In fields such as medicine, geography, and mechanics, spatial reasoning involves reasoning about entities that may coincide without overlapping. Some examples are: cavities and invading particles, passageways and valves, geographic regions and tropical storms. The purpose of this paper is to develop a formal theory of spatial relations for domains that include coincident entities. The core of the theory is a clear distinction between mereotopological relations, such as parthood and connection, and relative location relations, such as coincidence. To guide the (...) development of the formal theory, I construct mathematical models in which nontrivial relative location relations are defined. (shrink)

The Foundational Model of Anatomy (FMA) symbolically represents the structural organization of the human body from the macromolecular to the macroscopic levels, with the goal of providing a robust and consistent scheme for classifying anatomical entities that is designed to serve as a reference ontology in biomedical informatics. Here we articulate the need for formally clarifying the is-a and part-of relations in the FMA and similar ontology and terminology systems. We diagnose certain characteristic errors in the treatment of these relations (...) and show how these errors can be avoided through adoption of the formalism we describe. We then illustrate how a consistently applied formal treatment of taxonomy and partonomy can support the alignment of ontologies. (shrink)