\begin{definition}[Definition:Categorical Statement/Abbreviation]
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 $P$''.
Category:Definitions/Categorical Statements
\end{definition}