We study the inference on the interesting association rules. Then we define the concept of the representative basis for interesting association rules extracted from a dataset D, and an inference system, which is purely qualitative. We show that (i) all association rules derived from the representative basis using the inference system are interesting, and (ii) all interesting association rules (extracted from D) can be derived from the representative basis, using the inference system, without any computation of confidences or supports. The uniqueness and the minimality of the representative basis, and relationships with other concepts of bases are studied. Keywords : Data mining, association rules.