## Solution Set 3

### Problem 1

Example 1: "He and I had a meeting between 4:00 and 5:00."
Example 2: "The planned meeting between Fred and George never took place."

### Problem 2

Consider the following sentence, from the New York Times, 9/22/07:
Even many hawks within the Bush administration have expressed doubts that the Syrians have the money or technical depth to build a serious nuclear program like the one in Iran.
A. Give four examples of lexical ambiguity and two examples of syntactic ambiguity in the above sentence. (The examples of lexical ambiguity must be syntactically possible; for instance it is not possible (as far as I can see) to read "like" as a verb in the above sentence, so that would not count as lexical ambiguity.)

Lexical ambiguity
"hawks" = birds / (metaphorically) proponents of an aggressive policy.
"within" = spatially inside / part of
"administration" = ruling part of government / act of ruling something / act of applying or giving something (as in "the administration of a drug to the patient ...")
"have" = possess / be in a condition ("has a cold/wish") / many others
"technical" = technological / relating to technique ("technical brilliance of her piano playing")
"depth" = distance downward / sophistication / several others.
"build" = develop / physically construct
"serious" = substantial / in earnest / dangerous or critical ("serious illness/flaw")
"nuclear" = related to fission/fusion reactors/bombs / related to the atomic nucleus ("nuclear particle") / related to the cell nucleus / central or core ("nuclear family")
"program" = enterprise / computer program / written agenda at a performance / many others

Syntactic ambiguity
The phrase "have expressed doubts ..." has two different parses:

```VP ---> VG ---> Modal ---> "have"
|       |
|       |-> Verb ---> "expressed"
|
|-> NP ---> Noun ---> "doubts"
|
...

or

VP ---> VG ---> Verb ---> "have"
|
|-> NP ---> Participle ---> "expressed"
|
|-> Noun ---> "doubts"
|
...
```
(The second one is like "The manuscript collection has handwritten notes from Lincoln ...")

The conjunction "or technical depth" can apply to "money" or to "doubts".
The infinitive phrase "to build a serious nuclear program like the one in Iran" in fact attaches to "money or technical depth", but syntactically it could attach to "depth", or "expressed".
The prepositional phrase "like the one in Iran" attaches to "program" but could attach to "build", "depth", "money or technical depth", "have", "Syrians", "doubts" or "expressed".
The prepositional phrase "in Iran" attaches to "one" but could attach to "program", "build", "depth", "money or technical depth", "doubts" or "expressed".

B. Discuss how selectional restrictions can be used to resolve two of these ambiguities. Be specific about the features and constraints involved.

The SUBJECT of the verb "expressed" (under the meaning "stated") must have feature PERSON which rules out the interpretation of "hawks" as birds.

The OBJECT of "within" meaning "spatially within" must be either have the feature PLACE or PHYSICAL OBJECT. Since "the Bush administration" has neither of these, this rules that out.

There are several others.

### Problem 3

Convert the following sentences to CNF:

P <=> [Q V R].