---
title: "Multidimensional Mereotopology with Betweenness"
authors:
  - "Torsten Hahmann"
  - "Michael Grüninger"
doi: "10.5591/978-1-57735-516-8/IJCAI11-157"
url: "https://ijcai.org/proceedings/2011/157"
pdf: "https://ijcai.org/proceedings/2011/0157.pdf"
venue: "Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence"
year: 2011
pages: "906-910"
track: ""
keywords:
---

# Multidimensional Mereotopology with Betweenness

Torsten Hahmann, Michael Grüninger

*Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence*, pages 906-910. DOI: [10.5591/978-1-57735-516-8/IJCAI11-157](https://doi.org/10.5591/978-1-57735-516-8/IJCAI11-157)

## Abstract

Qualitative reasoning about commonsense space often involves entities of different dimensions. We present a weak axiomatization of multidimensional qualitative space based on `relative dimension' and dimension-independent `containment' which suffice to define basic dimension-dependent mereotopological relations. We show the relationships to other meoreotopologies and to incidence geometry. The extension with betweenness, a primitive of relative position, results in a first-order theory that qualitatively abstracts ordered incidence geometry.