The Birkhoff Completion of Finite Lattices

被引：0

作者：

Abdulla, Mohammad ^{[1
,2
]}

Hirth, Johannes ^{[1
,2
]}

Stumme, Gerd ^{[1
,2
]}

机构：

[1] Univ Kassel, Knowledge & Data Engn Grp, Kassel, Germany

[2] Univ Kassel, Interdisciplinary Res Ctr Informat Syst Design, Kassel, Germany

来源：

CONCEPTUAL KNOWLEDGE STRUCTURES, CONCEPTS 2024 | 2024年 / 14914卷

关键词：

Formal Concept Analysis; Distributive Lattices; Implicational Theories;

D O I：

10.1007/978-3-031-67868-4_2

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We introduce the Birkhoff completion as the smallest distributive lattice in which a given finite lattice can be embedded as semilattice. 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.

引用

页码：20 / 35

页数：16

共 11 条

[1] The lattices of closure systems, closure operators, and implicational systems on a finite set: a survey [J].