In this paper we describe an approach for integrating abduction and induction in the ILP setting of learning from interpretations with the aim of solving the problem of incomplete information both in the background knowledge and in the interpretations. The approach is inspired by the techniques developed in the learning from entailment setting for performing induction from an incomplete background knowledge. Similarly to those techniques, we exploit an abductive proof procedure for completing the available background knowledge and input interpretations. The approach has been implemented in a system called AICL that is based on the ILP system ICL. Preliminary experiments have been performed on a toy domain where knowledge has been gradually removed. The experiments show that AICL has a superior accuracy for levels of incompleteness between 5% and 20%.