Atomicity vs. Infinite Divisibility of Space

This paper investigates the possibility of characterizing properties of space such as divisibility, density and atomicity in spaces modeled by mereologies and mereotopologies, and properties of atoms like extension and self-connectedness will be considered.

Abstract

In qualitative spatial reasoning, the last ten years have brought a lot of results on theories of spatial properties and relations taking regions of space as primitive entities. In particular, the axiomatization of mereotopologies has been extensively studied. However, properties of space such as divisibility, density and atomicity haven't attracted much attention in this context. Nevertheless, atomicity is especially important if one seeks to build a bridge between spatial reasoning and spatial databases approaches in areas like vision or GIS. In this paper we will investigate the possibility of characterizing such properties in spaces modeled by mereologies and mereotopologies. In addition, properties of atoms like extension and self-connectedness will be considered.