Merging frameworks for interaction

Journal of Philosophical Logic 38 (5):491-526 (2009)
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Abstract

A variety of logical frameworks have been developed to study rational agents interacting over time. This paper takes a closer look at one particular interface, between two systems that both address the dynamics of knowledge and information flow. The first is Epistemic Temporal Logic (ETL) which uses linear or branching time models with added epistemic structure induced by agents’ different capabilities for observing events. The second framework is Dynamic Epistemic Logic (DEL) that describes interactive processes in terms of epistemic event models which may occur inside modalities of the language. This paper systematically and rigorously relates the DEL framework with the ETL framework. The precise relationship between DEL and ETL is explored via a new representation theorem characterizing the largest class of ETL models corresponding to DEL protocols in terms of notions of Perfect Recall , No Miracles , and Bisimulation Invariance . We then focus on new issues of completeness . One contribution is an axiomatization for the dynamic logic of public announcements constrained by protocols, which has been an open problem for some years, as it does not fit the usual ‘reduction axiom’ format of DEL. Finally, we provide a number of examples that show how DEL suggests an interesting fine-structure inside ETL.

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Author Profiles

Eric Pacuit
University of Maryland, College Park
Johan Van Benthem
University of Amsterdam
Tomohiro Hoshi
Stanford University

References found in this work

Modal Logic: Graph. Darst.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - New York: Cambridge University Press. Edited by Maarten de Rijke & Yde Venema.
Facing the future: agents and choices in our indeterminist world.Nuel D. Belnap - 2001 - New York: Oxford University Press. Edited by Michael Perloff & Ming Xu.
The Logic of Reliable Inquiry.Kevin T. Kelly - 1996 - Oxford, England: Oxford University Press USA. Edited by Kevin Kelly.
Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.

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