((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.
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.
(& (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.
((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.
(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.
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