Ontologies for Plane, Polygonal Mereotopology

Notre Dame Journal of Formal Logic 38 (2):225-245 (1997)
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
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David Bostock (2010). Whitehead and Russell on Points. Philosophia Mathematica 18 (1):1-52.
Stefano Borgo & Claudio Masolo (2010). Full Mereogeometries. Review of Symbolic Logic 3 (4):521-567.
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