The way I see play. How "smart" your character is based on all the mental attributes . With the strengths weaknesses giving the flavor about areas that they're good or bad at.
There are a great many multi-factor theories of intelligence out there; each mental stat would wind up correlating to more than one factor in such theories.
Actually, I've got a Personality textbook I could grab that had, as I recall, a very nice breakdown... Will edit in a few.
EDIT: Most useful thing I could find, after mining through a few books, was
this. In this model, Logic would likely correlate with logical-mathematical, linguistic, and naturalist. Intuition correlates with linguistic, musical, spatial, bodily-kinesthetic, and to a limited extent interpersonal. Charisma would correlate with intrapersonal, interpersonal, and linguistic. Willpower, to me, seems like another factor entirely.