Abstract : In this paper, we address the problem of the usefulness of the set of discovered association rules. This problem is important since real-life databases yield most of the time several thousands of rules with high conﬁdence. We propose new algorithms based on Galois closed sets to reduce the extraction to small covers (or bases) for exact and approximate rules, adapted from lattice theory and data analysis domain. Once frequent closed itemsets – which constitute a generating set for both frequent itemsets and association rules – have been discovered, no additional database pass is needed to derive these bases. Experiments conducted on real-life databases show that these algorithms are efﬁcient and valuable in practice.