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<p><b>Abstract</b>—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 <it>IRC-refuting problem</it>, 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 <it>acyclic</it> 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.</p>
Semantic integrity constraints, implication constraints, referential constraints, query containment, semantic query optimization, refutation, database system.

Z. M. Ozsoyoglu and X. Zhang, "Implication and Referential Constraints: A New Formal Reasoning," in IEEE Transactions on Knowledge & Data Engineering, vol. 9, no. , pp. 894-910, 1997.
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