Hierarchical Decision Making by Autonomous Agents

  • Stijn Heymans
  • Davy Van Nieuwenborgh
  • Dirk Vermeir
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3229)

Abstract

Often, decision making involves autonomous agents that are structured in a complex hierarchy, representing e.g. authority. Typically the agents share the same body of knowledge, but each may have its own, possibly conflicting, preferences on the available information.

We model the common knowledge base for such preference agents as a logic program under the extended answer set semantics, thus allowing for the defeat of rules to resolve conflicts. An agent can express its preferences on certain aspects of this information using a partial order relation on either literals or rules. Placing such agents in a hierarchy according to their position in the decision making process results in a system where agents cooperate to find solutions that are jointly preferred.

We show that a hierarchy of agents with either preferences on rules or on literals can be transformed into an equivalent system with just one type of preferences. Regarding the expressiveness, the formalism essentially covers the polynomial hierarchy. E.g. the membership problem for a hierarchy of depth n is \(\sum{_{n+2}^P}\) -complete. We illustrate an application of the approach by showing how it can easily express a generalization of weak constraints, i.e. “desirable” constraints that do not need to be satisfied but where one tries to minimize their violation.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alferes, J.J., Pereira, L.M.: Updates plus preferences. In: Brewka, G., Moniz Pereira, L., Ojeda-Aciego, M., de Guzmán, I.P. (eds.) JELIA 2000. LNCS (LNAI), vol. 1919, pp. 345–360. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  2. 2.
    Baral, C.: Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge Press, Cambridge (2003)MATHCrossRefGoogle Scholar
  3. 3.
    Baral, C., Gelfond, M.: Reasoning agents in dynamic domains. In: Logic-based artificial intelligence, pp. 257–279. Kluwer Academic Publishers, Dordrecht (2000)Google Scholar
  4. 4.
    Brewka, G.: Logic programming with ordered disjunction. In: Proceedings of the 18th National Conference on Artificial Intelligence and Fourteenth Conference on Innovative Applications of Artificial Intelligence, Edmonton, Canada, July 2002, pp. 100–105. AAAI Press, Menlo Park (2002)Google Scholar
  5. 5.
    Brewka, G., Eiter, T.: Preferred answer sets for extended logic programs. Artificial Intelligence 109(1-2), 297–356 (1999)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Brewka, G., Niemela, I., Syrjanen, T.: Implementing ordered disjunction using answer set solvers for normal programs. In: Flesca et al. [14], pp. 444–455Google Scholar
  7. 7.
    Buccafurri, F., Faber, W., Leone, N.: Disjunctive logic programs with inheritance. In: De Schreye, D. (ed.) Logic Programming: The 1999 International Conference, Las Cruces, New Mexico, December 1999, pp. 79–93. MIT Press, Cambridge (1999)Google Scholar
  8. 8.
    Buccafurri, F., Gottlob, G.: Multiagent compromises, joint fixpoints, and stable models. In: Kakas, A.C., Sadri, F. (eds.) Computational Logic: Logic Programming and Beyond. LNCS (LNAI), vol. 2407, pp. 561–585. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  9. 9.
    Buccafurri, F., Leone, N., Rullo, P.: Strong and weak constraints in disjunctive datalog. In: Fuhrbach, U., Dix, J., Nerode, A. (eds.) LPNMR 1997. LNCS, vol. 1265, pp. 2–17. Springer, Heidelberg (1997)Google Scholar
  10. 10.
    Buccafurri, F., Leone, N., Rullo, P.: Disjunctive ordered logic: Semantics and expressiveness. In: Cohn, A.G., Schubert, L.K., Shapiro, S.C. (eds.) Proceedings of the 6th International Conference on Principles of Knowledge Representation and Reasoning, Trento, June 1998, pp. 418–431. Morgan Kaufmann, San Francisco (1998)Google Scholar
  11. 11.
    Buccafurri, F., Leone, N., Rullo, P.: Enhancing disjunctive datalog by constraints. Knowledge and Data Engineering 12(5), 845–860 (2000)CrossRefGoogle Scholar
  12. 12.
    Faber, W.: Disjunctive datalog with strong and weak constraints: Representational and computational issues. Master’s thesis, Institut for Informationssysteme, Technische Universit ätWien (1998)Google Scholar
  13. 13.
    Faber, W., Leone, N., Pfeifer, G.: Representing school timetabling in a disjunctive logic programming language. In: Proceedings of the 13th Workshop on Logic Programming, WLP 1998 (1998)Google Scholar
  14. 14.
    Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.): JELIA 2002. LNCS (LNAI), vol. 2424. Springer, Heidelberg (2002)MATHGoogle Scholar
  15. 15.
    Gabbay, D., Laenens, E., Vermeir, D.: Credulous vs. Sceptical Semantics for Ordered Logic Programs. In: Allen, J., Fikes, R., Sandewall, E. (eds.) Proceedings of the 2nd International Conference on Principles of Knowledge Representation and Reasoning, Cambridge, Mass, pp. 208–217. Morgan Kaufmann, San Francisco (1991)Google Scholar
  16. 16.
    Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R.A., Bowen, K.A. (eds.) Logic Programming, Proceedings of the Fifth International Conference and Symposium, Seattle, Washington, August 1988, pp. 1070–1080. The MIT Press, Cambridge (1988)Google Scholar
  17. 17.
    Kowalski, R.A., Sadri, F.: Logic programs with exceptions. In: Warren, D.H.D., Szeredi, P. (eds.) Proceedings of the 7th International Conference on Logic Programming, Jerusalem, pp. 598–613. The MIT Press, Cambridge (1990)Google Scholar
  18. 18.
    Laenens, E., Vermeir, D.: A logical basis for object oriented programming. In: van Eijck, J. (ed.) JELIA 1990. LNCS, vol. 478, pp. 317–332. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  19. 19.
    Van Nieuwenborgh, D., Heymans, S., Vermeir, D.: On programs with linearly ordered multiple preferences. In: Demoen, B., Lifschitz, V. (eds.) ICLP 2004. LNCS, vol. 3132, pp. 180–194. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  20. 20.
    Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)MATHGoogle Scholar
  21. 21.
    Sakama, C., Inoue, K.: Representing priorities in logic programs. In: Maher, M.J. (ed.) Proceedings of the 1996 Joint International Conference and Symposium on Logic Programming, Bonn, September 1996, pp. 82–96. MIT Press, Cambridge (1996)Google Scholar
  22. 22.
    Van Nieuwenborgh, D., Vermeir, D.: Preferred answer sets for ordered logic programs. In: Flesca et al. [14], pp. 432–443Google Scholar
  23. 23.
    Van Nieuwenborgh, D., Vermeir, D.: Order and negation as failure. In: Palamidessi, C. (ed.) ICLP 2003. LNCS, vol. 2916, pp. 194–208. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  24. 24.
    Van Nieuwenborgh, D., Vermeir, D.: Ordered diagnosis. In: Y. Vardi, M., Voronkov, A. (eds.) LPAR 2003. LNCS, vol. 2850, pp. 244–258. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  25. 25.
    Van Nieuwenborgh, D., Vermeir, D.: Ordered programs as abductive systems. In: Proceedings of the APPIA-GULP-PRODEConference on Declarative Programming (AGP 2003), pp. 374–385. Regio di Calabria, Italy (2003)Google Scholar
  26. 26.
    DeVos, M., Vermeir, D.: Logic programming agents playing games. In: Research and Development in Intelligent Systems XIX (ES 2002), BCS Conference Series, pp. 323–336. Springer, Heidelberg (2002)Google Scholar
  27. 27.
    Wang, K., Zhou, L., Lin, F.: Alternating fixpoint theory for logic programs with priority. In: Palamidessi, C., Moniz Pereira, L., Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS (LNAI), vol. 1861, pp. 164–178. Springer, Heidelberg (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Stijn Heymans
    • 1
  • Davy Van Nieuwenborgh
    • 1
  • Dirk Vermeir
    • 1
  1. 1.Dept. of Computer ScienceVrije Universiteit Brussel, VUBBrusselsBelgium

Personalised recommendations