You can find any number of books on the physiological processes of the brain, but learning how it functions logically, you might have to scrounge around a bit.
Evolve your Brain, J. Dispenza and Genie in your Genes, Dawson Church, might get you thinking.
You mentioned not being interested in the chemistry, but also being interested in hormones, hormones are all about chemistry. It is rather an important part of brain function, one that would be worth becoming acquainted with.
All cognitive processes involve or produce chemical reactions. If you were to examine any thought in the brain you would find chemistry. The electrical impulses in the brain are all chemical based, and every thought you have produces an accompanying chemical/hormonal/emotional reaction within the body.
When inquiring about how logic works in the brain you would need to understand how the brain operates, both from the intellectual side and emotional side of the brain, and what importance does this have with the experiential aspects of life.
Conscious processes are another thing altogether, separate from cognitive thought, but vitally important as conscious perception initiates cognitive function.