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Implication and Referential Constraints: A New Formal Reasoning
November-December 1997 (vol. 9 no. 6)
pp. 894-910

Abstract—In this paper, we address the issue of reasoning with two classes of commonly used semantic integrity constraints in database and knowledge-base systems: implication constraints and referential constraints. We first consider a central problem in this respect, the IRC-refuting problem, which is to decide whether a conjunctive query always produces an empty relation on (finite) database instances satisfying a given set of implication and referential constraints. Since the general problem is undecidable, we only consider acyclic referential constraints. Under this assumption, we prove that the IRC-refuting problem is decidable, and give a novel necessary and sufficient condition for it. Under the same assumption, we also study several other problems encountered in semantic query optimization, such as the semantics-based query containment problem, redundant join problem, and redundant selection-condition problem, and show that they are polynomially equivalent or reducible to the IRC-refuting problem. Moreover, we give results on reducing the complexity for some special cases of the IRC-refuting problem.

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Index Terms:
Semantic integrity constraints, implication constraints, referential constraints, query containment, semantic query optimization, refutation, database system.
Citation:
Xubo Zhang, Z. Meral Ozsoyoglu, "Implication and Referential Constraints: A New Formal Reasoning," IEEE Transactions on Knowledge and Data Engineering, vol. 9, no. 6, pp. 894-910, Nov.-Dec. 1997, doi:10.1109/69.649315
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