Ken Ueno

On a Sufficient Condition for the Existence of Most Specific Hypothesis in Progol

In this paper, we give a sufficient condition for the existence of the most specific hypothesis (MSH) in Progol. Muggleton [2] showed that for any first order theory (background knowledge) B and a single clause (a positive example) E, there exists the most specific hypothesis ¬bot(B, E) which satisfies B ≈ ¬,bot(B, E) ⊨ E and for any hypothesis H satisfying B ≈ H ⊨ E, H entails bot(B, E) assuming that hypotheses are all single clauses. Yamamoto[8] gave a counter example and indicated that Muggletons proof contains error. He also gave a sufficient condition under which the MSH exists. In this paper, we give another and more realistic sufficient condition to guarantee the existence of the MSH.