Hypothesis finding based on upward refinement of residue hypotheses

For given logical formulae B and E such that B n E, hypothesis finding means the generation of a formula H such that B ∧ H ⊧ E. Hypothesis finding constitutes a basic technique for fields of inference, like inductive inference and knowledge discovery. In order to put various hypothesis finding methods proposed previously on one general ground, we use upward refinement and residue hypotheses. We show that their combination is a complete method for solving any hypothesis finding problem in clausal logic. We extend the relative subsumption relation, and show that some hypothesis finding methods previously presented can be regarded as finding hypotheses which subsume examples relative to a given background theory. Noting that the weakening rule may make hypothesis finding difficult to solve, we propose restricting this rule either to the inverse of resolution or to that of subsumption. We also note that this work is related to relevant logic.