It seems temporal logic is back via trying to understand computers. It seems it has never disappeared. Perhaps it has found an important niche. I was already interested in computers in 1954 but I had no idea then that the semantics of a program would sometimes be so important; I made no connection.
The “Logic” in this “Temporal Logic” seems to come down via electrical engineering; yet relevant.
I cannot find a clear description of the semantics or axiomatics of any particular temporal logic. A model would help perhaps.