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what is the scope of quantifier and What is the scopal relation of negation and quantifier?

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  • 2
    Pretty much infinite.
    – user6726
    Jan 12 '16 at 5:59
  • Depends on a quite a few parametres, beginning with what language you're in and what particular sentence/construction that is. Jan 12 '16 at 7:15
  • @IvanKapitonov in English
    – M.S
    Jan 13 '16 at 6:35
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In logic, the scope of negation is everything in the sentence that is formed by combining negation with another sentence. Similarly, the scope of a quantifier is everything in the sentence that is formed by combining the quantifier with a sentence. In the syntax of a human language sentence, the scopes are as they would be in the corresponding logical form.

The scopal relation of negation and quantifier concerns which is in the scope of the other (if either is):

  1. negation in scope of quantifier: "Mary didn't see someone." (Ex)(not(Mary saw x))
  2. quantifier in scope of negation: "Mary didn't see anyone." not((Ex)(Mary saw x))
  3. neither in the scope of the other: "Someone left, but Mary didn't." ((Ex)(x left)) and (not(Mary left))
  4. negation and quantifier in the scope of each other: not possible.
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  • Could you give more examples with information and what about the ambiguity case?
    – M.S
    Jan 13 '16 at 6:36
  • Ambiguous: "Mary didn't see a person." could have either sense 1 or 2 above. Sense 1 is referred to as the wide scope interpretation. A quantifier must have all coreferential nouns in its scope, so "Mary didn't see a person, but he saw her" has only the wide scope interpretation, because of the "he". Some speakers may find the wide scope reading impossible, so for them, the last example is unacceptable.
    – Greg Lee
    Jan 13 '16 at 17:07
  • You said scope of negation and quantifier together is not possible. It is not possible even in Arabic? Look at this sentence in Arabic: did not she go anywhere. Is there a relation between scope of negation and scope of quantifier?
    – M.S
    Jan 18 '16 at 15:33
  • I didn't say that scope of negation and quantifier together is not possible -- constituents can be in the scope of both. I said it's not possible for a given quantifier and negation to be in the scope of each other. I don't know Arabic. In the English version you give, the existential quantifier for anywhere is in the scope of the negation, but not vice versa.
    – Greg Lee
    Jan 18 '16 at 16:44
  • could you help me with the given quantifiers that make scope with negation and vice versa?
    – M.S
    Jan 18 '16 at 22:01

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