0440949	Andreas van Cranenburgh
Cognitive Models of Language
Assignment 5a

NB: instead of calculating all this by hand I decided to implemement a DOP and
PCFG model in python using nltk. Hence any mistakes here are mistakes in my
implementation. The code is available at:

	https://unstable.nl/andreas/dop.py

1.
S -> NP VP 			2 / 2
NP -> 'Harry' 			1 / 3
NP -> 'pizza' 			1 / 3
NP -> 'Hermione' 		1 / 3
VP -> V NP 			1 / 2
VP -> 'eats' 			1 / 2
V -> 'eats' 			1 / 1

2.
S -> NP V NP 			1 / 14
S -> NP V 'pizza' 		1 / 14
S -> NP VP 			2 / 14
S -> NP 'eats' 			1 / 14
S -> NP 'eats' NP		1 / 14
S -> NP 'eats' 'pizza' 		1 / 14
S -> 'Harry' V NP 		1 / 14
S -> 'Harry' V 'pizza' 		1 / 14
S -> 'Harry' VP 		1 / 14
S -> 'Harry' 'eats' NP 		1 / 14
S -> 'Harry' 'eats' 'pizza' 	1 / 14
S -> 'Hermione' VP 		1 / 14
S -> 'Hermione' 'eats' 		1 / 14
NP -> 'Harry' 			1 / 3
NP -> 'Hermione'	 	1 / 3
NP -> 'pizza' 			1 / 3
VP -> V NP 			1 / 5
VP -> V 'pizza' 		1 / 5
VP -> 'eats' 			1 / 5
VP -> 'eats' NP 		1 / 5
VP -> 'eats' 'pizza' 		1 / 5
V -> 'eats' 			1 / 1

3. Prefix probabilities:
PCFG
prefix prob: Hermione 1.33333333333
prefix prob: Hermione eats 2.33333333333
prefix prob: Hermione eats pizza 0.888888888889
prefix prob: pizza 1.33333333333
prefix prob: pizza eats 2.33333333333
prefix prob: pizza eats Harry 0.888888888889

PTSG:
prefix prob: Hermione 0.252380952381
prefix prob: Hermione eats 0.471428571429
prefix prob: Hermione eats pizza 0.342857142857
prefix prob: pizza 0.180952380952
prefix prob: pizza eats 0.357142857143
prefix prob: pizza eats Harry 0.133333333333

4. Surprisals:
PCFG:
surprisal:  Hermione -0.287682072452
surprisal:  Hermione eats -0.559615787935
surprisal:  Hermione eats pizza 0.965080896044
surprisal:  pizza -0.287682072452
surprisal:  pizza eats -0.559615787935
surprisal:  pizza eats Harry 0.965080896044

PTSG:
surprisal:  Hermione 1.37681561717
surprisal:  Hermione eats -0.624827936582
surprisal:  Hermione eats pizza 0.318453731119
surprisal:  pizza 1.70952137099
surprisal:  pizza eats -0.67990195381
surprisal:  pizza eats Harry 0.985283603361


5. 
The surprisals for the PCFG are the same for both sentences, whereas for the
PTSG they differ, which immediately makes the PTSG model superior. However, it
is strange to me that "pizza eats" is less surprising than "Hermione eats",
whereas the fact that "Hermione" is less surprising than "pizza" and "Hermione
eats pizza" less than "pizza eats Harry" is just as expected. 

More generally, DOP's modus operandi is more cognitively plausible. For
example, memory damage in a DOP implementation can result in graceful
degradation.  Compare losing one subtree in a DOP model with losing one PCFG
rule: the former slightly alters the probability distribution, while the latter
can be disastrous since there are surely many sentences depending for their
parsability on that rule.