The Birkhoff completion of finite lattices
Discrete Mathematics
2024-05-07 v1 Artificial Intelligence
Logic in Computer Science
Abstract
We introduce the Birkhoff completion as the smallest distributive lattice in which a given finite lattice can be embedded as semi-lattice. We discuss its relationship to implicational theories, in particular to R. Wille's simply-implicational theories. By an example, we show how the Birkhoff completion can be used as a tool for ordinal data science.
Keywords
Cite
@article{arxiv.2405.02342,
title = {The Birkhoff completion of finite lattices},
author = {Mohammad Abdulla and Johannes Hirth and Gerd Stumme},
journal= {arXiv preprint arXiv:2405.02342},
year = {2024}
}