Axiomatic theory of betweenness

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Archive for Mathematical Logic 60 (1):227-239 (2020)
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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.

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2021

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10.1007/s00153-020-00744-5

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Pavel Naumov
University of Southampton

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References found in this work

Introduction to mathematical logic.Elliott Mendelson - 1964 - Princeton, N.J.,: Van Nostrand.
The Foundations of Geometry.David Hilbert - 1899 - Open Court Company (This Edition Published 1921).
Logic of secrets in collaboration networks.Sara More & Pavel Naumov - 2011 - Annals of Pure and Applied Logic 162 (12):959-969.
Logic of secrets in collaboration networks.Sara Miner More & Pavel Naumov - 2011 - Annals of Pure and Applied Logic 162 (12):959-969.

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