Definition:Value of Formula under Assignment/Sentence
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Definition
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 $\O$.
Also see
Sources
- 2009: Kenneth Kunen: The Foundations of Mathematics ... (previous) ... (next): $\text{II}.7$ First-Order Logic Semantics: Definition $\text{II}.7.8$