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arXiv · 2405.02342

The Birkhoff completion of finite lattices

Mohammad Abdulla·Johannes Hirth·Gerd Stumme
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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.

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Mohammad Abdulla, Johannes Hirth, Gerd Stumme. 2024-05-02. The Birkhoff completion of finite lattices. https://arxiv.org/abs/2405.02342

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