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Genetic Algorithms (GAs) are known for their capacity to explore large search spaces and due to this ability, they were to some extent applied to Inductive Logic Programming (ILP) problem. Although Estimation of Distribution Algorithms (EDAs) perform better in most problems when compared to standard GAs, this kind of algorithm have not been applied to ILP. This work presents an ILP system based on EDA. Preliminary results show that the proposed system is superior when compared to a "standard" GA and it is very competitive when compared to the state of the art ILP system Aleph.