Jérémy Ledent

Selected papers

1. Epistemic Logic,
   Concurrency

   Simplicial Models for the Epistemic Logic of Faulty Agents

   Éric Goubault, Roman Kniazev, Jérémy Ledent, and Sergio Rajsbaum

   Boletín de la Sociedad Matemática Mexicana, 2024

   Abstract Bibtex URL arXiv

   In recent years, several authors have been investigating simplicial models, a model of epistemic logic based on higher-dimensional structures called simplicial complexes. In the original formulation, simplicial models are always assumed to be pure, meaning that all worlds have the same dimension. This is equivalent to the standard S5 semantics of epistemic logic, based on Kripke models. By removing the assumption that models must be pure, we can go beyond the usual Kripke semantics and study epistemic logics where the number of agents participating in a world can vary. This approach has been developed in a number of papers, with applications in fault-tolerant distributed computing where processes may crash during the execution of a system. A difficulty that arises is that subtle design choices in the definition of impure simplicial models can result in different axioms of the resulting logic. In this paper, we classify those design choices systematically, and axiomatize the corresponding logics. We illustrate them via distributed computing examples of synchronous systems where processes may crash.

   @Article{GoubaultKLR2024faulty,
     author={Goubault, {\'E}ric and Kniazev, Roman and Ledent, J{\'e}r{\'e}my and Rajsbaum, Sergio},
     title={Simplicial models for the epistemic logic of faulty agents},
     journal={Bolet{\'i}n de la Sociedad Matem{\'a}tica Mexicana},
     year={2024},
     month={Sep},
     day={09},
     volume={30},
     number={3},
     pages={90},
     issn={2296-4495},
     doi={10.1007/s40590-024-00656-x},
     url={https://doi.org/10.1007/s40590-024-00656-x},
   }

2. Epistemic Logic

   A Many-Sorted Epistemic Logic for Chromatic Hypergraphs

   Éric Goubault, Roman Kniazev, and Jérémy Ledent

   In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)

   Abstract Bibtex URL arXiv PDF

   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 previous attempts at epistemic logic with variable number of agents. 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.

   @InProceedings{goubault2023manysorted,
     author =	{Goubault, \'{E}ric and Kniazev, Roman and Ledent, J\'{e}r\'{e}my},
     title =	{{A Many-Sorted Epistemic Logic for Chromatic Hypergraphs}},
     booktitle =	{32nd EACSL Annual Conference on Computer Science Logic (CSL 2024)},
     pages =	{30:1–30:18},
     series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
     ISBN =	{978-3-95977-310-2},
     ISSN =	{1868-8969},
     year =	{2024},
     volume =	{288},
     editor =	{Murano, Aniello and Silva, Alexandra},
     publisher =	{Schloss Dagstuhl – Leibniz-Zentrum f{\"u}r Informatik},
     address =	{Dagstuhl, Germany},
     doi =		{10.4230/LIPIcs.CSL.2024.30},
   }