At least in the sciences I'm familiar with, there's really no logical "proof" of things, just evidence that supports a theory -- for now. The stronger the evidence, the greater the confidence you can have in a theory. But that stops when good contradictory evidence appears. Then you need a better theory.

If you wish, think about the reasons why you think it's a good idea to accept reincarnation, or any belief, at face value. It might be a worthwhile exercise.