In the context of the Semantic Web, learning implicit knowledge in terms of axioms from Linked Open Data has been the object of much current research. In this paper, we propose a method based on grammar-based genetic programming to automatically discover disjoint-ness axioms between concepts from the Web of Data. A training-testing model is also implemented to overcome the lack of benchmarks and comparable research. The acquisition of axioms is performed on a small sample of DBpedia with the help of a Grammatical Evolution algorithm. The accuracy evaluation of mined axioms is carried out on the whole DBpe-dia. Experimental results show that the proposed method gives high accuracy in mining class disjointness axioms involving complex expressions .