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<p><b>Abstract</b>—Numerous frameworks have been proposed in recent years for deductive databases with uncertainty. On the basis of how uncertainty is associated with the facts and rules in a program, we classify these frameworks into <it>implication-based</it> (IB) and <it>annotation-based</it> (AB) frameworks. In this paper, we take the IB approach and propose a generic framework, called the <it>parametric framework</it>, as a unifying umbrella for IB frameworks. We develop the declarative, fixpoint, and proof-theoretic semantics of programs in our framework and show their equivalence. Using the framework as a basis, we then study the query optimization problem of containment of conjunctive queries in this framework and establish necessary and sufficient conditions for containment for several classes of parametric conjunctive queries. Our results yield tools for use in the query optimization for large classes of query programs in IB deductive databases with uncertainty.</p>
Conjunctive query containment, deductive databases, fixpoint computation, multisets, proof theory, query optimization, semantics, uncertainty.

N. Shiri and L. V. Lakshmanan, "A Parametric Approach to Deductive Databases with Uncertainty," in IEEE Transactions on Knowledge & Data Engineering, vol. 13, no. , pp. 554-570, 2001.
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