Аннотация:

In this article, we continue the investigation of deductive systems within the class of linear step-like temporal logics. For the case of the temporal logic $\mathcal{LTL}.sl$ we proved the finite model property and the projective unification. Building on the results of P. Balbiani and T. Tinchev for modal logic $Alt_1$, we formally define the tuple and relational semantics for $\mathcal{LTL}.sl$ and prove their equivalence.