Definition:Logical NAND/Boolean Interpretation

Definition
Let $\mathbf A$ and $\mathbf B$ be propositional formulas.

Let $\mathbf A \uparrow \mathbf B$ denote the logical NAND operator.

The boolean interpretations for $\mathbf A \uparrow \mathbf B$ under the model $\mathcal M$ are:


 * $\left({\mathbf A \uparrow \mathbf B}\right)_\mathcal M = \begin{cases}

F & : \mathbf A_\mathcal M = T \text{ and } \mathbf B_\mathcal M = T \\ T & : \text {otherwise} \end{cases}$