Advertisement

Possibilistic Conditional Tables

  • Olivier Pivert
  • Henri Prade
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9616)

Abstract

On the one hand possibility theory and possibilistic logic offer a powerful representation setting in artificial intelligence for handling uncertainty in a qualitative manner. On the other hand conditional tables (c-tables for short) and their probabilistic extension provide a well-known setting for representing respectively incomplete and uncertain information in relational databases. Although these two settings rely on the idea of possible worlds, they have been developed and used independently. This paper investigates the links between possibility theory, possibilistic logic and c-tables, before introducing possibilistic c-tables and discussing their relation with a recent certainty-based approach to uncertain databases and their differences with probabilistic c-tables.

Keywords

Classical Logic Relational Algebra Possibility Distribution Possibilistic Logic Uncertain Information 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. Addison-Wesley, Reading (1995)zbMATHGoogle Scholar
  2. 2.
    Abiteboul, S., Kanellakis, P.C., Grahne, G.: On the representation and querying of sets of possible worlds. Theor. Comput. Sci. 78(1), 158–187 (1991)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Antova, L., Jansen, T., Koch, C., Olteanu, D.: Fast and simple processing of uncertain data. In: Proceedings of the 24th International Conference on Data Engineering (ICDE 2008), pp. 983–992 (2008)Google Scholar
  4. 4.
    Benjelloun, O., Das Sarma, A., Halevy, A., Theobald, M., Widom, J.: Databases with uncertainty and lineage. VLDB J. 17(2), 243–264 (2008)CrossRefGoogle Scholar
  5. 5.
    Benjelloun, O., Das Sarma, A., Halevy, A., Widom, J.: ULDBs: databases with uncertainty and lineage. In: Proceedings of VLDB 2006, pp. 953–964 (2006)Google Scholar
  6. 6.
    Bosc, P., Pivert, O.: About projection-selection-join queries addressed to possibilistic relational databases. IEEE T. Fuzzy Syst. 13(1), 124–139 (2005)CrossRefGoogle Scholar
  7. 7.
    Codd, E.F.: Extending the relational database model to capture more meaning. ACM Trans. Database Syst. 4(4), 397–434 (1979)CrossRefGoogle Scholar
  8. 8.
    Dalvi, N., Suciu, D.: Management of probabilistic data: foundations and challenges. In: Proceedings of PODS 2007, pp. 1–12 (2007)Google Scholar
  9. 9.
    Dubois, D., Lang, J., Prade, H.: Possibilistic logic. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A., Nute, D. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 3, pp. 439–513. Oxford University Press, Oxford (1994)Google Scholar
  10. 10.
    Dubois, D., Prade, H.: Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York (1988). (with the collaboration of H. Farreny, R. Martin-Clouaire, and C. Testemale)CrossRefzbMATHGoogle Scholar
  11. 11.
    Dubois, D., Prade, H.: Possibility theory: qualitative and quantitative aspects. In: Gabbay, D.M., Smets, P. (eds.) Quantified Representation of Uncertainty and Imprecision. Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 1, pp. 169–226. Kluwer Academic Publishers, Dordrecht (1998)CrossRefGoogle Scholar
  12. 12.
    Dubois, D., Prade, H.: Possibilistic logic – an overview. In: Siekmann, J.H. (ed.) Computational Logic. Handbook of the History of Logic, vol. 9, pp. 283–342. Elsevier, Amsterdam (2014)Google Scholar
  13. 13.
    Dubois, D., Prade, H., Schockaert, S.: Stable models in generalized possibilistic logic. In: Brewka, G., Eiter, T., McIlraith, S.A. (eds.) Proceedings of the 13th International Conference on Principles of Knowledge Representation and Reasoning (KR 2012), pp. 519–529. AAAI Press, Menlo Park (2012)Google Scholar
  14. 14.
    Gallaire, H., Minker, J.J. (eds.): Advances in Data Base Theory. In: Proceedings of the Symposium on Logic and Data Bases, Centre d’ Etudes et de Recherches de Toulouse, 1977. Plenum Press (1978)Google Scholar
  15. 15.
    Grahne, G.: The Problem of Incomplete Information in Relational Databases. LNCS, vol. 554. Springer, Heidelberg (1991)zbMATHGoogle Scholar
  16. 16.
    Green, C.: Theorem-proving by resolution as a basis for question-answering systems. In: Michie, D., Meltzer, B. (eds.) Machine Intelligence, vol. 4, pp. 183–205. Edinburgh University Press, Edinburgh (1969)Google Scholar
  17. 17.
    Green, T.J., Tannen, V.: Models for incomplete and probabilistic information. In: Proceedings of the IIDB 2006 Workshop, pp. 278–296 (2006)Google Scholar
  18. 18.
    Imielinski, T., Lipski, W.: Incomplete information in relational databases. J. ACM 31(4), 761–791 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Lang, J.: Possibilistic logic: complexity and algorithms. In: Kohlas, J., Moral, S. (eds.) Algorithms for Uncertainty and Defeasible Reasoning. Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol. 5, pp. 179–220. Kluwer Academic Publisher, Dordrecht (2001). (Gabbay, D.M. and Smets, Ph., eds.)Google Scholar
  20. 20.
    Lipski, W.: On semantic issues connected with incomplete information databases. ACM Trans. Database Syst. 4(3), 262–296 (1979)CrossRefGoogle Scholar
  21. 21.
    Lipski, W.: On databases with incomplete information. J. ACM 28, 41–70 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Pivert, O., Prade, H.: A certainty-based model for uncertain databases. IEEE Trans. Fuzzy Syst. 23(4), 1181–1196 (2015)CrossRefGoogle Scholar
  23. 23.
    Prade, H.: The connection between Lipski’s approach to incomplete information data bases and Zadeh’s possibility theory. In: Proceedings of the International Conference on Systems Methodology, Washington, D.C., 5–9 January, pp. 402–408 (1982)Google Scholar
  24. 24.
    Prade, H.: Lipski’s approach to incomplete information data bases restated and generalized in the setting of Zadeh’s possibility theory. Inf. Syst. 9(1), 27–42 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Prade, H., Testemale, C.: Generalizing database relational algebra for the treatment of incomplete/uncertain information and vague queries. Inf. Sci. 34(2), 115–143 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Shimizu, S., Ishihara, Y., Takarabe, T., Ito, M.: A probabilistic database model with representability of dependency among tuples. In: Proceedings of the 4th World Multiconference on Systemics, Cybernetics and Informatics (SCI 2000), pp. 221–225 (2000)Google Scholar
  27. 27.
    Suciu, D., Olteanu, D., Ré, C., Koch, C.: Probabilistic Databases. Synthesis Lectures on Data Management. Morgan & Claypool Publishers (2011)Google Scholar
  28. 28.
    Zadeh, L.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1(1), 3–28 (1978)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Irisa – EnssatUniversity of Rennes 1Lannion CedexFrance
  2. 2.IRIT, CNRS and University of ToulouseToulouse Cedex 9France
  3. 3.QCIS, University of TechnologySydneyAustralia

Personalised recommendations