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

Linker, S, Papacchini, F ORCID: 0000-0002-0310-7378 and Sevegnani, M (2021) Finite Models for a Spatial Logic with Discrete and Topological Path Operators. .

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Official URL: https://www.dagstuhl.de/dagpub/978-3-95977-201-3

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 or Workshop Item (Unspecified)
Divisions:	Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	12 Oct 2021 07:39
Last Modified:	22 Nov 2023 11:36
DOI:	10.4230/LIPIcs.MFCS.2021.72
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3140064