Definition:Boolean Interpretation/Formula

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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 $\phi$ be a WFF of propositional logic.

Then $v$ is called a boolean interpretation for $\phi$ iff $v$ is defined at $\phi$.

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