Admissibility and Unification in a Certain Class of Multimodal Logics

Protsenko Nikita Aleksandrovich, Vladimir Vladimirovich Rybakov

Keywords: modal logic, multimodal logics, unification, admissibility, reasoning under uncertainty

Abstract: This paper investigates unification and admissibility of inference rules in a novel class of multimodal logics designed for multi-agent systems with dynamic information quality. We introduce a logic with cluster-based semantics and moderator agents, where the $Next$ and $Prev$ operators model the flow of time and knowledge revision. Our main technical contribution is the construction of a projective unifier for any unifiable formula in this logic, which allows us to prove that the logic is almost structurally complete - i.e., every admissible inference rule with unifiable premises is derivable. We can also conclude that the admissibility problem in this logic is decidable.

Submission Number: 15