Definition:Logical NOR/Boolean Interpretation

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Definition

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

Let $\downarrow$ denote the logical NOR operator.


The truth value of $\mathbf A \downarrow \mathbf B$ under a boolean interpretation $v$ is given by:

$v \left({\mathbf A \downarrow \mathbf B}\right) = \begin{cases} T & : v \left({\mathbf A}\right) = v \left({\mathbf B}\right) = F\\ F & : \text{otherwise} \end{cases}$