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Challenges in Fixpoint Computation with Multisets

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Foundations of Information and Knowledge Systems (FoIKS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2942))

Abstract

Uncertainty management has been a challenging issue in AI and database research. Logic database programming with its declarative advantage and its top-down and bottom-up query processing techniques has been an attractive formalism for representing and manipulating uncertain information, and numerous frameworks with uncertainty has been proposed. These proposals address fundamental issues of modeling, semantics, query processing and optimization, however, one important issue which remains unaddressed is efficient implementation of such frameworks. In this paper, we illustrate that the standard semi-naive evaluation method does not have a counterpart in general in these frameworks. We then propose a desired semi-naive algorithm, which extends the corresponding standard method, and establish its equivalence with the naive method with uncertainty. We implemented the algorithm and conducted numerous tests. Our experimental results indicate that the proposed technique is practical and supports efficient fixpoint computation with uncertainty. We believe that the method is also useful in a more general context of fixpoint computation with aggregations.

This research was supported in part by grants from the National Sciences and Engineering Research Council of Canada (NSERC).

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References

  1. Ceri, S., Gottlob, G., Tanca, L.: Logic programming and Databases. Springer, Berlin (1990)

    Google Scholar 

  2. Didier, D., Jérôme, L., Henri, P.: Towards possibilistic logic programming. In: Proc. 8th Intl. Conf. on Logic Programming, pp. 581–596 (1991)

    Google Scholar 

  3. Fitting, M.C.: Logic programming on a topological bilattice. Fundamenta Informaticae 11, 209–218 (1988)

    MATH  MathSciNet  Google Scholar 

  4. Fitting, M.C.: Bilattices and the semantics of logic programming. Journal of Logic Programming 11, 91–116 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  5. Kifer, M., Li, A.: On the semantics of rule-based expert systems with uncertainty. In: Gyssens, M., Van Gucht, D., Paredaens, J. (eds.) ICDT 1988. LNCS, vol. 326, pp. 102–117. Springer, Heidelberg (1988)

    Google Scholar 

  6. Kifer, M., Subrahmanian, V.S.: Theory of generalized annotated logic programming and its applications. Journal of Logic Programming 12, 335–367 (1992)

    Article  MathSciNet  Google Scholar 

  7. Lakshmanan, L.V.S.: An epistemic foundation for logic programming with uncertainty. In: Thiagarajan, P.S. (ed.) FSTTCS 1994. LNCS, vol. 880, Springer, Heidelberg (1994)

    Google Scholar 

  8. Lakshmanan, L.V.S., Sadri, F.: Probabilistic deductive databases. In: Proc. Intl. Logic Programming Symposium, Ithaca, NY, November 1994, pp. 254–268. MIT Press, Cambridge (1994)

    Google Scholar 

  9. Lakshmanan, L.V.S., Sadri, F.: Modeling uncertainty in deductive databases. In: Karagiannis, D. (ed.) DEXA 1994. LNCS, vol. 856, Springer, Heidelberg (1994)

    Google Scholar 

  10. Lakshmanan, L.V.S., Shiri, N.: A parametric approach to deductive databases with uncertainty. In: Pedreschi, D., Zaniolo, C. (eds.) LID 1996. LNCS, vol. 1154, pp. 61–81. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  11. Lakshmanan, L.V.S., Shiri, N.: Logic programming and deductive databases with uncertainty: A survey. In: Enclyclopedia of Computer Science and Technology, vol. 45, pp. 153–176. Marcel Dekker, Inc., New York (2001)

    Google Scholar 

  12. Lakshmanan, L.V.S., Nematollaah, S.: A parametric approach to deductive databases with uncertainty. IEEE Transactions on Knowledge and Data Engineering 13(4), 554–570 (2001)

    Article  Google Scholar 

  13. Leach Sonia, M., Lu James, J.: Query processing in annotated logic programming: Theory and implementation. Journal of Intelligent Information Systems 6(1), 33–58 (1996)

    Article  Google Scholar 

  14. Lloyd, J.W.: Foundations of Logic Programming, 2nd edn. Springer, Heidelberg (1987)

    MATH  Google Scholar 

  15. Ng, R.T., Subrahmanian, V.S.: Relating Dempster-Shafer theory to stable semantics. Tech. Report UMIACS-TR-91-49, CS-TR-2647, Institute for Advanced Computer Studies and Department of Computer Science University of Maryland, College Park, MD 20742 (April 1991)

    Google Scholar 

  16. Ng, R.T., Subrahmanian, V.S.: Probabilistic logic programming. Information and Computation 101(2), 150–201 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  17. Ng, R.T., Subrahmanian, V.S.: A semantical framework for supporting subjective and conditional probabilities in deductive databases. Automated Reasoning 10(2), 191–235 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  18. Parsons, S.: Current approaches to handling imperfect information in data and knowledge bases. IEEE Transactions on Knowledge and Data Engineering 8(3), 353–372 (1996)

    Article  MathSciNet  Google Scholar 

  19. Ramakrishnan, R., Srivastava, D., Sudarshan, S.: CORAL: Control, relations, and logic. In: Proc. Intl. Conf. on Very Large Databases (1992)

    Google Scholar 

  20. Konstantinos, S., Terrance, S., Warren David, S.: XSB as an efficient deductive database engine. In: Proc. of the ACM SIGMOD Intl. Conf. on the Management of Data, Minneapolis, Minnesota, May 1994, pp. 442–453 (1994)

    Google Scholar 

  21. Shapiro, E.: Logic programs with uncertainties: a tool for implementing expert systems. In: Proc. IJCAI 1983, pp. 529–532. William Kaufmann, San Francisco (1983)

    Google Scholar 

  22. Shiri, N.: Towards a Generalized Theory of Deductive Databases with Uncertainty. PhD thesis, Department of Computer Science, Concordia University, Montreal, Canada (August 1997)

    Google Scholar 

  23. Subrahmanian, V.S.: On the semantics of quantitative logic programs. In: Proc. 4th IEEE Symposium on Logic Programming, pp. 173–182. Computer Society Press, Washington (1987)

    Google Scholar 

  24. van Emden, M.H.: Quantitative deduction and its fixpoint theory. Journal of Logic Programming 4(1), 37–53 (1986)

    Article  Google Scholar 

  25. Loyer, Y., Straccia, U.: The well-founded semantics in normal logic programs with uncertainty. In: Hu, Z., Rodríguez-Artalejo, M. (eds.) FLOPS 2002. LNCS, vol. 2441, pp. 67–78. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  26. Loyer, Y., Straccia, U.: Default knowledge in logic programs with uncertainty. In: Palamidessi, C. (ed.) ICLP 2003. LNCS, vol. 2916, pp. 466–480. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, Concordia University, 1400 Maisonneuve Blvd., West Montreal, Quebec, Canada, H3G 1M8

    Nematollaah Shiri & Zhi Hong Zheng

Authors
  1. Nematollaah Shiri
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  2. Zhi Hong Zheng
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Editor information

Editors and Affiliations

  1. Universität Würzburg, Am Hubland, 97074, Würzburg, Germany

    Dietmar Seipel

  2. Department of Information Systems, Massey University, Information Science Research Centre, PO Box 756, Wellington, New Zealand

    José María Turull-Torres

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© 2004 Springer-Verlag Berlin Heidelberg

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Shiri, N., Zheng, Z.H. (2004). Challenges in Fixpoint Computation with Multisets. In: Seipel, D., Turull-Torres, J.M. (eds) Foundations of Information and Knowledge Systems. FoIKS 2004. Lecture Notes in Computer Science, vol 2942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24627-5_18

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  • DOI: https://doi.org/10.1007/978-3-540-24627-5_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20965-2

  • Online ISBN: 978-3-540-24627-5

  • eBook Packages: Springer Book Archive

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