Logic is dependent on God. God is not dependent on logic. God is not restricted by the rules of logic because He is logic, and what He does is logical. Logic is defined by what God does. The reason why we don't see logic changing all the time is because God does not change.
True, since the principles of logic are congruent on God, He could change them, but He doesn't. Yes, it is absurd to think that a law such as the law of non-contradiction can be false but only because God set it to be that way. It would know longer be absurd if God were to say that something is true and false at the same time. It does not make sense in our infinite, Earthly minds because that is the way we were created to think.
This is how and why miracles are possible with God. Miracles do not make sense logically. God can change that logic and work a miracle. God changes things that that temporarily to display His Glory so that we will have no doubt in our minds that that was the work of God.
God is not and couldn't have been bound to the rules of logic. He created the universe out of nothing. That doesn't seem very logical to the human mind. That is why we can trust God to work the good out of every situation, no matter how bad it seems or how illogical it seems that any good will come of it.