SIGIR ’94 pp 122-130 | Cite as

A Probabilistic Terminological Logic for Modelling Information Retrieval

  • Fabrizio Sebastiani
Conference paper

Abstract

Some researchers have recently argued that the task of Information Retrieval (IR) may successfully be described by means of mathematical logic; accordingly, the relevance of a given document to a given information need should be assessed by checking the validity of the logical formula dn,where d is the representation of the document, n is the representation of the information need and “→” is the conditional connective of the logic in question. In a recent paper we have proposed Terminological Logics (TLs) as suitable logics for modelling IR within the paradigm described above. This proposal, however, while making a step towards adequately modelling IR in a logical way, does not account for the fact that the relevance of a document to an information need can only be assessed up to a limited degree of certainty. In this work, we try to overcome this limitation by introducing a model of IR based on a Probabilistic TL, i.e. a logic allowing the expression of real-valued terms representing probability values and possibly involving expressions of a TL. Two different types of probabilistic information, i.e. statistical information and information about degrees of belief, can be accounted for in this logic. The paper presents a formal syntax and a denotational (possible-worlds) semantics for this logic, and discusses, by means of a number of examples, its adequacy as a formal tool for describing IR.

Keywords

Entropy 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    F. Bacchus. Representing and reasoning with probabilistic knowledge. MIT Press, Cambridge, MA,. 1990.Google Scholar
  2. 2.
    F. Bacchus, A. Grove, J. Y. Halpern, and D. Koller. From statistics to beliefs. In Proceedings of AAAI-92, 10th Conference of the American Association for Artificial Intelligence, pages 602–608, San Jose, CA, 1992.Google Scholar
  3. 3.
    A. Grove, J. Y. Halpern, and D. Koller. Random worlds and maximum entropy. In Proceedings of the 7th annual IEEE Symposium in Logic in Computer Science, pages 22–33, Santa Cruz, CA, 1992.CrossRefGoogle Scholar
  4. 4.
    J. Y. Halpern. An analysis of first-order logics of probability. Artificial Intelligence, 46: 311–350, 1990.MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    J. Y. Halpern and Y. O. Moses. A guide to completeness and complexity for modal logics of knowledge and belief. Artificial Intelligence, 54: 319–379, 1992.MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    W. L. Harper, R. Stalnaker, and G. Pearce, editors. Ifs. Conditionals, belief, decision, chance and time. Reidel, Dordrecht, NL, 1981.Google Scholar
  7. 7.
    S. A. Kripke. Semantical analysis of modal logic. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 9: 67–96, 1963.MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    H. Kyburg. The reference class. Philosophy of science, 50: 374–397, 1983.MathSciNetGoogle Scholar
  9. 9.
    C. Meghini, F. Sebastiani, U. Straccia, and C. Thanos. A model of information retrieval based on a terminological logic. In Proceedings of SIGIR-93, 16th ACM International Conference on Research and Development in Information Retrieval, pages 298–307, Pittsburgh, PA, 1993.CrossRefGoogle Scholar
  10. 10.
    F. Sebastiani. A model of information retrieval based on a probabilistic terminological logic (extended version). Technical report, Istituto di Elaborazione dell’Informazione, Consiglio Nazionale delle Ricerche, Pisa, Italy, 1994. Forthcoming.Google Scholar
  11. 11.
    C. J. van Rijsbergen. A non-classical logic for information retrieval. The Computer Journal, 29: 48 1485, 1986.Google Scholar
  12. 12.
    C. J. van Rijsbergen. Probabilistic retrieval revisited. The Computer Journal, 35: 291–298, 1992.MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 1994

Authors and Affiliations

  • Fabrizio Sebastiani
    • 1
  1. 1.Istituto di Elaborazione dell’InformazioneConsiglio Nazionale delle RicerchePisaItaly

Personalised recommendations