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Review of Homework 4

Review of Homework 4. November 20, 2003. 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.

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Review of Homework 4

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  1. Review of Homework 4 November 20, 2003

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

  4. 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

  5. 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

  6. 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

  7. 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

  8. (i) A sentence with two levels of embedding using subject relative clauses mary,saw,the,cat,that,hissed,at,the,man,that,hit,john subject subject

  9. (ii) A sentence with two levels of embedding using one subject and one object relative clause mary,saw,the,cat,that,hissed,at,the,man,that,john,hit subject object object subject mary,saw,the,man,that,the,cat,that,hit,hohn,hissed,at

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

  11. Your sentence has to be grammatical!

  12. 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

  13. s(s(X,Y),EC) --> np(X), vp(Y), {(nonvar(EC), X = np(x)) -> EC == overt}. vp(vp(X,Y)) --> transitive_verb(X), np(Y). np(np(X)) --> proper_noun(X). np(np(x)) --> []. np(np(np(Y,Z),U)) --> det(Y), common_noun(Z), sbar(U). sbar(lambda(x,Y)) --> complementizer(EC), s(Y,EC). complementizer(overt) --> [that]. complementizer(empty) --> [].

  14. 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: • You’ll need to add more than one clause to visit/1

  15. 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.

  16. 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?

  17. 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

  18. 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

  19. 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).

  20. 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".)

  21. 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.

  22. Big Picture • Relative clauses: John saw the man that the cat hissed at.

  23. Big Picture • Relative clauses: John saw the man that the cat hissed at e. np(x)

  24. Big Picture • Relative clauses: John saw the manthat the cat hissed at e. np(x) l

  25. Big Picture • The relation between l and np(x): John saw the manthat the cat hissed at e. np(x) l ok 0 0 1 2+ 0 1 1 2+ * F1 * F1 * F2new ok * F2old

  26. 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.

  27. 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

  28. 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

  29. 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).

  30. *Mary hit the man that the cat that John saw Mary hissed at lambda x s np vp np lambda v np det n x s hissed at x the cat np vp john v np saw mary

  31. 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)

  32. An alternative filter2(X) :- \+ ( operator(X,F), var(F)).

  33. A better solution that takes care of even the 2nd extra credits • lt2vars(np(x),F) :- (var(F) -> 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)

  34. Term projects? Final take-home exam: 12/9-12/16

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