6.2.x. Exercise questions

1.

Expand each of the following in two different ways, (i) on a single occurrence of a single individual term, and (ii) on all terms together. In each case express the expanded form in English using is such that and in a partially symbolic way, as in

[x wrote Moby Dick]x Melville
  a. Romney is north of Linden.
  b. Mike gave the package to Nancy.
  c. Tom spoke of Ed to Sue.
  d. Sam traveled to Atlanta by way of Chicago.
2.

Analyze each of the following in a way that uses abstracts and variables to represent pronouns instead of replacing them by their antecedents. Since you will not replace pronouns by their antecedents, you should end up with as many occurrences of each individual term in your result as in the original sentence. Also, restate your symbolic analysis in reduced form.

  a. Ann nominated herself
  b. Ralph tried the motor, and it started
  c. If the alarm is touched, it will go off
  d. Ralph fixed Sam’s car, and he drove it back to him
  e. Ann and Bill each left a message for the other
3.

Each of the following sentences exhibits an ambiguity (in pronoun reference) between meanings that can be indicated by alternative analyses using abstracts. Use abstracts to give two complete analyses of each sentence that express different interpretations of it. You will find it easier to distinguish interpretations if you expand for all terms involved in the ambiguity whether or not all have pronouns referring to them on each interpretation (see the last example of 6.2.3).

In c, the word so serves to apply the same predicate to Bill as was applied to Al, so each of your analyses of it should have a repeated abstract.

  a. Al called Bill, and he called Carol.
  b. Sam gave the book to Tom, but he didn’t read it.
  c. Al washed his car, and so did Bill.
4.

For each of the following abstracts (i) diagram the pattern of binding using lines rather than variables (in the manner shown in 6.2.2) and (ii) give an alphabetic variant (i.e., abstract which indicates the same pattern of binding using different variables).

In the case of e, remember that, as noted in 6.2.2, a bracketed sentence-with-blanks amounts to an abstract whose body has a different variable in each blank and whose abstractor lists the variables in the same order. Also, the lower-case f in c means that it is a functor rather than a predicate; but that won’t make for any differences in the way you handle it.

  a. [Fx]x
  b. [Fz → Gz]z
  c. [Tyxy]xy
  d. [fyz]zy
  e. [S _ _ _ ]
  f. [[Rxy]xa ∧ Rby]y
  g. [[Rcy]ya ∧ Rby]y
Glen Helman 01 Aug 2011