Categorical Logic (The Traditional Square of Opposition)

Contradictories

Two standard-form categorical propositions are contradictories when one if the negation of the other. (A- and O-propositions, and E- and I-propositions are contradictories.)

Contraries

Two standard-form categorical propositions are contraries when both cannot be true at the same time, but both can be false at the same time. (A- and E-propositions are contraries.)

Opposition

Two standard-form categorical propositions are opposed when they refer to the same subject and predicate classes, but differ in quality, quantity, or both.

Subcontraries

Two standard-form propositions are subcontraries when both cannot be false at the same time, but both can be true at the same time. (I- and O-propositions are subcontraries.

Subalterns

A standard-form proposition is the subaltern of its corresponding universal (superaltern) proposition. The I-proposition is the subaltern of the A-proposition; the O-proposition is the subaltern of the E-proposition. The subaltern is true if, and only if, the superaltern is true.

Superalterns

A standard-form proposition is the superaltern of its corresponding particular (subaltern) proposition. The A-proposition is the sueraltern of the I-proposition; the E-proposition is the superaltern of the O-proposition. The superaltern is false if, and only if, the subaltern is false.