In the Semantic Web, OWL ontologies play the key role of domain conceptualizations, while the corresponding assertional knowledge is given by the heterogeneous Web resources referring to them. However, being strongly decoupled, ontologies and assertional knowledge can be out of sync. In particular, an ontology may be incomplete, noisy, and sometimes inconsistent with the actual usage of its conceptual vocabulary in the assertions. Despite of such problematic situations, we aim at discovering hidden knowledge patterns from ontological knowledge bases, in the form of multi-relational association rules, by exploiting the evidence coming from the (evolving) assertional data. The final goal is to make use of such patterns for (semi-)automatically enriching/completing existing ontologies. An evolutionary search method applied to populated ontological knowledge bases is proposed for the purpose. The method is able to mine intensional and assertional knowledge by exploiting problem-aware genetic operators, echoing the refinement operators of inductive logic programming, and by taking intensional knowledge into account, which allows to restrict the search space and direct the evolutionary process. The discovered rules are represented in SWRL, so that they can be straightforwardly integrated within the ontology, thus enriching its expressive power and augmenting the assertional knowledge that can be derived from it. Discovered rules may also suggest new (schema) axioms to be added to the ontology. We performed experiments on publicly available ontologies, validating the performances of our approach and comparing them with the main state-of-the-art systems.