@The Pentacle Queen,
I think a definition of "logic" is a bit tricky.
Initially, it might seem that it is no more than a process of "correct reasoning". But to determine what is correct reasoning, we have to trust our motives, and we need to have a clear idea of our objective.
In most situations logic is applied on multiple levels simultaneously, both with choosing which aspects of a subject should be considered and with the actual consideration of those subjects. Therefore, there is bound to be a degree of intuition and subjective preference to the process of logical thinking.
Or, to say it in another way, how you approach a problem can decide how logic will be applied. Even deciding how to approach is often a matter of logic. But to apply logic we need to make choices, which also can be a matter of logic. But in most real life situations a purely logical approach isn't necessarily the best or logical choice.
Considering this, I am inclined to say that logic is a process of evaluating and acting on the information you have, making the choices that will ensure an outcome that is as close to your initial objective as you can manage. I would say that it is not a purely intellectual process. Not unless the subject logic is applied to is purely intellectual.