A logic-based framework for database repairs

We introduce a general abstract framework for database repairing in which the repair notions are defined using formal logic. We differentiate between integrity constraints and the so-called query constraints. The former are used to model consistency and desirable properties of the data (such as functional dependencies and independencies), while the latter relates two database instances according to their answers for the query constraints. The framework also admits a distinction between hard and soft queries, allowing to preserve the answers of a core set of queries as well as defining a distance between instances based on query answers. We exemplify how various notions of repairs from the literature can be modelled in our unifying framework. Furthermore, we initiate a complexity-theoretic analysis of the problems of consistent query answering, repair computation, and existence of repair within the new framework. We present both coNP- and NP-hard cases that illustrate the interplay between computationally hard problems and more flexible repair notions. We show general upper bounds in NP and the second level of the polynomial hierarchy. Finally, we relate the existence of a repair to model checking of existential second-order logic.