An operator O has narrow scope with respect to an operator O' if O occurs in the subformula which corresponds to the scope of O':
(i) ... O' [ ... O [ .... ] ... ]
The operator O' is then said to have wide scope with respect to O or to have scope over O.
the existential quantifier ThereIs(y) in (ii) has narrow scope with respect to the universal quantifier All(x), but wide scope with respect to negation Neg:
(ii) All(x) [ P(x) -> ThereIs(y) [ Neg R(x,y) ]]
- Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.