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2010 Point-free Foundation of Geometry and Multivalued Logic
Cristina Coppola, Giangiacomo Gerla, Annamaria Miranda
Notre Dame J. Formal Logic 51(3): 383-405 (2010). DOI: 10.1215/00294527-2010-024

Abstract

Whitehead, in two basic books, considers two different approaches to point-free geometry: the inclusion-based approach, whose primitive notions are regions and inclusion relation between regions, and the connection-based approach, where the connection relation is considered instead of the inclusion. We show that the latter cannot be reduced to the first one, although this can be done in the framework of multivalued logics.

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Cristina Coppola. Giangiacomo Gerla. Annamaria Miranda. "Point-free Foundation of Geometry and Multivalued Logic." Notre Dame J. Formal Logic 51 (3) 383 - 405, 2010. https://doi.org/10.1215/00294527-2010-024

Information

Published: 2010
First available in Project Euclid: 18 August 2010

zbMATH: 1194.03019
MathSciNet: MR2675690
Digital Object Identifier: 10.1215/00294527-2010-024

Subjects:
Primary: 03B30 , 18A15
Secondary: 54E99

Keywords: foundation of geometry , multivalued logic , point-free geometry , Whitehead

Rights: Copyright © 2010 University of Notre Dame

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Vol.51 • No. 3 • 2010
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