Generalization under Implication by

The present paper discusses a generalization operator based on the-subsumption ordering between Horn clauses introduced by the author elsewhere. It has been shown that-subsumption is strictly stronger than-subsumption and a local equivalent of generalized subsumption. With some language restrictions it is decidable and possesses some other useful properties. Most importantly it allows deening a non-trivial upper bound of the-subsumption generalization hierarchy without the use of negative examples. Consequently this allows solving a version of the ILP task with positive-only examples.