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Our paper investigates the linear logic of knowledge and time LTK_r withreflexive intransitive time relation. The logic is defined semantically, -- asthe set of formulas which are true at special frames with intransitive andreflexive time binary relation. The LTK_r -frames are linear chains of clustersconnected by a reflexive intransitive relation $R_T$. Elements inside a clusterare connected by several equivalence relations imitating the knowledge ofdifferent agents. We study the decidability problem for formulas and inferencerules. Decidability for formulas follows from decidability w.r.t. admissibleinference rules.To study admissibility, we introduce some special constructiveKripke models useful for description of admissibility of inference rules. Witha special technique of definable valuations we find an algorithm determiningadmissible inference rules in LTK_r. That is, we show that the logic LTK_r isdecidable and decidable with respect to admissibility of inference rules.

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