Notre Dame Journal of Formal Logic

Ontologies for Plane, Polygonal Mereotopology

Abstract

Several authors have suggested that a more parsimonious and conceptually elegant treatment of everyday mereological and topological reasoning can be obtained by adopting a spatial ontology in which regions, not points, are the primitive entities. This paper challenges this suggestion for mereotopological reasoning in two-dimensional space. Our strategy is to define a mereotopological language together with a familiar, point-based interpretation. It is proposed that, to be practically useful, any alternative region-based spatial ontology must support the same sentences in our language as this familiar interpretation. This proposal has the merit of transforming a vague, open-ended question about ontologies for practical mereotopological reasoning into a precise question in model theory. We show that (a version of) the familiar interpretation is countable and atomic, and therefore prime. We conclude that useful alternative ontologies of the plane are, if anything, less parsimonious than the one which they are supposed to replace.

Article information

Source
Notre Dame J. Formal Logic Volume 38, Number 2 (1997), 225-245.

Dates
First available in Project Euclid: 12 December 2002

http://projecteuclid.org/euclid.ndjfl/1039724888

Digital Object Identifier
doi:10.1305/ndjfl/1039724888

Mathematical Reviews number (MathSciNet)
MR1489411

Zentralblatt MATH identifier
0897.03014

Citation

Pratt, Ian; Lemon, Oliver. Ontologies for Plane, Polygonal Mereotopology. Notre Dame J. Formal Logic 38 (1997), no. 2, 225--245. doi:10.1305/ndjfl/1039724888. http://projecteuclid.org/euclid.ndjfl/1039724888.

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