Chasing Relational Database Constraints Backwards

Data dependencies are well known in the context of relational database. They aim to specify constraints that the data must satisfy to model correctly the part of the world under consideration. The implication problem for dependencies is to decide whether a given dependency is logically implied by a given set of dependencies. A proof procedure for the implication problem called "chase", has already been studied in the generalized case of tuple-generating and equality-generating dependencies. The chase is a bottom-up procedure: from hypotheses to conclusion, and thus is not goal-directed. It also requires the dynamic creation of new symbols. This paper introduces a new proof procedure which is top-down: from conclusion to hypothesis, that is goal-directed. The originality of this procedure is that it does not act as classical theorem proving procedures, by requiring a special form of expresions, such as clausal form, obtained after skolemisation. We show, with out procedure, that this step is useless, and that the notion of piece allows inferring directly on dependencies, without dynamically creating new symbols. With the recent introduction of constrained dependencies, some interesting perspectives also arise.

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