Bases of closure systems

Kira Adaricheva, J. B. Nation

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)


In Section 4-2.2 we discussed the fundamental connection between closure systems and sets of implications. In this chapter, we will look into the canonical forms of representations of a closure system by implications. Most of the results are inspired by the structure of the closure lattice and its properties. In particular, we will be concerned with effective representations of closure systems whose closure lattices are join-semidistributive, lower bounded or locally distributive.

Original languageEnglish
Title of host publicationLattice Theory
Subtitle of host publicationSpecial Topics and Applications
PublisherSpringer International Publishing
Number of pages33
ISBN (Electronic)9783319442365
ISBN (Print)9783319442358
Publication statusPublished - Jan 1 2016


ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Adaricheva, K., & Nation, J. B. (2016). Bases of closure systems. In Lattice Theory: Special Topics and Applications (Vol. 2, pp. 181-213). Springer International Publishing.