RAIRO-Theor. Inf. Appl.
Volume 54, 2020
|Number of page(s)||10|
|Published online||16 December 2020|
Betweenness of partial orders
LaBRI, CNRS and Bordeaux University,
* Corresponding author: firstname.lastname@example.org
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
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