Spaces of Theories with Ideal Refinement Operators

Refinement operators for theories avoid the problems related to the myopia of many relational learning algorithms based on the operators that refine single clauses. However, the non-existence of ideal refinement operators has been proven for the standard clausal search spaces based on 0-subsumption or logical implication, which scales up to the spaces of theories. By adopting different generalization models constrained by the assumption of object identity, we extend the theoretical results on the existence of ideal refinement operators for spaces of clauses to the case of spaces of theories.