Assignment 4 grading and comments

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Problem 1

2 marks per item, total 6

Most people did well on that. Only 1 common mistake - not completing the transformation. For example, in expression 2, we can apply lambda conversion once and get
  ((lambda x (x A)) (lambda y (Q y))) = ((lambda y (Q y)) A)
  
This is correct, but this is not again. After applying 1 more lambda expression, we get
  ((lambda y (Q y)) A) = (Q A)
  
which should be the final result.

Problem 2

5 marks per tree, total 40 (a and e had 2 trees each)

Some people forgot to specify subcat features, as required by the assignment. I take off some marks for that, especially in cases where incorrect trees were produced as a result of neglecting it.

(a)

The sentence was easy, but the problem requested that you draw both predicate logic and thematic representation. Several people missed that.

The most common problem with thematic representation is that people didn't realize that the predicates defining thematic arguments originate on the lexical level. So, if we are using predicate logic, the lexical entry for "find" is

  (find (v _NP var ?v sem FIND1)) 
  
However, for thematic representation we need to define what are the verb arguments, and the lexical entry is
  (*) (find (v _NP var ?v sem (lambda x (lambda y 
                            (& (FIND ?v) (AGENT ?v y) (THEME ?v x))))))
  
This semantics is carried up to the level of verb phrase where THEME variable will be bound, and then to sentence level, where AGENT variable will be bound. You cannot simply introduce thematic argument names on verb phrase level because different verbs have different arguments in different positions, e.g. a preposition phrase in the same position can be TO-LOC or TO-POSS (cf ex. 4), and the only way to account for the variation is to include the relevant information in verb semantics.

Another common point of confusion is the notation used in the book. The entry

  
  (find (v _NP var ?v sem (lambda x (lambda y 
                            (FIND ?v [AGENT y] [THEME x])))))
  
is a shorthand for the previous entry that allows to omit conjunction and event variables from the form, indicating the changes by using square brackets, and therefore they cannot be replaced with parenthesis etc, or the meaning of the form as (*) will be lost.

(b)

The most common mistake here was forgetting that logical connectives are unscoped and not indicated it in the logical form.

(c)

No one here realized that even though must does not have tense morphology, it is still a main verb and should have tense. We discussed in class several reasons for that, and the common assumption is that all auxiliaries are tensed, regardless of whether they show this in morphology.

(d)

A common mistake here is interpreting "a charlatan" as "Ex x (charlatan x)". Note that indefinite noun phrases can be interpreted in 2 different ways. The meaning we most often encountered in class is existential, basically declaring that there is an object with a given property, that can be used as an argument for other predicates in the sentence. This would be the interpretation of "a bird" in "Birds generally fly". However, if we say "Tweety is a bird", we do not simply state that there is some bird, we declare that Tweety is that bird. Therefore, we need to interpret BIRD as a predicate that can be applied to TWEETY to produce (BIRD TWEETY). Note that we cannot say something like
  (& (Ex x (BIRD x)) (BIRD TWEETY))
  
because it can imply existence of other birds except tweety, and this is not entailed by the original sentence. Another interpretation is possible,
  (Ex x (& (BIRD x) (= x TWEETY))
  
but it is more difficult to obtain it compositionally.

(e)

There was a lot of confusion here about how the actual LF should look like. Consider rules
  ((vp (var ?v) (sem (lambda x (& (?semvp x) (?sempp ?v)))))
           -10> ;; John saw Mary in London
    (head (vp (gap -) (sem ?semvp))) (pp (gap -) (pred +) (sem ?sempp)))
  
  ((vp (var ?v) (sem (LAMBDA ag2 (?semv ?v ag2 ?sempp))))
           -11> ;; John decided on a car
            (head (v (subcat _pp-on) (sem ?semv))) 
            (pp (pred -) (pform on) (sem ?sempp)))
  
After applying the sentence rules we get
  (s (gap -) (var v117) (sem (& (sees1 v117 John Mary) (IN v117 London))
  
for "john saw Mary in London", and so we're talking about the event in which John saw Mary, and that event happened in London.
  (s (var v217) (sem (DECIDEDON1 v217 John (the v223 car)))
  
for "John decided on a car". Now we're talking about an event in which John decides on the car. The corresponding LF's are
  Ex e Sees1(e, John, Mary) /\ In(e, London)
  Ex e ( (The x (CAR x): DecidedOn(e, John, Car))
  
The main difference in the representation that in one case you do get a conjunction of predicates over the event, and in another just 1 predicate. The reason is more or less that in the first case you may or may not specify the place, but you're required to specify the theme (whom John saw). In the second case, you're certainly required to specify theme (on what John decided). This distinction works in most cases, except the weird case with meaningful prepositions in "put the box on the table" where you get conjunction even though all arguments are required, because you have to ahve a complex predicate to specify "on the table". The representation are similar, and that is why many people like Neo-Davidsonian representation - the thematic rolse give you conjunction in both cases and you don't have to bother yourself by the distinctions between complementsand adjuncts.

(d)

Generally, few problems with this sentence. One common mistake: non-finite forms of the verb do not carry tense information. So, in "has read", "has" should be interpreted as < pres HAVE >, but read is interpreted as READ, producing
  (lambda x (< pres HAVE> (READ x)))
  
Further processing may determine that the event is in the past, but the initial semantic interpretation will have a present reference, which is not so surprising given the tense name - Present Perfect.

Another common problem, here and in (c), is forgetting that auxiliaries subcategorize for a verb phrase and therefore "read", or "leave", must be a VP and interpreted as such, producing a lambda expression.

Problem 3

5 marks per sentence, total 10

People did a good job here. No one got (c) completely, because no one had the correct interpretation to start with. I didn't take points off for that.

Problem 4

3 marks per sentence, total 9

People did a good job here, except that there was a confusion about notation, which I explained in (2a). Also, some people believed "The owner" in the third sentence to be EXPERIENCER. This is not possible, because EXPERIENCER is used to denote someone who is an inactive participant of an action, usually with verbs denoting some kind of physical experience, usually caused by some kind of natural phenomena rather than direct actions of others, like "seeing", which has more to do with light and properties of our eyes than anything anyone else can do. On the other hand, the receiver does not experience anything - he just gets something in his possession usually as a result of someone else's action.

Problem 5

Optional for undergrads, a - 8, b - 3, total 11

I put individual comments on the papers. This was not an easy question, and not extensively covered in class. Please come talk to me if you need more explanation about model theory.

Problem 6

Optional for undergrads, 2 points per item, total 14, up to 4 points extra credit for using linguistic tests

Most people got the idea well, though there was a question on whether it is necessary to be entered in the show to get a place in it. I think it is necessary, and the situations where the dog ends up entered automatically etc. still mean that it was entered into the competition. The question is debatable, though, so I took only half point off for that.

Statistics

Here are the scores so that you can compare your performance to others.

(grads max 90, undergrads max 65)

     50.00
     59.00
     67.00
     70.50
     87.00