Categorical Logic · Standard Form

The Four
AEIO Propositions

Every standard form categorical proposition is one of these four types. Each makes a claim about the relationship between a Subject (S) class and a Predicate (P) class.

Shaded region = empty (nothing exists there)
= at least one thing exists there
A
Universal
Affirmative
All S are P.
"All dogs are mammals."
S P
The S-only region is shaded — nothing exists in S that isn't also in P. Every member of S is inside P too.
E
Universal
Negative
No S are P.
"No fish are mammals."
S P
The overlapping region is shaded — nothing can be both S and P at the same time. The two classes are completely separate.
I
Particular
Affirmative
Some S are P.
"Some students are athletes."
S P
A ✕ in the overlap — at least one thing exists that is both S and P. No regions are shaded; we're not ruling anything out.
O
Particular
Negative
Some S are not P.
"Some birds are not songbirds."
S P
A ✕ in the S-only region — at least one thing is in S but outside P. Something exists in S that is not a member of P.