Perfect refinement operators can be flexible

A (weakly) perfect ILP refinement operator was described in [I]. It's main disadvantage however is that it is static and inflexible: for ensuring non-redundancy, some refinements of a hypothesis are disallowed in advance, regardless of the search heuristic which may recommend their immediate exploration. (Similar problems are faced by Progol and other complete and non-redundant systems). On the other hand, there are systems, like FOIL, which give up completeness for maximum flexibility. But if the heuristic fails to guide the search to a solution, such a system cannot rely on a complete refinement operator to explore alternative paths. In this paper we construct a dynamically perfect refinement operator which combines the advantages of completeness, non-redundancy and flexibility, and which represents one of the best tractable ILP operators one can hope for.