Tractable Computation of Representative ABox Repairs in Description Logic Ontologies
Computing all ABox repairs is a key to cautious or brave reasoning over inconsistent description logic (DL) ontologies. However, the number of ABox repairs can be exponential in the number of assertions in the ABox even for very lightweight DLs. Hence we propose to compute a minimal representative set of ABox repairs. A set of ABox repairs is representative, if every assertion occurring in at least one ABox repair also occurs in at least one element of this set, while every assertion occurring in all ABox repairs occurs in all elements of this set. Cautious or brave reasoning then can be approximated by standard reasoning over a minimal representative set other than the complete set of ABox repairs. However, computing a minimal representative set of ABox repairs is still intractable in general. To guarantee the tractability in data complexity for computing a minimal representative set, we focus on a class of DL ontologies called the first-order rewritable class. We propose a tractable method for computing a minimal representative set of ABox repairs in an inconsistent first-order rewritable ontology. Experimental results demonstrate the high efficiency and scalability of the proposed method.
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