Definition:Boolean Interpretation/Set of Formulas

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Let $\mathcal L_0$ be the language of propositional logic.

Let $v: \mathcal L_0 \to \left\{{T, F}\right\}$ be a (partial) boolean interpretation.

Let $\mathcal F$ be a set of WFFs of $\mathcal L_0$.

Then $v$ is called a boolean interpretation for $\mathcal F$ iff $v$ is defined on $\mathcal F$.

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