Definition:Boolean Interpretation/Set of Formulas

Definition

Let $\LL_0$ be the language of propositional logic.

Let $v: \LL_0 \to \set {\T, \F}$ be a (partial) boolean interpretation.

Let $\FF$ be a set of WFFs of $\LL_0$.

Then $v$ is called a boolean interpretation for $\FF$ if and only if $v$ is defined on $\FF$.

Otherwise, $v$ is called a partial (boolean) interpretation for $\FF$.

Sources

• 2012: M. Ben-Ari: Mathematical Logic for Computer Science (3rd ed.) ... (previous) ... (next): $\S 2.2.4$: Definition $2.24$