Induction on Failure: Learning Connected Horn Theories

Abstract

Several learning systems based on Inverse Entailment (IE) have been proposed, some that compute single clause hypotheses, exemplified by Progol, and others that produce multiple clauses in response to a single seed example. A common denominator of these systems is a restricted hypothesis search space, within which each clause must individually explain some example E, or some member of an abductive explanation for E. This paper proposes a new IE approach, called Induction on Failure (IoF), that generalises existing Horn clause learning systems by allowing the computation of hypotheses within a larger search space, namely that of Connected Theories. A proof procedure for IoF is proposed that generalises existing IE systems and also resolves Yamamoto’s example. A prototype implementation is also described. Finally, a semantics is presented, called Connected Theory Generalisation, which is proved to extend Kernel Set Subsumption and to include hypotheses constructed within this new IoF approach.