1. With respect to a deductive system $\text{L}$, describes an $n$-ary connective $\circ$ or quantifier $\text{Q}$ such that there exists a semantics employing truth values such that the truth value of a sentence with $\circ$ or $\text{Q}$ as its primary connective is completely determined by the truth values assigned to its subformulae. More formally, a connective $\circ$ is truth functional when there exists an $n$-ary function $f^{\circ }$ such that for every valuation $v$ and sentence $\circ \left({\phi }_0,...,{\phi }_{n-1}\right)$,

with an analogous definition for the truth functionality of quantifiers.

2. Describes a logic $\text{L}$ when $\text{L}$ can be provided with a semantics in which all connectives and operators are truth functional in the foregoing sense.