Skip to main content
SpringerLink
Log in

Hope for Epistemic Reasoning with Faulty Agents!

  • Conference paper
  • First Online:
Selected Reflections in Language, Logic, and Information (ESSLLI 2019)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14354))

Included in the following conference series:

  • 69 Accesses

Abstract

In this paper, we study a new epistemic modal operator, termed hope, which has been introduced recently in the context of a novel epistemic reasoning framework for distributed multi-agent systems with arbitrarily (“byzantine”) faulty agents. It has been proved that both preconditions of actions used in agent protocols, as well as assertions about the epistemic states of agents obtained for analysis purposes, need to be restricted in a particular way for such systems. Hope has been proposed as the most promising candidate for analysis purposes, and defined in terms of the standard knowledge operator. To support the challenging next step of defining the semantics of common hope and eventual common hope, which are crucial for the analysis of fault-tolerant distributed agreement algorithms, we provide a suitable axiomatization of individual hope that avoids knowledge altogether, and prove its (strong) soundness and (strong) completeness.

PhD student in the Austrian Science Fund (FWF) doctoral program LogiCS (W1255).

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Notes

  1. 1.

    In case of synchronous systems, a causal structure called centipede is both necessary and sufficient for verifying knowledge (when considering full-information protocols) as shown in [1].

  2. 2.

    We note that this paper has been accepted to ESSLLI2019 Student Session. Since then (building on top of the results presented here), new results have been obtained. See [5] for an example of a distributed computing problem analyzed using epistemic logic where the notion of eventual common hope shows up. See [2] where it is shown how one can make the logic of hope (introduced here) not depend on the \(\textit{correct}_{i}\) atomic propositions. It turns out that, essentially, the logic of \(\mathsf {KB4_n}\) can be taken as an alternative logic for hope. Interestinly, in [6] Goubault et al. show that the logic of \(\mathsf {KB4_n}\) also plays a crucial role in studying systems with crash failures. See [2] for further discussion.

  3. 3.

    In literature on modal logics, a statement of this type is called Lindenbaum’s Lemma.

  4. 4.

    In literature on modal logics, a statement of this type is called Truth Lemma.

  5. 5.

    In literature on modal logics, a statement of this type is called Correctness Lemma.

  6. 6.

    Note that \(W^{c} \ne \emptyset \) since any \(\mathscr {H}\)-consistent set can be extended to a maximal \(\mathscr {H}\)-consistent set according to Lemma 2.

  7. 7.

    We again note that this paper has been accepted to ESSLLI2019 Student Session. Since then (building on top of the results presented here), new results have been obtained. See [2] where a logic containing both individual knowledge and individual hope has been introduced as well as a logic containing both common knowledge and common hope.

References

  1. Ben-Zvi, I., Moses, Y.: On interactive knowledge with bounded communication. J. Appl. Non Class. Logics 21(3–4), 323–354 (2011). https://doi.org/10.3166/jancl.21.323-354

    Article  MathSciNet  Google Scholar 

  2. van Ditmarsch, H., Fruzsa, K., Kuznets, R.: A new hope. In: Fernández-Duque, D., Palmigiano, A., Pinchinat, S. (eds.) Advances in Modal Logic, AiML 2022, Rennes, France, 22–25 August 2022, pp. 349–370. College Publications (2022)

    Google Scholar 

  3. Dwork, C., Moses, Y.: Knowledge and common knowledge in a Byzantine environment: crash failures. Inf. Comput. 88, 156–186 (1990). https://doi.org/10.1016/0890-5401(90)90014-9

    Article  MathSciNet  Google Scholar 

  4. Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning About Knowledge. MIT Press (1995)

    Google Scholar 

  5. Fruzsa, K., Kuznets, R., Schmid, U.: Fire! In: Halpern, J., Perea, A. (eds.) Proceedings Eighteenth Conference on Theoretical Aspects of Rationality and Knowledge. EPTCS, vol. 335, pp. 139–153. Open Publishing Association (2021). https://doi.org/10.4204/EPTCS.335.13

  6. Goubault, É., Ledent, J., Rajsbaum, S.: A simplicial model for \(\textbf{KB4} _{\textbf{n} }\): Epistemic logic with agents that may die. In: Berenbrink, P., Monmege, B. (eds.) 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), vol. 219, pp. 33:1–33:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPIcs.STACS.2022.33

  7. Halpern, J.Y., Moses, Y.: A guide to completeness and complexity for modal logics of knowledge and belief. Artif. Intell. 54, 319–379 (1992). https://doi.org/10.1016/0004-3702(92)90049-4

    Article  MathSciNet  Google Scholar 

  8. Halpern, J.Y., Moses, Y., Waarts, O.: A characterization of eventual Byzantine agreement. SIAM J. Comput. 31, 838–865 (2001). https://doi.org/10.1137/S0097539798340217

    Article  MathSciNet  Google Scholar 

  9. Kuznets, R., Prosperi, L., Schmid, U., Fruzsa, K.: Causality and epistemic reasoning in byzantine multi-agent systems. In: Moss, L.S. (ed.) TARK 2019. EPTCS, vol. 297, pp. 293–312. Open Publishing Association (2019). https://doi.org/10.4204/EPTCS.297.19

  10. Kuznets, R., Prosperi, L., Schmid, U., Fruzsa, K.: Epistemic reasoning with byzantine-faulty agents. In: Herzig, A., Popescu, A. (eds.) FroCoS 2019. LNCS (LNAI), vol. 11715, pp. 259–276. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-29007-8_15

    Chapter  Google Scholar 

  11. Kuznets, R., Prosperi, L., Schmid, U., Fruzsa, K., Gréaux, L.: Knowledge in Byzantine message-passing systems I: Framework and the causal cone. Tech. Rep. TUW-260549, TU Wien (2019). https://publik.tuwien.ac.at/files/publik_260549.pdf

  12. Lamport, L.: Time, clocks, and the ordering of events in a distributed system. Commun. ACM 21, 558–565 (1978). https://doi.org/10.1145/359545.359563

    Article  Google Scholar 

  13. Lamport, L., Shostak, R., Pease, M.: The Byzantine generals problem. ACM Trans. Program. Lang. Syst. 4, 382–401 (1982). https://doi.org/10.1145/357172.357176

    Article  Google Scholar 

  14. McKinsey, M.: Skepticism and content externalism. In: Stanford Encyclopedia of Philosophy (2018). https://plato.stanford.edu/entries/skepticism-content-externalism/

  15. Moses, Y.: Relating knowledge and coordinated action: the knowledge of preconditions principle. In: Ramanujam, R. (ed.) TARK 2015, pp. 231–245 (2015). https://doi.org/10.4204/EPTCS.215.17

  16. Moses, Y., Shoham, Y.: Belief as defeasible knowledge. Artif. Intell. 64, 299–321 (1993). https://doi.org/10.1016/0004-3702(93)90107-M

    Article  MathSciNet  Google Scholar 

  17. Moses, Y., Tuttle, M.R.: Programming simultaneous actions using common knowledge. Algorithmica 3, 121–169 (1988). https://doi.org/10.1007/BF01762112

    Article  MathSciNet  Google Scholar 

  18. Schlögl, T., Schmid, U., Kuznets, R.: The persistence of false memory: brain in a vat despite perfect clocks. In: Uchiya, T., Bai, Q., Marsá-Maestre, I. (eds.) PRIMA 2020. LNCS, vol. 12568, pp. 403–411. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-69322-0_30

Download references

Acknowledgments

I am immensly grateful to Ulrich Schmid and Roman Kuznets for inspiring discussions, suggestions and constructive comments on earlier versions of this paper. I would also like to thank the anonymous reviewers for their very much appreciated suggestions, in particular, regarding the need to justify the axiomatization, which allowed me to considerably strengthen the paper.

Author information

Authors and Affiliations

  1. TU Wien, Vienna, Austria

    Krisztina Fruzsa

Authors
  1. Krisztina Fruzsa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Krisztina Fruzsa .

Editor information

Editors and Affiliations

  1. Institute of Logic and Computation, TU Wien, Vienna, Austria

    Alexandra Pavlova

  2. Department of Information Science and Media Studies, University of Bergen, Bergen, Norway

    Mina Young Pedersen

  3. University of Trento, Rovereto, Italy

    Raffaella Bernardi

Rights and permissions

Reprints and permissions

Copyright information

© 2024 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

Fruzsa, K. (2024). Hope for Epistemic Reasoning with Faulty Agents!. In: Pavlova, A., Pedersen, M.Y., Bernardi, R. (eds) Selected Reflections in Language, Logic, and Information. ESSLLI 2019. Lecture Notes in Computer Science, vol 14354. Springer, Cham. https://doi.org/10.1007/978-3-031-50628-4_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-50628-4_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-50627-7

  • Online ISBN: 978-3-031-50628-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Societies and partnerships

Search

Navigation