Ideal Refinement of Datalog Clauses Using Primary Keys

Inductive Logic Programming (ILP) algorithms are frequently used to data mine multi-relational databases. However, in many ILP algorithms the use of primary key constraints is limited. We show how primary key constraints can be incorporated in a downward refinement operator. This refinement operator is proved to be finite, complete, proper and therefore ideal for clausal languages defined by primary keys. As part of our setup, we introduce a weak Object Identity subsumption relation between clauses which generalizes over traditional, full Object Identity. We find that the restrictions on the language and the subsumption relation are not very restrictive. We demonstrate the feasibility of our setup by showing how the refinement operator can be incorporated in the refinement strategy of common ILP algorithms.