Sample problems from 2nd half of course

Let me emphasize that this is just a collection of sample problems, not a sample final exam.

Multiple choice problems

Problem 1

Consider the following CFG grammar:
S -> NP VP
NP -> NG | NG "and" NG
NG -> pronoun | noun
VP -> verb | verb NP | VP "and" VP

Lexicon:
I : pronoun.
cook : noun, verb
eggs : noun
fish : noun, verb.
Which of the following parse tree are correct:
 
i.  S ---> NP ---> NG ---> pronoun ---> I
       |
       |-> VP ---> verb ---> cook
               |
               |-> NP ---> NG ---> noun ---> eggs
                       |
                       |-> "and"
                       |
                       |-> NG ---> noun ---> fish


ii. S ---> NP ---> NG ---> pronoun ---> I
       |
       |-> VP ---> verb ---> cook
               |
               |-> NP ---> NG ---> noun ---> eggs
                       |
                       |-> "and"
                       |
                       |-> VP ---> verb ---> fish


iii.S ---> NP ---> NG ---> pronoun ---> I
       |
       |-> VP ---> VP ---> verb ---> cook
               |       |       
               |       |-> NP ---> NG ---> noun ---> eggs
               |               
               |-> "and"
               |
               |-> VP ---> verb ---> fish


iv. S ---> NP ---> NG ---> pronoun ---> I
       |
       |-> VP ---> verb ---> cook
               |       
               |-> NP ---> NG ---> noun ---> eggs
               |       
               |-> "and"
               |
               |-> VP ---> verb ---> fish
A. All four.
B. Only (i)
C. (i), (iii), and (iv).
D. (i) and (iii).
E. (i) and (iv).

Problem 2

In a chart parser, the "EXTENDER" module could combine edge [2,4,VP -> VG * NP] with
A. edge [2,4,VG -> modal verb *] to create edge [2,4,VP -> VG NP *]
B. edge [4,6,VG -> modal verb *] to create edge [2,6,VP -> VG NP *]
C. edge [2,6,VG -> modal verb *] to create edge [2,6,VP -> VG * NP]
D. edge[2,4,NP -> determiner noun *] to create edge [2,4,VP -> VG NP *]
E. edge[4,6,NP -> determiner noun *] to create edge [2,6,VP -> VG NP *]
F. edge[2,6,NP -> determiner noun *] to create edge [2,6,VP -> VG * NP]

Problem 3

Compositional semantics is

Problem 4

Bayes' Law states that

Problem 5

In a feed-forward, back-propagation network, learning proceeds by

Long Answer Problems

Problem 6

Consider the following pair of sentences:
A. Joe wore a wool suit. ("suit" = pants and jacket)
B. The suit is in the court. ("suit" = lawsuit).
Explain how the disambiguation techniques of selectional restriction and frequency in context can be applied in these two sentences.

Problem 7

List the major modules of a natural language interpretation system and explain their function.

Problem 8

A. Give an example of a sentence or pair of sentences in which selectional restrictions can be used to disambiguate potential anaphoric ambiguity. Explain the ambiguity and the selectional restriction used.

B. Give an example of a sentence or pair of sentences in which there is a potential anaphoric ambiguity that cannot be disambiguated using selectional restrictions. Explain why not. Give a method for carrying out the disambiguation.

Problem 9

Consider the sentence "Hammers are for driving nails into surfaces." Name two words in this sentence that are lexically ambiguous. (There are at least four.) For each of these two words, describe a disambiguation technique which will choose the right interpretation over at least one of the wrong interpretations. Be specific.

Problem 10

In this problem and in problem 10, we consider a data set with three Boolean predictive attributes, A,B,C, and a Boolean classification, Z.

A. Suppose that your data is completely characterized by the following rules:

Construct a decision tree whose predictions correspond to these rules.

B. True or false: Given any consistent set of rules like those above, it is possible to construct a decision tree that executes that set of rules. By "consistent", I mean that there are no examples where two different rules give different answers.

Problem 11

Which of the following expresses the independence assumption that is used in deriving the formula for Naive Bayesian learning, for the classification problem in problem ???.

Problem 12

Consider the following data set T. A and B are numerical attributes and Z is a Boolean classification.
      A   B   Z
      1   2   T
      2   1   F
      3   2   T
      1   1   F
A. Let P be the perceptron with weights wA = 2, wB = 1, and threshhold T=4.5. What is the value of the standard error function for this perceptron?

B. Find a set of weights and a threshhold that categorizes all this data correctly. (Hint: Sketch a graph of the instances in the plane where the coordinates are A and B.)