  Our manuscript studies linear temporal (with UNTIL and NEXT) logic based at a
conception of intransitive time. non-transitive time. In particular, we
demonstrate how the notion of knowledge might be represented in such a
framework (here we consider logical operation NN and the operation UNTIL
(actually, the time overall) to be directed to past). The basic mathematical
problems we study are the fundamental ones for any logical system
  - decidability and decidability w.r.t. admissible rules. First, we consider
the logic with non-uniform non-transitivity, and describe how to solve the
decidability problem for this logic. Then we consider a modification of this
logic - linear temporal logic with uniform intransitivity and solve the problem
of admissibility for inference rules. A series of open problems is enumerated
in the concluding part of the paper.
