Mining association rules is an important problem in Knowledge Extraction (KE). This paper proposes an efficient method for mining simultaneously informative positive and negative association rules, using a new selective pair support-$$M_{GK}$$. For this, we define four new bases of positive and negative association rules, based on Galois connection semantics. These bases are characterized by frequent closed itemsets, maximal frequent itemsets, and their generator itemsets; it consists of the non-redundant exact and approximate association rules having minimal premise and maximal conclusion, i.e. the informative association rules. We introduce Nonred algorithm allowing to generate these bases and all valid informative association rules. Results experiments carried out on reference datasets show the usefulness of this approach.