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.