Skip to main content

Reasoning about knowledge and messages in asynchronous multi-agent systems


We propose a variant of public announcement logic for asynchronous systems. To capture asynchrony, we introduce two different modal operators for sending and receiving messages. The natural approach to defining the semantics leads to a circular definition, but we describe two restricted cases in which we solve this problem. The first case requires the Kripke model representing the initial epistemic situation to be a finite tree, and the second one only allows announcements from the existential fragment. After establishing some validities, we study the model checking problem and the satisfiability problem in cases where the semantics is well-defined, and we provide several complexity results.

Hide All
Aucher, G. and Schwarzentruber, F. (2013). On the complexity of dynamic epistemic logic. In: TARK '13.
Balbiani, P., Baltag, A., van Ditmarsch, H.P., Herzig, A., Hoshi, T. and Lima, T.D. (2007). What can we achieve by arbitrary announcements?: A dynamic take on Fitch's knowability. In: TARK '07.
Balbiani, P., Gasquet, O. and Schwarzentruber, F. (2013). Agents that look at one another. Logic Journal of the IGPL 21 (3) 438467.
Balbiani, P., van Ditmarsch, H., Herzig, A. and Lima, T.D. (2010). Tableaux for public announcement logic. Journal of Logic and Computation 20 (1).
Baltag, A., Ditmarsch, H.P.V. and Moss, L.S. (2008). Epistemic logic and information update. In: Adriaans, P. and van Benthem, J. (eds.) Philosophy of Information, Elsevier Science Publishers, 361455.
Baltag, A. and Moss, L.S. (2004). Logics for epistemic programs. Synthese 139 (2) 165224.
Baltag, A., Moss, L.S. and Solecki, S. (1998). The logic of public announcements and common knowledge and private suspicions. In: Proceedings of the 7th Conference on Theoretical Aspects of Rationality and Knowledge (TARK-98), Evanston, IL, USA, July 22–24, 1998, 43– 56.
Benthem, J.V. (2011). Logical Dynamics of Information and Interaction, Cambridge University Press.
Brand, D. and Zafiropulo, P. (1983). On communicating finite-state machines. Journal of the ACM (JACM) 30 (2) 323342.
Braüner, T., Blackburn, P. and Polyanskaya, I. (2016). Second-order false-belief tasks: Analysis and formalization. In: Proceedings of the Logic, Language, Information, and Computation - 23rd International Workshop, WoLLIC 2016, Puebla, Mexico, August 16–19th, 2016, 125– 144.
Chambart, P. and Schnoebelen, P. (2008). Mixing lossy and perfect fifo channels. In: International Conference on Concurrency Theory, Springer, 340–355.
Charrier, T. and Schwarzentruber, F. (2015). Arbitrary public announcement logic with mental programs. In: Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2015, Istanbul, Turkey, May 4–8, 2015, 1471–1479.
Charrier, T. and Schwarzentruber, F. (2017). Arbitrary public announcement logic with mental programs. In: Proceedings of the 2017 International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2017 (to appear).
Corradini, F., Berardini, M.R.D. and Vogler, W. (2003). Relating fairness and timing in process algebras. In: Proceedings of the CONCUR '03.
Dégremont, C., Löwe, B. and Witzel, A. (2011). The synchronicity of dynamic epistemic logic. In: Proceedings of the TARK '11.
Fagin, R., Halpern, J., Moses, Y. and Vardi, M. (2004). Reasoning About Knowledge, The MIT Press.
Fagin, R., Halpern, J.Y. and Vardi, M.Y. (1992). What can machines know?: On the properties of knowledge in distributed systems. Journal of ACM 39 (2) 328376.
French, T. and van Ditmarsch, H. P. (2008). Undecidability for arbitrary public announcement logic. In: Proceedings of the AiML '08.
Gasquet, O., Goranko, V. and Schwarzentruber, F. (2015). Big brother logic: Visual-epistemic reasoning in stationary multi-agent systems. Autonomous Agents and Multi-Agent Systems 30 133.
Gerbrandy, J. and Groeneveld, W. (1997). Reasoning about information change. Journal of Logic, Language and Information 6 (2) 147169.
Griesmayer, A. and Lomuscio, A. (2013). Model checking distributed systems against temporal-epistemic specifications. In: Formal Techniques for Distributed Systems, Springer 130145.
Halpern, J. Y. and Moses, Y. (1990). Knowledge and common knowledge in a distributed environment. Journal of the ACM 37 (3) 549587.
Hintikka, J. (1962). Knowledge and Belief: An Introduction to the Logic of the Two Notions, Vol. 4, Cornell University Press Ithaca.
Jones, B.D. (1999). Bounded rationality. Annual Review of Political Science 2 297321.
Knight, S., Maubert, B. and Schwarzentruber, F. (2015). Asynchronous announcements in a public channel. In: Proceedings of the ICTAC '15.
Kutschera, F. (1976). Einführung in die Intensionale Semantik, Grundlagen der Kommunikation und Kognition.
Lamport, L. (1978). Time, clocks, and the ordering of events in a distributed system. Communications of the ACM 21 55565., doi:10.1145/359545.359563
Lenzen, W. (1978). Recent work in epistemic logic. Acta Philosophica Fennica 30 1219.
Lutz, C. (2006). Complexity and succinctness of public announcement logic. In: Proceedings of the AAMAS '06.
Moses, Y. and Tuttle, M.R. (1988). Programming simultaneous actions using common knowledge. Algorithmica 3 121169.
Panangaden, P. and Taylor, K. (1992). Concurrent common knowledge: Defining agreement for asynchronous systems. Distributed Computing 6 7393.
Plaza, J. (2007). Logics of public communications. Synthese 158 (2).
Raynal, M. (2013). Distributed Algorithms for Message-Passing Systems, Springer.
Schnoebelen, P. (2002). The complexity of temporal logic model checking. Advances in Modal Logic 4 (393–436), 35.
Sipser, M. (1997). Introduction to the Theory of Computation, PWS Publishing Company.
Tarski, A. (1955). A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics 5 (2) 285309.
van Benthem, J., van Eijck, J., Gattinger, M. and Su, K. (2015). Symbolic model checking for dynamic epistemic logic. In: Proceedings of the Logic, Rationality, and Interaction – 5th International Workshop, LORI 2015 Taipei, Taiwan, October 28–31, 2015, 366–378.
van der Hoek, W. (1990). Systems for knowledge and beliefs. In: Proceedings of the Logics in AI, European Workshop, JELIA '90, Amsterdam, The Netherlands, September 10–14, 1990, 267–281.
van Ditmarsch, H. (2017). Asynchronous announcements. CoRR abs/1705.03392.
van Ditmarsch, H., French, T. and Hales, J. Positive announcements (submitted).
van Ditmarsch, H., van der Hoek, W. and Kooi, B.P. (2007). Dynamic Epistemic Logic, Vol. 337.
van Emde Boas, P. (1997). The convenience of tilings. Lecture Notes in Pure and Applied Mathematics.
van Lambalgen, M. (2010). Logical form as a determinant of cognitive processes. In: Proceedings of the Logic, Language, Information and Computation, 17th International Workshop, WoLLIC 2010, Brasilia, Brazil, July 6–9, 2010, 59–83.
Winskel, G. (1993). The Formal Semantics of Programming Languages - An Introduction, MIT Press.
Yu, Y.-T. and Gouda, M. (1982). Deadlock detection for a class of communicating finite state machines. IEEE Transactions on Communications 30 (12) 25142518.
Zhang, J., Johansson, K.H., Lygeros, J. and Sastry, S. (2001). Zeno hybrid systems. International Journal of Robust and Nonlinear Control 11 (5), 435451.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 28 *
Loading metrics...

Abstract views

Total abstract views: 208 *
Loading metrics...

* Views captured on Cambridge Core between 10th November 2017 - 25th April 2018. This data will be updated every 24 hours.