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2008 Approximate Similarities and Poincaré Paradox
Giangiacomo Gerla
Notre Dame J. Formal Logic 49(2): 203-226 (2008). DOI: 10.1215/00294527-2008-008

Abstract

De Cock and Kerre, in considering Poincaré paradox, observed that the intuitive notion of "approximate similarity" cannot be adequately represented by the fuzzy equivalence relations. In this note we argue that the deduction apparatus of fuzzy logic gives adequate tools with which to face the question. Indeed, a first-order theory is proposed whose fuzzy models are plausible candidates for the notion of approximate similarity. A connection between these structures and the point-free metric spaces is also established.

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Giangiacomo Gerla. "Approximate Similarities and Poincaré Paradox." Notre Dame J. Formal Logic 49 (2) 203 - 226, 2008. https://doi.org/10.1215/00294527-2008-008

Information

Published: 2008
First available in Project Euclid: 15 May 2008

zbMATH: 1144.03022
MathSciNet: MR2402042
Digital Object Identifier: 10.1215/00294527-2008-008

Subjects:
Primary: 03A05 , 03B52

Keywords: approximate reasoning , fuzzy equivalence, , , , Poincaré paradox , point-free geometry

Rights: Copyright © 2008 University of Notre Dame

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