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## quantifier

```  2  definitions  found

From  WordNet  r  1.6  [wn]:

quantifier
n  1:  a  word  (such  as  `some'  or  `all`  or  `no')  that  binds  the
variables  in  a  logical  proposition
2:  a  word  that  expresses  a  quantity  (as  `fifteen'  or  `many')

From  The  Free  On-line  Dictionary  of  Computing  (13  Mar  01)  [foldoc]:

quantifier

An  operator  in  mathematics  and  logic  specifying  for  which
values  of  a  variable  a  formula  is  true.  Universally
quantified  means  "for  all  values"  (written  with  an  inverted  A,
{LaTeX}  \forall)  and  existentially  quantified  means  "there
exists  some  value"  (written  with  a  reversed  E,  {LaTeX}
\exists).  To  be  unambiguous,  the  set  to  which  the  values  of
the  variable  belong  should  be  specified,  though  this  is  often
omitted  when  it  is  clear  from  the  context.  E.g.

Forall  x  .  P(x)  <=>  not  (Exists  x  .  not  P(x))

meaning  that  any  x  (in  some  unspecified  set)  has  property  P
which  is  equivalent  to  saying  that  there  does  not  exist  any  x
which  does  not  have  the  property.

If  a  variable  is  not  quantified  then  it  is  a  {free  variable}.
In  {logic  programming}  this  usually  means  that  it  is  actually
universally  quantified.

See  also  {first  order  logic}.

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