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We describe a new approach for improving the evaluation of queries with quantifiers. We first introduce the concept of constructive evaluation as a formalization of a principle common to the methods that have been proposed for answering quantified queries. Relying on this concept, we define the class of constructively domain independent (cdi) formulas. We show that cdi queries can be constructively evaluated by searching only the relations they refer to. Therefore, cdi queries admit domain independent evaluations as soon as they do not explicitly refer to the database domain. Then, we define rewritings that translate general quantified queries into expressions amenable to efficient constructive evaluations. These rewritings preserve logical equivalence, hence do not compromise the semantics of queries. They are based on the generation from a query of the ranges and co-ranges of its variables. We show that the rewritings we propose permit to optimize the evaluation of cdi queries. They also reduce queries from several solvable subclasses of domain independent formulas to cdi queries, hence permitting their domain independent evaluation.

Logical rewritings for improving the evaluation of quantified queries