English

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}
}