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We focus on the problem of handling inconsistency in lightweight ontologies. We assume that the terminological knowledge base (TBox) is specified in DL-Lite and that the set of assertional facts (ABox) is partially preordered and may be inconsistent with respect to the TBox. One of the main contributions of this paper is the provision of an efficient and safe method, called Elect, to restore the consistency of the ABox with respect to the TBox. In the case where the assertional base is flat (i.e. no priorities are associated with the ABox) or totally preordered, we show that our method collapses with the well-known intersection ABox repair semantics and the non-defeated semantics, respectively. The semantic justification of the Elect method is obtained by first viewing a partially preordered ABox as a family of totally preordered ABoxes and then applying non-defeated inference to each of the totally preordered ABoxes. We introduce the notion of elected assertions which allows us to provide an equivalent characterization of the Elect method without explicitly generating all the totally preordered ABoxes. We show that computing the set of elected assertions is done in polynomial time with respect to the size of the ABox. The second part of the paper discusses how to go beyond the Elect method. In particular, we discuss to what extent the Elect method can be generalized to description logics that are more expressive than DL-Lite.

Handling inconsistency in partially preordered ontologies: the Elect method