User:Sapo02/sandbox/Scope (linguistics)

Scope in linguistics refers to the ability of an operator to affect the meaning of other expressions. Commonly accepted instances of an operator’s scope affecting the interpretation of an expression are quantifier—quantifier, quantifier—pronoun and quantifier—negative polarity item. The notion of scope in linguistics is closely related although distinct to that of scope in logic. An example the scope of a quantifier affecting the interpretation of another quantifier is

(1) every boy read a book

(1) can be interpreted as every boy reading one specific book, for example ... or that each boy read a different book.

The study of scope usually involves the assumption of a logical form, which postulates that there exists a mental representation of an expression that is derived solely from the surface structure.

Examples
Quantifier Quantifier

a. Every boy named a planet. `for every boy, there is a possibly different planet that he named'

b. I showed every boy a planet. `for every boy, there is a possibly different planet that I showed him'

c. That every boy left upset a teacher. `for every boy, there is a possibly different teacher who was upset by the fact that the boy left'

Q -- Pron

(3)      a.        Every       boyi read hisi book.

b. I showed every boyi hisi book.

c.* That every boyi left upset hisi teacher.

Q-- NPI

a. Few boys read any of the books.

b. I showed few boys any of the books.

c.* That few boys came upset any of the teachers.

Determining Scope
Reinhart claims that

(9) If a rule assigns node A some kind of prominence over node B, B must be within the domain of A.

(10) "First branching node" c-command: The domain of a node A consists of all and only the nodes dominated by the (nonunary) branching node α which most immediately dominates A.

(11) A logical structure in which a quantifier binding a variable x has wide scope over a quantifier binding a (distinct) variable y is a possible interpretation for a given sentence S just in case in the surface structure of S the quantified expression (QE) corresponding to y is in the domain of the QE corresponding to x.

Montague
Montague's classical  paper,  The  proper  treatment  of  quantification  in  ordinary  English  (1974)  presents  a  grammar  for  a  small  fragment  of  English  which,  however,  contains  the  logico-syntactic  and  semantic  devices  to  handle  practically  any  scope  phenomenon.

May proposes that syntax does not end with producing the surface string. Instead, movement operations somewhat reminiscent  of  wh-movement  continue  to  operate  at  an  abstract  level  called  Logical  Form  and  append  each  phrase  containing  a  quantifier  to  its  domain. This rule  is  called Quantifier Raising (QR). For example, the two readings of Everyone loves someonehave the following LF structures

einhart's approach and the Montague/May approach represent two extremes. On the former,  independently  motivated  phrase  structure  imposes  an  absolute  limitation  on  scope options; on the latter, there is no such absolute limitation, because stucture may be built  solely  for  the  purposes  of  scope  assignment. Nevertheless, syntactic  considerations  bear on scope on the latter approach as well.

The Scope Principle: If two operators govern each other, they can be interpreted in either scopal order.