Open Access
Spring 1997 Ontologies for Plane, Polygonal Mereotopology
Oliver Lemon, Ian Pratt
Notre Dame J. Formal Logic 38(2): 225-245 (Spring 1997). DOI: 10.1305/ndjfl/1039724888


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.


Download Citation

Oliver Lemon. Ian Pratt. "Ontologies for Plane, Polygonal Mereotopology." Notre Dame J. Formal Logic 38 (2) 225 - 245, Spring 1997.


Published: Spring 1997
First available in Project Euclid: 12 December 2002

zbMATH: 0897.03014
MathSciNet: MR1489411
Digital Object Identifier: 10.1305/ndjfl/1039724888

Primary: 03B30
Secondary: 03C65

Rights: Copyright © 1997 University of Notre Dame

Vol.38 • No. 2 • Spring 1997
Back to Top