The Birkhoff completion of finite lattices
This work addresses a theoretical problem in lattice theory with potential applications in data science, but it appears incremental as it builds on existing concepts like implicational theories.
The paper introduces the Birkhoff completion as the smallest distributive lattice for embedding finite lattices as semi-lattices, and demonstrates its application as a tool for ordinal data science through an example.
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.