We present our research produced about Higher-order Logic Learning (HOLL), which consists of adapting First-order Logic Learning (FOLL), like Inductive Logic Programming (ILP), within a Higher-order Logic (HOL) context. We describe a first working implementation of lambda-Progol, a HOLL system adapting the ILP system Progol and the HOL formalism lambda-Prolog. We compare lambda-Progol and Progol on the learning of recursive theories showing that HOLL can, in these cases, outperform FOLL.
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