Notes on computational linguistics.pdf - UCLA Department of ...

Stabler - Lx 185/209 2003
Example: Many adjectives are “intersective” in the sense that [A N] signifies ([[A]] ∧ [[N]]). For example, Greek
student signifies (Greek ∧ student). Allowing ourselves this treatment of intersective adjectives, we have
Every student sings
Therefore, every Greek student sings
We can recognize this now as one instance of the Q↑ rule:
(sings (every student)) (student(every (Greek∧student)))
sings(every (Greek∧student))
The second premise says that the step from the property [student] to [Greek student] is a “decrease,” and
since we know ↓every, the step from the first premise to the conclusion preserves truth. Notice that this does
not work with other quantifiers!
[↓Q]
every student sings ⇒ every Greek student sings
every Greek student sings ⇒ every student sings
some student sings ⇒ some Greek student sings
some Greek student sings⇒ some student sings
exactly 1 student sings ⇒ exactly 1 Greek student sings
exactly 1 Greek student sings ⇒ exactly 1 student sings
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