Brazilianlogic is the dual of intuitionistic logic, where you drop the law of excluded middle (i.e.
Intuitionistic logic is modeled by open sets in a topological space: and stands for intersection, or for union, and not for the interior of the complement.
In intuitionistic logic a slight gap (at the boundary) between A and ¬A is allowed, whereas in Brazilianlogic a slight overlap is allowed.