Temporal Epistemic Gossip Problems

  • Martin C. CooperEmail author
  • Andreas Herzig
  • Frédéric Maris
  • Julien Vianey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11450)


Gossip problems are planning problems where several agents have to share information (‘secrets’) by means of phone calls between two agents. In epistemic gossip problems the goal can be to achieve higher-order knowledge, i.e., knowledge about other agents’ knowledge; to that end, in a call agents communicate not only secrets, but also agents’ knowledge of secrets, agents’ knowledge about other agents’ knowledge about secrets, etc. Temporal epistemic gossip problems moreover impose constraints on the times of calls. These constraints are of two kinds: either they stipulate that a call between two agents must necessarily be made at some time point, or they stipulate that a call can be made within some possible (set of) interval(s). In the non-temporal version, calls between two agents are either always possible or always impossible. We investigate the complexity of the plan existence problem in this general setting. Concerning the upper bound, we prove that it is in NP in the general case, and that it is in P when the problem is non-temporal and the goal is a positive epistemic formula. As for the lower bound, we prove NP-completeness for two fragments: problems with possibly negative goals even in the non-temporal case, and problems with temporal constraints even if the goal is a set of positive atoms.


Epistemic planning Temporal planning Gossip problem Complexity Epistemic logic 


  1. 1.
    Apt, K.R., Grossi, D., van der Hoek, W.: Epistemic protocols for distributed gossiping. In: Ramanujam, R. (ed.) Proceedings Fifteenth Conference on Theoretical Aspects of Rationality and Knowledge, TARK 2015. EPTCS, vol. 215, pp. 51–66 (2015). Scholar
  2. 2.
    Apt, K.R., Grossi, D., van der Hoek, W.: When are two gossips the same? Types of communication in epistemic gossip protocols. CoRR abs/1807.05283 (2018).
  3. 3.
    Apt, K.R., Kopczynski, E., Wojtczak, D.: On the computational complexity of gossip protocols. In: Sierra, C. (ed.) Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI 2017, pp. 765–771. (2017).
  4. 4.
    Apt, K.R., Wojtczak, D.: Common knowledge in a logic of gossips. In: Lang, J. (ed.) Proceedings Sixteenth Conference on Theoretical Aspects of Rationality and Knowledge, TARK 2017. EPTCS, vol. 251, pp. 10–27 (2017). Scholar
  5. 5.
    Apt, K.R., Wojtczak, D.: Decidability of fair termination of gossip protocols. In: Eiter, T., Sands, D., Sutcliffe, G., Voronkov, A. (eds.) IWIL@LPAR 2017 Workshop and LPAR-21 Short Presentations, vol. 1. Kalpa Publications in Computing, EasyChair (2017).
  6. 6.
    Attamah, M., van Ditmarsch, H., Grossi, D., van der Hoek, W.: A framework for epistemic gossip protocols. In: Bulling, N. (ed.) EUMAS 2014. LNCS (LNAI), vol. 8953, pp. 193–209. Springer, Cham (2015). Scholar
  7. 7.
    Aucher, G., Bolander, T.: Undecidability in epistemic planning. In: Rossi, F. (ed.) Proceedings of the 23rd International Joint Conference on Artificial Intelligence, IJCAI 2013, 3–9 August 2013, Beijing, China, pp. 27–33. IJCAI/AAAI (2013).
  8. 8.
    Bolander, T., Andersen, M.B.: Epistemic planning for single and multi-agent systems. J. Appl. Non-Classical Logics 21(1), 9–34 (2011). Scholar
  9. 9.
    Bylander, T.: The computational complexity of propositional STRIPS planning. Artif. Intell. 69(1–2), 165–204 (1994). Scholar
  10. 10.
    Cooper, M.C., Herzig, A., Maffre, F., Maris, F., Régnier, P.: A simple account of multi-agent epistemic planning. In: Kaminka et al. [19], pp. 193–201.
  11. 11.
    Cooper, M.C., Herzig, A., Maffre, F., Maris, F., Régnier, P.: Simple epistemic planning: generalised gossiping. In: Kaminka et al. [19], pp. 1563–1564.
  12. 12.
    Cooper, M.C., Herzig, A., Maffre, F., Maris, F., Régnier, P.: Simple epistemic planning: generalised gossiping. CoRR abs/1606.03244 (2016).
  13. 13.
    Cooper, M.C., Maris, F., Régnier, P.: Monotone temporal planning: tractability, extensions and applications. J. Artif. Intell. Res. 50, 447–485 (2014). Scholar
  14. 14.
    van Ditmarsch, H., van Eijck, J., Pardo, P., Ramezanian, R., Schwarzentruber, F.: Epistemic protocols for dynamic gossip. J. Appl. Logic 20, 1–31 (2017). Scholar
  15. 15.
    van Ditmarsch, H., Grossi, D., Herzig, A., van der Hoek, W., Kuijer, L.B.: Parameters for epistemic gossip problems. In: Proceedings of LOFT 2016 (2016)Google Scholar
  16. 16.
    Hedetniemi, S.M., Hedetniemi, S.T., Liestman, A.L.: A survey of gossiping and broadcasting in communication networks. Networks 18(4), 319–349 (1988). Scholar
  17. 17.
    Herzig, A., Lorini, E., Maffre, F.: A poor man’s epistemic logic based on propositional assignment and higher-order observation. In: van der Hoek, W., Holliday, W.H., Wang, W. (eds.) LORI 2015. LNCS, vol. 9394, pp. 156–168. Springer, Heidelberg (2015). Scholar
  18. 18.
    Herzig, A., Maffre, F.: How to share knowledge by gossiping. AI Commun. 30(1), 1–17 (2017). Scholar
  19. 19.
    Kaminka, G.A., et al. (eds.): 22nd European Conference on Artificial Intelligence, Frontiers in Artificial Intelligence and Applications, ECAI 2016, vol. 285. IOS Press (2016)Google Scholar
  20. 20.
    Löwe, B., Pacuit, E., Witzel, A.: DEL planning and some tractable cases. In: van Ditmarsch, H., Lang, J., Ju, S. (eds.) LORI 2011. LNCS (LNAI), vol. 6953, pp. 179–192. Springer, Heidelberg (2011). Scholar
  21. 21.
    Maffre, F.: Ignorance is bliss: observability-based dynamic epistemic logics and their applications. Ph.D. thesis, Paul Sabatier University, Toulouse, France (2016).
  22. 22.
    Muise, C.J., et al.: Planning over multi-agent epistemic states: a classical planning approach. In: Bonet, B., Koenig, S. (eds.) Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, 25–30 January 2015, Austin, Texas, USA, pp. 3327–3334. AAAI Press (2015).

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Martin C. Cooper
    • 1
    Email author
  • Andreas Herzig
    • 1
  • Frédéric Maris
    • 1
  • Julien Vianey
    • 1
  1. 1.IRIT, CNRS, Univ. ToulouseToulouse Cedex 9France

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