Abstract
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 individuals rather than to particular individuals. Since it is the purpose of these standards and ontologies to facilitate interoperability, it is important to give a clear semantics to statements like (1) and (2). For example, (1) should be understood to claim that every waterfall is part of some watercourse, but NOT that every watercourse has a waterfall as its part. In (2), by contrast, the term “part-of” has a stronger meaning: every ecoregion of continental scale is part of some ecoregion of global scale AND every ecoregion of global scale has some ecoregion of continental scale as a part. To overcome this kind of semantic heterogeneity, we propose a Mereotopology for Individuals and Classes (MIC) in which we define parthood, location, and connection relations among classes based on parthood, location, and connection relations between individuals. We then demonstrate the usefulness of this formal theory for making the logical structure of spatial information more precise. Although we focus here on the simplest and most pervasive of the spatial relations (parthood, location, and connection), the strategy employed in this paper can be used in analogous treatments of other kinds of relations among classes.
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References
Asher, N., Vieu, L.: Towards a geometry of commonsense: semantics and a complete axiomatization of mereotopology. In: Proceedings of IJCAI 1995, pp. 846–852. Morgan Kaufmann, San Francisco (1995)
Beck, R., Schulz, S.: Logic-based remodeling of the Digital Anatomist Foundational Model. In: AIMA Annual Symposium Proceedings, pp. 71–75 (2003)
Bittner, T., Donnelly, M., et al.: Individuals, universals, and collections: on the foundational relations of ontology. In: Proceedings of FOIS 2004, pp. 37–48 (2004)
Casati, R., Varzi, A.C.: Parts and Places. MIT Press, Cambridge (1999)
Cleland, D.T., Avers, P.E., et al.: National hierarchical framework of ecological units. In: Boyce, M.S.A.H., Haven, A.W.N. (eds.) Ecosystem Management Applications for Sustainable Forest and Wildlife Resources, pp. 181–200. CT (1997)
Cohn, A.G., Bennett, B., et al.: Qualitative spatial representation and reasoning with the Region Connection Calculus. Geoinformatica 1(3), 1–44 (1997)
Donnelly, M.: A formal theory for reasoning about parthood, connection, and location. Journal of Artificial Intelligence 160, 145–172 (2004)
Donnelly, M.: Relative places. Applied Ontology (2005) (in press)
Donnelly, M., Bittner, T., et al.: A formal theory for spatial representation and reasoning in biomedical ontologies. In: Artificial Intelligence in Medicine (in press)
Levesque, H., Brachman, R.: Fundamental Trade-off in Knowledge Representation and Reasoning. In: Brachman, R., Levesque, H. (eds.) Readings in Knowledge Representation, pp. 41–70. Morgan Kaufmann, Los Altos (1985)
McNab, W.H., Avers, P.E.: Ecological subregions of the United States, WO-WSA-5 (1994), http://www.fs.fed.us/land/pubs/ecoregions/index.html
Mejino, J.L.V., Agoncillo, A.V., et al.: Representing complexity in part-whole relationships within the Foundational Model of Anatomy. In: Proceedings of the American Medical Informatics Association Fall Symposium, pp. 450–454 (2003)
Rector, A.L., Rogers, J.E.: Ontological issues in using a description logic to represent medical concepts: experience from GALEN: part 1 - principles. In: Methods of Information in Medicine (2002a)
Rector, A.L., Rogers, J.E.: Ontological issues in using a description logic to represent medical concepts: experience from GALEN: part II - the GALEN high level schemas. In: Methods of Information in Medicine (2002b)
Rogers, J., Rector, A.: GALEN’s model of parts and wholes: experience and comparisons. In: Proceedings of the AMIA Symp 2000, pp. 714–718 (2000)
Rosse, C., Mejino, J.L.V.: A reference ontology for bioinformatics: the Foundational Model of Anatomy. Journal of Biomedical Informatics 36, 478–500 (2003)
SDTS, American national standard for information systems - Spatial Data Transfer Standard (SDTS) (1997), http://mcmcweb.er.usgs.gov/sdts/standard.html
Smith, B., Ceusters, W., et al.: Relations in biomedical ontologies. Genome Biology (2005) (in press)
Smith, B., Rosse, C.: The role of foundational relations in the alignment of biomedical ontologies. In: Fieschi, M., Coiera, E., Li, Y.J. (eds.) Proceedings of the 11th World Congress on Medical Informatics, pp. 444–448 (2003)
Sorokine, A., Bittner, T.: Understanding taxonomies of ecosystems: a case study. In: Fisher, P. (ed.) Developments in Spatial Data Handling, pp. 559–572 (2005)
Sorokine, A., Bittner, T., et al.: Ontological Investigation of Ecosystem Hierarchies and Formal Theory for Multiscale Ecosystem Classifications. In: Proceedings of GI-Science (2004)
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Donnelly, M., Bittner, T. (2005). Spatial Relations Between Classes of Individuals. In: Cohn, A.G., Mark, D.M. (eds) Spatial Information Theory. COSIT 2005. Lecture Notes in Computer Science, vol 3693. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11556114_12
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DOI: https://doi.org/10.1007/11556114_12
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