Definition:Categorical Statement/Abbreviation

Definition
Let $S$ and $P$ be predicates. A categorical statement connecting $S$ and $P$ can be abbreviated as:
 * $\mathbf{\Phi} \left({S, P}\right)$

where $\Phi$ is one of either $\mathbf{A}$, $\mathbf{E}$, $\mathbf{I}$ or $\mathbf{O}$, signifying Universal Affirmative, Universal Negative, Particular Affirmative and Particular Negative respectively.

Thus:
 * $\mathbf{A} \left({S, P}\right)$ denotes All $S$ are $P$
 * $\mathbf{E} \left({S, P}\right)$ denotes No $S$ are $P$
 * $\mathbf{I} \left({S, P}\right)$ denotes Some $S$ are $P$
 * $\mathbf{O} \left({S, P}\right)$ denotes Some $S$ are not $P$.