Definition:Boolean Interpretation/Formal Semantics

Definition
Let $\mathcal L_0$ be the language of propositional logic. The boolean interpretations for $\mathcal L_0$ can be interpreted as a formal semantics for $\mathcal L_0$, which we denote by $\mathrm{BI}$.

The structures of $\mathrm{BI}$ are the boolean interpretations.

A WFF $\phi$ is declared ($\mathrm{BI}$-)valid in a boolean interpretation $v$ iff:


 * $v \left({\phi}\right) = T$

Symbolically, this can be expressed as:


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

Also see

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


 * Definition:Formal Semantics