Bases of closure systems

Kira Adaricheva; J. B. Nation

doi:10.1007/978-3-319-44236-5_6

Bases of closure systems

Kira Adaricheva, J. B. Nation

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

3 Citations (Scopus)

Abstract

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 language	English
Title of host publication	Lattice Theory
Subtitle of host publication	Special Topics and Applications
Publisher	Springer International Publishing
Pages	181-213
Number of pages	33
Volume	2
ISBN (Electronic)	9783319442365
ISBN (Print)	9783319442358
DOIs	https://doi.org/10.1007/978-3-319-44236-5_6
Publication status	Published - Jan 1 2016

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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. https://doi.org/10.1007/978-3-319-44236-5_6

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Access to Document

10.1007/978-3-319-44236-5_6