This paper presents the concept of the disjunctive bottom set and discusses its computation. The disjunctive bottom set differs from existing extensions of the bottom set, such as kernel sets, by being the weakest minimal single hypothesis for the whole hypothesis space. The disjunctive bottom set may be characterized in terms of minimal models. Therefore, as minimal models can be computed in polynomial space complexity, so can the disjunctive bottom set. We outline a flexible inductive logic programming framework based on the disjunctive bottom set. Compared with existing systems based on bottom set, such as Progol, it can probe an enlarged hypothesis space without increasing space complexity. Another novelty of the framework is that it provides an avenue, via hypothesis selection function, for the integration of more advanced hypothesis selection mechanisms.