\begin{definition}[Definition:Expansion of Structure]
Let $\LL, \LL'$ be signatures of the language of predicate logic.
Let $\LL'$ be a supersignature of $\LL$.
Let $\AA, \AA'$ be structures for $\LL, \LL'$, respectively.
Then $\AA'$ is called an '''expansion of $\AA$ to $\LL'$''' {{iff}}:
:For all function symbols $f$ of $\LL$, one has $f_{\AA'} = f_\AA$
:For all predicate symbols $p$ of $\LL$, one has $p_{\AA'} = p_\AA$
where $f_{\AA'}$ is the interpretation of the function symbol $f$ in the structure $\AA'$.
\end{definition}