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An Axiomatization of the d-logic of Planar Polygons

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Language, Logic, and Computation (TbiLLC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11456))

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Abstract

We introduce the modal logic of planar polygonal subsets of the plane, with the modality interpreted as the Cantor-Bendixson derivative operator. We prove the finite model property of this logic and provide a finite axiomatization for it.

D. Gabelaia, M. Jibladze, E. Kuznetsov and L. Uridia—Supported by Shota Rustaveli National Science Foundation grant #DI-2016-25.

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Notes

  1. 1.

    We introduce this terminology extending the terminology of [6] where reduction means taking a p-morphic image and subreduction means taking a p-morphic image of a subframe of the frame. Thus, up-reductions are special cases of subreduction, where the subframe under question is an up-set.

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Author information

Authors and Affiliations

  1. Ivane Javakhishvili Tbilisi State University, Tbilisi, Georgia

    David Gabelaia, Kristina Gogoladze, Mamuka Jibladze & Levan Uridia

  2. TSU Razmadze Mathematical Institute, Tbilisi, Georgia

    David Gabelaia, Mamuka Jibladze, Evgeny Kuznetsov & Levan Uridia

Authors
  1. David Gabelaia
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  2. Kristina Gogoladze
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  3. Mamuka Jibladze
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  4. Evgeny Kuznetsov
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  5. Levan Uridia
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Corresponding author

Correspondence to David Gabelaia .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University College London, London, UK

    Alexandra Silva

  2. Department of Computer Science, University of Oxford, Oxford, UK

    Sam Staton

  3. Department of Linguistics, Heinrich Heine University Düsseldorf, Düsseldorf, Germany

    Peter Sutton

  4. Leibniz-Zentrum Allgemeine Sprachwissenschaft, Berlin, Germany

    Carla Umbach

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Gabelaia, D., Gogoladze, K., Jibladze, M., Kuznetsov, E., Uridia, L. (2019). An Axiomatization of the d-logic of Planar Polygons. In: Silva, A., Staton, S., Sutton, P., Umbach, C. (eds) Language, Logic, and Computation. TbiLLC 2018. Lecture Notes in Computer Science(), vol 11456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-59565-7_8

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  • DOI: https://doi.org/10.1007/978-3-662-59565-7_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-59564-0

  • Online ISBN: 978-3-662-59565-7

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