A categorical statement is any statement that asserts a whole or partial relationship between the subject and predicate terms of the statement.

There are four standard categorical propositional forms.
Using the variables *S* and *P* (for the subject and predicate terms respectively) they are:

- All
*S*are*P*. -**universal affirmative** - No
*S*are*P*. -**universal negative** - Some
*S*are*P*. -**particular affirmative** - Some
*S*are not*P*. -**particular negative**

The four categorical propositions can be arranged by *quantity* (universal/particular) and *quality*
(affirmative/negative) to form a grid known as the **Square of Opposition** which demonstrate the logical
relationships between any two propositions on the grid. The four relationships are:

**Contrary**- cannot both be true simultaneously**Subcontrary**- cannot both be false simultaneously**Contradiction**- opposite truth value**Sub-alternation**- truth of the universal entails the truth of the particular, falseness of particular entails the falseness of the universal.