Union and Intersection of all Justifications

We present new algorithms for computing the union and intersection of all justifications for a given ontological consequence without first computing the set of all justifications. Our goal is to use these sets to explain the consequences and, if needed, repair them. Through an empirical evaluation, we show that our approach behaves well in practice for expressive description logics. In particular, the union of all justifi cations can be computed much faster than with existing justificationenumeration approaches.