Foundations of Inductive Logic Programming
Foundations of Inductive Logic Programming
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Refinement Operators Can Be (Weakly) Perfect
ILP '99 Proceedings of the 9th International Workshop on Inductive Logic Programming
Searching the Subsumption Lattice by a Genetic Algorithm
ILP '00 Proceedings of the 10th International Conference on Inductive Logic Programming
Learning from good data and bad
Learning from good data and bad
On generalization and subsumption for ordered clauses
JSAI'05 Proceedings of the 2005 international conference on New Frontiers in Artificial Intelligence
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ILP systems which use some form of Inverse Entailment (IE) are based on clause refinement through a hypotheses space bounded by a most specific clause. In this paper we give a new analysis of refinement operators in this setting. In particular, Progol's refinement operator is revisited and discussed. It is known that Progol's refinement operator is incomplete with respect to the general subsumption order. We introduce a subsumption order relative to a most specific (bottom) clause. This subsumption order, unlike previously suggested orders, characterises Progol's refinement space. We study the properties of this subsumption order and show that ideal refinement operators exist for this order. It is shown that efficient operators can be implemented for least generalisation and greatest specialisation in the subsumption order relative to a bottom clause. We also study less restricted subsumption orders relative to a bottom clause and show how Progol's incompleteness can be addressed.