Bases of closure systems

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.