# The Birkhoff completion of finite lattices

arXiv: https://arxiv.org/abs/2405.02342 · HTML: https://mlsanity.com/paper/2405.02342/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 12 references that are in the map.
- First posted on arXiv 2 May 2024.

## Built on by (most cited first, 1 of 1)

- [Rises for Measuring Local Distributivity in Lattices](https://mlsanity.com/paper/2506.23168/) (2025)

## Abstract (arXiv)

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.