<p>The class of CNFs such that every clause is either positive or negative, that is, there are no clauses containing positive and negative literals at the same time, has been called "monotone CNFs" for example by Hans Kleine Buening in his book on propositional logic. A recent paper on monotone CNFs is
<a href="https://arxiv.org/abs/1603.07881" rel="nofollow noreferrer">https://arxiv.org/abs/1603.07881</a>
"Monotone 3-Sat-4 is NP-complete"
It is not hard to see by standard techniques, that  monotone 3-SAT (all clauses are either positive or negative, all clauses have length (at most) 3) is NP-complete, and the above paper refines this, by showing NP-completeness for the case where every variable occurs at most four time.</p>
What is this special CNF called?
<p>Suppose you have an instance of the boolean satisfiability where the formula in given in CNF. Furthermore, each clause contains only positive literals or negative literals. For example:</p>

<pre><code>(a || b) &amp;&amp; (!a || !c || !d) &amp;&amp; (b || d)
</code></pre>

<p>Does such a boolean formula have a special name? Is there a faster way to test satisfiability with this type of formula, compared to standard CNF formulas?</p>