Recognizing determinism in prioritized repairing of inconsistent databases

A repair of an inconsistent database is traditionally defined as a consistent database that differs from the inconsistent one in a "minimal way." As there are often reasons to prefer one repair over another, researchers have introduced and investigated the framework of preferred repairs, where a priority relation between facts is lifted towards a priority relation between consistent databases, and repairs are restricted to ones that are optimal in the lifted sense. In this paper we describe our recent results on the complexity of deciding whether the priority relation suffices to clean the database unambiguously, or in other words, whether there is exactly one optimal repair. In particular, we show that different conventional semantics of priority lifting entail highly different complexities.