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Complexity of multi-agent conformant planning with group knowledge

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Abstract

In this paper, we propose a dynamic epistemic framework to capture the knowledge evolution in multi-agent systems where agents are not able to observe. We formalize multi-agent conformant planning with group knowledge, and reduce planning problems to model checking problems. We prove that multi-agent conformant planning with group knowledge is Pspace-complete on the size of dynamic epistemic models. We also consider the alternative Kripke semantics, and show that for each Kripke model with perfect recall and no miracles, there is an equivalent dynamic epistemic model and vice versa.

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References

  • Ågotnes, T., & Wáng, Y. N. (2017). Resolving distributed knowledge. Artificial Intelligence, 252, 1–21. https://doi.org/10.1016/j.artint.2017.07.002

    Article  Google Scholar 

  • Alur, R., Henzinger, T. A., & Kupferman, O. (2002). Alternating-time temporal logic. Journal of the ACM, 49(5), 672–713. https://doi.org/10.1145/585265.585270

    Article  Google Scholar 

  • Andersen, M. B., Bolander, T., & Jensen, M. H. (2012). Conditional epistemic planning. In L. F. del Cerro, A. Herzig, & J. Mengin (Eds.), Logics in artificial intelligence (pp. 94–106). Springer.

    Chapter  Google Scholar 

  • Andersen, M. B., Bolander, T., & Jensen, M. H. (2015). Don’t plan for the unexpected: Planning based on plausibility models. Logique et Analyse, 58, 145–176.

    Google Scholar 

  • Aucher, G., & Bolander, T. (2013). Undecidability in epistemic planning. In: Proceedings of IJCAI ’13 (pp. 27–33).

  • Bolander, T., & Andersen, M. B. (2011). Epistemic planning for single and multi-agent systems. Journal of Applied Non-classical Logics, 21(1), 9–34.

    Article  Google Scholar 

  • Bolander, T., Charrier, T., Pinchinat, S., et al. (2020). DEL-based epistemic planning: Decidability and complexity. Artificial Intelligence, 287, 1–34.

    Article  Google Scholar 

  • Bolander, T., Engesser, T., & Herzig, A., et al. (2019). The dynamic logic of policies and contingent planning. In: JELIA.

  • Bonet, B. (2010). Conformant plans and beyond: Principles and complexity. Artificial Intelligence, 174(3–4), 245–269.

    Article  Google Scholar 

  • Douéneau-Tabot, G., Pinchinat, S., & Schwarzentruber, F. (2018). Chain-monadic second order logic over regular automatic trees and epistemic planning synthesis. In: Advances in modal logic.

  • Fagin, R., Halpern, J., Moses, Y., et al. (1995). Reasoning about knowledge. MIT Press.

    Google Scholar 

  • Fervari, R., Herzig, A., & Li, Y., et al. (2017). Strategically knowing how. In: Proceedings of IJCAI’17 (pp. 1031—1038).

  • Gabbay, D. M., Kurucz, A., Wolter, F., et al. (2003). Many-dimensional modal logics: Theory and applications. Elsevier.

    Google Scholar 

  • Geffner, H., & Bonet, B. (2013). A concise introduction to models and methods for automated planning. Synthesis Lectures on Artificial Intelligence and Machine Learning, 8(1), 1–141.

    Google Scholar 

  • Ghallab, M., Nau, D., & Traverso, P. (2004). Automated planning: Theory and practice. Morgan Kaufmann.

    Google Scholar 

  • Halpern, J. Y., & Vardi, M. Y. (1989). The complexity of reasoning about knowledge and time. I. Lower bounds. Journal of Computer and System Sciences, 38(1), 195–237. https://doi.org/10.1016/0022-0000(89)90039-1

    Article  Google Scholar 

  • Haslum, P., & Jonsson, P. (2000). Some results on the complexity of planning with incomplete information. In: Biundo, S., Fox, M. (Eds.), Recent advances in AI planning. Springer, Lecture Notes in Computer Science, (pp 308–318). https://doi.org/10.1007/10720246_24.

  • Jamroga, W., & Ågotnes, T. (2007). Constructive knowledge: What agents can achieve under imperfect information. Journal of Applied Non-classical Logics, 17(4), 423–475.

    Article  Google Scholar 

  • Li, K., & Wang, Y. (2015). From rules to runs: A dynamic epistemic take on imperfect information games. Studies in Logic (pp. 74–107)

  • Li, Y., & Wang, Y. (2017). Achieving while maintaining: A logic of knowing how with intermediate constraints. In: Proceedings of ICLA’17 (pp 154–167).

  • Li, Y. (2016). Stopping means achieving: A weaker logic of knowing how. Studies in Logic, 9(4), 34–54.

    Google Scholar 

  • Li, Y. (2021). Multi-agent conformant planning with distributed knowledge. In S. Ghosh & T. Icard (Eds.), Logic, rationality, and interaction (pp. 128–140). Springer.

    Chapter  Google Scholar 

  • Li, Y., & Wang, Y. (2019). Multi-agent knowing how via multi-step plans: A dynamic epistemic planning based approach. In P. Blackburn, E. Lorini, & M. Guo (Eds.), Logic, rationality, and interaction (pp. 126–139). Springer.

    Chapter  Google Scholar 

  • Li, Y., Yu, Q., & Wang, Y. (2017). More for free: A dynamic epistemic framework for conformant planning over transition systems*. Journal of Logic and Computation, 27(8), 2383–2410.

    Article  Google Scholar 

  • Liu, Q., & Liu, Y. (2018). Multi-agent epistemic planning with common knowledge. In: Proceedings of the twenty-seventh international joint conference on artificial intelligence (pp. 1912–1920)

  • Lomuscio, A., & Penczek, W. (2012). Symbolic model checking for temporal-epistemic logic. In: Artikis A, Craven R, Kesim Çiçekli N, et al (Eds.), Logic Programs, Norms and Action: Essays in Honor of Marek J. Sergot on the Occasion of His 60th Birthday. Lecture Notes in Computer Science, Springer, (pp. 172–195) https://doi.org/10.1007/978-3-642-29414-3_10.

  • Maubert, B., Murano, A., & Pinchinat, S., et al. (2020). Dynamic epistemic logic games with epistemic temporal goals. arXiv:2001.07141

  • Maubert, B., Pinchinat, S., & Schwarzentruber, F. (2019). Reachability games in dynamic epistemic logic. In: Proceedings of the twenty-eighth international joint conference on artificial intelligence. (pp. 499–505). https://www.ijcai.org/proceedings/2019/71.

  • Maubert, B., Pinchinat, S., & Schwarzentruber, F., et al. (2020). Concurrent games in dynamic epistemic logic. pp 1877–1883. https://doi.org/10.24963/ijcai.2020/260.

  • Rintanen, J. (2004). Complexity of planning with partial observability. In: Proceedings of the 14th International Conference on Automated Planning and Scheduling, ICAPS 2004.

  • Savitch, W. J. (1970). Relationships between nondeterministic and deterministic tape complexities. Journal of Computer and System Sciences, 4(2), 177–192. https://doi.org/10.1016/S0022-0000(70)80006-X

    Article  Google Scholar 

  • Schmidt, R. A., & Tishkovsky, D. (2002). Combining dynamic logic with doxastic modal logics. Advances in Modal Logic, 4, 371–391.

    Google Scholar 

  • Smith, D. E., & Weld, D. S. (1998). Conformant graphplan. AAAI-98 proceedings (pp. 889–896). American Association for Artificial Intelligence.

    Google Scholar 

  • van Benthem, J., Gerbrandy, J., Hoshi, T., et al. (2009). Merging frameworks for interaction. Journal of Philosophical Logic, 38(5), 491–526.

    Article  Google Scholar 

  • van der Hoek, W., & Wooldridge, M. (2003). Cooperation, knowledge, and time: Alternating-time temporal epistemic logic and its applications. Studia Logica, 75, 125–157. https://doi.org/10.1023/A:1026185103185

    Article  Google Scholar 

  • van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic epistemic logic. Springer. https://doi.org/10.1007/978-1-4020-5839-4

    Article  Google Scholar 

  • van Otterloo, S., & Jonker, G. (2005). On epistemic temporal strategic logic. Electronic Notes in Theoretical Computer Science, 126, 77–92. https://doi.org/10.1016/j.entcs.2004.11.014

    Article  Google Scholar 

  • van der Hoek, W., & Wooldridge, M. (2002). Tractable multiagent planning for epistemic goals. In: Proceedings of AAMAS’02 (pp. 1167–1174).

  • Wang, Y. (2015). A logic of knowing how. In: Proceedings of LORI’15 (pp. 392–405). https://doi.org/10.1007/978-3-662-48561-3_32.

  • Wang, Y. (2018). A logic of goal-directed knowing how. Synthese, 195, 4419–4439.

    Article  Google Scholar 

  • Wang, Y., & Cao, Q. (2013). On axiomatizations of public announcement logic. Synthese, 190, 103–134. https://doi.org/10.1007/s11229-012-0233-5

    Article  Google Scholar 

  • Warshall, S. (1962). A theorem on Boolean matrices. Journal of the ACM, 9(1), 11–12. https://doi.org/10.1145/321105.321107

    Article  Google Scholar 

  • Wu, P., & Li, Y. (2020). A logic for multi-agent conformant planning over transition systems. IEEE Access, 8, 193621–193631. https://doi.org/10.1109/ACCESS.2020.3032901

    Article  Google Scholar 

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Acknowledgements

The author thanks the support from the National Social Science Foundation for Young Scholars of China (Grant No. 18CZX062). The author is also grateful to the anonymous reviewers of this journal, whose detailed comments helped to improve the presentation of the paper.

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  1. College of Philosophy, Nankai University, Tianjin, China

    Yanjun Li

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  1. Yanjun Li
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Correspondence to Yanjun Li.

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A preliminary version of this paper is appeared in the proceedings of LORI-VIII (Li, 2021).

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Li, Y. Complexity of multi-agent conformant planning with group knowledge. Synthese 201, 131 (2023). https://doi.org/10.1007/s11229-023-04095-5

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