By logic, do you mean the study of symbolic forms or generic rationality?
I'm not inclined to think formal consistency (or inconsistency) has much to do with God. Rationality, however, I think may well be the Archimedian (sp?) point upon which an important distinction may turn. On one side of this see-saw, we have the notion that God must, by definition, be beyond rationality, some(thing?) that can never be caputured in words or in conceptual thought. I think this is where the existential tension, the sickness unto death, comes from: That urge to make sense of the nonsensical. So, I suppose the goal of the Christian existenialist is to follow his/her lights and attempt to say the unsayable, and in some way get closer by God by failing miserably -- by defining the limits of what God is not. On the other side of this fulcrum is the possibility that God is not so different from us, that he/she is a proper object of contemplation. This second alternative is, I admit, more palatable to me, at least partly because it does not enshrine an impossibly perverse mindset, i.e., a mindset that must tilt at windmills by attempting to grasp the Absolute (whatever that is). This second alternative also gives a God we can cuddle with, one who might be a pal as well as a savior. Perhaps this removes some of the awe and majesty that has pervaded Christianity since medieval days, but it is a God I'd be more inclined to believe in.

J. Climacus