A consistent query answer in an inconsistent database is an answer obtained in every (minimal) repair. The repairs are obtained by resolving all conflicts in all possible ways. Often, however, the user is able to provide a preference on how conflicts should be resolved. We investigate here the framework of preferred consistent query answers, in which user preferences are used to narrow down the set of repairs to a set of preferred repairs. We axiomatize desirable properties of preferred repairs. We present three different families of preferred repairs and study their mutual relationships. Finally, we investigate the complexity of preferred repairing and computing preferred consistent query answers.
The first article to notice the importance of priorities in information systems is @cite_21 . There, the problem of conflicting updates in (propositional) databases is solved in a manner similar to @math . The considered priorities are transitive, which in our framework is too restrictive. Also, in our framework this restriction does not bring any computational benefits (the reductions can be modified to use only transitive priorities). @cite_0 is another example of @math -like prioritized conflict resolution of first-order theories. The basic framework is defined for priorities which are weak orders. A partial order is handled by considering every extension to weak order. This approach also assumes the transitivity of the priority.
@cite_0 @cite_21
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We present a general framework for defining nonmonotonic systems based on the notion of preferred maximal consistent subsets of the premises. This framework subsumes David Poole's THEORIST approach to default reasoning as a particular instance. A disadvantage of THEORIST is that it does not allow to represent priorities between defaults adequately (as distinct from blocking defaults in specific situations). We therefore propose two generalizations of Poole's system: in the first generalization several layers of possible hypotheses representing different degrees of reliability are introduced. In a second further generalization a partial ordering between premises is used to distinguish between more and less reliable formulas. In both approaches a formula is provable from a theory if it is possible to construct a consistent argument for it based on the most reliable hypotheses. This allows for a simple representation of priorities between defaults. We suggest here a methodology for updating databases with integrity constraints and rules for deriving inexphcit information. First we consider the problem of updating arbitrary theories by inserting into them or deleting from them arbitrary sentences. The solution involves two key ideas when replacing an old theory by a new one we wish to minimize the change in the theory, and when there are several theories that involve minimal changes, we look for a new theory that reflects that ambiguity. The methodology is also adapted to updating databases, where different facts can carry different priorities, and to updating user views.