This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Parametric Approach to Deductive Databases with Uncertainty
July/August 2001 (vol. 13 no. 4)
pp. 554-570

Abstract—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 implication-based (IB) and annotation-based (AB) frameworks. In this paper, we take the IB approach and propose a generic framework, called the parametric framework, 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.

[1] G. Birkhoff, Lattice Theory, third ed. Providence: American Math. Soc., 1967.
[2] H.A. Blair and V.S. Subrahmanian, “Paraconsistent Logic Programming,” Theoretical Computer Science, vol. 68, pp. 135-154, 1989.
[3] B.G. Buchanan and E.D. Shortliffe, “A Model of Inexact Reasoning in Medicine,” Math. Biosciences, vol. 23, pp. 351-379, 1975.
[4] A.K. Chandra and P.M. Merlin, “Optimal Implementation of Conjunctive Queries in Relational Databases,” Proc. Ninth Ann. ACM Symp. Theory of Computing, pp. 77-90, 1977.
[5] S. Debray and R. Ramakrishnan, “Generalized Horn Clause Programs,” manuscript, Jan. 1994.
[6] D. Dubois, J. Lang, and H. Prade, “Towards Possibilistic Logic Programming,” Proc. Eighth Int'l Conf. Logic Programming, pp. 581-596, 1991.
[7] G. Escalada-Imaz and F. Manyà, “Efficient Interpretation of Propositional Multi-Valued Logic Programs,” Advances in Intelligent Computing, Proc. Fifth Int'l Conf. Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU '94), B. Bouchon-Meunier, R.R. Yager, and L.A. Zadeh, eds., pp. 428-439, 1995.
[8] R. Fagin, “Combining Fuzzy Information from Multiple Systems,” Proc. ACM Symp. Principles of Database Systems (PODS), pp. 216-226, June 1996.
[9] M.C. Fitting, “Logic Programming on a Topological Bilattice,” Fundamenta Informaticae, vol. 11, pp. 209-218, 1988.
[10] M.C. Fitting, “Bilattices and the Semantics of Logic Programming,” J. Logic Programming, vol. 11, pp. 91-116, 1991.
[11] R. Hähnle, “Exploiting Data Dependencies in Many-Valued Logics,” J. Applied Non-Classical Logics, vol. 6, no. 1, pp. 49-69, 1996.
[12] Y.E. Ioannidis and R. Ramakrishnan, “Containment of Conjunctive Queries: Beyond Relations as Sets,” ACM Trans. Database Systems, vol. 20, no. 3, pp. 288-324, Sept. 1995.
[13] 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.
[14] 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.
[15] 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.
[16] L.V.S. Lakshmanan and F. Sadri, “Uncertain Deductive Databases: A Hybrid Approach,” Information Systems, vol. 22, no. 8, pp. 483-508, 1997. Preliminary version appeared in Proc. Int'l Conf. Database Expert Systems and Applications (DEXA '94), 1994.
[17] L.V.S. Lakshmanan, “An Epistemic Foundation for Logic Programming with Uncertainty,” Proc. 14th Conf. Foundations of Software Technology and Theoretical Computer Science (FST and TCS '94), Dec. 1994.
[18] L. Lakshmanan and F. Sadri, “Probabilistic Deductive Databases,” Proc. Int'l Logic Programming Symp., pp. 254-268, 1994.
[19] S.M. Leach and J.J. Lu, “Query Processing in Annotated Logic Programming: Theory and Implementation,” J. Intelligent Information Systems, vol. 6, no. 1, pp. 33-58, Jan. 1996.
[20] J.W. Lloyd, Foundations of Logic Programming, Springer Series in Symbolic Computation, second ed. New York: Springer-Verlag, 1987.
[21] R.T. Ng and V.S. Subrahmanian, “Relating Dempster-Shafer Theory to Stable Semantics,” Technical Report UMIACS-TR-91-49, CS-TR-2647, Inst. for Advanced Computer Studies and Dept. of Computer Science, Univ. of Maryland, College Park, Apr. 1991.
[22] R. Ng and V.S. Subrahmanian, "Probabilistic Logic Programming," Information and Computation, vol. 101, no. 2, pp. 150-201, 1992.
[23] R.T. Ng and V.S. Subrahmanian, “A Semantical Framework for Supporting Subjective and Conditional Probabilities in Deductive Databases,” Automated Reasoning, vol. 10, no. 2, pp. 191-235, 1993.
[24] F. Sadri, “Modeling Uncertainty in Databases,” Proc. Seventh IEEE Int'l Conf. Data Eng., pp. 122-131, Apr. 1991.
[25] Y. Sagiv, “Optimizing Datalog Programs,” Foundations of Deductive Databases and Logic Programming, J. Minker, ed., pp. 659-698, Morgan-Kaufmann, 1988. Extended abstract of this paper appears in Proc. ACM Symp. Principles of Database Systems (PODS), pp. 237-249, 1987.
[26] E. Shapiro, “Logic Programs with Uncertainties: A Tool for Implementing Expert Systems,” Proc. Int'l Joint Conf. Artificial Intelligence (IJCAI '83), pp. 529-532, 1983.
[27] N. Shiri, “Towards a Generalized Theory of Deductive Databases with Uncertainty,” PhD thesis, Dept. of Computer Science, Concordia Univ., Montreal, Canada, Aug. 1997.
[28] V.S. Subrahmanian, “On the Semantics of Quantitative Logic Programs,” Proc. Fourth IEEE Symp. Logic Programming, pp. 173-182, 1987.
[29] J.D. Ullman, Principles of Database and Knowledge-Base Systems, vol. II: The New Tech nologies. New York: Computer Science Press, 1989.
[30] M.H. van Emden, “Quantitative Deduction and Its Fixpoint Theory,” J. Logic Programming, vol. 4, no. 1, pp. 37-53, 1986.
[31] 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.
[32] L.A. Zadeh, “Fuzzy Sets,” Information and Control, vol. 8, pp. 338-353, 1965.
[33] L.A. Zadeh, “Fuzzy Sets as a Basis for a Theory of Possibility,” Fuzzy Sets and Systems, vol. 1, no. 1, pp. 3-28, 1978.

Index Terms:
Conjunctive query containment, deductive databases, fixpoint computation, multisets, proof theory, query optimization, semantics, uncertainty.
Citation:
Laks V.S. Lakshmanan, Nematollaah Shiri, "A Parametric Approach to Deductive Databases with Uncertainty," IEEE Transactions on Knowledge and Data Engineering, vol. 13, no. 4, pp. 554-570, July-Aug. 2001, doi:10.1109/69.940732
Usage of this product signifies your acceptance of the Terms of Use.