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

Stabler - Lx 185/209 2003
15 Exercises
1. Consider the inferences below, and list the English quantifiers that make them always true. Try to name at
least 2 different quantifiers for each inference pattern:
a.
b.
c.
d.
e.
B(Q(A))
(A∧B)(Q(A))
What English quantifiers are conservative?
B(Q(A)) C(Q(B))
C(Q(A))
What English quantifiers are transitive?
B(Q(A))
A(Q(B))
What English quantifiers are symmetric?
A(Q(A))
What English quantifiers are reflexive?
B(Q(A))
B(Q(B))
What English quantifiers are weakly reflexive?
[conser vativity] (f or any conser vative quantif ier Q)
[tr ansitivity] (f or any tr ansitive quantif ier Q)
[symmetr y] (f or any symmetr ic quantif ier Q)
[r ef lexivity] (f or any r ef lexive quantif ier Q)
[weak ref lexivity] (f or any weakly ref lexive quantif ier Q)
2. Following the examples in the previous sections, do any of our rules cover the following “Celarent syllogism”?
(If not, what rule is missing?)
No mammals are birds
All whales are mammals
Therefore, no whales are birds
(I think we did this one in a rush at the end of class? So I am not sure we did it right, but it’s not too hard)
3. Following the examples in the previous sections, do any of our rules cover the following “Ferio syllogism”?
(If not, what rule is missing?)
No student is a toddler
Some skaters are students
Therefore, some skaters are not toddlers
241