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


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

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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)


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
  • Modal logics
  • epistemic logics
  • multi-agent systems
  • hypergraphs


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