The Prioritized Inductive Logic Programs

The limit behaviors of an inductive logic program should be an important research topic which has not been explored. An inductive logic program is convergent if given an increasing sequence of example sets, the inductive logic program should produce a corresponding sequence of the Horn logic programs which has the settheoretic limit; limit-correct if the limit of the produced sequence of the Horn logic programs is correct with respect to the limit of the sequence of the example sets. We will show by examples that there exist incremental learning algorithms which are not limit-correct in some cases. A priority order is defined on the literals, and the prioritized version of the learning algorithm is proposed such that the prioritized version is limit-correct with respect to any increasing infinite sequence {Ek} of the positive literal sets.