Constraint Inductive Logic Programming and Its Application to Knowledge Discovery in Databases

this paper, hence not very relevant to KDD. We think that the idea of CILP can be applied to the standard Empirical ILP problem and various ILP techniques: Least General Generalization Relative to Background Knowledge (rlgg) [6], Inverse Resolution [7], Top-Down Specialization [10], etc. Let us look at the Inverse Resolution technique as a case study. This method consists of backward proof steps. An ordinary resolution step takes two clauses C 1 and C 2 and resolves them to produce the resolvent C: Then an inverse resolution step takes C (could be a positive example) and C 1 (could be a piece of background knowledge) and produces C 2 (could be a hypothesis). Certainly the hypothesis C 2 will cover the positive example C; but may fail to reject some negative examples. In CILP, instead of giving up the hypothesis C 2 ; we may add some constraints to the body of the clause C 2 so that it rejects the negative examples while still covering the positive example. For example, suppose we have positive example p(5; 15) and negative exampl