# Model Checking Spatial Logics for Closure Spaces

arXiv: https://arxiv.org/abs/1609.06513 · HTML: https://mlsanity.com/paper/1609.06513/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Sep 2016.

## Built on by (most cited first, 4 of 4)

- [MacroSwarm: A Field-based Compositional Framework for Swarm Programming](https://mlsanity.com/paper/2401.10969/) (2024)
- [Certified Control for Train Sign Classification](https://mlsanity.com/paper/2311.09778/) (2023)
- [Geometric Model Checking of Continuous Space](https://mlsanity.com/paper/2105.06194/) (2021)
- [Programming Distributed Collective Processes in the eXchange Calculus](https://mlsanity.com/paper/2401.11212/) (2024)

## Abstract (arXiv)

Spatial aspects of computation are becoming increasingly relevant in Computer Science, especially in the field of collective adaptive systems and when dealing with systems distributed in physical space. Traditional formal verification techniques are well suited to analyse the temporal evolution of programs; however, properties of space are typically not taken into account explicitly. We present a topology-based approach to formal verification of spatial properties depending upon physical space. We define an appropriate logic, stemming from the tradition of topological interpretations of modal logics, dating back to earlier logicians such as Tarski, where modalities describe neighbourhood. We lift the topological definitions to the more general setting of closure spaces, also encompassing discrete, graph-based structures. We extend the framework with a spatial surrounded operator, a propagation operator and with some collective operators. The latter are interpreted over arbitrary sets of points instead of individual points in space. We define efficient model checking procedures, both for the individual and the collective spatial fragments of the logic and provide a proof-of-concept tool.