The Birkhoff completion of finite lattices

Mohammad Abdulla, Johannes Hirth, Gerd Stumme
5/2/2024
cs.DMcs.AIcs.LO

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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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Cite this paper

@article{abdulla2024birkhoff,
  title  = {The Birkhoff completion of finite lattices},
  author = {Mohammad Abdulla and Johannes Hirth and Gerd Stumme},
  year   = {2024},
  eprint = {2405.02342},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2405.02342v1}
}

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