Thomas Bittner

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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)
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)
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)
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(More)
Parthood, componenthood, and containment relations are commonly assumed in biomedical ontologies and terminology systems, but are not usually clearly distinguished from another. This paper contributes towards a unified theory of parthood, componenthood, and containment relations. Our goal in this is to clarify distinctions between these relations as well as(More)
Reasoning about the location of regions in 2-dimensional space is necessarily based on finite approximations to such regions. These finite approximations are often derived by describing how a region (the figure) relates to a frame of reference (the ground). The frame of reference generally consists of regions, or cells, forming a partition of the space(More)
We propose an ontological theory that is powerful enough to describe both complex spatio-temporal processes (occurrents) and the enduring entities (continuants) that participate therein. The theory is divided into two major categories of sub-theories: (sub-) theories of type SPAN and (sub-)theories of type SNAP. These theories represent two complementary(More)
In the Spatial Data Transfer Standard and many other geographic standards and ontologies, we find statements such as (1) “waterfalls are parts of watercourses” and (2) “ecoregions of continental scale are parts of ecoregions of global scale”, etc. In these examples, the terms “waterfall”, “watercourse”, “ecoregion of scale X”, etc. refer to classes of(More)