Note: This is due in TWO weeks. If you are submitting this by email, please send it to Ernie Davis, firstname.lastname@example.org, not to the TA.
Answer: The subject of "drank" must have the feature ANIMATE; hence, not the container of liquid.
Answer: The source of a "pouring" action must have the feature CONTAINER; hence, not the baseball player.
Answer: The adjective "excited" must modify an object that is has the feature ANIMATE; hence, not toys.
Answer: The subject of the verb "broke" must have the feature INANIMATE; hence, not children.
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.
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.
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"
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:
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)
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."