In logic, Brazilian logic is a name given by Chris Mortensen , in his book Inconsistent Mathematics, to a system R# of relevance logic. It is named this way because the inventor of the approach, Newton da Costa, is Brazilian.
This approach is a way to get rid of (A ∧ ¬A) → B without getting rid of material implication (i.e. the rule that states that A ∧ ¬A is false).
Brazilian logic is the dual of intuitionistic logic, where you drop the law of excluded middle (i.e. the law that states that A ∨ ¬A is true). 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. Similarly, Brazilian logic is modeled by closed sets. In intuitionistic logic a slight gap between A and ¬A is allowed, whereas in Brazilian logic a slight overlap is allowed.