A Re-De nition of Least Generalizations, and Construction Modes as a New Declarative Bias for ILP

The classical deenition of the concept of least generalization of a clause set C is that it is a single clause. Since such a unique clause is sometimes over-general, we re-deene this concept as being a minimal-sized set of clauses, each member of this set being the classical least generalization of some subset of C. The elements of these subsets are two by two compatible, in the sense that their classical least generalizations are not too general according to some over-generality criterion. We give an algorithm for computing this re-deened concept, providing thus a new approach to disjunctive concept learning. The criterion for over-generality is problem-speciic. We introduce a new such criterion: two clauses are compatible, i.e., their classical least generalization is not over-general, if this least generalization is admissible wrt a construction mode capturing the required dataaow of each involved relation. We design a language for expressing such construction modes, and we deene a powerful admissibility criterion. We also prove a few theorems relating the problem-independent concept of compatibility with the problem-speciic concept of admissibility (our over-generality criterion): these theorems show how to speed up certain computations for these concepts. Finally, we outline an application of these considerations to a frequently occurring problem in the inductive synthesis of recursive (logic) programs, namely the induction of the operator combining the partial results (obtained through recursion) into the overall result.