Constructing Reenement Operators by Decomposing Logical Implication

Inductive learning models 14] 17] often use a search space of clauses, ordered by a generalization hierarchy. To nd solutions in the model, search algorithms use diierent generalization and specialization operators. In this article we will decompose the quasi-ordering induced by logical implication into six increasingly weak orderings. The diierence between two successive orderings will be small, and can therefore be understood easily. Using this decomposition, we will describe upward and downward reenement operators for all orderings, including-subsumption and logical implication.