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Partially Preordered Inconsistent Lightweight Ontologies in Possibility Theory

In the context of DL-Lite, a family of lightweight fragments of description logics, this paper introduces an extension of standard possibilistic DL-Lite to the case where the knowledge base is partially preordered. We consider the assertional base, a.k.a. ABox, to be represented as a symbolic weighted base and we assume a strict partial preorder is applied on the weights. We introduce a tractable method for computing a single repair for a partially preordered weighted ABox. Basically, this repair is computed from possibilistic repairs associated with compatible bases of a partially preordered ABox, which intuitively encode all possible extensions of a partial preorder. We provide an equivalent characterization using the notion of π-accepted assertions, which ensures that the possibilistic repair is computed in polynomial time.