Linear step-like logic of knowledge $\mathcal{LTK}.{sl}$

This paper proposes a description of linear multi-agent logic of knowledge $\mathcal{LTK}.{sl}$ that models a linear non-reflexive non-transitive (step-like) temporal process of transition between information clusters — time points.
Using modified techniques, we proved the finite approximability of logic. We proposed an approach for solving the main unification problem in logics of a step-like temporal relation. The projectivity and, as a consequence, unitary type of unification in logic are proved.