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Proof Systems for Planning Under Cautious Semantics

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Abstract

Planning with incomplete knowledge becomes a very active research area since late 1990s. Many logical formalisms introduce sensing actions and conditional plans to address the problem. The action language \(\mathcal{A}_{K}\) invented by Son and Baral is a well-known framework for this purpose. In this paper, we propose so-called cautious and weakly cautious semantics for \(\mathcal{A}_{K}\), in order to allow an agent to generate and execute reliable plans in safety-critical environments. Intuitively speaking, cautious and weakly cautious semantics enable the agent to know exactly what happens after the execution of an action. Computational complexity analysis shows that cautious semantics reduces the reasoning complexity of \(\mathcal{A}_{K}\), it is also worth to point out that many useful domains could still be expressed with this setting. Another important contribution of our work is the development of Hoare style proof systems. These proof systems are served as inference mechanisms for the verification of conditional plans, and proved to be sound and complete. In addition, they could also be used for plan generation, in the sense that constructing a derivation is indeed a procedure to finding a plan. We point out that the proof systems posses a nice property for off-line planning, that is, the agent could generate and store short proofs in her spare time, and perform quick plan query by easily constructing a long proof from the stored shorter ones (under the assumption that sufficient proofs are stored).

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Notes

  1. A state is defined as a set of fluents in Son and Baral (2001), it is essentially the same as our definition here.

  2. It is equivalent to: check; If alarm_off Then defuse Else {switch; defuse}

  3. In fact, it has been pointed out in Malik Ghallab Dana (2004) that logical proof systems can play two roles in planning, i.e., the plan generator and validator.

  4. The term off-line planning is also mentioned in (Lin and Reiter 1997), but in a different context.

References

  • Apt, K. R., de Boer, F. S., & Olderog, E. R. (2009). Verification of sequential and concurrent programs, (3rd ed). Berlin: Springer.

  • Baldoni, M., Giordano, L., Martelli, A., & Patti, V. (2001). Reasoning about complex actions with incomplete knowledge: A modal approach. In ICTCS ’01, Vol. LNCS 2202. London, UK. UK:Springer.

  • Baral, C., Kreinovich, V., & Trejo, R. (2000). Computational complexity of planning and approximate planning in the presence of incompleteness. Artificial Intelligence 122, 241–267.

    Article  MathSciNet  MATH  Google Scholar 

  • Cadoli, M., & Donini, F. M. (1997). A survey on knowledge compilation. AI Communications, 10, 137–150.

    Google Scholar 

  • Etzioni, O., Hanks, S., Weld, D., Draper, D., Lesh, N., & Williamson, M. (1992). An approach to planning with incomplete information. In: In Proceedings of 3rd international conference on principles of knowledge representation and reasoning (pp. 115–125). Morgan Kaufmann.

  • Gerevini, A. E., Haslum, P., Long, D., Saetti, A., & Dimopoulos, Y. (2009). Deterministic planning in the fifth international planning competition: Pddl3 and experimental evaluation of the planners. Artificial Intelligence, 173(5C6), 619–668.

    Article  MathSciNet  MATH  Google Scholar 

  • Hähnle, R. (2001). Tableaux and related methods. Handbook of Automated Reasoning.

  • Herzig, A., Lang, J., & Marquis, P. (2003). Action representation and partially observable planning using epistemic logic. In IJCAI2003 (pp. 1067–1072).

  • Hoare, C. A. R. (1969). An axiomatic basis for computer programming. Communications of the ACM, 12, 576–580.

    Article  MATH  Google Scholar 

  • Howey, R., & Long, D. (2003). Val’s progress: The automatic validation tool for pddl2.1 used in the international planning competition.

  • Kartha, G. N. (1993). Soundness and completeness theorems for three formalizations of action. In IJCAI93 (pp. 724–731).

  • Levesque, H. J. (1996). What is planning in the presence of sensing? In: Proceedings of the national conference on artificial intelligence (AAAI) (pp. 1139–1146). Portland, Oregon: American Association for Artificial Intelligence.

  • Lifschitz, V. (1995). Nested abnormality theories. Artificial Intelligence, 74, 351–365.

    Article  MathSciNet  MATH  Google Scholar 

  • Lin, F. (2007). Situation calculus, chap. 16, pp. 649–669. Elsevier.

  • Lin, F., & Reiter, R. (1997). How to progress a database. Artificial Intelligence, 92, 131–167.

    Article  MathSciNet  MATH  Google Scholar 

  • Malik Ghallab Dana Nau, P. T. (2004). Automated planning: Theorey and practice. Los Altos, CA: Morgan Kaufmann Publishers.

    Google Scholar 

  • Moore, R. C. (1985). A formal theory of knowledge and action. In J. R. Hobbs, & R. C. Moore (Eds), Formal theories of the commonsense world (pp. 319–358). Norwood, NJ: Ablex.

  • Nieuwenborgh, D. V., Eiter, T., & Vermeir, D. (2007). Conditional planning with external functions. Lecture Notes in Computer Science, 4483, 214–227.

    Article  Google Scholar 

  • Oglietti, M. (2005). Understanding planning with incomplete information and sensing. Artificial Intelligence, 164(1–2), 171–208.

    Article  MathSciNet  MATH  Google Scholar 

  • Petrick, R. P. A., & Bacchus, F. (2004). Extending the knowledge-based approach to planning with incomplete information and sensing. In ICAPS-04 (pp. 2–11). AAAI Press.

  • Raimondi, F., Pecheur, C., & Brat, G. (2009). Pdver, a tool to verify pddl planning domains. In ICAPS workshop on VVPS (pp. 76–82).

  • Russell, S. J., & Norvig, P. (2009). Artificial intelligence: A modern approach (3rd ed). Englewood Cliffs, NJ: Prentice Hall.

    Google Scholar 

  • Sanjeev Arora, B. B. (2009). Computational complexity:a modern approach. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  • Scherl, R. B., & Levesque, H. J. (1993). The frame problem and knowledge-producing actions. In AAAI (pp. 689–695).

  • Scherl, R. B., & Levesque, H. J. (2003). Knowledge, action, and the frame problem. Artificial Intelligence, 144, 1–39.

    Article  MathSciNet  MATH  Google Scholar 

  • Son, T. C., & Baral, C. (2001). Formalizing sensing actions: A transition function based approach. Artificial Intelligence, 125(1–2), 19–91.

    Article  MathSciNet  MATH  Google Scholar 

  • Thielscher, M. (2005). Flux: A logic programming method for reasoning agents. Theory and Practice of Logic Programming, 5, 533–565.

    Article  MATH  Google Scholar 

  • Tu, P. H., Son, T. C., & Baral, C. (2007). Reasoning and planning with sensing actions, incomplete information, and static causal laws using answer set programming. Theory and Practice of Logic Programming, 7(4), 377–450.

    Article  MathSciNet  MATH  Google Scholar 

  • Vassos, S., & Levesque, H. J. (2007). Progression of situation calculus action theories with incomplete information. In IJCAI.

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Acknowledgments

This research was partially supported by the NSFC project under grant number 60970040, 61272059; the MOE project under grant number 05JJD72040122, 11JJD720020 and projects under grant numbers GD10YZX03 and WYM10114.

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Authors and Affiliations

  1. Department of Philosophy, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of China

    Yuping Shen

  2. Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of 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 Cautious Semantics. Minds & Machines 23, 5–45 (2013). https://doi.org/10.1007/s11023-012-9288-9

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