# Specifying and Verifying Properties of Space - Extended Version

arXiv: https://arxiv.org/abs/1406.6393 · HTML: https://mlsanity.com/paper/1406.6393/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2014.

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

- [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)
- [A Hybrid Deep Learning and Model-Checking Framework for Accurate Brain Tumor Detection and Validation](https://mlsanity.com/paper/2501.01991/) (2024)
- [Model Checking in Medical Imaging for Tumor Detection and Segmentation](https://mlsanity.com/paper/2501.02024/) (2025)

## Abstract (arXiv)

The interplay between process behaviour and spatial aspects of computation has become more and more relevant in Computer Science, especially in the field of collective adaptive systems, but also, more generally, when dealing with systems distributed in physical space. Traditional verification techniques are well suited to analyse the temporal evolution of programs; properties of space are typically not explicitly taken into account. We propose a methodology to verify 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 a more general setting, also encompassing discrete, graph-based structures. We further extend the framework with a spatial until operator, and define an efficient model checking procedure, implemented in a proof-of-concept tool.