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

Stabler - Lx 185/209 2003
A, B for the predicates and Q for the determiner in sentences like every student laugh -s, QAB,whichgets
a syntactic analysis of the form B(Q(A)) since Q selects A and then B selects Q. We capture many entailment
relations among sentences of this form with schemes like the following, depending on the determiners Q. 53
B(Q(A)) C(every(B))
C(Q(A))
[Q↑]
(f or any r ight monotone incr easing Q: all, most,
the, at least N, inf initely many,...)
B(Q(A)) B(every(C))
C(Q(A))
(f or any r ight monotone decr easing Q: no, f ew,
[Q↓]
f ewer than N, at most N,...)
B(Q(A)) C(every(A))
B(Q(C))
(f or any lef t monotone increasing Q: some, at least N,
[↑Q]
...)
B(Q(A)) A(every(C))
B(Q(C))
(f or any lef t monotone decreasing Q: no, ever y, all,
[↓Q]
at most N, at most f initely many,...)
There is an absolutely fundamental insight here: substitution of a “greater” constituent is sound in a increasing
context, and substitution of a “lesser” constituent is sound in an decreasing context. It is worth spelling out
this notion of “context” more carefully.
A competent language user learns more specific information about each verb too, some of which can be
encoded in schemes roughly like this:
v(praise(Obj),Subj)
v(think,Subj)
v(eat(Obj),Subj)
v(eat,Subj)
v(prefer(Obj),Subj)
v(think,Subj)
v(eat,Subj)
v(eat(some(thing)),Subj)
v(doubt(Obj),Subj)
v(think,Subj)
v(wonder(Obj),Subj)
v(think,Subj)
53Since ↑every↓, the “Barbara” syllogism is an instance of the rule [Q ↑]. Since ↓no↓, the “Celarent” syllogism is an instance of the
rule [↓ Q].
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