Towards E cient Higher-order Logic Learning in a First-order Datalog Framework

Within ILP, the concepts to be learned are normally considered as being succinctly representable in rst-order logic. In a previous paper the authors demonstrated that increased predictive accuracy can be achieved by employing higher-order logic (HOL) in the background knowledge. In this paper, the exible higher-order Horn clauses (FHOHC) framework is introduced. It is more expressive than the formalism used previously and can be emulated (with the use of holds statements and attening) in a fragment of Datalog. The decidability, compatibility with ILP systems like Progol and positive learnability results of Datalog are then used towards e cient higher-order logic learning (HOLL). We show with experiments that this approach outperforms the HOLL system λProgol and that it can learn concepts in other HOLL settings like learning HOL and using HOL for abduction.