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Modal Logic and the Vietoris Functor

  • Yde Venema
  • Jacob Vosmaer
Chapter
Part of the Outstanding Contributions to Logic book series (OCTR, volume 4)

Abstract

In [16], Esakia uses the Vietoris topology to give a coalgebra-flavored definition of topological Kripke frames, thus relating the Vietoris topology, modal logic and coalgebra. In this chapter, we sketch some of the thematically related mathematical developments that followed. Specifically, we look at Stone duality for the Vietoris hyperspace and the Vietoris powerlocale, and at recent work combining coalgebraic modal logic and the Vietoris functor.

Keywords

Modal logic Vietoris topology Stone duality Coalgebra 

Notes

Acknowledgments

We would like to thank Liang-Ting Chen and Steve Vickers for providing helpful pointers to the literature. Additionally, we would like to thank the anonymous referee, whose thorough criticism contributed significantly to the quality of this chapter, and in particular to the presentation and choice of contents in Sect. 6.3.2.3. Finally, we are grateful to Guram Bezhanishvili, who provided many suggestions for improving the presentation of the chapter.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Institute for Logic, Language and ComputationUniversity of AmsterdamAmsterdamThe Netherlands

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