1. For each of the following sentences, state whether it is ambiguous or not, and why. In particular, you should indicate what sort of ambiguity (if any) is present - word sense, syntactic structure, or a combination of the two. (Sentences c-f are supposed to have been actual newspaper headlines.)

   a. We saw her duck.
   b. A man stopped at every truck stop.
   c. Killer sentenced to die for second time in 10 years.
   d. Teacher strikes idle kids.
   e. Prostitutes appeal to Pope.
   f. Squad helps dog bite victim.

   If you are not a native speaker of English, then you may not be aware of some alternative meanings of some of the words used in these examples. If I give the relevant meanings here, it will take some of the point of the exercises for students who are native speakers of English, so instead, you will find the relevant extra meanings explained in the solutions.

   In an exam situation, either the relevant meanings and parts of speech would be given, or the example sentence would be one already seen in lectures or in these exercises.

2. Expand out the following ambiguous logical forms, giving a complete list of the full logical forms allowed by the ambiguous logical form:

   {run1 run2}(ev1, agent[pro(h1, male1)])

   sees1(s1, agent[pro(h1, male1)], theme[every<b1, { ball1 ball2} >])

   gives1(l1, agent[every<m1, man1>], theme[a<g1, gift1>])

   not<({run1 run2}>)(r1, agent[every<m1, &(man1(m1), happy(m1))>])

   How would each of these logical forms read in English?

3. Simplify the following formulae using lambda reduction:

   lambda(X, p(X)) a

   lambda(X, X(a) lambda(Y, q(Y))

   lambda(X, (lambda(Y, p(Y)) X)) a

4. Using the interpretation rules defined in Chapter 9 of Allen and shown in lectures, and defining any others that you need, give a detailed trace of the interpretation of the sentence The man gave the apple to Bert. In particular, give the analysis of each constituent and show its SEM feature.

© Bill Wilson, 1996-2008.
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