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quantifiermore about quantifier


  2  definitions  found 
  From  WordNet  r  1.6  [wn]: 
  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]: 
  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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