Pour le prochain séminaire de l’équipe Cosynus, nous aurons le plaisir d’accueillir Jérémy Ledent qui nous parlera de logique épistémique.

Résumé: Epistemic logic is the logic of knowledge; it studies what a set of agents know about the world and about each other. The usual model for multi-agent epistemic logic S5 is based on a Kripke frame, which is a graph whose edges are labeled with agents that do not distinguish between two states. We show that this structure is related to the chromatic simplicial complexes that are used in the topological approach to distributed computability. This allows us to view the input, output and protocol complexes as models of epistemic logic, on which we can interpret formulas saying what the processes know about the system. We then extend this duality to the setting of dynamic epistemic logic in order to describe how the epistemic model evolves when communication happens between the agents. By doing so, we are able to prove impossibility results for task solvability, using logical arguments.