Modal logic of planar polygons

David Gabelaia; Kristina Gogoladze; Mamuka Jibladze; Evgeny Kuznetsov; Maarten Marx

Modal logic of planar polygons

Logic 2018-07-10 v1

Authors: David Gabelaia , Kristina Gogoladze , Mamuka Jibladze , Evgeny Kuznetsov , Maarten Marx

Abstract

We study the modal logic of the closure algebra $P_2$ , generated by the set of all polygons in the Euclidean plane $\mathbb{R}^2$ . We show that this logic is finitely axiomatizable, is complete with respect to the class of frames we call "crown" frames, is not first order definable, does not have the Craig interpolation property, and its validity problem is PSPACE-complete.

Keywords

mathematical logic rational maps set theory

Cite

@article{arxiv.1807.02868,
  title  = {Modal logic of planar polygons},
  author = {David Gabelaia and Kristina Gogoladze and Mamuka Jibladze and Evgeny Kuznetsov and Maarten Marx},
  journal= {arXiv preprint arXiv:1807.02868},
  year   = {2018}
}

Modal logic of planar polygons

Abstract

Keywords

Cite

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