The paper presents an attempt to combine a linear temporal logic which employs modalities for past with a justification logic and to modal in this way a development of agent’s knowledge through an interaction between justifications and time. The constructed logical system \(\mathsf{LPLTL^P}\) uses a rather ramified language, which includes such temporal operators as next, weak previous, until, since, through which one can define some further operators, strong previous, always from now on, sometime, has-always-been and once among them. The constructed system is based on classical propositional logic, and has axioms for future and past modalities (and for interaction between them), as well as axioms for justification together with some connecting principles. Two types of semantics are proposed – one based on interpreted systems and fitting models and another based on Mkrtychev models. Soundness and completeness are established. It is shown that the internalization property holds in some of the temporal justification logics. It is also demonstrated how the proposed logical construction can be applied to investigation of the two well-known epistemic-temporal notions of no forgetting and no learning.