Publication

Logics of communication and change

van Benthem, J., van Eijck, J. & Kooi, B. Nov-2006 In : Information and Computation. 204, 11, p. 1620-1662 43 p.

Research output: Scientific - peer-reviewArticle

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DOI

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. (c) 2006 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)1620-1662
Number of pages43
JournalInformation and Computation
Volume204
Issue number11
StatePublished - Nov-2006

    Keywords

  • epistemic logic, update, dynamic logic, common knowledge, reduction axioms, product update, finite automata, Kleene's theorem

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