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Analysing Spatial Properties on Neighbourhood Spaces

Authors Sven Linker , Fabio Papacchini, Michele Sevegnani

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Author Details

Sven Linker
  • Department of Computer Science, University of Liverpool, UK
Fabio Papacchini
  • Department of Computer Science, University of Liverpool, UK
Michele Sevegnani
  • School of Computing Science, University of Glasgow, UK

Funding

This work was supported by the Engineering and Physical Sciences Research Council, under the grant EP/N007565/1 (S4: Science of Sensor Systems Software).
  • Papacchini, Fabio: supported by the EPSRC through grant EP/R026084 and grant EP/R026173.
  • Sevegnani, Michele: supported by PETRAS SRF grant MAGIC (EP/S035362/1).

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.MFCS.2020.66

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.

Subject Classification

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

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