Definition:Value of Formula under Assignment/Sentence

Definition
Let $\mathcal A$ be a structure for predicate logic. Let $\mathbf A$ be a sentence in the language of predicate logic.

The value of $\mathbf A$ in $\mathcal A$, denoted $\operatorname{val}_{\mathcal A} \left({\mathbf A}\right)$, is defined as:


 * $\operatorname{val}_{\mathcal A} \left({\mathbf A}\right) := \mathop{ \operatorname{val}_{\mathcal A} \left({\mathbf A}\right) } \left[{\varnothing}\right]$

where $\varnothing$ is the empty mapping considered as an assignment for $\mathbf A$ and $\mathop{ \operatorname{val}_{\mathcal A} \left({\mathbf A}\right) } \left[{\varnothing}\right]$ is the value of $\mathbf A$ under $\varnothing$.

Also see

 * Definition:Model (Predicate Logic)