License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2021.72
URN: urn:nbn:de:0030-drops-145120
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14512/
Linker, Sven ;
Papacchini, Fabio ;
Sevegnani, Michele
Finite Models for a Spatial Logic with Discrete and Topological Path Operators
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.
BibTeX - Entry
@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/opus/volltexte/2021/14512},
URN = {urn:nbn:de:0030-drops-145120},
doi = {10.4230/LIPIcs.MFCS.2021.72},
annote = {Keywords: spatial logic, topology, finite models}
}
Keywords: |
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spatial logic, topology, finite models |
Collection: |
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46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021) |
Issue Date: |
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2021 |
Date of publication: |
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18.08.2021 |