\begin{definition}[Definition:Categorical Syllogism/Shorthand]
In order to specify the pattern of a categorical syllogism completely, it is necessary and sufficient to specify:
:$(1) \quad$ The figure ($\text I$ to $\text {IV}$) of the syllogism
and
:$(2) \quad$ The types of the three categorical statements that compose the syllogism.
Hence, for example, the following categorical syllogism, which is of the first figure:
:$\begin{array}{r|rl}
\text I & & \\
\hline \\
\text{Major Premise}: & \mathbf E & \left({M, P}\right) \\
\text{Minor Premise}: & \mathbf I & \left({S, M}\right) \\
\hline \\
\text{Conclusion}: & \mathbf O & \left({S, P}\right) \\
\end{array}$
is specified completely by:
:$\text I: EIO$
\end{definition}