This was covered in my undergraduate (second-year) SR course. The idea is that if you accept that Maxwell's equations apply in all inertial frames (speed of light is constant) and that causality is conserved in all frames, the result is that Newtonian mechanics requires adjustments for effects that are called "special relativity".
ED: This is the starting point of the Causal Set [1] program. Don’t
ask me for details, I don’t know any. But the wikipedia article looks
interesting. Seems they are trying to figure out how causality
restricts models with some level of discreteness.