The problem of the relevance and the usefulness of extracted association rules is becoming of primary importance, since an overwhelming number of association rules may be derived from even reasonably sized real-life databases. In this paper, we introduce a novel generic base of association rules, based on the Galois connection semantics. The novel generic base is sound and informative. We also present a sound axiomatic system, allowing to derive all association rules that can be drawn from an extraction context.