Categorical proposition

https://en.wikipedia.org/wiki/Categorical_proposition

A categorical proposition is a statement that asserts/denies that all/some of the members of one category (the subject term) are included in another category (the predicate term). Syllogisms are categorical statements.

Aristotle had identified 4 primary types of categorical propositions and gave them standard forms: A, E, I, O.

Syllogistic logic	Propositional logic
A: All S are P	∀x. S(x) -> P(x) or ¬∃x. S(x) ∧ ¬P(x)
E: All S are not P	∀x. S(x) ->¬P(x) or ¬∃x. S(x) ∧ P(x)
I: Some S are P	∃x. S(x) ∧ P(x)
O: Some S are not P	∃x. S(x) ∧ ¬P(x)

S is the subject category, P is and the predicate category.

Aristotle's square of opposition codifies the logical relations among the different forms (e.g. that an A-statement is contradictory to an O-statement). The relations of the square of opposition may allow immediate inference, whereby the truth or falsity of one of the forms may follow directly from the truth or falsity of a statement in another form.

Arguments consisting of 3 categorical propositions, 2 premises and a conclusion, are called categorical syllogisms.

Formal arguments using categorical syllogisms have fallen away due to the increased expressive power of modern logic systems.