In recent years Predicate Invention has been underexplored within Inductive Logic Programming due to difficulties in formulating efficient search mechanisms.However,a recent paper demonstrated that both predicate invention and the learning of recursion can be efficiently implemented for regular and context-free grammars,by way of abduction with respect to a meta-interpreter.New predicate symbols are introduced as constants representing existentially quantified higher-order variables.In this paper we generalise the approach of Meta-Interpretive Learning (MIL) to that of learning higher-order dyadic datalog programs.We show that with an infinite signature the higher-order dyadic datalog class H2 2 has universal Turing expressivity though H2 2 is decidable given a finite signature.Additionally we show that Knuth-Bendix ordering of the hypothesis space together with logarithmic clause bounding allows our Dyadic MIL implementation MetagolD to PAC-learn minimal cardinailty H2 2 definitions.This result is consistent with our experiments which indicate that MetagolD efficiently learns compact H2 2 definitions involving predicate invention for robotic strategies and higher-order concepts in the NELL language learning domain.
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