Linear Intransitive Temporal Logic of Knowledge LTK_r, Decision Algorithms, Inference Rules

Our paper investigates the linear logic of knowledge and time LTKr with reflexive intransitive time relation. The logic is defined semantically, – as the set of formulas true at special frames with intransitive and reflexive time binary relation. The LTKr-frames are linear chains of clusters connected by a reflexive intransitive relation RT . Elements inside a cluster are connected by several equivalence relations imitating the knowledge of different agents. We study the decidability problem for formulas and inference rules. Decidability for formulas follows from decidability w.r.t. admissible inference rules.To study admissibility, we introduce some special constructive Kripke models suitable to describe admissibility of inference rules. With a special technique of definable valuations we find an algorithm determining admissible inference rules in LTKr.. That is, we show that the logic LTKr is decidable and decidable with respect to admissibility of inference rules.