what is the scope of quantifier and What is the scopal relation of negation and quantifier?
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):
- negation in scope of quantifier: "Mary didn't see someone." (Ex)(not(Mary saw x))
- quantifier in scope of negation: "Mary didn't see anyone." not((Ex)(Mary saw x))
- neither in the scope of the other: "Someone left, but Mary didn't." ((Ex)(x left)) and (not(Mary left))
- negation and quantifier in the scope of each other: not possible.