David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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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Citations of this work BETA
Alexandru Baltag & Sonja Smets (2008). Probabilistic Dynamic Belief Revision. Synthese 165 (2):179 - 202.
Rineke Verbrugge (2009). Logic and Social Cognition. Journal of Philosophical Logic 38 (6):649 - 680.
Swarup Mohalik & R. Ramanujam (2010). Automata for Epistemic Temporal Logic with Synchronous Communication. Journal of Logic, Language and Information 19 (4):451-484.
Johan van Benthem, Jelle Gerbrandy, Tomohiro Hoshi & Eric Pacuit (2009). Merging Frameworks for Interaction. Journal of Philosophical Logic 38 (5):491-526.
Tomohiro Hoshi (2010). Merging DEL and ETL. Journal of Logic, Language and Information 19 (4):413-430.
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