1. An occasion in which a truth functional valuation is underdetermined and fails to assign a truth value to a formula $\phi$, i.e., when $v\left(\phi \right)$ is undefined. Archetypal instances of truth value gaps are in the presentation of three-valued logic by mathematician Stephen Cole Kleene (1909–1994). Kleene generalized classical valuations from formulae to the set $\left\{0,1\right\}$, i.e., falsity and truth, by relaxing the condition of totality and admitting partial valuations to $\left\{0,1\right\}$ as well. In such partial evaluations, there may be formulae $\phi$ for which $v\left(\phi \right)$ is not defined. Truth value gaps are related to a dual notion of a truth value glut, in which the evaluation of a formula is overdetermined

2. A truth value in a semantics for a deductive system $\text{L}$ serving as a formal representation of a gap. For example, in Kleene’s three valued semantics, the state of being undefined is represented by a novel truth value $\frac{1}{2}$; although $1$ and $0$ correspond to authentic semantic values while $\frac{1}{2}$ is only a semantic device.