Communicating ASP and the Polynomial Hierarchy

  • Kim Bauters
  • Steven Schockaert
  • Dirk Vermeir
  • Martine De Cock
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6645)


Communicating answer set programming is a framework to represent and reason about the combined knowledge of multiple agents using the idea of stable models. The semantics and expressiveness of this framework crucially depends on the nature of the communication mechanism that is adopted. The communication mechanism we introduce in this paper allows us to focus on a sequence of programs, where each program in the sequence may successively eliminate some of the remaining models. The underlying intuition is that of leaders and followers: each agent’s decisions are limited by what its leaders have previously decided. We show that extending answer set programs in this way allows us to capture the entire polynomial hierarchy.


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  1. 1.
    Bauters, K., Janssen, J., Schockaert, S., Vermeir, D., De Cock, M.: Communicating answer set programs. In: Tech. Comm. of ICLP 2010, vol. 7, pp. 34–43 (2010)Google Scholar
  2. 2.
    Brain, M., De Vos, M.: Implementing OCLP as a front-end for answer set solvers: From theory to practice. In: Proc. of ASP 2005 (2003)Google Scholar
  3. 3.
    Brewka, G., Eiter, T.: Equilibria in heterogeneous nonmonotonic multi-context systems. In: Proc. of AAAI 2007, pp. 385–390 (2007)Google Scholar
  4. 4.
    Brewka, G., Roelofsen, F., Serafini, L.: Contextual default reasoning. In: Proc. of. IJCAI 2007, pp. 268–273 (2007)Google Scholar
  5. 5.
    Buccafurri, F., Caminiti, G., Laurendi, R.: A logic language with stable model semantics for social reasoning. In: Garcia de la Banda, M., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 718–723. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Bylander, T.: The computational complexity of propositional STRIPS planning. Artificial Intelligence 69, 165–204 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Dao-Tran, M., Eiter, T., Fink, M., Krennwallner, T.: Modular nonmonotonic logic programming revisited. In: Hill, P.M., Warren, D.S. (eds.) ICLP 2009. LNCS, vol. 5649, pp. 145–159. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    De Vos, M., Crick, T., Padget, J., Brain, M., Cliffe, O., Needham, J.: LAIMA: A multi-agent platform using ordered choice logic programming. In: Baldoni, M., Endriss, U., Zhang, S.-W., Torroni, P. (eds.) DALT 2005. LNCS (LNAI), vol. 3904, pp. 72–88. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Dell’Acqua, P., Sadri, F., Toni, F.: Communicating agents. In: Proc. of MASL 1999 (1999)Google Scholar
  10. 10.
    Eiter, T., Gottlob, G.: The complexity of logic-based abduction. Journal of the ACM 42, 3–42 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Eiter, T., Ianni, G., Lukasiewicz, T., Schindlauer, R., Tompits, H.: Combining answer set programming with description logics for the semantic web. Artifial Intelligence 172(12-13), 1495–1539 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Eiter, T., Ianni, G., Schindlauer, R., Tompits, H.: A uniform integration of higher-order reasoning and external evaluations in answer-set programming. In: Proc. of IJCAI 2005, pp. 90–96 (2005)Google Scholar
  13. 13.
    Eiter, T., Ianni, G., Schindlauer, R., Tompits, H.: dlvhex: A tool for semantic-web reasoning under the answer-set semantics. In: Proc. of ALPSWS 2006, pp. 33–39 (2006)Google Scholar
  14. 14.
    Gelder, A.V., Ross, K.A., Schlipf, J.S.: The well-founded semantics for general logic programs. Journal of the ACM 38(3), 620–650 (1991)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Gelfond, M., Lifzchitz, V.: The stable model semantics for logic programming. In: Proc. of ICLP 1988, pp. 1081–1086 (1988)Google Scholar
  16. 16.
    Giunchiglia, F., Serafini, L.: Multilanguage hierarchical logics or: How we can do without modal logics. Artifial Intelligence 65(1), 29–70 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Jeroslow, R.: The polynomial hierarchy and a simple model for competitive analysis. Mathematical Programming 32, 146–164 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Luo, J., Shi, Z., Wang, M., Huang, H.: Multi-agent cooperation: A description logic view. In: Lukose, D., Shi, Z. (eds.) PRIMA 2005. LNCS, vol. 4078, pp. 365–379. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    Papadimitriou, C.: Computational complexity. Addison-Wesley, Reading (1994)zbMATHGoogle Scholar
  20. 20.
    Roelofsen, F., Serafini, L.: Minimal and absent information in contexts. In: Proc. of IJCAI 2005, pp. 558–563 (2005)Google Scholar
  21. 21.
    Van Nieuwenborgh, D., De Vos, M., Heymans, S., Hadavandi, E.: Hierarchical decision making in multi-agent systems using answer set programming. In: Inoue, K., Satoh, K., Toni, F. (eds.) CLIMA 2006. LNCS (LNAI), vol. 4371, pp. 20–40. Springer, Heidelberg (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Kim Bauters
    • 1
  • Steven Schockaert
    • 1
  • Dirk Vermeir
    • 2
  • Martine De Cock
    • 1
  1. 1.Department of Applied Mathematics and Computer ScienceUniversiteit GentGentBelgium
  2. 2.Department of Computer ScienceVrije Universiteit BrusselBrusselBelgium

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