# Analysing Spatial Properties on Neighbourhood Spaces

arXiv: https://arxiv.org/abs/2007.01266 · HTML: https://mlsanity.com/paper/2007.01266/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2020.

## Built on by (most cited first, 1 of 1)

- [Geometric Model Checking of Continuous Space](https://mlsanity.com/paper/2105.06194/) (2021)

## Abstract (arXiv)

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.