*Svetla Boytcheva and Zdravko Markov*

Inductive Logic Programming (ILP) deals with inducing clausal theories from examples basically through generalization or specialization. The specialization and generalization operators used are mainly based on three generality orderings - subsumption, implication and implication relative to background knowledge. Implication is stronger than subsumption, but relative implication is more powerful because background knowledge can be used to model all sorts of useful properties and relations. The least generalization under relative implication (LGRI) does not exist in the general case, but it exists if both the set to be generalized and the background knowledge satisfy some special conditions. The present paper discusses an algorithm for computing LGRI in cases when the latter exists.

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