I sit here, pondering whether that type of logic is math or philosophy. Most likely, it is the intersection of the two. Of course, spending even a few minutes pondering such things tells me that I personally need to avoid the math and embrace the philosophy.
Philosophy includes the study of mathematical reasoning, but you don't get practice at it while you're studying it. It's like taking a music theory class versus learning to play an instrument.
Hm. When I was studying philosophy, we did have logic classes, and did diagram out the logic of arguments. It was a critical component for success in later courses, so I'd say we absolutely practiced it.
I own a modal logic textbook used by a course in a philosophy department, and on any given page it looks an awful lot like a math textbook except that the presentation is far friendlier and the explanations are better than are in 99% of math books.
