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Quickly, explain what you think logic is. I'm interested to know because so much of your position rests on this definition and from reading your post it seems like you have no idea.

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Logic and intuition are both (kind of) the same neurological function, but rely on different inputs and happen within different areas of the neo-cortical hierarchy. Logic is the phenomenon that occurs in the higher levels, which receives information from the lower levels but not directly from sensory inputs. The information higher levels receives is processed through the lower levels, so it is not PURE sensory information, it is interpreted and simplified sensory information.

Just think of the neo-cortex as a general learning algorithm. The same kind of stuff is happening everywhere, just different input is influencing every different level.

I hope that answers your question.

EDIT

Sorry, I have to add on to this thought. The reason why I suspect logic is a function of higher levels within the neo-cortical hierarchy is because of the type of cells that exist within the higher levels. Cells in the higher levels are generally fewer in number, but much larger in size. These cells also have a vast amount of connections running to all levels of the hierarchy. These cells are thought to represent conceptual thought. The highest levels of the neo-cortex is what distinguishes our cortex from those of other mammals, which is why some are led to this conclusion. Logic, for the most part, requires conceptual and symbolic thought which is what these large cells can provide.