Scope is that part of a formula to which an operator is prefixed.
phi is the scope of Neg in Neg phi and of All(x) in All(x) [ phi ]. The scope of an operator in complex formulas is determined by brackets. In the formula in (i) the subformula P(x) -> Q(y) is the scope of All(x), but R(x) is outside the scope of All(x).
(i) All(x) [ P(x) -> Q(y) ] & R(x)
It is usually assumed that for those syntactic elements which are interpreted as elements with scope (e.g. NPs such as everyone and who, which are interpreted as (quantificational) operators), the scope assigned to the element that is the interpretation of the syntactic element is determined as a function of the syntactic context of the syntactic element. It has often been assumed, furthermore, that the notion c-command plays a crucial role in the determination of the scope of (the interpretation of) quantificational and other scopal elements. Thus, May (1977) states that "the scope of a quantifier phi is everything which it c-commands" (meaning: at LF). Thus, if the relevant syntactic level of representation where scope is determined is the level of LF (which is denied, e.g., by Williams (1986)) then which LFs can be derived from a given S-structure determines the possible scopal orders of the scopal elements in the structure (see scope ambiguity, QR).
- Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.