Semi-simplicial set models for distributed knowledge

Goubault, Éric and Kniazev, Roman and Ledent, Jérémy and Rajsbaum, Sergio; (2023) Semi-simplicial set models for distributed knowledge. In: 2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). IEEE, USA. ISBN 9798350335873 (https://doi.org/10.1109/LICS56636.2023.10175737)

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Abstract

In recent years, a new class of models for multi-agent epistemic logic has emerged, based on simplicial complexes. Since then, many variants of these simplicial models have been investigated, giving rise to different logics and axiomatizations. In this paper, we present a further generalization, which encompasses all previously studied variants of simplicial models. Geometrically, this is achieved by generalizing beyond simplicial complexes, and considering instead semi-simplicial sets. By doing so, we define a new semantics for epistemic logic with distributed knowledge, where a group of agents may distinguish two worlds, even though each individual agent in the group is unable to distinguish them. As it turns out, these models are the geometric counterpart of a generalization of Kripke models, called “pseudo- models”. We show how to recover the previously defined variants of simplicial models as sub-classes of our models; and give a sound and complete axiomatization for each of them.

  • Item type:Book Section
    ID code:88354
    Dates:
    Date
    Event
    14 July 2023
    Published
    29 June 2023
    Published Online
    5 April 2023
    Accepted
    Notes:© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
    Subjects:Bibliography. Library Science. Information Resources > Library Science. Information Science
    Department:Faculty of Science > Computer and Information Sciences
    Depositing user: Pure Administrator
    Date deposited:06 Mar 2024 12:40
    Last modified:22 Apr 2024 00:11
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/88354
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