Possibilistic planning: Representation and complexity

  • Célia Da Costa Pereira
  • Frédérick Garcia
  • Jérôme Lange
  • Roger Martin-Clouaire
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1348)


A possibilistic approach of planning under uncertainty has been developed recently. It applies to problems in which the initial state is partially known and the actions have graded nondeterministic effects, some being more possible (normal) than the others. The uncertainty on states and effects of actions is represented by possibility distributions. The paper first recalls the essence of possibilitic planning concerning the representational aspects and the plan generation algorithms used to search either plans that lead to a goal state with a certainty greater than a given threshold or optimally safe plans that have maximal certainty to succeed. The computational complexity of possibilistic planning is then studied, showing quite favorable results compared to probabilistic planning.


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  1. 1.
    C. Bäckström. Computational complexity of reasoning about plans. PhD thesis, University of Linköping, 1992.Google Scholar
  2. 2.
    B. Bonet and H. Geffner. Arguing for decisions: a qualitative model for decision making. In Proc. of UAI'96, 1996.Google Scholar
  3. 3.
    C. Boutilier, T. Dean, and S. Hanks. New Directions in AI Planning, chapter Planning under uncertainty: structural assumptions and computational leverage, pages 157–172. IOS Press, Amsterdam, 1996.Google Scholar
  4. 4.
    C. Boutilier and R. Dearden. Using abstractions for decision-theoretic plCéliaanning with time constraints. In Proceedings AAAI, pages 1016–1022, 1994.Google Scholar
  5. 5.
    C. Boutilier and D. Poole. Computing optimal policies for partially observable decision processes using compact representations. In Proceedings AAAI'96, pages 1168–1175, 1996.Google Scholar
  6. 6.
    T. Bylander. The computational complexity of propositional strips planning. Artificial Intelligence, 69:161–204, 1994.Google Scholar
  7. 7.
    A.R. Cassandra, L.P. Kaelbling, and M.L. Littman. Acting optimally in partially observable stochastic domains. In Proceedings AAAI, pages 1023–1028, 1994.Google Scholar
  8. 8.
    D. Chapman. Planning for Conjunctive Goals. Artificial Intelligence, 32, 1987.Google Scholar
  9. 9.
    L. Chrisman. Abstract probabilistic modeling of action. In Proceedings AAAI, pages 28–36, 1992.Google Scholar
  10. 10.
    C. Da Costa Pereira, F. Garcia, J. Lang, and R. Martin-Clouaire. Planning with graded nondeterministic actions: a possibilistic approach. Int. J. of Intelligent Systems, 12(12), 1997.Google Scholar
  11. 11.
    M. De Glas and E. Jacopin. An algebric framework for uncertain strips planning. In Proceedings AIPS, 1994.Google Scholar
  12. 12.
    T. Dean and M. Boddy. Reasoning about Partially Ordered Events. Artificial Intelligence, 36:375–399, 1988.Google Scholar
  13. 13.
    A. Doan. Modeling probabilistic actions for practical decision-theoretic planning. In Proc. of AIPS'96, 1996.Google Scholar
  14. 14.
    D. Dubois and H. Prade. Possibility theory — an approach to computerized processing of uncertainty. Plenum Press, 1988.Google Scholar
  15. 15.
    D. Dubois and H. Prade. Fuzzy sets and probability: misunderstanding, bridges and gaps. In Proceeding of 2nd IEEE Int. Conf. on Fuzzy Systems, pages 1059-1068, 1993.Google Scholar
  16. 16.
    H. Erol, D. Nau, and V.S. Subrahmanian. Complexity, decidability and undecidability results for domain-independent planning. Artificial Intelligence, 76:75–88, 1995.Google Scholar
  17. 17.
    H. Fargier, J. Lang, and R. Sabbadin. Towards qualitative approaches to multistage decision making. In Proc. of IPMU'96, 1996.Google Scholar
  18. 18.
    F. Garcia and P. Laborie. New Directions in AI Planning, chapter Hierarchisation of the Search Space in Temporal Planning, pages 217–232. IOS Press, Amsterdam, 1996.Google Scholar
  19. 19.
    R. Goldman and M. Boddy. Epsilon-safe planning. In Proc. of UAI'94, pages 253–261, 1994.Google Scholar
  20. 20.
    J. Goldsmith, M. Littman, and M. Mundhenk. The complexity of plan existence and evaluation in probabilistic domains. In Proc. of UAI'97, pages 182–189, 1997.Google Scholar
  21. 21.
    P. Haddawy, A. Doan, and R. Goodwin. Efficient decision-theoretic planning: Techniques and empirical analysis. In Proc. of UAI'95, pages 229–236, 1995.Google Scholar
  22. 22.
    P. Haddawy and P. Hanks. Issues in decision-theoretic planning: utility functions for deadline goals. In Proc. of the.3rd Int. Conf. on Principles of Knowledge Representation and Reasoning (KR'92), pages 71–82, 1992.Google Scholar
  23. 23.
    S. Kambhampati and D.S. Nau. On the nature and role of modal truth criteria in planning. Artificial Intelligence, 1996.Google Scholar
  24. 24.
    C. Knoblock. Automatically generating abstractions for planning. Artificial Intelligence, 68:243–302, 1994.Google Scholar
  25. 25.
    N. Kushmerick, S. Hanks, and D.W Weld. An algorithm for probabilistic planning. Artificial Intelligence, 76:239–286, 1995.Google Scholar
  26. 26.
    M.L. Littman. Probabilistic propositional planning: representations and complexity. In Proceedings AAAI, pages 748–754, 1997.Google Scholar
  27. 27.
    D. McAllester and D. Rosenblitt. Systematic nonlinear planning. In Proceedings AAAI, pages 634–639, 1991.Google Scholar
  28. 28.
    C.H. Papadimitriou. Computational complexity. Addison-Wesley, 1994.Google Scholar
  29. 29.
    J.S. Penberthy and D. Weld. UCPOP: A sound, complete, partial-order planner for ADL. In Proc. of the 3rd Int. Conf. on Principles of Knowledge Representation and Reasoning (KR'92), pages 103–114, 1992.Google Scholar
  30. 30.
    L. Stockmeyer. The polynomial-time hierarchy. Theoretical Computer Science, 3:1–22, 1977.Google Scholar
  31. 31.
    S. Thiébaux, J. Hertzberg, W. Shoaff, and M. Schneider. A stochastic model of actions and plans for anytime planning under uncertainty. Int. J. of Intelligent Systems, 10(2):155–183, 1995.Google Scholar
  32. 32.
    Q. Yang and J. D. Tenenberg. Abstracting a nonlinear least commitment planner. In Proceedings AAAI, pages 204–209, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Célia Da Costa Pereira
    • 1
  • Frédérick Garcia
    • 1
  • Jérôme Lange
    • 2
  • Roger Martin-Clouaire
    • 1
  1. 1.INRA/BIA, AuzevilleCastanet Tolosan cedexFrance
  2. 2.IRITUniversité Paul SabatierToulouse cedexFrance

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