Finitary boolean function

A finitary boolean function is a function of the type $$ f : \mathbb{B}^k \to \mathbb{B} $$, where $$ \mathbb{B} $$ is a generic 2-element set, typically $$ \mathbb{B} = \left \{ 0, 1 \right \} $$, frequently interpreted for logical applications as $$ \mathbb{B} = \left \{ false, true \right \} $$, and where k is a positive integer.