Definition:Johansson's Minimal Logic

 Johansson's minimal calculus is a system of propositional logic of the intuitionist school.

The philosophical position behind it is that it may be the case that one or both of: does not hold.
 * The Law of the Excluded Middle (a statement is either true or false);
 * The Rule of Bottom-Elimination (from a contradiction anything can be deduced),

Thus this philosophical school allows for the foundation of the study of fuzzy logic.