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DOI: 10.4230/LIPIcs.MFCS.2021.72

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

Authors: Sven Linker, Fabio Papacchini, and Michele Sevegnani

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract

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.

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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)

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@InProceedings{linker_et_al:LIPIcs.MFCS.2021.72,
  author =	{Linker, Sven and Papacchini, Fabio and Sevegnani, Michele},
  title =	{{Finite Models for a Spatial Logic with Discrete and Topological Path Operators}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{72:1--72:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.72},
  URN =		{urn:nbn:de:0030-drops-145120},
  doi =		{10.4230/LIPIcs.MFCS.2021.72},
  annote =	{Keywords: spatial logic, topology, finite models}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2020.66

Analysing Spatial Properties on Neighbourhood Spaces

Authors: Sven Linker, Fabio Papacchini, and Michele Sevegnani

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract

We present a bisimulation relation for neighbourhood spaces, a generalisation of topological spaces. We show that this notion, path preserving bisimulation, preserves formulas of the spatial logic SLCS. We then use this preservation result to show that SLCS cannot express standard topological properties such as separation and connectedness. Furthermore, we compare the bisimulation relation with standard modal bisimulation and modal bisimulation with converse on graphs and prove it coincides with the latter.

Cite as

Sven Linker, Fabio Papacchini, and Michele Sevegnani. Analysing Spatial Properties on Neighbourhood Spaces. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 66:1-66:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{linker_et_al:LIPIcs.MFCS.2020.66,
  author =	{Linker, Sven and Papacchini, Fabio and Sevegnani, Michele},
  title =	{{Analysing Spatial Properties on Neighbourhood Spaces}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{66:1--66:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.66},
  URN =		{urn:nbn:de:0030-drops-127352},
  doi =		{10.4230/LIPIcs.MFCS.2020.66},
  annote =	{Keywords: spatial logic, topology, bisimulation}
}

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Documents authored by Papacchini, Fabio

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

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Analysing Spatial Properties on Neighbourhood Spaces

Abstract

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