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Convergence, Continuity and Recurrence in Dynamic Epistemic Logic

  • Dominik Klein
  • Rasmus K. Rendsvig
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10455)

Abstract

The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the latter, used as an analytical aid. We show maps induced by action model transformations continuous with respect to the Stone topology and present results on the recurrent behavior of said maps.

Keywords

Dynamic epistemic logic Limit behavior Convergence Recurrence Dynamical systems Metric spaces General topology Modal logic 

Notes

Acknowledgements

The contribution of R.K. Rendsvig was funded by the Swedish Research Council through the Knowledge in a Digital World project and by The Center for Information and Bubble Studies, sponsored by The Carlsberg Foundation. The contribution of D. Klein was partially supported by the Deutsche Forschungsgemeinschaft (DFG) and Grantová agentura České republiky (GAČR) as part of the joint project From Shared Evidence to Group Attitudes [RO 4548/6-1].

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of PhilosophyBayreuth UniversityBayreuthGermany
  2. 2.Department of Political ScienceUniversity of BambergBambergGermany
  3. 3.Theoretical PhilosophyLund UniversityLundSweden
  4. 4.Center for Information and Bubble StudiesUniversity of CopenhagenCopenhagenDenmark

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