Skip to main content

Synergistic Knowledge

  • Conference paper
  • First Online:
Stabilization, Safety, and Security of Distributed Systems (SSS 2023)

Abstract

In formal epistemology, group knowledge is often modelled as the knowledge that the group would have if the agents shared all their individual knowledge. However, this interpretation does not account for relations between agents. In this work, we propose the notion of synergistic knowledge, which makes it possible to model those relationships. As examples, we investigate the use of consensus objects and the problem of the dining cryptographers. Moreover, we show that our logic can also be used to model certain aspects of information flow in networks.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Chaum, D.: The dining cryptographers problem: unconditional sender and recipient untraceability. J. Cryptol. 1(1), 65–75 (1988). https://doi.org/10.1007/BF00206326

    Article  MathSciNet  MATH  Google Scholar 

  2. van Ditmarsch, H., Goubault, É., Ledent, J., Rajsbaum, S.: Knowledge and simplicial complexes. In: Lundgren, B., Nuñez Hernández, N.A. (eds.) Philosophy of Computing, vol. 143, pp. 1–50. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-75267-5_1

    Chapter  Google Scholar 

  3. van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic, 1st edn. Springer, Dordrecht (2007). https://doi.org/10.1007/978-1-4020-5839-4

    Book  MATH  Google Scholar 

  4. van Ditmarsch, H., Kuznets, R.: Wanted dead or alive: epistemic logic for impure simplicial complexes. J. Log. Comput. (to appear)

    Google Scholar 

  5. Goubault, É., Ledent, J., Rajsbaum, S.: A simplicial complex model for dynamic epistemic logic to study distributed task computability. Inf. Comput. 278, 104597 (2021). https://doi.org/10.1016/j.ic.2020.104597

    Article  MathSciNet  MATH  Google Scholar 

  6. Goubault, É., Ledent, J., Rajsbaum, S.: A simplicial model for KB4\(_n\): epistemic logic with agents that may die. In: Berenbrink, P., Monmege, B. (eds.) 39th International Symposium on Theoretical Aspects of Computer Science, STACS 2022. LIPIcs, Marseille, France, 15–18 March 2022 (Virtual Conference), vol. 219, pp. 33:1–33:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPIcs.STACS.2022.33

  7. Goubault, É.G., Kniazev, R., Ledent, J., Rajsbaum, S.: Semi-simplicial set models for distributed knowledge (2023)

    Google Scholar 

  8. Halpern, J.Y., Moses, Y.: Knowledge and common knowledge in a distributed environment. In: Kameda, T., Misra, J., Peters, J.G., Santoro, N. (eds.) Proceedings of the Third Annual ACM Symposium on Principles of Distributed Computing, Vancouver, B.C., Canada, 27–29 August 1984, pp. 50–61. ACM (1984). https://doi.org/10.1145/800222.806735

  9. Herlihy, M.: Wait-free synchronization. ACM Trans. Program. Lang. Syst. 13(1), 124–149 (1991). https://doi.org/10.1145/114005.102808

    Article  Google Scholar 

  10. Herlihy, M., Kozlov, D.N., Rajsbaum, S.: Distributed Computing Through Combinatorial Topology. Morgan Kaufmann (2013). https://store.elsevier.com/product.jsp?isbn=9780124045781

  11. Herlihy, M., Shavit, N.: The topological structure of asynchronous computability. J. ACM 46(6), 858–923 (1999). https://doi.org/10.1145/331524.331529

    Article  MathSciNet  MATH  Google Scholar 

  12. Randrianomentsoa, R.F., van Ditmarsch, H., Kuznets, R.: Impure simplicial complexes: complete axiomatization. Log. Methods Comput. Sci. (to appear)

    Google Scholar 

Download references

Acknowledgments

This work has been funded by the Swiss National Science Foundation (SNSF) under grant agreement Nr. 200021_188443 (Advanced Consensus Protocols).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to David Lehnherr .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Cachin, C., Lehnherr, D., Studer, T. (2023). Synergistic Knowledge. In: Dolev, S., Schieber, B. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2023. Lecture Notes in Computer Science, vol 14310. Springer, Cham. https://doi.org/10.1007/978-3-031-44274-2_41

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-44274-2_41

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-44273-5

  • Online ISBN: 978-3-031-44274-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics