You can read online James N. Anderson and Greg Welty’s paper, “The Lord of Non-Contradiction: An Argument for God from Logic,” Philosophia Christi 13:2 (2011): 321-338.
Here’s a summary:
In this paper we offer a new argument for the existence of God. We contend that the laws of logic are metaphysically dependent on the existence of God, understood as a necessarily existent, personal, spiritual being; thus anyone who grants that there are laws of logic should also accept that there is a God. We argue that if our most natural intuitions about them are correct, and if they’re to play the role in our intellectual activities that we take them to play, then the laws of logic are best construed as necessarily existent thoughts — more specifically, as divine thoughts about divine thoughts. We conclude by highlighting some implications for both theistic arguments and antitheistic arguments.
Next year Crossway will release a book from Vern Poythress that will include a similar line of argument; it’s entitled Logic: A God-Centered Approach to the Foundation of Western Thought.