Axiomatic Theory of Betweenness
Logic
2020-06-16 v2
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.
Keywords
Cite
@article{arxiv.1902.00847,
title = {Axiomatic Theory of Betweenness},
author = {Sanaz Azimipour and Pavel Naumov},
journal= {arXiv preprint arXiv:1902.00847},
year = {2020}
}