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2013 Complementation in Representable Theories of Region-Based Space
Torsten Hahmann, Michael Grüninger
Notre Dame J. Formal Logic 54(2): 177-214 (2013). DOI: 10.1215/00294527-1731344

Abstract

Through contact algebras we study theories of mereotopology in a uniform way that clearly separates mereological from topological concepts. We identify and axiomatize an important subclass of closure mereotopologies (CMT) called unique closure mereotopologies (UCMTs) whose models always have orthocomplemented contact algebras (OCAs), an algebraic counterpart. The notion of MT-representability, a weak form of spatial representability but stronger than topological representability, suffices to prove that spatially representable complete OCAs are pseudocomplemented and satisfy the Stone identity. Within the resulting class of contact algebras the strength of the algebraic complementation delineates two classes of mereotopology according to the key ontological choice between mereological and topological closure operations. All closure operations are defined mereologically if and only if the corresponding contact algebras are uniquely complemented while topological closure operations highly restrict the contact relation but allow not uniquely complemented and nondistributive contact algebras. Each class contains a single ontologically coherent theory that admits discrete models.

Citation

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Torsten Hahmann. Michael Grüninger. "Complementation in Representable Theories of Region-Based Space." Notre Dame J. Formal Logic 54 (2) 177 - 214, 2013. https://doi.org/10.1215/00294527-1731344

Information

Published: 2013
First available in Project Euclid: 21 February 2013

zbMATH: 1262.68164
MathSciNet: MR3028795
Digital Object Identifier: 10.1215/00294527-1731344

Subjects:
Primary: 68T27
Secondary: 06C15, 54H10

Rights: Copyright © 2013 University of Notre Dame

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Vol.54 • No. 2 • 2013
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