# External negation

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**External negation** is the external negation Neg Q of a generalized quantifier Q is the set of sets that are not in Q (i.e. the complement of Q with regard to the power set of E). Formally, external negation is defined as follows:

(i) Neg Q = { X subset E : X not_in Q }

The external negation of *all* is *not all* and the external negation of *a(n)* is *no*. See also internal negation.

### Link

Utrecht Lexicon of Linguistics

### References

- Gamut, L.T.F. 1991.
*Logic, language, and meaning,*Univ. of Chicago Press, Chicago.