Authors
Johan Van Benthem
University of Amsterdam
Jan Van Eijck
University of Amsterdam
Barteld Kooi
University of Groningen
Abstract
Current dynamic epistemic logics for analyzing effects of informational events often become cumbersome and opaque when common knowledge is added for groups of agents. Still, postconditions involving common knowledge are essential to successful multi-agent communication. We propose new systems that extend the epistemic base language with a new notion of ‘relativized common knowledge’, in such a way that the resulting full dynamic logic of information flow allows for a compositional analysis of all epistemic postconditions via perspicuous ‘reduction axioms’. We also show how such systems can deal with factual alteration, rather than just information change, making them cover a much wider range of realistic events. After a warm-up stage of analyzing logics for public announcements, our main technical results are expressivity and completeness theorems for a much richer logic that we call LCC. This is a dynamic epistemic logic whose static base is propositional dynamic logic (PDL), interpreted epistemically. This system is capable of expressing all model-shifting operations with finite action models, while providing a compositional analysis for a wide range of informational events. This makes LCC a serious candidate for a standard in dynamic epistemic logic, as we illustrate by analyzing some complex communication scenarios, including sending successive emails with both ‘cc’ and ‘bcc’ lines, and other private announcements to subgroups. Our proofs involve standard modal techniques, combined with a new application of Kleene’s theorem on finite automata, as well as new Ehrenfeucht games of model comparison
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The Ethics of Nudge.Luc Bovens - 2008 - In Mats J. Hansson & Till Grüne-Yanoff (eds.), Preference Change: Approaches from Philosophy, Economics and Psychology. Berlin: Springer, Theory and Decision Library A. pp. 207-20.
Dynamic Logic for Belief Revision.Johan van Benthem - 2007 - Journal of Applied Non-Classical Logics 17 (2):129-155.
Dynamic Logic of Preference Upgrade.Johan van Benthem & Fenrong Liu - 2007 - Journal of Applied Non-Classical Logics 17 (2):157-182.
Merging Frameworks for Interaction.Johan van Benthem, Jelle Gerbrandy, Tomohiro Hoshi & Eric Pacuit - 2009 - Journal of Philosophical Logic 38 (5):491-526.

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