A type of generalized quantifier that permits an element of independence in the evaluation of quantified formulae. In first-order classical logic, the formula $\forall x\forall y\exists z\exists wR\left(x,y,z,w\right)$ would indicate that each of $z$ and $w$ depend on both $x$ and $y$, a feature apparent in the selection of Skolem functions in the process of Skolemization. By contrast, the branching quantifier $\left(\forall x,\exists z\right)\left(\forall y\exists w\right)R\left(x,y,z,w\right)$ indicates that $z$ depends only on $x$, and $w$ depends only on $y$.