Semi-Simplicial Set Models for Distributed Knowledge

Éric Goubault (1) , Roman Kniazev , Jérémy Ledent , Sergio Rajsbaum

1 X - École polytechnique

In recent years, a new class of models for multiagent 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 "pseudomodels". 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.

Mots clés: Epistemic logic Simplicial sets Distributed knowledge; Epistemic logic; Simplicial sets; Distributed knowledge

Domaines: Informatique [cs]

Éric Goubault, Roman Kniazev, Jérémy Ledent, Sergio Rajsbaum. Semi-Simplicial Set Models for Distributed Knowledge. Logic in Computer Science, Jun 2023, Boston (MA), United States. ⟨10.1109/lics56636.2023.10175737⟩. ⟨hal-04336328⟩