A Taxonomy of Granular Partitions

In this paper we propose a formal theory of granular partitions (ways of dividing up or sorting or mapping reality) and we show how the theory can be applied in the geospatial domain. We characterize granular partitions at two levels: as systems of cells, and in terms of their projective relation to reality. We lay down conditions of well-formedness for granular partitions, and we define what it means for partitions to project transparently onto reality in such a way as to be structure-preserving. We continue by classifying granular partitions along three axes, according to: (a) the degree to which a partition represents the mereological structure of the domain it is projected onto; (b) the degree of completeness and exhaustiveness with which a partition represents reality; and (c) the degree of redundancy in the partition structure. This classification is used to characterize three types of granular partitions that play an important role in spatial information science: cadastral partitions, categorical coverages, and the partitions involved in folk categorizations of the geospatial domain.