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.
Axiomatization, Betweenness, Completeness theorem
227-239
Azimipour, Sanaz
b6f3cca5-3fc1-43e3-9c2d-2f87409a37ee
Naumov, Pavel
8b6c40fb-b199-44d5-a8e2-0ebd021566b0
1 February 2021
Azimipour, Sanaz
b6f3cca5-3fc1-43e3-9c2d-2f87409a37ee
Naumov, Pavel
8b6c40fb-b199-44d5-a8e2-0ebd021566b0
Azimipour, Sanaz and Naumov, Pavel
(2021)
Axiomatic Theory of Betweenness.
Archive for Mathematical Logic, 60 (1-2), .
(doi:10.1007/s00153-020-00744-5).
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.
Text
2020-aml
- Accepted Manuscript
More information
Accepted/In Press date: 3 July 2020
e-pub ahead of print date: 13 July 2020
Published date: 1 February 2021
Keywords:
Axiomatization, Betweenness, Completeness theorem
Identifiers
Local EPrints ID: 452124
URI: http://eprints.soton.ac.uk/id/eprint/452124
ISSN: 0933-5846
PURE UUID: 9accc0cf-8db0-47c6-84cf-978f06287435
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Date deposited: 25 Nov 2021 16:46
Last modified: 17 Mar 2024 04:10
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Contributors
Author:
Sanaz Azimipour
Author:
Pavel Naumov
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