Subalternation

In Categorical Logic, the relationship between universal and particular propositions of the same quality: The truth of the universal entails the truth of the particular; the falsity of the particular entails the falsity of the universal.

For example, if we know the statement “all cats are mammals” is true, then it must be true that any particular cat will be a mammal. Therefore, the statement “some cats are mammals” will be necessarily true whenever “all cats are mammals” is true (the truth of the universal statement entails the truth of the particular).

The inverse relationship holds if we move from particular to universal. If it is false that there is at least one cat that is a mammal, then the claim that All cats are mammals must be false as well (the falsity of the particular entails the falsity of the universal).