Definition:Model (Boolean Interpretations)

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

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

Then $v$ models a WFF $\phi$ :


 * $\map v \phi = \T$

and this relationship is denoted as:


 * $v \models_{\mathrm {BI} } \phi$

When pertaining to a collection of WFFs $\FF$, one says $v$ models $\FF$ :


 * $\forall \phi \in \FF: v \models_{\mathrm {BI} } \phi$

that is, it models all elements of $\FF$.

This can be expressed symbolically as:


 * $v \models_{\mathrm {BI}} \FF$

Also denoted as
Often, when the formal semantics is clear to be $\mathrm {BI}$, the formal semantics of boolean interpretations, the subscript is omitted, yielding:


 * $v \models \phi$

Also see

 * Definition:Boolean Interpretation
 * Definition:Model (Logic)