Paper ID: 2405.02342

The Birkhoff completion of finite lattices

Mohammad Abdulla, Johannes Hirth, Gerd Stumme

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.

Submitted: May 2, 2024