An overview of contemporary part-whole theories, with reference to both their axiomatic developments and their philosophical underpinnings.

A critical survey of the fundamental philosophical issues in the logic and formal ontology of space, with special emphasis on the interplay between mereology (the theory of parthood relations), topology (broadly understood as a theory of qualitative spatial relations such as continuity and contiguity), and the theory of spatial location proper.

To enhance the treatment of relations in biomedical ontologies we advance a methodology for providing consistent and unambiguous formal definitions of the relational expressions used in such ontologies in a way designed to assist developers and users in avoiding errors in coding and annotation. The resulting Relation Ontology can promote interoperability of ontologies and support new types of automated reasoning about the spatial and temporal dimensions of biological and medical phenomena.

We analyze and compare geometrical theories based on mereology (mereogeometries). Most theories in this area lack in formalization, and this prevents any systematic logical analysis. To overcome this problem, we concentrate on specific interpretations for the primitives and use them to isolate comparable models for each theory. Relying on the chosen interpretations, we introduce the notion of environment structure, that is, a minimal structure that contains a (sub)structure for each theory. In particular, in the case of mereogeometries, the domain of (...) an environment structure is composed of particular subsets of Rn. The comparison of mereogeometrical theories within these environment structures shows dependencies among primitives and provides (relative) definitional equivalences. With one exception, we show that all the theories considered are equivalent in these environment structures. (shrink)

A taxonomy of part‐whole or meronymic relations is developed to explain the ordinary English‐speaker's use of the term “part of” and its cognates. The resulting classification yields six types of meronymic relations: 1. component‐integral object (pedal‐bike), 2. member‐collection (ship‐fleet), 3. portion‐mass (slice‐pie), 4. stuff‐object (steel‐car), 5. feature‐activity (paying‐shopping), and 6. place‐area (Everglades‐Florida). Meronymic relations ore further distinguished from other inclusion relations, such as spatial inclusion, and class inclusion, and from several other semantic relations: attribution, attachment, and ownership. This taxonomy is (...) then used to explain cases of apparent intransitivity in merological syllogisms, and standard form syllogisms whose premises express different inclusion relations. The data suggest that intransitivities arise due to equivocations between different types of semantic relations. These results are then explained by means of the relation element theory which accounts for the character and behavior of semantic relations in terms of more primitive relational elements. The inferential phenomena observed are then explained by means of a single principle of element matching. (shrink)