A premise is something that is a previous statement or proposition from which another is inferred or follows as a conclusion. if the premise is true, then the conclusion must be true Something to base an argument, theory, or undertaking on. The basis, or the idea being proposed or expounded.
In The Oath of the Horatii, the main message David wishes to communicate is that of men going to battle for the sake of loyalty, with possible sacrifice. There are several signs that allow the viewer to read this narrative, then further associate it with the ancient story from which the image was born.
The oath to which President Kennedy referred in his inaugural  address was the Presidential Oath of Office. It was administered  just before his speech.   Washington, D.C, where all the other ones happen, too. If a free society cannot help the many who are poor, it cannot save the few who are rich.