Refining Logic Theories under OI-Implication

We present a framework for theory refinement operators ful- filling properties that ensure the efficiency and effectiveness of the learning process. A refinement operator satisfying these requirements is de- fined ideal. Past results have demonstrated the impossibility of defining ideal operators in search spaces ordered by the logical implication or the θ-subsumption relationships. By assuming the object identity bias over a space defined by a clausal language ordered by logical implication, we obtain OI-implication, a novel ordering relationship, and show that ideal operators can be defined for the resulting search space.