Well, if I don't, there isn't much to talk about is there. So, yes. I exist. As for the logic, I am going along with Rene Descartes concusion in his Meditations on First Philosophy. After much thought about existance, he concludes:
I am, however, a real thing, and really existent; but what thing? The answer was, a thinking thing.
But what is a thinking thing? It is a thing that doubts, understands, conceives, affirms, denies, wills, refuses; that imagines also, and perceives.
This thinking thing that Descartes describes is called a Soul by the English speaking world. It is a semi-imortal or immortal mind that exists separate from the physical body but it interacts with the physical body. Having a Soul is essential to the concept of the afterlife.
Rene Descartes was a Dualist. And I am right there with him. Although there are many, many, many, philosophical arguments agaisnt Duailsm, I think the arguments for it can withstand the onslaught.