Several logical formalisms have been proposed in the literature for expressing structural and semantic integrity constraints of Linked Open Data (LOD). Still, the integrity of the datasets published in the LOD cloud needs to be improved, as published data often violate such constraints, jeopardising the value of applications consuming linked data in an automatic way. In this work, we propose a novel, fully automatic framework for detecting and repairing violations of integrity constraints, by considering both explicit and implicit ontological knowledge. Our framework relies on the ontology language DL-LiteA for expressing several useful types of constraints, while maintaining good computational properties. The experimental evaluation shows that our framework is scalable for large datasets and numbers of invalidities exhibited in reality by reference linked datasets (e.g., DBpedia).