Scott Oliphint, Westminster Seminary apologetics professor, discusses God and logic at some point in this discussion about Gordon Clark and Cornelius van Til, about half-way or three-quarters-of-the-way through.
http://reformedforum.org/podcasts/ctc163/
Our logic is analogical of - or iconic of, i.e. an image of - God's logic.
Our logic is founded on God's, otherwise logic would just be a convention, which is impossible.
God's mind is very different to ours, because He knows all things in an eternal moment, but if God was a man He would think - sinlessly - like us, and He has indeed become a Man in Christ.