Logic is neither above God nor arbitrarily decreed by God. Its ultimate basis is in God's eternal nature. God is a rational God and necessarily so. Therefore logic is necessary. Human logical systems don't always reflect God's logic perfectly. But insofar as they do, they are necessarily true.
I've been discussing this with some Christians recently and it seems I'm in the minority agreeing with the above statment. I don't have an issue saying that God is "bound" by logic becasue I believe it is in his nature to be logical (IE. Following the law of Identity, Non-Contradiction and Excluded Middle).
But I would like a more learned opinion then my own
If God wasn't "bound" by logic then He wouldn't be able to make any sense to us; we couldn't know anything about Him, right?