Finite Models for a Spatial Logic with Discrete and Topological Path Operators

Authors Sven Linker , Fabio Papacchini , Michele Sevegnani

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Author Details

Sven Linker
  • Lancaster University in Leipzig, Germany
Fabio Papacchini
  • University of Liverpool, UK
Michele Sevegnani
  • University of Glasgow, UK

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Sven Linker, Fabio Papacchini, and Michele Sevegnani. Finite Models for a Spatial Logic with Discrete and Topological Path Operators. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 72:1-72:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


This paper analyses models of a spatial logic with path operators based on the class of neighbourhood spaces, also called pretopological or closure spaces, a generalisation of topological spaces. For this purpose, we distinguish two dimensions: the type of spaces on which models are built, and the type of allowed paths. For the spaces, we investigate general neighbourhood spaces and the subclass of quasi-discrete spaces, which closely resemble graphs. For the paths, we analyse the cases of quasi-discrete paths, which consist of an enumeration of points, and topological paths, based on the unit interval. We show that the logic admits finite models over quasi-discrete spaces, both with quasi-discrete and topological paths. Finally, we prove that for general neighbourhood spaces, the logic does not have the finite model property, either for quasi-discrete or topological paths.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
  • Mathematics of computing → Topology
  • spatial logic
  • topology
  • finite models


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