Computing and visualizing closure objects using relation algebra and relview

Abstract

Closure systems and closure operations play an important role in both mathematics and computer science. In addition there are a number of concepts which have been proven to be isomorphic to closure systems and we refer to all such concepts as closure objects. In this work we develop relation-algebraic specifications to recognize several classes of closure objects, compute the complete lattices they constitute and transform any of these closure objects into another. All specifications are algorithmic and can directly be translated into the programming language of the computer algebra system RelView, which is a special purpose tool for computing with relations. We show that the system is well suited for computing and visualizing closure objects and their complete lattices. © 2009 Springer Berlin Heidelberg.