Dynamically Ordered Probabilistic Choice Logic Programming

  • Marina De Vos
  • Dirk Vermeir
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1974)

Abstract

We present a framework for decision making under uncertainty where the priorities of the alternatives can depend on the situation at hand. We design a logic-programming language, DOP-CLP, that allows the user to specify the static priority of each rule and to declare, dynamically, all the alternatives for the decisions that have to be made. In this paper we focus on a semantics that reflects all possible situations in which the decision maker takes the most rational, possibly probabilistic, decisions given the circumstances. Our model theory, which is a generalization of classical logic-programming model theory, captures uncertainty at the level of total Herbrand interpretations. We also demonstrate that DOP-CLPs can be used to formulate game theoretic concepts.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Fahiem Bacchus. LP, a Logic for Representing and Reasoning with Statistical Knowledge. Computational Intelligence, 6:209–231, 1990.CrossRefGoogle Scholar
  2. [2]
    Gerhard Brewka. Well-Founded Semantics for Extended Logic Programs with Dynamic Preferences. Journal of Articficial Intelligence Research, 4:19–36, 1996.MATHMathSciNetGoogle Scholar
  3. [3]
    Francesco Buccafurri, Wolfgang Faber, and Nicola Leone. Disjunctive Logic Programs with Inheritance. In Danny De Schreye, editor, International Conference on Logic Pro-gramming (ICLP), pages 79–93, Las Cruces, New Mexico, USA, 1999. The MIT Press.Google Scholar
  4. [4]
    Marina De Vos and Dirk Vermeir. Choice Logic Programs and Nash Equilibria in Strategic Games. In Jörg Flum and Mario Rodríguez-Artalejo, editors, Computer Science Logic (CSL’99), volume 1683 of Lecture Notes in Computer Science, pages 266–276, Madrid, Spain, 1999. Springer Verslag.CrossRefGoogle Scholar
  5. [5]
    Marina De Vos and Dirk Vermeir. On the Role of Negation in Choice Logic Programs. In Michael Gelfond, Nicola Leone, and Gerald Pfeifer, editors, Logic Programming and Non-Monotonic Reasoning Conference (LPNMR’99), volume 1730 of Lecture Notes in Artificial Intelligence, pages 236–246, El Paso, Texas, USA, 1999. Springer Verslag.Google Scholar
  6. [6]
    Marina De Vos and Dirk Vermeir. A Logic for Modelling Decision Making with Dynamic Preferences. Accepted at Jelia 2000. Lecture Notes in Artificial Intelligence. Springer Ver-slag.Google Scholar
  7. [7]
    Phan Minh Dung. On the acceptability of arguments and its fundamental role in nonmono-tonic reasoning, logic programming and n-person games. Artificial Intelligence, 77(2):321–358, 1995.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    D. Gabbay, E. Laenens, and D. Vermeir. Credulous vs. Sceptical Semantics for Ordered Logic Programs. In J. Allen, R. Fikes, and E. Sandewall, editors, Proceedings of the 2nd In-ternational Conference on Principles of Knowledge Representation and Reasoning, pages 208–217, Cambridge, Mass, 1991. Morgan Kaufmann.Google Scholar
  9. [9]
    Raymond Ng and V.S. Subrahmanian. A semantical framework for supporting subjective and conditional probabilities in deductive databases. In Koichi Furukawa, editor, Proceed-ings of the 8th International Conference on Logic Programming, pages 565–580. MIT, June 1991.Google Scholar
  10. [10]
    Liem Ngo. Probabilistic Disjunctive Logic Programming. In Eric Horvitz and Finn Jensen, editors, Proceedings of the 12th Conference on Uncertainty in Artificial Intelligence (AI-96), pages 387–404, San Francisco, aug 1996. Morgan Kaufmann Publishers.Google Scholar
  11. [11]
    Martin J. Osborne and Ariel Rubinstein. A Course in Game Theory. The MIT Press, Cambridge, Massachusets, London, Engeland, third edition, 1996.Google Scholar
  12. [12]
    David Poole. Logic programming, abduction and probability. In Institute for New Gener-ation Computer Technology (ICOT), editor, Proceedings for the International Conference on Fifth Generation Computer Systems, pages 530–538. IOS Press, 1992.Google Scholar
  13. [13]
    David Poole. The independent choice logic for modeling multiple agents under uncertainty. Artificial Intelligence, 94(1–2):7–56, 1997.MATHCrossRefMathSciNetGoogle Scholar
  14. [14]
    Chiaki Sakama and Katsumi Inoue. Representing Priorities in Logic Programs. In Michael Maher, editor, Proceedings of the 1996 Joint International Conference and Symposium on Logic Programming, pages 82–96, Cambridge, September2-6 1996. MIT Press.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Marina De Vos
    • 1
  • Dirk Vermeir
    • 1
  1. 1.Dept. of Computer ScienceFree University of BrusselsBrusselsBelgium

Personalised recommendations