Temporal Epistemic Gossip Problems

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.

[1]  Martin C. Cooper,et al.  Monotone Temporal Planning: Tractability, Extensions and Applications , 2014, J. Artif. Intell. Res..

[2]  Wiebe van der Hoek,et al.  A Framework for Epistemic Gossip Protocols , 2014, EUMAS.

[3]  Martin C. Cooper,et al.  Simple Epistemic Planning: Generalised Gossiping , 2016, ECAI.

[4]  Krzysztof R. Apt,et al.  On the Computational Complexity of Gossip Protocols , 2017, IJCAI.

[5]  Tom Bylander,et al.  The Computational Complexity of Propositional STRIPS Planning , 1994, Artif. Intell..

[6]  Andreas Herzig,et al.  How to Share Knowledge by Gossiping , 2015, EUMAS/AT.

[7]  Krzysztof R. Apt,et al.  Common Knowledge in a Logic of Gossips , 2017, TARK.

[8]  Wiebe van der Hoek,et al.  Epistemic Protocols for Distributed Gossiping , 2016, TARK.

[9]  Faustine Maffre.  Ignorance is bliss : observability-based dynamic epistemic logics and their applications. (Le bonheur est dans l'ignorance : logiques épistémiques dynamiques basées sur l'observabilité et leurs applications) , 2016 .

[10]  Jan van Eijck,et al.  Epistemic protocols for dynamic gossip , 2017, J. Appl. Log..

[11]  Martin C. Cooper,et al.  A simple account of multiagent epistemic planning , 2015 .

[12]  Wiebe van der Hoek,et al.  When Are Two Gossips the Same? Types of Communication in Epistemic Gossip Protocols , 2018, ArXiv.

[13]  Arthur L. Liestman,et al.  A survey of gossiping and broadcasting in communication networks , 1988, Networks.

[14]  Thomas Bolander,et al.  Epistemic planning for single- and multi-agent systems , 2011, J. Appl. Non Class. Logics.

[15]  Emiliano Lorini,et al.  A Poor Man's Epistemic Logic Based on Propositional Assignment and Higher-Order Observation , 2015, LORI.

[16]  Andreas Herzig,et al.  Parameters for Epistemic Gossip Problems , 2016 .

[17]  Andreas Witzel,et al.  DEL Planning and Some Tractable Cases , 2011, LORI.

[18]  Christian J. Muise,et al.  Planning Over Multi-Agent Epistemic States: A Classical Planning Approach , 2015, AAAI.

[19]  Thomas Bolander,et al.  Undecidability in Epistemic Planning , 2013, IJCAI.

[20]  Krzysztof R. Apt,et al.  Decidability of Fair Termination of Gossip Protocols , 2017, IWIL@LPAR.

[21]  Martin C. Cooper,et al.  A Simple Account of Multi-Agent Epistemic Planning , 2016, ECAI.