1. When $𝒱$ is a set of truth values, the property holding of a set of truth functions $\left\{f_0,...,f_{n-1}\right\}$ when every truth function $g$ on $𝒱$ is definable by composing functions from $\left\{f_0,...,f_{n-1}\right\}$.

2. Describes a logic $\text{L}$ characterized by a logical matrix if there exist connectives ${\circ }_0,...,{\circ }_{n-1}$ such that the set of associated truth functions $f^{{\circ }_0},...,f^{{\circ }_{n-1}}$ is functionally complete. Functional completeness of $\text{L}$ may be equivalently defined as the property that for every $n$-ary truth function $f$, there exists a formula $\phi$ containing atomic formulae $p_0,...,p_{n-1}$ such that for every $\text{L}$ valuation $v$, $v\left(\phi \right)=f\left(v\left(p_0\right),...,v\left(p_{n-1}\right)\right)$. When $\text{L}$ is functionally complete, any enrichment of $\text{L}$ by new extensional connectives is redundant, as every formula of the extended language will have an equivalent formula in the original language.