I have three nonnegativity constraints
\begin{equation}
A\_1>0, A\_2>0, A\_3>0.
\end{equation}
I want to create a single List consisting of all possible/inequivalent Boolean configurations of none (trivial), one (also trivial), two, and three of them, using the AND, NOT and OR operations. 

How long will this List be?

Well--in response to the initial comment/answer--I was really thinking of a (multi-element) List such as 

```
{B1 && B2 && ! B3, B1 || (B2 && B3), ! (B1 && B2) && B3,  B1 || (! B2 && B3), B1 || ! (B2 && B3), ! B1 && B2 && B3}

```

Given such a List, I would make the substitutions 

```
{B1 -> A1 > 0, B2 -> A2 > 0, B3 -> A3 > 0}

```

and then attempt Boolean integrations using Boole[each element of the resulting list].