The Traditional Square of Opposition

 
 Beside the relation of contradiction between A and O, and I and E, part of traditional logic concerned itself with figuring out what other relations held among A,I,E, and O categorical propositions. We will now take a look at those putative semantical relations.

(1) Subalternation: This is the inference from either a universal affirmative to a particular affirmative, or from a universal negative to a particular negative. The traditional Square claims that subalternation is a valid form of inference. The universal categorical proposition is called the superaltern and the particular is called the subaltern.

Examples:

All dogs are mammals.
Some dogs are mammals.

No husband is happy.
Some husbands are not happy.

(2) Contraries: Two categorical propositions are said to be contraries when they cannot both be true. According to the traditional square, universal categorical sentences are contraries.

(3) Subcontraries: Two categorical sentences are said to be subcontraries if they cannot both be false. Particular categorical sentences are said to be subcontraries.