11.4 Scope rules
That is, a quantifier or a coreference link need not apply to all parts of a graph. Let us say that a quantifier or coreference link is defined in the referent of a certain concept C. Then that quantifier or coreference link only applies to:
Consider the following graph:
[If: [If: [Rhino: *x] [Then: [Mammal: ?x] ] ] [If: [Mammal: *y] [Then: [Animal: ?y] ] ] [Then: [If: [Rhino: *x] [Then: [Animal: ?x] ] ] ] ]
The defining label "*y" is in the same scope as the bound label "?y". This is because the bound label "?y" is in the referent of a concept ([Animal]) which is nested inside a concept [Then] which is co-nested with the concept ([Mammal]) in which the defining label "*y" occurs.
Likewise, the first occurrence of "*x" is in the same scope as the first occurrence of "?x" because the defining label "*x" occurs in the referent of a concept ([Rhino]) which is co-nested with a concept ([Then]) inside which we find the nested concept ([Mammal]) in whose referent we find the bound label "?x".
Because of the scope rules, the first occurrence of "*x" is distinct from the second occurrence of "*x". That is, the two do not refer to the same coreference link. This is the same as saying that they occur in different scopes.
This is because the first "*x" occurs inside a concept ([Rhino]) which is not co-nested with the concept in which the second "*x" occurs.
Instead, there is a so-called export-barrier, namely the concept [If] (first occurrence) outside of which the first defining label "*x" does not have scope.
This amounts to saying that quantifiers and coreference-links have scope over everything in the immediately surrounding context (i.e., over those concepts that are co-nested with the concept in which the quantifier or defining label occurs), but not outside the immediately surrounding context.
Two types of quantifier
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