Abstract
The “Muddy Children” puzzle is a well known problem in the multi-agent epistemic reasoning literature, however it has not been studied in other fields of Artificial Intelligence. In this paper, we present the “Muddy Children” problem as a challenge to the Artificial Intelligence and Computer Science community. The interesting aspect of this problem is that agents have asymmetric and incomplete information; and each agent needs to reason about his own knowledge as well as knowledge of other agents. The existing solutions use Kripke structure and possible world semantics which are not scalable for large problem sizes. Hence we stimulate for alternative solution methodologies and discover its relation to the other problems in the applied sciences. We go over several variations of the Muddy Children puzzle and discuss the challenges for future research.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
When we omit the set of agents in the formulae \(C_{\alpha }\), we assume \(\alpha = \mathcal{A}\mathcal{G}\).
References
Baral, C., Gelfond, G., Son, T.C., Pontelli, E.: Using answer set programming to model multi-agent scenarios involving agents’ knowledge about other’s knowledge. In: Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems, vol. 1, pp. 259–266 (2010)
Barwise, J.: Scenes and other situations. J. Philos. 78(7), 369–397 (1981)
Bolander, T., Andersen, M.: Epistemic planning for single and multi-agent systems. J. Appl. Non-Classical Logics 21(1) (2011)
Bolander, T.: A gentle introduction to epistemic planning: the del approach. arXiv preprint arXiv:1703.02192 (2017)
Van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic, 1st edn. Springer, Heidelberg (2007)
Engesser, T., Bolander, T., Mattmüller, R., Nebel, B.: Cooperative epistemic multi-agent planning for implicit coordination. In: Ghosh, S., Ramanujam, R. (eds.) Proceedings of the Ninth Workshop on Methods for Modalities, M4M@ICLA 2017, Indian Institute of Technology, Kanpur, India, 8th to 10th January 2017. EPTCS, vol. 243, pp. 75–90 (2017)
Fagin, R., Halpern, J., Moses, Y., Vardi, M.: Reasoning About Knowledge. MIT Press, Cambridge (1995)
Gierasimczuk, N., Szymanik, J.: A note on a generalization of the muddy children puzzle. In: Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge, pp. 257–264 (2011)
Huang, X., Fang, B., Wan, H., Liu, Y.: A general multi-agent epistemic planner based on higher-order belief change. In: Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence (IJCAI 2017) (2017)
Kominis, F., Geffner, H.: Beliefs in multiagent planning: from one agent to many. In: Proceedings of the Twenty-Fifth International Conference on Automated Planning and Scheduling, ICAPS 2015, Jerusalem, Israel, 7–11 June 2015, pp. 147–155 (2015)
Liu, Q., Liu, Y.: Multi-agent epistemic planning with common knowledge. In: Lang, J. (ed.) Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, IJCAI 2018, Stockholm, Sweden, 13–19 July 2018, pp. 1912–1920. ijcai.org (2018)
McCarthy, J.: Formalization of two puzzles involving knowledge. Formalizing Common Sense: Papers by John McCarthy, pp. 158–166 (1990)
Son, T.C., Pontelli, E., Baral, C., Gelfond, G.: Finitary S5-theories. In: Fermé, E., Leite, J. (eds.) JELIA 2014. LNCS (LNAI), vol. 8761, pp. 239–252. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11558-0_17
van Tilburg, G.: Doe wel en zie niet om (do well and don’t look back). Katholieke Illustratie (Catholic Illustrated Journal) 90(32), 47 (1956)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Izmirlioglu, Y., Pham, L., Son, T.C., Pontelli, E. (2023). A Review of the Muddy Children Problem. In: Dovier, A., Montanari, A., Orlandini, A. (eds) AIxIA 2022 – Advances in Artificial Intelligence. AIxIA 2022. Lecture Notes in Computer Science(), vol 13796. Springer, Cham. https://doi.org/10.1007/978-3-031-27181-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-031-27181-6_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-27180-9
Online ISBN: 978-3-031-27181-6
eBook Packages: Computer ScienceComputer Science (R0)