Computing a Possibility Theory Repair for Partially Preordered Inconsistent Ontologies

We address the problem of handling inconsistency in uncertain knowledge bases that are specified in the lightweight fragments of description logics DL-Lite. More specifically, we assume that the TBox component is coherent, stable, and fully reliable. However, the ABox component may be inconsistent with respect to the TBox, partially preordered and uncertain. Uncertainty is encoded in the framework of possibility theory. In this context, we propose an extension of standard possibilistic DL-Lite. We represent the ABox as a symbolic weighted base, where the weights attached to the assertions are ordered according to a strict partial order. We define a tractable method for computing a single possibilistic repair for a partially preordered weighted ABox. The idea is to consider the possibilistic compatible bases of such an ABox, which intuitively encode all the possible extensions of a partial order, and compute the possibilistic repair of each compatible base. We then compute the intersection of all these possibilistic repairs to obtain a single repair for the initial ABox. We also provide an equivalent characterization by introducing the notion of
$\pi$
-accepted assertions. This ensures that the computation of the partially preordered possibilistic repair can be achieved in polynomial time in DL-Lite.