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A Many-Sorted Epistemic Logic for Chromatic Hypergraphs

Authors Éric Goubault , Roman Kniazev , Jérémy Ledent



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Author Details

Éric Goubault
  • LIX, CNRS, École Polytechnique, IP-Paris, Palaiseau Cedex, France
Roman Kniazev
  • LIX, CNRS, École Polytechnique, IP-Paris, Palaiseau Cedex, France
  • Université Paris-Saclay, ENS Paris-Saclay, CNRS, LMF, 91190, Gif-Sur-Yvette, France
  • Université Paris Cité, CNRS, IRIF, F-75013, Paris, France
Jérémy Ledent
  • Université Paris Cité, CNRS, IRIF, F-75013, Paris, France

Acknowledgements

This work benefited from various discussions during https://www.dagstuhl.de/23272.

Cite AsGet BibTex

Éric Goubault, Roman Kniazev, and Jérémy Ledent. A Many-Sorted Epistemic Logic for Chromatic Hypergraphs. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 30:1-30:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CSL.2024.30

Abstract

We propose a many-sorted modal logic for reasoning about knowledge in multi-agent systems. Our logic introduces a clear distinction between participating agents and the environment. This allows to express local properties of agents and global properties of worlds in a uniform way, as well as to talk about the presence or absence of agents in a world. The logic subsumes the standard epistemic logic and is a conservative extension of it. The semantics is given in chromatic hypergraphs, a generalization of chromatic simplicial complexes, which were recently used to model knowledge in distributed systems. We show that the logic is sound and complete with respect to the intended semantics. We also show a further connection of chromatic hypergraphs with neighborhood frames.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
Keywords
  • Modal logics
  • epistemic logics
  • multi-agent systems
  • hypergraphs

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References

  1. Samson Abramsky, Rui Soares Barbosa, Kohei Kishida, Raymond Lal, and Shane Mansfield. Contextuality, cohomology and paradox. In Stephan Kreutzer, editor, 24th EACSL Annual Conference on Computer Science Logic, CSL 2015, volume 41 of LIPIcs, pages 211-228. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015. URL: https://doi.org/10.4230/LIPIcs.CSL.2015.211.
  2. Yifeng Ding, Jixin Liu, and Yanjing Wang. Someone knows that local reasoning on hypergraphs is a weakly aggregative modal logic. Synthese, 201(2):1-27, 2023. URL: https://doi.org/10.1007/s11229-022-04032-y.
  3. Hans van Ditmarsch. Wanted Dead or Alive: Epistemic Logic for Impure Simplicial Complexes. In Alexandra Silva, Renata Wassermann, and Ruy J. G. B. de Queiroz, editors, Logic, Language, Information, and Computation - 27th International Workshop, WoLLIC 2021, Proceedings, volume 13038 of Lecture Notes in Computer Science, pages 31-46. Springer, 2021. URL: https://doi.org/10.1007/978-3-030-88853-4_3.
  4. Hans van Ditmarsch, Éric Goubault, Jérémy Ledent, and Sergio Rajsbaum. Knowledge and simplicial complexes. In Björn Lundgren and Nancy Abigail Nuñez Hernández, editors, Philosophy of Computing, volume 143, pages 1-50, Cham, 2022. Springer International Publishing. URL: https://doi.org/10.1007/978-3-030-75267-5_1.
  5. Hans van Ditmarsch, Wiebe van der Hoek, and Barteld Kooi. Dynamic Epistemic Logic, volume 337 of Synthese Library. Springer, 2007. URL: https://doi.org/10.1007/978-1-4020-5839-4.
  6. Ronald Fagin, Joseph Y. Halpern, Yoram Moses, and Moshe Y. Vardi. Reasoning About Knowledge. MIT Press, Cambridge, MA, USA, 2003. Google Scholar
  7. Jelle Gerbrandy and Willem Groeneveld. Reasoning about information change. Journal of Logic, Language and Information, 6:147-169, 1997. Google Scholar
  8. Éric Goubault, Roman Kniazev, Jérémy Ledent, and Sergio Rajsbaum. Semi-simplicial set models for distributed knowledge. In 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), pages 1-13, 2023. URL: https://doi.org/10.1109/LICS56636.2023.10175737.
  9. Éric Goubault, Jérémy Ledent, and Sergio Rajsbaum. A simplicial complex model for dynamic epistemic logic to study distributed task computability. Inf. Comput., 278:104597, 2021. URL: https://doi.org/10.1016/j.ic.2020.104597.
  10. Éric Goubault, Jérémy Ledent, and Sergio Rajsbaum. A simplicial model for KB4: Epistemic logic with agents that may die. In 39th International Symposium on Theoretical Aspects of Computer Science, STACS 2022, pages 33:1-33:20, 2022. URL: https://doi.org/10.4230/LIPIcs.STACS.2022.33.
  11. Joseph Y. Halpern and Yoram Moses. Knowledge and common knowledge in a distributed environment. J. ACM, 37(3):549-587, 1990. URL: https://doi.org/10.1145/79147.79161.
  12. Joseph Y. Halpern and Moshe Y. Vardi. The complexity of reasoning about knowledge and time. I. lower bounds. J. Comput. Syst. Sci., 38(1):195-237, 1989. URL: https://doi.org/10.1016/0022-0000(89)90039-1.
  13. Maurice Herlihy, Dmitry Kozlov, and Sergio Rajsbaum. Distributed Computing Through Combinatorial Topology. Morgan Kaufmann, San Francisco, CA, USA, 2013. Google Scholar
  14. Maurice Herlihy and Sergio Rajsbaum. Algebraic topology and distributed computing: A primer. In Jan van Leeuwen, editor, Computer Science Today: Recent Trends and Developments, volume 1000 of Lecture Notes in Computer Science, pages 203-217. Springer, 1995. URL: https://doi.org/10.1007/BFb0015245.
  15. Maurice Herlihy, Sergio Rajsbaum, and Mark R. Tuttle. An overview of synchronous message-passing and topology. Electronic Notes in Theoretical Computer Science, 39(2):1-17, 2000. URL: https://doi.org/10.1016/S1571-0661(05)01148-5.
  16. Jaakko Hintikka. Knowledge and Belief. Cornell University Press, 1962. Google Scholar
  17. E. Pacuit. Neighborhood Semantics for Modal Logic. Short Textbooks in Logic. Springer International Publishing, 2017. URL: https://books.google.co.uk/books?id=WK4-DwAAQBAJ.
  18. Rojo Fanamperana Randrianomentsoa, Hans van Ditmarsch, and Roman Kuznets. Impure simplicial complexes: Complete axiomatization. CoRR, abs/2211.13543, 2022. URL: https://doi.org/10.48550/arXiv.2211.13543.
  19. Mehrnoosh Sadrzadeh and Roy Dyckhoff. Positive logic with adjoint modalities: Proof theory, semantics and reasoning about information. Electronic Notes in Theoretical Computer Science, 249:451-470, 2009. Proceedings of the 25th Conference on Mathematical Foundations of Programming Semantics (MFPS 2009). URL: https://doi.org/10.1016/j.entcs.2009.07.102.
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