How do the A, E, I, and O forms classify categorical propositions?

In traditional logic, categorical propositions are classified into four basic forms, designated by the letters A, E, I, and O. These letters are derived from the Latin terms affirmo (I affirm) and nego (I deny).1

The classification is based on two primary characteristics:
* Quality: Whether the proposition affirms or denies the predicate of the subject.1
* Quantity: Whether the proposition refers to the entire scope (universal) or only a part (particular) of the subject.1

The four forms are defined as follows:

| Form | Name | Logical Structure |
| :--- | :--- | :--- |
| A | Universal affirmative | Every S is P23|
| E | Universal negative | No S is P23|
| I | Particular affirmative | Some S is P23|
| O | Particular negative | Some S is not P23|

These forms are central to the syllogistic method, which analyzes how these statements interact within a square of opposition to determine the validity of logical inferences.12