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<p><b>Abstract</b>—In recent years, there has been a growing interest in reasoning with uncertainty in logic programming and deductive databases. However, most frameworks proposed, thus far, are either nonprobabilistic in nature or based on subjective probabilities. In this paper, we address the problem of incorporating empirical probabilities—that is, probabilities obtained from statistical findings—in deductive databases. To this end, we develop a formal model-theoretic basis for such databases. We also present a sound and complete algorithm for checking the consistency of such databases. Moreover, we develop consistency-preserving ways to optimize the algorithm for practical usage. Finally, we show how query answering for empirical deductive databases can be carried out.</p>
Deductive databases, empirical probabilities, model semantics, constraint satisfaction, optimizations, query answering.

R. T. Ng, "Semantics, Consistency, and Query Processing of Empirical Deductive Databases," in IEEE Transactions on Knowledge & Data Engineering, vol. 9, no. , pp. 32-49, 1997.
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