You will have to spell it out a little more so I can be certain of your point.
Did you see the point about logic not adding any new information, Ed? At the end there, I kinda switched topics, and you responded to that, but...
The point is that logic can and will never serve to convince someone who doesn't also accept the premises. Premises, by nature, do not come from logic, and can't be proved--at least not fundamental premises.
It is quite "logical" to conclude that god exists, if that's the premise you start with, but, like I said, that's just a matter of repeating yourself. Likewise, it's just as "logical" to conclude that there are no gods if you start with that premise.
But logic does not generate premises. Premises generate implications, which can be independently assessed for empirical consistency with other known facts, but they will necessarily be consistent with the premises, so that won't be a question. If they weren't, they wouldn't be implications.
People often like to think that logic "proves" their position. It doesn't (and can't). It can only show that their conclusions are entailed by their assumptions (or not).