Bases of Closure Systems

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.

Authors and Affiliations

1. School of Science and Technology, Nazarbayev University, 53 Kabanbay Batyr Ave, 010000, Astana, Kazakhstan

   K. Adaricheva

2. Department of Mathematics, University of Hawaii, 2565 McCarthy Mall, 96822, Honolulu, Hawaii, USA

   J. B. Nation

Editors and Affiliations

1. Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada

   George Grätzer

2. Department of Mathematics, University of Caen, Caen, France

   Friedrich Wehrung

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