I am inclined to doubt that anything very resembling formal logic could be a good model for human reasoning. In particular, I doubt 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 I can see, requires at least some capacity to reflect on what it does. If Russell shattered our hopes for making a completely reliable version of commonsense reasoning, still we can try to find the islands of "local consistency," in which naive reasoning remains correct.
Jokes and their Relation to the Cognitive Unconscious (1980)