Loading [a11y]/accessibility-menu.js
Lattice Data Analytics: The Poset of Irreducibles and the MacNeille Completion | IEEE Conference Publication | IEEE Xplore
Scheduled Maintenance: On Monday, 27 January, the IEEE Xplore Author Profile management portal will undergo scheduled maintenance from 9:00-11:00 AM ET (1400-1600 UTC). During this time, access to the portal will be unavailable. We apologize for any inconvenience.

Lattice Data Analytics: The Poset of Irreducibles and the MacNeille Completion


Abstract:

Automated and semi-automated systems that derive actionable information from massive, heterogeneous datasets are essential for many applications. The reasoning of such sy...Show More

Abstract:

Automated and semi-automated systems that derive actionable information from massive, heterogeneous datasets are essential for many applications. The reasoning of such systems must be as clear as possible in order to earn our trust. Lattices have begun to play a key role in computer science finding applications in distributed computing, programming languages, concurrency theory, and data mining, thereby justifying G. C. Rota's belief that lattice theory will play an important role in 21st Century mathematics [1]. In some instances, researchers must deal with posets that are not necessarily lattices and the question arises how these posets can be embedded in lattices. A classic way to answer this question is to construct the MacNeille completion of the lattice, which is the most compact way to embed a poset into a lattice. In 1973 G. Markowsky introduced the poset of irreducibles construction in his dissertation and demonstrated that this was a very compact way to represent a lattice. In addition, the poset of irreducibles has many of the properties of the poset of join-irreducibles of distributive lattices that was introduced by G. Birkhoff and described in his book [2]. In this paper, we show how to construct the poset of irreducibles for the MacNeille completion of a poset efficiently. We conclude with some applications of these ideas.
Date of Conference: 18-21 September 2019
Date Added to IEEE Xplore: 05 December 2019
ISBN Information:
Conference Location: Metz, France

References

References is not available for this document.