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Semantics, Consistency, and Query Processing of Empirical Deductive Databases
January-February 1997 (vol. 9 no. 1)
pp. 32-49

Abstract—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.

[1] F. Bacchus, "Representing and Reasoning with Probabilistic Knowledge," Research Report CS-88-31, Univ. of Waterloo, Ontario, Canada, 1988.
[2] J.F. Baldwin, "Evidential Support Logic Programming," Fuzzy Sets and Systems, vol. 24, pp. 1-26, 1987.
[3] C. Bell, A. Nerode, R. Ng, and V.S. Subrahmanian, "Implementing Deductive Databases by Linear Programming," Proc. ACM SIGACT/SIGART/SIGMOD Symp. Principles of Database Systems, pp. 283-292, 1992. Available as Univ. of Maryland Technical Report CS-TR-2747, 1991.
[4] H.A. Blair and V.S. Subrahmanian, “Paraconsistent Logic Programming,” Theoretical Computer Science, vol. 68, pp. 135-154, 1989.
[5] D. Dubois, H. Prade, and J. Lang, "Towards Possibilistic Logic Programming," Proc. Int'l. Conf. Logic Programming, K. Furukawa, ed., pp. 581-595, MIT Press, 1991.
[6] J.E. Fenstad, "The Structure of Probabilities Defined on First-Order Languages," Studies in Inductive Logic and Probabilities, vol. 2, R.C. Jeffrey, ed., pp. 251-262. Univ. of Calif. Press, 1980.
[7] M.C. Fitting, "Logic Programming on a Topological Bilattice," Fundamenta Informaticae, vol. 11, pp. 209-218, 1988.
[8] M.C. Fitting, “Bilattices and the Semantics of Logic Programming,” J. Logic Programming, vol. 11, pp. 91-116, 1991.
[9] U. Güntzer, W. Kießling, and H. Thöne, "New Directions for Uncertainty Reasoning in Deductive Databases," Proc. ACM SIGMOD Int'l Conf. Management of Data, pp. 178-187,Denver, 1991.
[10] J. Han, Y. Cai, and N. Cercone, “Knowledge Discovery in Databases: an Attribute-Oriented Approach,” Proc. 18th Conf. Very Large Databases, pp. 547–559, 1992.
[11] M. Kifer and A. Li, “On the Semantics of Rule-Based Expert Systems with Uncertainty,” Proc. Second Int'l Conf. Database Theory, M. Gyssens, J. Paradaens, and D. van Gucht, eds., pp. 102-117, 1988.
[12] M. Kifer and E. Lozinskii, "RI: A Logic for Reasoning with Inconsistency," Proc. Fourth Symp. Logic in Computer Science, pp. 253-262,Asilomar, Calif., 1989.
[13] M. Kifer and V.S. Subrahmanian, "Theory of Generalized Annotated Logic Programming and its Applications," J. Logic Programming, vol. 12, no. 4, pp. 335-368, 1992.
[14] H.E. Kyburg, Jr., "The Reference Class," Philosophy of Science, vol. 50, no. 3, pp. 374-397, 1983.
[15] H.E. Kyburg, Jr., "Semantics for Probabilistic Inference," Proc. Eighth Conf. Uncertainty in Artificial Intelligence, pp. 142-148, 1992.
[16] J.W. Lloyd, Foundations of Logic Programming, Springer Series in Symbolic Computation, second ed. New York: Springer-Verlag, 1987.
[17] D. Luenberger, Linear and Nonlinear Programming, Addison-Wesley, 1984.
[18] A. Nerode, R.T. Ng, and V.S. Subrahmanian, "Computing Circumscriptive Databases, Part I: Theory and Algorithms," Information and Computation, vol. 116, no. 1, pp. 58-90, 1995.
[19] R. Ng and V.S. Subrahmanian, "Probabilistic Logic Programming," Information and Computation, vol. 101, no. 2, pp. 150-201, 1992.
[20] R.T. Ng and V.S. Subrahmanian, "A Semantical Framework for Supporting Subjective and Conditional Probabilities in Deductive Databases," J. Automated Reasoning, vol. 10, no. 2, pp. 191-235, 1992. Preliminary version in Proc. Int'l. Conf. Logic Programming, K. Furukawa, ed., pp. 565-580, MIT Press, 1991.
[21] R.T. Ng and V.S. Subrahmanian, "Empirical Probabilities in Monadic Deductive Databases," Proc. Eighth Conf. Uncertainty in Artificial Intelligence, pp. 215-222,Stanford, 1992.
[22] N. Nilsson, "Probabilistic Logic," Artificial Intelligence, vol. 28, pp. 71-87, 1986.
[23] J. Pearl, Probabilistic Reasoning in Intelligent Systems. San Mateo, Calif.: Morgan Kaufman, 1988.
[24] G. Piatetsky-Shapiro and W.J. Frawley, Knowledge Discovery in Databases. AAAI/MIT Press, 1991.
[25] H. Reichenbach, Theory of Probability. Univ. of Calif. Press.
[26] E. Shapiro, "Logic Programs with Uncertainties: A Tool for Implementing Expert Systems," Proc. IJCAI '83, pp. 529-532, William Kauffman, 1983.
[27] H. Thöne, U. Güntzer, and W. Kießling, "Towards Precision of Probabilistic Bounds Propagation," Proc. Eighth Conf. Uncertainty in Artificial Intelligence, pp. 315-322,Stanford, 1992.
[28] M.H. van Emden, “Quantitative Deduction and Its Fixpoint Theory,” J. Logic Programming, vol. 4, no. 1, pp. 37-53, 1986.

Index Terms:
Deductive databases, empirical probabilities, model semantics, constraint satisfaction, optimizations, query answering.
Raymond T. Ng, "Semantics, Consistency, and Query Processing of Empirical Deductive Databases," IEEE Transactions on Knowledge and Data Engineering, vol. 9, no. 1, pp. 32-49, Jan.-Feb. 1997, doi:10.1109/69.567045
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