Updating inconsistent Description Logic knowledge bases

Finding an appropriate semantics for task of updating an inconsistent knowledge base is a challenging problem. In this paper, we consider knowledge bases expressed in Description Logics, and focus on ABox inconsistencies, i.e., the case where the TBox is consistent, but the whole knowledge base is not. Our first contribution is the definition of a new semantics for updating an inconsistent Description Logic knowledge base with both the insertion and the deletions of a set of ABox assertions. We then concentrate on the DL-Lite family of Description Logics, and present algorithms for updating a possibly inconsistent knowledge base expressed in the most expressive logic of such family. We show that, by virtue of both the characteristics of our semantics, and the limited expressive power of DL-Lite, both insertions and deletions can be done in polynomial time with respect of the size of the ABox.