# HOMEWORK 10

## Question 1 [3 points]

Zettlemoyer and Collins (2007) develop a CCG grammar with rules corresponding to the following operations: (i) functional application, (ii) functional composition, (iii) relaxed functional application, (iv) relaxed functional composition, (v) role-hypothesising [sic!] type shifting, (vi) null-head type shifting, and (vii) crossed functional composition.

For each of the following pairs of expressions, either indicate that the expressions cannot be combined according Z&C's grammar or give the result of combination and the name of the rule you used to combine them.

1. NP   ((S\NP)\NP)
2. ((S\NP)/NP)   NP
3. (S/(S\NP))   ((S\NP)/S)
4. (S/(S\NP))   ((S\NP)\S)
5. (S/(S/NP))   ((S\NP)/S)
6. NP   ((N\N)/NP)

## Question 2 [4 points]

Logical forms have a very different status for Liang et al. 2011 than they do for Zettlemoyer and Collins (2007). Articulate what this difference is (1-2 sentences), and give one practical consequence of this difference (1-2 sentences).

## Question 3 [3 points]

Compute the meaning of the following dependency structure in the world/database w, using the recursive interpretation rules defined by Liang et al. (2011), §2.2. (Assume array indexing begins at 1, in the leftmost position.) The final meaning wil be a set of arrays.

Database/world w
a
[A],
[B],
[γ],
[X]
b
[A, W, α],
[B, X, δ],
[C, Y, γ],
[D, Z, δ]
c
[X,α],
[γ,β],
[α,γ],
[B,Y]