## Problem Set 6

Assigned: Nov. 17
Due: Dec. 3.

Note: This is due in TWO weeks. If you are submitting this by email, please send it to Ernie Davis, davise@cs.nyu.edu, not to the TA.

### Problem 1

Explain how each of the ambiguities specified below can be resolved by selectional restrictions. Your explanation should specify what are the constraints and the features involved. Comment: It was careless on my part that 6 out of the 7 examples could be resolved on the ANIMATE feature.
• A. Resolve the lexical ambiguity of "pitcher" in "The pitcher drank a cup of coffee." ("pitcher" = baseball player vs. "pitcher" = container of liquid.

Answer: The subject of "drank" must have the feature ANIMATE; hence, not the container of liquid.

• B. Resolve the lexical ambiguity of "pitcher" in "Joe poured a cup of coffee from the pitcher". (Same ambiguity as in (A); different decision.)

Answer: The source of a "pouring" action must have the feature CONTAINER; hence, not the baseball player.

• C. Resolve the anaphoric ambiguity of "They" in "The children got new toys for Christmas. They were very excited." (They = "children" or "toys").

Answer: The adjective "excited" must modify an object that is has the feature ANIMATE; hence, not toys.

• D. Resolve the anaphoric ambiguity of "They" in "The children got new toys for Christmas, but they all broke within half an hour."

Answer: The subject of the verb "broke" must have the feature INANIMATE; hence, not children.

• E. Resolve the syntactic ambiguity of the conjunction in "The captain of the ship and the first mate swam to shore." (Is it "The captain of [the ship and the first mate]" or "[The captain of the ship] and the first mate."

Answer: The object of the relation "captain of" must either have the feature VEHICLE (captain of a ship / of an airplane) or the feature COLLECTION OF PEOPLE (captain of a brigade); not a single person like "the first mate". Hence "the first mate" cannot be conjoined with ship.

• F. Resolve the syntactic ambiguity of the conjunction in "The man with the red beard and the glass eye swam to shore". (Is it "[the red beard and the glass eye]" or "[The man with the red beard] and the glass eye"?)

Answer: The subject of the verb "swam" must have the feature ANIMATE; hence, not the glass eye. Therefore, "the glass eye" cannot be conjoined with "the man".

That's an adequate answer, but the truth is that the primary disambiguation strategy employed here is not selectional restrictions at all, but a parallelism constraint. There is a preference to understand a conjuction "and" as connecting two similar entities, rather than two dissimilar entities. Hence, it is preferred to interpret this as "the red beard and the glass eye" where two body parts (one prosthetic) are conjoined rather than "the man ... and the glass eye" which conjoins a person and a body part.

That this is the key disambiguation strategy here can be seen from the following two examples. If we change the sentence to "The man with the red beard and the glass eye sank in the lake," there's no violation of selectional restrictions in supposing that a glass eye can sink, but the preferred interpretation is still to connect "the glass eye" to "the red beard". In fact, if we change the sentence to force the opposite reading --- e.g. "The man with the red beard and the glass eye are in the living room," where the plural verb "are" means that the interpretation must be "the man ... and the glass eye" --- we get a so-called "garden path" sentence; that is, when you reach the word "are" you have to go back and rethink the sentence.

• G. Resolve the lexical ambiguity of the word "on" in the sentence "We have to write a paper on prohibition for "Twentieth Century American History" by Monday." ("on" = "about" vs. "on" = "on top of")

Answer: The object of the relation "on top of" must have the feature CONCRETE. Since the object is the abstract entity "prohibition", the relation involved cannot be "on top of"

### Problem 2

Explain how each of the ambiguities specified below can be resolved using selectional restrictions or world knowledge. You should be as precise as possible about what facts are being applied.
• A. John asked his father whether he would give him a car for his 16th birthday. ("him" and "his" = John; "he" = father.)

Answer: Obviously, selectional restrictions do not apply, since John and his father are entities of the same kind with the same features. Note also that the first "his" must unambiguously refer to "John". There are various ways to do this; here's one.

Facts of world knowledge:

• 1. The giver of a present is rarely the same as the recipient.
• 2. A person is more likely to receive than to give a present on his birthday (among us; the hobbits have the opposite custom.)
• 3. It is unlikely that A will ask B if A "would" do X. (as opposed to "should" do X.) I've worded this in terms of the word "would"; there are deeper explanations for this but those would take us deep into the theory of modal expressions and conditional time, which are, in fact, not wholly understood.
• 4. A person is (with very rare exceptions) at least 12 years younger than his/her parent.
• 5. A person does not generally receive a car until he/she is nearly 16 years old.
From (3) it follows that "he" is not John; hence "he" is the father. From (1) it follows that "him" is John. From (2) it follows that "his birthday" is John's birthday. (4) and (5) together are supporting evidence that the birthday involved is John's, rather than supposing that a 16 year old father will be giving a car to an infant John.

• B. President Bush proposed to cut taxes on inheritances because they are too high. ("proposed" = "formally suggested" rather than "offers marriage"; "cut" = "reduce" rather than literally slice; "they" = taxes rather than inheritances; "high" = large amount of money rather than physically elevated.)

Answer: Actually "proposed" always means "formally suggested". If there is evidence that the recipient of the proposal was a unique person and there is no indication of the content of the proposal, then the default interpretation is "proposed to X that they get married". In this case, the content is quite clearly unconnected to marriage, so that default does not apply. (Selectional restriction, of a unusual kind.)

The object of the action "slice" must have the feature CONCRETE OBJECT; since "taxes" does not have this feature, that interpretation of "cut" is excluded. (Selectional restriction)

The meaning "physically elevated" can only apply to entities with the features "PHYSICAL OBJECT", which is not a feature of either "taxes" or "inheritances" (generally), the two possible antecedents for "they". Hence "high" cannot mean "physically elevated." (Selectional restriction.)

The causal chain "A reduces X because X is too large" is coherent. The causal chain "A reduces X, a penalty associated with Y, because Y is too large," is much less coherent. Hence "they" is "taxes" not "inheritances". (World knowledge)

• C. Resolve the syntactic ambiguities of the prepositional phrase attachments in the sentence "We have to write a paper on prohibition for "Twentieth Century American History" by Monday." (Compare: "We have to read a book on prescription drug benefits for senior citizens by an expert on Medicare.")

Answer: Several people gave answers explaining how the meanings of the prepositions could be disambiguated, which is not what I asked here. I asked about the attachment .

"on prohibition" can be attached either to "paper" or to "write". This is actually genuinely ambiguous; it is an instance of the category, not rare in English, of syntactic ambiguities that don't actually make any difference. One can say "We have to write on prohibition," or one can say "The paper on prohibition was very dull;" either attachment is feasible. But in this case they mean the same thing; We will write about prohibition, and the paper will be about prohibition.

Syntactically, "for 'Twentieth Century American History'" can attach either to "prohibition", to "paper", or to "write" . We can exclude the attachment to "prohibition" using world knowledge; Prohibition was not enacted for the benefit of the course "Twentieth Century American History." The choice of attaching this to "paper" or to "write" is again a distinction without a difference.

Syntactically, "by Monday" can attach to "History", to "paper" or to "write". (Since we have decided that "for 'Twentieth Century American History'" does not attach to "prohibition", it is not syntactically possible that "by Monday" should attach to "prohibition".) "By" has many meanings, including as between "authored by", "next to", and "no later than"; however, since "Monday" has the feature "TIME DESIGNATION", the meaning "no later than" is by far the most probable (Selectional restriction.) A due date "by Monday" can only apply to an event, such as "write", not to "paper" or "Twentieth-Century American History."