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Merging Frameworks for Interaction

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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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Authors and Affiliations

  1. Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands

    Johan van Benthem

  2. School of Humanities and Social Sciences, Tsinghua University, Beijing, China

    Johan van Benthem

  3. Department of Philosophy, Stanford University, Stanford, CA, USA

    Johan van Benthem, Tomohiro Hoshi & Eric Pacuit

  4. Departimento di Informatica, University of Torino, Turin, Italy

    Jelle Gerbrandy

Authors
  1. Johan van Benthem
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  2. Jelle Gerbrandy
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  3. Tomohiro Hoshi
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  4. Eric Pacuit
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Corresponding author

Correspondence to Johan van Benthem.

Additional information

An early version of this paper was presented at TARK XI [14].

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van Benthem, J., Gerbrandy, J., Hoshi, T. et al. Merging Frameworks for Interaction. J Philos Logic 38, 491–526 (2009). https://doi.org/10.1007/s10992-008-9099-x

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  • DOI: https://doi.org/10.1007/s10992-008-9099-x

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