Analysing Spatial Properties on Neighbourhood Spaces

TL;DR

This paper introduces a bisimulation relation for neighbourhood spaces, a generalization of topological spaces, demonstrating its logical preservation properties and comparing it with standard modal bisimulations.

Contribution

It defines a new bisimulation for neighbourhood spaces, shows its logical invariance, and compares it with existing modal bisimulations, highlighting its unique properties.

Findings

Path preserving bisimulation preserves SLCS formulas.

SLCS cannot express separation and connectedness.

Bisimulation coincides with modal bisimulation with converse on graphs.

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.