Journal of Philosophical Logic
, Volume 31, Issue 5, pp 469498
First online:
Elementary Polyhedral Mereotopology
 Ian PrattHartmannAffiliated withDepartment of Computer Science, University of Manchester
 , Dominik SchoopAffiliated withDepartment of Computer Science, University of Manchester
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A regionbased model of physical space is one in which the primitive spatial entities are regions, rather than points, and in which the primitive spatial relations take regions, rather than points, as their relata. Historically, the most intensively investigated regionbased models are those whose primitive relations are topological in character; and the study of the topology of physical space from a regionbased perspective has come to be called mereotopology. This paper concentrates on a mereotopological formalism originally introduced by Whitehead, which employs a single primitive binary relation C(x,y) (read: “x is in contact with y”). Thus, in this formalism, all topological facts supervene on facts about contact. Because of its potential application to theories of qualitative spatial reasoning, Whitehead's primitive has recently been the subject of scrutiny from within the Artificial Intelligence community. Various results regarding the mereotopology of the Euclidean plane have been obtained, settling such issues as expressive power, axiomatization and the existence of alternative models. The contribution of the present paper is to extend some of these results to the mereotopology of threedimensional Euclidean space. Specifically, we show that, in a firstorder setting where variables range over tame subsets of R ^{3}, Whitehead's primitive is maximally expressive for topological relations; and we deduce a corollary constraining the possible regionbased models of the space we inhabit.
 Title
 Elementary Polyhedral Mereotopology
 Journal

Journal of Philosophical Logic
Volume 31, Issue 5 , pp 469498
 Cover Date
 200210
 DOI
 10.1023/A:1020184007550
 Print ISSN
 00223611
 Online ISSN
 15730433
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 mereotopology
 ontology of space
 spatial reasoning
 Authors

 Ian PrattHartmann ^{(1)}
 Dominik Schoop ^{(1)}
 Author Affiliations

 1. Department of Computer Science, University of Manchester, Manchester, M13 9PL, U.K.