Logical hexagon

In philosophical logic, the logical hexagon (also called the hexagon of opposition) is a conceptual model of the relationships between the truth values of six statements.

It was discovered independently by both Augustin Sesmat and Robert Blanché.

For instance, the statement A may be interpreted as "Whatever x may be, if x is a man, then x is white."

The statement I may be interpreted as "There exists at least one x that is both a man and white."

The statement O may be interpreted as "There exists at least one x that is both a man and non-white."

The logical hexagon extends the square of opposition to six statements.