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.

翻译：我们引入布尔霍夫完备化，作为能够将给定有限格作为半格嵌入其中的最小分配格。讨论了该完备化与蕴含理论之间的关系，特别是与R. Wille的简单蕴含理论之间的联系。通过实例展示了布尔霍夫完备化如何作为序数数据科学的一种工具。