Applications of Annotated Predicate Calculus to Querying Inconsistent Databases

We consider the problem of specifying and computing consistent answers to queries against databases that do not satisfy given integrity constraints. This is done by simultaneously embedding the database and the integrity constraints, which are mutually inconsistent in classical logic, into a theory in annotated predicate calculus — a logic that allows non trivial reasoning in the presence of inconsistency. In this way, several goals are achieved: (a) A logical specification of the class of all minimal “repairs” of the original database, and the ability to reason about them; (b) The ability to distinguish between consistent and inconsistent information in the database; and (c) The development of computational mechanisms for retrieving consistent query answers, i.e., answers that are not affected by the violation of the integrity constraints.