Learn More
A granular partition is a way of dividing up, or classifying, or mapping a certain portion of reality. We characterize partitions at two levels: as systems of cells and subcells, and in terms of their relation to reality. We define a notion of well-formedness for partitions, and we give an account of what it means for a partition to project onto objects in(More)
OBJECTIVE The objective of this paper is to demonstrate how a formal spatial theory can be used as an important tool for disambiguating the spatial information embodied in biomedical ontologies and for enhancing their automatic reasoning capabilities. METHOD AND MATERIALS This paper presents a formal theory of parthood and location relations among(More)
Reasoning about the location of regions in 2-dimensional space is necessarily based on nite approximations to such regions. These nite approximations are often derived by describing how a region (the gure) relates to a frame of reference (the ground). The frame of reference generally consists of regions, or cells, forming a partition of the space under(More)
Bridging levels of "granularity" and "scale" are frequently cited as key problems for biomedical informatics. However, detailed accounts of what is meant by these terms are sparse in the literature. We argue for distinguishing two notions: "size range," which deals with physical size, and "collectivity," which deals with aggregations of individuals into(More)
Parthood, componenthood, and containment relations are commonly assumed in biomedical ontolo-gies and terminology systems, but are not usually clearly distinguished from another. This paper contributes towards a unified theory of parthood, com-ponenthood, and containment relations. Our goal in this is to clarify distinctions between these relations as well(More)
This paper proposes a qualitative coordinate language of regional individuals. It is shown that representing a configuration of regions using a coordinate language of regional individuals supports a primary breakup of a spatial configuration into primary objects of focus and secondary objects of reference, i.e., in figure and ground. We define the notion of(More)
The relationship between less detailed and more detailed versions of data is one of the major issues in processing geographic information. Fundamental to much work in model-oriented generalization, also called semantic generalization , is the notion of an equivalence relation. Given an equivalence relation on a set, the techniques of rough set theory can be(More)
This paper provides an axiomatic formalization of a theory of foundational relations between three categories of entities: individuals, universals, and collections. We deal with a variety of relations between entities in these categories, including the is-a relation among universals and the part-of relation among individuals as well as cross-category(More)