The MathResource
restricted quantifier,
n. (Logic) a quantifier regarded as ranging over the extension of a predicate rather than over the entire domain of a logical theory. For example, predicate calculus standardly treats
all ravens are black
as equivalent to
if anything is a raven it is black,
and writes (∀x) Rx Bx (with the obvious translation scheme); however, Hempel's paradox suggests that non-ravens are irrelevant to the truth conditions of such a statement, and so that it might better be treated as quantifying only over those entities that satisfy the subject term. We might then write this as (∀Rx)Bx. Similarly, it is clear that
>most As are Bs
is not equivalent to
it is true of most things that if they are A they are B,
since the latter will be true if an absolute majority of the domain are not A, no matter what their relation to the Bs; thus logics of plurality require restricted quantification.