An inference method for the complete inverse of relative subsumption
We propose in this paper an inference method called Bottom Generalization for Inductive Logic Programming (ILP, for short). We give an inference procedure based on it, and prove that a hypothesis clause H is derived by the procedure from an example E under a background theory B iff H subsumes E relative to B in Plotkin's sense. The theory B can be any clausal theory, and the example E can be any clause which is not implied by B. The derived hypothesis H is a clause, but is not always definite. The result is proved by defining a declarative semantics for arbitrary consistent clausal theories, and showing that SE-resolution, which was originally introduced by Plotkin, gives their complete procedural semantics. We also show that Bottom Generalization is more powerful than both Jung's method based on the V-operator and Saturant Generalization by Rouveirol, but not than Inverse Entailment by Muggleton. At the ILP '97 workshop we called our inference method "Inverse Entailment," but we have renamed it "Bottom Generalization" because we found that it differs from the original definition of Inverse Entailment.
relative subsumption bottom generalization inductive logic programming the v-operator saturant generalization inverse entailment