| Issue |
RAIRO-Theor. Inf. Appl.
Volume 54, 2020
|
|
|---|---|---|
| Article Number | 7 | |
| Number of page(s) | 10 | |
| DOI | https://doi.org/10.1051/ita/2020007 | |
| Published online | 16 December 2020 | |
Betweenness of partial orders
LaBRI, CNRS and Bordeaux University,
33405
Talence, France.
* Corresponding author: courcell@labri.fr
Received:
20
April
2020
Accepted:
19
November
2020
We construct a monadic second-order sentence that characterizes the ternary relations that are the betweenness relations of finite or infinite partial orders. We prove that no first-order sentence can do that. We characterize the partial orders that can be reconstructed from their betweenness relations. We propose a polynomial time algorithm that tests if a finite relation is the betweenness of a partial order.
Mathematics Subject Classification: 06A06 / 03B10 / 03C13 / 03C15
Key words: Betweenness / partial order / axiomatization / monadic second-order logic / comparability graph
© The authors. Published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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