Four Kinds of Atheists.

[BluffTHIS!]

Those in in the 1st case don't seem likely to admit such, and will likely assert one of the other rationales. But I think you are giving too short a shrift to #3, simply because the existence of God or not, cannot be proven with 100% certainty either way, thus making the application of reason/logic suitable, even if it itself cannot be conclusive or even extremely convincing as to non-existence. Plus it is obvious that so many scientific theories were "reasoned" out decades before any technology existed to prove/disprove them empirically.