to much wider classes of algebras, which include, but are not limited to, arbitrary BAOs and arbitrary modal expansions of Heyting algebras . Thanks to this construction, the benefits and the wider scope of applications given by a point-free, intuitionistic theory of epistemic updates are made available. As an application of this dual characterization, we axiomatize the intuitionistic analogue of PAL, which we refer to as IPAL, prove soundness and completeness of IPAL w.r.t. both algebraic and relational models, and show that the well known Muddy Children Puzzle can be formalized in IPAL
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DOI 10.1016/j.apal.2013.11.004
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References found in this work BETA

Logics of Public Communications.Jan Plaza - 2007 - Synthese 158 (2):165 - 179.
Reasoning About Information Change.Jelle Gerbrandy & Willem Groeneveld - 1997 - Journal of Logic, Language and Information 6 (2):147-169.
The Structure of Lattices of Subframe Logics.Frank Wolter - 1997 - Annals of Pure and Applied Logic 86 (1):47-100.

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Citations of this work BETA

A Computational Learning Semantics for Inductive Empirical Knowledge.Kevin T. Kelly - 2014 - In Alexandru Baltag & Sonja Smets (eds.), Johan van Benthem on Logic and Information Dynamics. Springer International Publishing. pp. 289-337.
About Intuitionistic Public Announcement Logic.Philippe Balbiani & Didier Galmiche - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 97-116.

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