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

Linker, S., Papacchini, F. and Sevegnani, M. (2021) Finite Models for a Spatial Logic with Discrete and Topological Path Operators. In: 46th Mathematical Foundations of Computer Science Conference, Tallinn, Estonia, 23-27 Aug 2021, 72:1-72:16. ISBN 9783959772013 (doi: 10.4230/LIPIcs.MFCS.2021.72)

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.

• Item Type: Conference Proceedings
• Additional Information: Funding: Fabio Papacchini: partly supported by the EPSRC through grants EP/R026084 and EP/R026173. Michele Sevegnani: supported by the EPSRC under PETRAS SRF grant MAGIC (EP/S035362/1).
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Sevegnani, Dr Michele
• Authors: Linker, S., Papacchini, F., and Sevegnani, M.
• College/School: College of Science and Engineering > School of Computing Science
• ISSN: 1868-8969
• ISBN: 9783959772013
• Published Online: 18 August 2021
• Copyright Holders: Copyright © Sven Linker, Fabio Papacchini, and Michele Sevegnani 2021
• Publisher Policy: Reproduced under a Creative Commons licence

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