A Size-Based Qualitative Approach to the Representation of Spatial Granularity

Abstract

A local spatial context is an area currently under consideration in a spatial reasoning process. The boundary between this area and the surrounding space together with the spatial granularity of the representation separates what is spatially relevant from what is irrelevant at a given time. The approach discussed in this article differs from other approaches to spatial granularity as it focusses not on a partitioning of the spatial domain, but on the notions of grain-size and the limited extent of a spatial context as primary factors of spatial granularity. Starting from a mereotopological characterization of these concepts, the notions of relevant and irrelevant extension in a context are defined. The approach is qualitative in the sense that quantitative, metric concepts are not required. The axiomatic characterization is thoroughly evaluated: it is compared to other mereotopological characterizations of spatial granularity; soundness is proven with an example model; and applicability for Knowledge Representation is illustrated with definitions for common sense conceptualizations of sameness, and adjacency of locations.