I still see those as mathematics, rather than logic, and the same goes for all other non-classical systems, such as all the modal logics. All of these are more like group theory than they are like logic, in the fundamentalist sense of "logic" I read the poll as talking about. They axiomatise certain mathematical objects, but not the general process of valid reasoning itself. That, I claim, is a problem completely solved by the classical first-order predicate calculus.