1. Any one of a loose collection of unary negation operations $\sim$ whose intended interpretations generally follow the work of the logician David Nelson (1918–2003) on constructible falsity. Strong negation is frequently used to enrich the expressivity of intuitionistic logic; the ‘strength’ of a strong negation lies in the fact that in these contexts, a strongly negated formula $\sim \phi$ will imply the corresponding intuitionistically negated formula $\neg \phi$. From a semantic perspective, accounts of strong negation tend to identify the truth of a negated formula $\sim \phi$ with the falsity of the formula $\phi$ and often treat truth and falsity as independent notions. This independence, with negation ‘toggling’ between distinct relations governing a formula’s truth and falsity, leads to the frequent requirement that a strong negation is involutive (i.e., $\sim \sim \phi$ is logically equivalent to $\phi$).

2. In the field of fuzzy logic, any continuous unary function $\neg :\left[0,1\right]\to \left[0,1\right]$ such that

1. 1 $\neg \neg m=m$

2. 2 $\neg 0=1$ and $\neg 1=0$

3. 3 If $m\le n$ then $\neg n\le \neg m$

All strong negations in fuzzy logic are homeomorphic (i.e., topologically equivalent) to the Łukasiewicz negation $f\left(x\right)=1-x$.