\begin{definition}[Definition:Relative Semantic Equivalence/Term]
Let $\FF$ be a theory in the language of predicate logic.
Let $\tau_1, \tau_2$ be terms.
Then $\tau_1$ and $\tau_2$ are '''semantically equivalent with respect to $\FF$''' {{iff}}:
:$\map {\operatorname{val}_\AA} {\tau_1} \sqbrk \sigma = \map {\operatorname{val}_\AA} {\tau_2} \sqbrk \sigma$
for all models $\AA$ of $\FF$ and assignments $\sigma$ for $\tau_1,\tau_2$ in $\AA$.
Here $\map {\operatorname{val}_\AA} {\tau_1} \sqbrk \sigma$ denotes the value of $\tau_1$ under $\sigma$.
\end{definition}