Review of Homework 4

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Review of Homework 4

• November 20, 2003

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Exercise 1 (A) 1 pt

• Modify the DCG to accept the omission of the
  complementizer that for object relative clauses
• Your DCG should accept both of the following
• the cat John saw
• the cat that John saw
• as NPs

3

• s(s(X,Y)) --gt np(X), vp(Y).vp(vp(X,Y)) --gt
  transitive_verb(X), np(Y).np(np(X)) --gt
  proper_noun(X). Special rules for relative
  clausesnp(np(np(Y,Z),U)) --gt det(Y),
  common_noun(Z), sbar(U).np(np(x)) --gt
  .sbar(lambda(x,Y)) --gt complementizer,
  s(Y).complementizer --gt that.complementizer
  --gt . Lexicontransitive_verb(v(hit
  )) --gt hit.transitive_verb(v(saw)) --gt
  saw.transitive_verb(v(hissed_at)) --gt
  hissed,at.proper_noun(john) --gt
  john.proper_noun(mary) --gt mary.common_noun(
  n(man)) --gt man.common_noun(n(cat)) --gt
  cat.det(det(the)) --gt the.

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Exercise 1 (B) 3 pts
doubly-embedded object relative clause structure
Mary hit the mani that the catj that John
saw ej hissed at ei
object
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Exercise 1 (B) 3 pts
doubly-embedded object relative clause structure
Mary hit the mani that the catj that John
saw ej hissed at ei
object
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Exercise 1 (B) 3 pts
doubly-embedded object relative clause structure
Mary hit the mani that the catj that John
saw ej hissed at ei
object
object
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Without any further modification to the DCG,
construct and show parses for (i) A sentence
with two levels of embedding using subject
relative clauses (ii) A sentence with two levels
of embedding using one subject and one object
relative clause (iii) Any sentence with a
triply-embedded relative clause structure
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(i) A sentence with two levels of embedding using
subject relative clauses
subject
subject

• mary,saw,the,cat,that,hissed,at,the,man,that,hit,j
  ohn

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(ii) A sentence with two levels of embedding
using one subject and one object relative clause
subject
object

• mary,saw,the,cat,that,hissed,at,the,man,that,john,
  hit

object
subject
mary,saw,the,man,that,the,cat,that,hit,hohn,hissed
,at
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(iii) Any sentence with a triply-embedded
relative clause structure
subject
subject
object

• mary,saw,the,cat,that,hissed,at,the,man,that,hit,t
  he,cat,that,john,saw

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• Your sentence has to be grammatical!

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Extra Credit Homework Question3 pt

• Modify the DCG to allow that to be omitted only
  in the case of object relative clauses, i.e.
  grammar should still accept
• the cat John saw
• but reject its subject relative clause
  counterpart
• the cat saw John
• Hint (for one possible implementation)
• Look at how subject/verb agreement was enforced

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• s(s(X,Y),EC) --gt np(X), vp(Y),
• (nonvar(EC), X np(x)) -gt EC overt.
• vp(vp(X,Y)) --gt transitive_verb(X), np(Y).
• np(np(X)) --gt proper_noun(X).
• np(np(x)) --gt .
• np(np(np(Y,Z),U)) --gt det(Y), common_noun(Z),
  sbar(U).
• sbar(lambda(x,Y)) --gt complementizer(EC),
  s(Y,EC).
• complementizer(overt) --gt that.
• complementizer(empty) --gt .

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Exercise 2 Disjunctive Tree-Walker1 pt

• Homework Question
• Modify visit/1 to search for all NP nodes
• How many times should visit/1 succeed for the
  following sentence?
• Mary hit the cat that hissed at John
• Hint
• Youll need to add more than one clause to visit/1

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• visit(X) - X .. _,A1,_,visit(A1).visit(X)
  - X .. _,_,A2,visit(A2).visit(X) - X ..
  _,A,visit(A).visit(np(_)).
• visit(np(_,_)).
• It succeeds 5 times, visiting each np node.

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Exercise 3 Collecting Answers1 pt

• Homework Question
• Assuming the unmodified version of visit/1
• What does the query
• ?- s(X,mary,hit,the,cat,that,hissed,at,john,),
  
• findall(once,visit(X),L),
• length(L,N).
• do?

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• s(X,mary,hit,the,cat,that,hissed,at,john,),
• findall(once,visit(X),L),length(L,N).
• X s(np(mary), vp(v(hit), np(np(det(the),
  n(cat)), lambda(x, s(np(x), vp(v(hissed_at),
  np(john)))))))
• L once, once, once, once, once, once, once,
  once
• N 8

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Exercise 4 Operators and Variables

• Homework Question
• Determine the status of the following sentences
  with respect to the DCG, filter1 and filter2.
• Explain your answers when there is a violation.
• 1. hit 1pt
• 2. saw the man that hit 1pt

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• Two Filters
• All variables must be bound by an operator (lx)
• Operator (lx) can only bind one variable
• Implementation
• filter1(X) - \ ( variable(X,F), var(F) ).
• filter2(X) - operator(X).

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• EX4-1 hit violates both filter 1 and 2
• X s(np(x), vp(v(hit), np(x)))
• it violates filter1 because the variables np(x)
  are not bound by an operator.
• it violates filter2 because there is no
  operator.(This shows the inadequacy of this rule
  because it also rules out sentences like "john
  saw mary".)

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• EX4-2 X s(np(x),vp(v(saw),np(np(det(the),
  n(man)), lambda(x,s(np(x),vp(v(hit), np(x)))))))
• it violates filter1 because the first np(x) is
  not bound by an operator.
• it violates filter2 because there are two
  variables to be bound one operator under the man.

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Big Picture

• Relative clauses
• John saw the man that the cat hissed at.

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Big Picture

• Relative clauses
• John saw the man that the cat hissed at e.

np(x)
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Big Picture

• Relative clauses
• John saw the man that the cat hissed at e.

np(x)
l
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Big Picture

• The relation between l and np(x)
• John saw the man that the cat hissed at e.

np(x)
l
ok
0 0 1
2 0 1 1
2
F1
F1
F2new
ok
F2old
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Big Picture

• Relative clauses
• The operator and the np(x) has to be in the same
  branch.
• The operator has to dominate the np(x).
• There should be no intervening operators between
  the operator and the variable.

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Exercise 5

• 4. Mary hit the man that the cat that John saw
  hissed at
• 5. Mary hit the man that the cat that John saw
  Mary hissed at
• (4) is a doubly-embedded object relative sentence
• (4) and (5) satisfy both filters

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Exercise 5 Multiple Embeddings2pt

• Homework Question
• Modify filter2/1, i.e. operator/1, to reject
  example 5
• 5. Mary hit the man that the cat that John saw
  Mary hissed at
• In other words
• Modify operator/1 from succeeding for zero np(x)s
• Operator/1 should succeed only for the case where
  there is exactly one np(x) present

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Original clauses

• filter2(X) - operator(X).lt2vars(np(x),F) -
  var(F), F one.lt2vars(X,F) - X .. _,A1,A2,
  \ X lambda(x,_), lt2vars(A1,F),lt2vars(A2,F).
  lt2vars(X,F) - X .. _,A1,A2, X
  lambda(x,_).lt2vars(X,F) - \ X np(x), X ..
  _,A, lt2vars(A,F).lt2vars(X,_) -
  atom(X).operator(lambda(x,Y),F)-
  lt2vars(Y,F).operator(X,F) - X .. _,A1,_,
  operator(A1,F).operator(X,F) - X .. _,_,A2,
  operator(A2,F).operator(X,F) - X .. _,A,
  operator(A,F).

This successfully excludes cases where there are
two np(x)s bound by one operator.
BUT, this does NOT exclude an operator binding
ZERO np(x).
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Mary hit the man that the cat that John saw
Mary hissed at
lambda
x
s
np
vp
np
lambda
np
v
det
n
x
s
hissed at
x
the
cat
np
vp
np
v
john
saw
mary
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Solution

• lt2vars(np(x),F) - var(F), F one.
• operator(lambda(x,Y))- lt2vars(Y,F), var(F).
• filter2(X) - \ operator(X).

2 np(x)
1 np(x)
0 np(x)
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An alternative

• filter2(X) - \ ( operator(X,F), var(F)).

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A better solution that takes care of even the 2nd
extra credits

• lt2vars(np(x),F) -
• (var(F) -gt F one(_)) F one(two).
• operator(lambda(x,Y))- lt2vars(Y,F), (var(F) F
  one(two)).
• filter2(X) - \ operator(X).

2 np(x)
1 np(x)
0 np(x)
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• Term projects?
• Final take-home exam 12/9-12/16