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In the generative syntax, binding refers to a relation in which the reference of a certain element is dependent on the reference of another element.

In semantics, binding is a term that is used to refer the relation obtaining between a quantifier All(v) or Exists(v) and the occurrences of the variable v in its scope:

 (i)      All(v)[ ... v ... ]
 (ii)  Exists(v)[ ... v ... ]


In the following formula only the first occurrence of x is bound by All but not the second (which is not in the scope of All):

 (iii) All(x)[P(x) -> Q(y)] & R(x)

The first occurrence of x is called a bound variable, the second occurrence is called a free variable.

See also


Utrecht Lexicon of Linguistics


Gamut, L.T.F. 1991. Logic, language, and meaning. Chicago: University of Chicago Press.