A Graded Multi-Agent Logic of Knowledge in Forward–Backward Time

Grekovich Konstantin Vikentyevich, Vladimir Vladimirovich Rybakov

Keywords: multi-agent logic, bidirectional time, cluster semantics, graded modalities, forward and backward operators, knowledge and reliability, decidability, intransitive frames

Abstract: This paper introduces an extension of a non‑linear multi‑agent modal logic of clusters, designed to formalize reasoning about knowledge in a temporal framework that allows movement both forward and backward in time. The logic is equipped with primitive temporal transition operators, modal necessity operators, and a temporal unreliability operator. The syntax and semantics of the logic are formally defined, and the problem of proving its decidability is formulated.

Submission Number: 20