On E cient Reasoning with Implication Constraints

In this paper, we address the complexity issue of reasoning with implication constraints. We consider the IC-RFT problem, which is the problem of deciding whether a conjunctive yes/no query always produces the empty relation (\no" answer) on database instances satisfying a given set of implication constraints, as a central problem in this respect. We show that several other important problems, such as the query containment problem, are polynomially equivalent to the IC-RFT problem. More importantly, we give criteria for designing a set of implication constraints so that an eecient \units-refutation" process can be used to solve the IC-RFT problem.