In ontology engineering, it is essential to develop techniques for module extraction, ontology reuse and ontology comparison. Since it was introduced in DL-Lite , forgetting has become into a major method of extracting modules in DL ontologies. It has been applied in some other domains such as ontology comparison . Given a (consistent) ontology K and a set of concepts and roles F , the result of forgetting is a new ontology K′ that does not contain symbols in F and preserves certain reasoning or query answering tasks. In existing approaches, forgetting is defined for only consistent ontologies. However, ontologies can be error-prone and inconsistent. To our best knowledge, the problem of establishing a framework for inconsistent ontologies has not been investigated yet. In order to provide a definition of forgetting for a possibly inconsistent DL ontology, we could first repair it and then perform standard forgetting on the repaired ontology. However, there are some issues with this naive approach. In particular, it can give unwanted results for some ontologies.