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Proof systems for planning under 0-approximation semantics

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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.

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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 

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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

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  1. YuPing Shen
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  2. XiShun Zhao
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Correspondence to XiShun Zhao.

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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

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