Journal of Philosophical Logic

, Volume 38, Issue 5, pp 491–526 | Cite as

Merging Frameworks for Interaction

  • Johan van Benthem
  • Jelle Gerbrandy
  • Tomohiro Hoshi
  • Eric Pacuit
Article

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.

Keywords

Dynamic epistemic logic Epistemic temporal logic Epistemic logic 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Johan van Benthem
    • 1
    • 2
    • 3
  • Jelle Gerbrandy
    • 4
  • Tomohiro Hoshi
    • 3
  • Eric Pacuit
    • 3
  1. 1.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.School of Humanities and Social SciencesTsinghua UniversityBeijingChina
  3. 3.Department of PhilosophyStanford UniversityStanfordUSA
  4. 4.Departimento di InformaticaUniversity of TorinoTurinItaly

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