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. Through an empirical evaluation, we show that our approach works well in practice for expressive description logics. In particular, the union of all justifications can be computed much faster than with existing justification-enumeration approaches. We further discuss how to use these results to repair ontologies.