The discovery of interesting patterns in relational databases is an important data mining task. In the framework of descriptive Inductive Logic Progamming (ILP), we present a refinement operator and hypothesis language declaration formalism that successfully combine a function-free first-order hypothesis language with the levelwise search principle. In particular, the hypothesis space is structured by the subset relation between hypotheses, and the refinement operator is based on the candidate generation procedure of the Apriori algorithm which is extended to allow for user-defined constraints on the combinations of literals. Experimental results show the usefulness of the approach.