Certain conjunctive query answering in first-order logic

Abstract

Primary key violations provide a natural means for modeling uncertainty in the relational data model. A repair (or possible world) of a database is then obtained by selecting a maximal number of tuples without ever selecting two distinct tuples that have the same primary key value. For a Boolean query q , the problem CERTAINTY( q ) takes as input a database db and asks whether q evaluates to true on every repair of db . We are interested in determining queries q for which CERTAINTY( q ) is first-order expressible (and hence in the low complexity class AC °). For queries q in the class of conjunctive queries without self-join, we provide a necessary syntactic condition for first-order expressibility of CERTAINTY( q ). For acyclic queries (in the sense of Beeri et al. [1983]), this necessary condition is also a sufficient condition. So we obtain a decision procedure for first-order expressibility of CERTAINTY( q ) when q is acyclic and without self-join. We also show that if CERTAINTY( q ) is first-order expressible, its first-order definition, commonly called certain first-order rewriting, can be constructed in a rather straightforward way.