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Linear Intransitive Temporal Logic of Knowledge LTK_r, Decision Algorithms, Inference Rules
Our paper investigates the linear logic of knowledge and time LTK_r with
reflexive intransitive time relation. The logic is defined semantically, -- as
the set of formulas which are true at special frames with intransitive and
reflexive time binary relation. The LTK_r -frames are linear chains of clusters
connected by a reflexive intransitive relation . 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 useful for description of admissibility of inference rules. With
a special technique of definable valuations we find an algorithm determining
admissible inference rules in LTK_r. That is, we show that the logic LTK_r is
decidable and decidable with respect to admissibility of inference rules