Definition:Value of Formula under Assignment/Sentence

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Let $\AA$ be a structure for predicate logic.

Let $\mathbf A$ be a sentence in the language of predicate logic.

The value of $\mathbf A$ in $\AA$, denoted $\map {\operatorname{val}_\AA} {\mathbf A}$, is defined as:

$\map {\operatorname{val}_\AA} {\mathbf A} := \map {\operatorname{val}_\AA} {\mathbf A} \sqbrk \O$

where $\O$ is the empty mapping considered as an assignment for $\mathbf A$ and $\map { \operatorname{val}_\AA} {\mathbf A} \sqbrk \O$ is the value of $\mathbf A$ under $\O$.

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