Skip to main content
SpringerLink
Log in

Proof systems for planning under 0-approximation semantics

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

In this paper we propose Hoare style proof systems called PR 0 D and PRKW 0 D for plan generation and plan verification under 0-approximation semantics of the action language A K . In PR 0 D (resp. PRKW 0 D ), a Hoare triple of the form {X}c{Y} (resp. {X}c{KW p }) means that all literals in Y become true (resp. p becomes known) after executing plan c in a state satisfying all literals in X. The proof systems are shown to be sound and complete, and more importantly, they give a way to efficiently generate and verify longer plans from existing verified shorter plans by applying so-called composition rule, provided that an enough number of shorter plans have been properly stored. The idea behind is a tradeoff between space and time, we refer it to off-line planning and point out that it could be applied to general planning problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Moore R C. A formal theory of knowledge and action. In: Hobbs J R, Moore R C, eds. Formal Theories of the Commonsense World. New Jersey: Norwood, 1985. 319–358

    Google Scholar 

  2. Scherl R B, Levesque H J. Knowledge, action, and the frame problem. Artif Intell, 2003, 144: 1–39

    Article  MATH  MathSciNet  Google Scholar 

  3. Tu P H, Son T C, Baral C. Reasoning and planning with sensing actions, incomplete information, and static causal laws using answer set programming. Theory Pract Log Program, 2007, 7: 377–450

    Article  MATH  MathSciNet  Google Scholar 

  4. Petrick R P A, Bacchus F. Extending the knowledge-based approach to planning with incomplete information and sensing. In: Proceedings of the 9th International Conference on Principles of Knowledge Representation and Reasoning, Whistler, 2004. 613-622

  5. Oglietti M. Understanding planning with incomplete information and sensing. Artif Intell, 2005, 164: 171–208

    Article  MATH  MathSciNet  Google Scholar 

  6. Nieuwenborgh D V, Eiter T, Vermeir D. Conditional planning with external functions. In: Proceedings of the 9th International Conference on Logic Programming and Nonmonotonic Reasoning, Tempe, 2007. 214–227

    Chapter  Google Scholar 

  7. Son T C, Baral C. Formalizing sensing actions: a transition function based approach. Artif Intell, 2001, 125: 19–91

    Article  MATH  MathSciNet  Google Scholar 

  8. Baral C, Kreinovich V, Trejo R. Computational complexity of planning and approximate planning in the presence of incompleteness. Artif Intell, 2000, 122: 241–267

    Article  MATH  MathSciNet  Google Scholar 

  9. Gerevini A E, Haslum P, Long D, et al. Deterministic planning in the fifth international planning competition: Pddl3 and experimental evaluation of the planners. Artif Intell, 2009, 173: 619–668

    Article  MATH  MathSciNet  Google Scholar 

  10. Raimondi F, Pecheur C, Brat G. Pdver, a tool to verify pddl planning domains. In: Proceedings of Workshop on Verification and Validation of Planning and Scheduling Systems, Thessaloniki, 2009. 76–82

    Google Scholar 

  11. Howey R, Long D. Val’s progress: the automatic validation tool for pddl2.1 used in the international planning competition. In: Proceedings of the 13th International Conference on Automated Planning and Scheduling, Trento, 2003. 52–61

    Google Scholar 

  12. Traverso P, Ghallab M, Nau D. Automated Planning: Theorey and Practice. Amsterdam: Morgan Kaufmann Publishers, 2004

    Google Scholar 

  13. Rintanen J. Planning and SAT, Handbook of Satisfiability. Amsterdam: IOS Press, 2009. 483–503

    Google Scholar 

  14. Kautz H A, Selman B, Hoffmann J. Planning as satisfiability. In: Proceedings of the 10th European conference on Artificial intelligence, Vienna, 1992. 359–363

    Google Scholar 

  15. Dimopoulos Y, Hashmi M A, Moraitis P. µ-satplan: multi-agent planning as satisfiability. Knowl-Based Syst, 2012, 29: 54–62

    Article  Google Scholar 

  16. Otwell C, Remshagen A, Truemper K. An effective QBF solver for planning problems. In: MSV/AMCS. CSREA Press, 2004. 311–316

    Google Scholar 

  17. Luca M D, Giunchiglia E, Narizzano M, et al. “Safe planning” as a QBF evaluation problem. In: Proceedings of the 2nd RoboCare Workshop, Genova, 2005

    Google Scholar 

  18. Reiter R. Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems. Cambridge: MIT Press, 2001

    Google Scholar 

  19. Kartha G N. Soundness and completeness theorems for three formalizations of action. In: Proceedings of the 13th International Joint Conference on Artificial Intelligence, Chambéry, 1993. 724–731

    Google Scholar 

  20. Lin F, Shoham Y. Provably correct theories of action. J ACM, 1995, 42: 293–320

    Article  MATH  MathSciNet  Google Scholar 

  21. Lin F, Reiter R. How to progress a database. Artif Intell, 1997, 92: 131–167

    Article  MATH  MathSciNet  Google Scholar 

  22. Hoare C A R. An axiomatic basis for computer programming. Commun ACM, 1969, 12: 576–580

    Article  MATH  Google Scholar 

  23. Ernst-Rüdiger O, Krzysztof R A, Frank S B. Verification of Sequential and Concurrent Programs. Springer, 2009

    MATH  Google Scholar 

  24. Barak B, Arora S. Computational Complexity: a Modern Approach. Cambridge: Cambridge University Press, 2009

    Google Scholar 

  25. Cadoli M, Donini F M. A survey on knowledge compilation. AI Commun, 1997, 10: 137–150

    Google Scholar 

  26. Russell S J, Norvig P. Artificial Intelligence: a Modern Approach. Englewood Cliffs: Prentice Hall, 2009

    Google Scholar 

  27. Robinson A, Voronkov A, eds. Handbook of Automated Reasoning. Cambridge: Elsevier and MIT Press, 2001

    MATH  Google Scholar 

  28. Li W. Logical verification of scientific discovery. Sci China Inf Sci, 2010, 53: 677–684

    Article  MathSciNet  Google Scholar 

  29. Hinchey M, Bowen J P, Vassev E. Formal methods. In: Marciniak J J, ed. Encyclopedia of Software Engineering. Taylor & Francis, 2010. 308–320

    Google Scholar 

  30. Grumberg O, Clarke E M, Peled D A. Model Checking. Cambridge: MIT Press, 1999

    MATH  Google Scholar 

  31. Grumberg O, Veith H. 25 Years of Model Checking—History, Achievements, Perspectives. Berlin/Heidelberg: Springer-Verlag, 2008

    Book  MATH  Google Scholar 

  32. Cimatti A, Roveri M, Traverso P. Automatic obdd-based generation of universal plans in non-deterministic domains. In: Proceedings of the 15th National/10th Conference on Artificial Intelligence/Innovative Applications of Artificial Intelligence, Madison, 1998. 875–881

    Google Scholar 

  33. Cimatti A, Roveri M. Conformant planning via symbolic model checking. J Artif Intell Res, 2000, 13: 305–338

    MATH  Google Scholar 

  34. Biere A, Cimatti A, Clarke EM, et al. Symbolic model checking without BDDs. In: Proceedings of the 5th International Conference on Tools and Algorithms for Construction and Analysis of Systems, London, 1999. 193–207

    Chapter  Google Scholar 

  35. Tu P H, Son T C, Gelfond M, et al. Approximation of action theories and its application to conformant planning. Artif Intell, 2011, 175: 79–119

    Article  MATH  MathSciNet  Google Scholar 

  36. Eiter T, Faber W, Leone N, et al. Answer set planning under action costs. J Artif Intell Res, 2003, 19: 25–71

    MATH  MathSciNet  Google Scholar 

  37. Stephan W, Biundo S. A new logical framework for deductive planning. In: Proceedings of the 13th International Joint Conference on Artificial Intelligence, Chambéry, 1993. 32–38

    Google Scholar 

  38. Levesque H J, Reiter R, Lin F, et al. GOLOG: a logic programming language for dynamic domains. J Log Progr, 1997, 31: 59–83

    Article  MATH  MathSciNet  Google Scholar 

  39. Thielscher M. Flux: a logic programming method for reasoning agents. Theor Pract Log Prog, 2005, 5: 533–565

    Article  MATH  Google Scholar 

  40. Krogt R V D, Weerdt M D. Plan repair as an extension of planning. In: Proceedings of the 15th International Conference on Automated Planning and Scheduling, Monterey, 2005. 161–170

    Google Scholar 

  41. Fox M, Gerevini A, Long D, et al. Plan stability: replanning versus plan repair. In: Proceedings of the 16th International Conference on Automated Planning and Scheduling, Ambleside, 2006. 212–221

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Philosophy, Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou, 510275, China

    YuPing Shen

  2. Institute of Logic and Cognition, Department of Philosophy, Sun Yat-sen University, Guangzhou, 510275, China

    XiShun Zhao

Authors
  1. YuPing Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. XiShun Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to XiShun Zhao.

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shen, Y., Zhao, X. Proof systems for planning under 0-approximation semantics. Sci. China Inf. Sci. 57, 1–12 (2014). https://doi.org/10.1007/s11432-013-4854-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-013-4854-1

Keywords

Search

Navigation