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A Simplicial Model for KB4_n: Epistemic Logic with Agents That May Die

Authors Éric Goubault , Jérémy Ledent , Sergio Rajsbaum

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Author Details

Éric Goubault
  • LIX, CNRS, École Polytechnique, Institut Polytechnique de Paris, France
Jérémy Ledent
  • MSP Group, University of Strathclyde, Glasgow, Scotland
Sergio Rajsbaum
  • National Autonomous University of Mexico, Mexico City, Mexico

Funding

Supported by UNAM-PAPIIT IN106520
  • Goubault, Éric: This author was partially funded by AID project "Swarm of drones".
  • Rajsbaum, Sergio: This work was partially done while this author was at École Polytechnique, France.

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Éric Goubault, Jérémy Ledent, and Sergio Rajsbaum. A Simplicial Model for KB4_n: Epistemic Logic with Agents That May Die. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 33:1-33:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.STACS.2022.33

Abstract

The standard semantics of multi-agent epistemic logic S5_n is based on Kripke models whose accessibility relations are reflexive, symmetric and transitive. This one dimensional structure contains implicit higher-dimensional information beyond pairwise interactions, that we formalized as pure simplicial models in a previous work in Information and Computation 2021 [Éric Goubault et al., 2021]. Here we extend the theory to encompass simplicial models that are not necessarily pure. The corresponding class of Kripke models are those where the accessibility relation is symmetric and transitive, but might not be reflexive. Such models correspond to the epistemic logic KB4_n. Impure simplicial models arise in situations where two possible worlds may not have the same set of agents. We illustrate it with distributed computing examples of synchronous systems where processes may crash.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
Keywords
  • Epistemic logic
  • Simplicial complexes
  • Distributed computing

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