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Modal Logic and the Vietoris Functor

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Leo Esakia on Duality in Modal and Intuitionistic Logics

Part of the book series: Outstanding Contributions to Logic ((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.

Dedicated to the memory of Leo Esakia, who was and will remain a great source of inspiration, both as a logician and as a person

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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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Authors and Affiliations

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

    Yde Venema & Jacob Vosmaer

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  1. Yde Venema
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  2. Jacob Vosmaer
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Correspondence to Yde Venema .

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Editors and Affiliations

  1. New Mexico State University, Las Cruces, New Mexico, USA

    Guram Bezhanishvili

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Venema, Y., Vosmaer, J. (2014). Modal Logic and the Vietoris Functor. In: Bezhanishvili, G. (eds) Leo Esakia on Duality in Modal and Intuitionistic Logics. Outstanding Contributions to Logic, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8860-1_6

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