Hybrid abductive inductive learning: A generalisation of Progol

Abstract

Abstract. The learning system Progol5 and the underlying inference method of Bottom Generalisation are rmly established within Induc-tive Logic Programming (ILP). But despite their success, it is known that Bottom Generalisation, and therefore Progol5, are restricted to nding hypotheses that lie within the semantics of Plotkin's relative sub-sumption. This paper exposes a previously unknown incompleteness of Progol5 with respect to Bottom Generalisation, and proposes a new ap-proach, called Hybrid Abductive Inductive Learning, that integrates the ILP principles of Progol5 with Abductive Logic Programming (ALP). A proof procedure is proposed, called HAIL, that not only overcomes this newly discovered incompleteness, but further generalises Progol5 by computing multiple clauses in response to a single seed example and de-riving hypotheses outside Plotkin's relative subsumption. A semantics is presented, called Kernel Generalisation, which extends that of Bottom Generalisation and includes the hypotheses constructed by HAIL.