The Birkhoff completion of finite lattices

2024/05/02 by Abdulla, Mohammad, Hirth, Johannes, Stumme, Gerd · 1 citation
#Artificial Intelligence (cs.AI) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Logic in Computer Science (cs.LO)

paper · doi:10.48550/arxiv.2405.02342

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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