This Article 
 Bibliographic References 
 Add to: 
Probabilistic Knowledge Bases
October 1995 (vol. 7 no. 5)
pp. 691-698

Abstract—We define a new fixpoint semantics for rule-based reasoning in the presence of weighted information. The semantics is illustrated on a real-world application requiring such reasoning. Optimizations and approximations of the semantics are shown so as to make the semantics amenable to very large scale real-world applications. We finally prove that the semantics is probabilistic and reduces to the usual fixpoint semantics of stratified Datalog if all information is certain. We implemented various knowledge discovery systems which automatically generate such probabilistic decision rules. In collaboration with a bank in Hong Kong we use one such system to forecast currency exchange rates.

[1] K. Apt, H.A. Blair, and A. Walker, "Towards a Theory of Declarative Knowledge," Foundations of Deductive Databases and Logic Programming, J. Minker, ed., pp. 89-148. Morgan Kaufmann, 1988.
[2] F. Baader,“A formal definition for the expressive power of knowledge representation languages,” Proc. European Conf. Artificial Intelligence, L.C. Aiello, ed., pp. 53-58, 1990.
[3] F. Bacchus,Representing and reasoning with probabilistic knowledge, MIT Press, 1990.
[4] D. Barbara,H. Garcia-Molina,, and D. Porter,“A probabilistic relational data model,” Proc. Advances in Database Technology (EDBT 90), F. Bancilhon, C. Thanos, and D. Tsichritzis, eds., pp. 60-74, 1990.
[5] A.K. Chandra, "Theory of Database Queries," Proc. PODS-88, 1988.
[6] P. Dagum and M. Luby,“Approximating probabilistic inference in Bayesian belief networks is NP-hard,” Aritificial Intelligence, vol. 60, pp.141-153, 1993.
[7] S. Dzeroski and N. Lavrac,“Inductive learning in deductive databases,” IEEE Trans. Knowledge and Data Engineering, vol. 5, no. 6, pp. 939-949, 1993.
[8] M.H. van Emden, “Quantitative Deduction and Its Fixpoint Theory,” J. Logic Programming, vol. 4, no. 1, pp. 37-53, 1986.
[9] M.H. van Emden and R.A. Kowalski, “The Semantics of Predicate Logic as a Programming Language,” J. ACM, vol. 23, no. 4, pp. 733-742, Oct. 1976.
[10] N. Fuhr, “A Probabilistic Framework for Vague Queries and Imprecise Information in Databases,” Proc. 16th Int'l Conf. Very Large Data Bases, pp. 696-707, Aug. 1990.
[11] 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.
[12] T. Hailperin,“Probability logic,” Notre Dame J. Formal Logic, vol. 25, no. 3, pp. 198-212, 1984.
[13] D. Heckermann,“Probabilistic interpretation for MYCIN’s certainty factors,” Uncertainty in Artificial Intelligence, North-Holland, L.N. Kanal and J. F. Lemmer, eds., pp. 167-196, 1986.
[14] 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.
[15] M. Kifer and V.S. Subrahmanian,“On the expressive power of annotated logic programs,” Proc. North Am. Conf. Logic Programming, E.L. Lusk and R.A. Overbeek, eds., pp. 1,069-1,089, 1989.
[16] J.W. Lloyd, Foundations of Logic Programming, Springer Series in Symbolic Computation, second ed. New York: Springer-Verlag, 1987.
[17] R. Ng and V.S. Subrahmanian, "Probabilistic Logic Programming," Information and Computation, vol. 101, no. 2, pp. 150-201, 1992.
[18] R. Ng and V.S. Subrahmanian,“Stable semantics for probabilistic deductive databases,” Information and Computation, vol. 110, pp. 42-83, 1994.
[19] R.T. Ng and V.S. Subrahmanian,“A semantical framework for supporting subjective and conditional probabilities in deductive databases,” Proc. Int’l Conf. Logic Programming, K. Furukawa, ed., pp. 565-580, 1991.
[20] R.T. Ng and V.S. Subrahmanian,“Relating Dempster-Shafer theory to stable semantics,” Proc. Int’l Symp. Logic Programming, V. Saraswat and K. Ueda, eds., pp. 551-565, 1991.
[21] N. Nilsson, "Probabilistic Logic," Artificial Intelligence, vol. 28, pp. 71-87, 1986.
[22] E. Parzen,Modern Probability Theory and its Applications, John Wiley&Sons, 1960.
[23] J. Pearl,“Probabilistic semantics for nonmonotonic reasoning: A survey,” Readings in Uncertain Reasoning, G. Shafer and J. Pearl, eds., Morgan Kaufmann, pp. 699-710, 1990.
[24] P. Schäble and B. Wüthrich,“On the expressive power of query languages,” ACM TOIS, vol. 12, no. 1, pp. 67-91, 1994.
[25] E.Y. Shapiro,“Logic programs with uncertainties: A tool for implementing rule-based systems,“ Proc. Eighth Int’l Joint Conf. Artificial Intelligence, A. Bundy, ed., pp. 329-352, 1983.
[26] B. Wüthrich,“Towards probabilistic knowledge bases,” Proc. Logic Programming and Automated Reasoning, Springer-Verlag, Lecture Notes in Artifical Intelligence, pp. 66-67, 1992.
[27] B. Wüthrich,“Knowledge discovery in databases,” Technical Report No. CS94-2,Hong Kong Univ. of Science and Tech nology, draft of manuscript of postgraduate course, 1994.
[28] B. Wüthrich,“Some proofs about probabilistic knowledge bases,” Technical Report No. CS94-18,Hong Kong Univ. of Science and Tech nology, 1994.

Index Terms:
Axiomatic probability theory, data mining, incomplete information, knowledge discovery in databases, query optimization and approximation, stratified Datalog.
Beat Wüthrich, "Probabilistic Knowledge Bases," IEEE Transactions on Knowledge and Data Engineering, vol. 7, no. 5, pp. 691-698, Oct. 1995, doi:10.1109/69.469827
Usage of this product signifies your acceptance of the Terms of Use.