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Succinctness and tractability of closure operator representations. (English) Zbl 1418.06001

Summary: It is widely known that closure operators on finite sets can be represented by sets of implications (also known as inclusion dependencies) as well as by formal contexts. In this article, we consider these two representation types, as well as generalizations of them: extended implication sets and context families. We discuss the mutual succinctness of these four representations and the tractability of certain operations used to compare and modify closure operators.

MSC:

06A15 Galois correspondences, closure operators (in relation to ordered sets)
68T30 Knowledge representation
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