Inductive Logic Programming (ILP) is frequently used to data mine in multi-relational databases. However, most ILP algorithms disregard primary key information which is often available for such databases. This work demonstrates several disadvantages of the mode refinement operator that has been used in many multi-relational data mining algorithms in combination with both traditional subsumption and subsumption under Object Identity. We show how primary key information can be incorporated in this refinement operator and provide evidence that the resulting operator has several desirable properties in comparison with the traditional approaches. Especially, we will show that our refinement operator is proper.