I am inclined to doubt that anything very resembling formal logic could be a good model for human reasoning... In particular, 1doubt that any logic that prohibits self-reference can be adequate for psychology: no mind can have enough power - without the power to think about Thinking itself. Without Self-Reference it would seem immeasurably harder to achieve Self-Consciousness -- which, so far as Ican see, requires at least some capacity ot reflect on what it does.
Since we have no systematic way to avoid all the inconsistencies of commonsense logic, each person must find his own way by building a private collection of "cognitive censors" to suppress the kinds of mistakes he has discovered in the past.