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Axiomatic theory of betweenness

Axiomatic theory of betweenness Betweenness as a relation between three individual points has been widely studied in geometry and axiomatized by several authors in different contexts. The article proposes a more general notion of betweenness as a relation between three sets of points. The main technical result is a sound and complete logical system describing universal properties of this relation between sets of vertices of a graph. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Axiomatic theory of betweenness

Azimipour, Sanaz; Naumov, Pavel
Archive for Mathematical Logic , Volume 60 (1-2): 13 – Jul 13, 2020
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References (8)

Publisher
Springer Journals
Copyright
Copyright © Springer-Verlag GmbH Germany, part of Springer Nature 2020
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s00153-020-00744-5
Publisher site
See Article on Publisher Site

Abstract

Betweenness as a relation between three individual points has been widely studied in geometry and axiomatized by several authors in different contexts. The article proposes a more general notion of betweenness as a relation between three sets of points. The main technical result is a sound and complete logical system describing universal properties of this relation between sets of vertices of a graph.

Journal

Archive for Mathematical Logic – Springer Journals

Published: Jul 13, 2020

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