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To answer database queries over incomplete data the gold standard is findingcertain answers: those that are true regardless of how incomplete data isinterpreted. Such answers can be found efficiently for conjunctive queries andtheir unions, even in the presence of constraints. With negation added, theproblem becomes intractable however. We concentrate on the complexity ofcertain answers under constraints, and on effficiently answering queriesoutside the usual classes of (unions) of conjunctive queries by means ofrewriting as Datalog and first-order queries. We first notice that there arethree different ways in which query answering can be cast as a decisionproblem. We complete the existing picture and provide precise complexity boundson all versions of the decision problem, for certain and best answers. We thenstudy a well-behaved class of queries that extends unions of conjunctivequeries with a mild form of negation. We show that for them, certain answerscan be expressed in Datalog with negation, even in the presence of functionaldependencies, thus making them tractable in data complexity. We show that ingeneral Datalog cannot be replaced by first-order logic, but withoutconstraints such a rewriting can be done in first-order. The paper is underconsideration in Theory and Practice of Logic Programming (TPLP).

Querying Incomplete Data : Complexity and Tractability via Datalog and First-Order Rewritings