We introduce the Birkhoff completion as the smallest dis-
tributive 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.
%0 Journal Article
%1 abdulla2024birkhoff
%A Abdulla, Mohammad
%A Hirth, Johannes
%A Stumme, Gerd
%D 2024
%K fca myown
%T The Birkhoff completion of finite lattices
%X We introduce the Birkhoff completion as the smallest dis-
tributive 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.
@article{abdulla2024birkhoff,
abstract = {We introduce the Birkhoff completion as the smallest dis-
tributive 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.},
added-at = {2024-04-17T10:15:39.000+0200},
author = {Abdulla, Mohammad and Hirth, Johannes and Stumme, Gerd},
biburl = {https://www.bibsonomy.org/bibtex/259749eb2797ad9ae2118a0743f57f5af/hirth},
interhash = {355b596181c1da2be951cc376f8bdf9d},
intrahash = {59749eb2797ad9ae2118a0743f57f5af},
keywords = {fca myown},
timestamp = {2024-04-17T10:15:51.000+0200},
title = {The Birkhoff completion of finite lattices},
year = 2024
}