External negation

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.