The Mereotopology of Discrete Space

Antony Galton

In C. Freksa and D. M. Mark (eds.) Spatial Information Theory: Cognitive and Computational Foundations of Geographic Science, Proceedings of the International Conference COSIT'99, Stade, Germany, August 1999 (Lecture Notes in Computer Science 1661), pp. 251-266. Berlin: Springer, 1999 (ISBN 3-540-66365-7).

Abstract

High-level qualitative approaches to handling spatial information are widely perceived as having little relevance to the domain of low-level quantitative data inhabited by "real-world" applications. Amongst many possible reasons for this, we concentrate on the incongruity between the continuous-space models favoured by high-level approaches and the discrete, digital representations used at the lower level. In this paper a preliminary attempt is made to bridge this gap by developing a high-level qualitative spatial theory premissed on a discrete model of space. The axioms and definitions of mereotopology are replaced by analogous axioms and definitions that are appropriate to the discrete framework. In the development of the theory, many analogies and disanalogies between the continuous and discrete models are revealed. In particular, we exploit the intrinsic metric of the discrete framework to define a measure of distinctness for regions, which in turn affords an analogue of continuous change, thus allowing the temporal dimension to be introduced in a natural way.