Found:
Dual
SEMANTICS: the dual Q^{*} of a generalized quantifier Q can be made by taking both the external negation and the internal negation of Q, i.e.:
(i) Q^{*} = Neg Q NegThis can be written out as:
(ii) Q^{*} = { X subset E : (E - X) not_in Q }All N and some N, for instance are pairs of quantifiers which are each other's duals:
(iii) a All dogs bark <-> b It is not the case that some dogs do not barkSome dogs is the dual of all dogs because every set X that belongs to the interpretation of some dogs contains at least one dog; so there is no set (E - X) that belongs to the interpretation of all dogs. If Q = Q^{*}, then Q is called self-dual. Proper names, for instance, are self-dual.
LIT. | Gamut, L.T.F. (1991) |