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External negation

SEMANTICS: 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.
LIT. Gamut, L.T.F. (1991)