The condition of covering in the definition of generalized subsumption has the effect, that generalization depends on the actual representation of the clauses. Defining generalization in terms of implication (see Plotkin's definition [\protect\citeauthoryearPlotkin1971]) instead of subset-relation would be more suitable. This would lead to a combination of techniques from inductive logic programming (ILP) and explanation-based learning (EBL) [\protect\citeauthoryearMooney and Zelle1994] by using deduction when deciding the generalization of clauses.
Unfortunately, doing so, the test for generalization becomes undecidable. On the other hand, Buntine states that generalized subsumption is semidecidable, although it is guaranteed to terminate if contains no recursion. Generalized subsumption w.r.t. a DATALOG program, however, is decidable.
Also, for practical applications, least general generalization as defined by [\protect\citeauthoryearPlotkin1970] can still be too general. Consider the least generalization of the two literals additive(ppn_1060, fluent) and additive(r_5320, flame-retardent) for which we get the very general term additive(X,Y) loosing nearly all information from and connection to the original terms that have been generalized.
Thus, in order to overcome the problems raised by theory revision with background knowledge, namely its undecidability and its results being too general, we study two approaches in the following: