Assignment 7 solutions, Ling 645/CMSC 723, Fall 1997

# Assignment 7 solutions, Ling 645/CMSC 723, Fall 1997

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7.1  These solutions are based on what Allen's parser does.  As discussed
below, however, there are some problems with the examples, even
going by what is in the book.

(a)  George ate a pizza at every road stop

(i) Interpretation with PP attached to 'pizza'

(<PAST EAT> e1
(NAME g1 George)
<A p1:(PIZZA p1) (AT p1 <EVERY r1 (ROADSTOP r1)))>)

(ii) Interpretation with PP modifying 'ate'

(&
(<PAST EAT> e1 (NAME g1 George) <A p1 (PIZZA p1)>)
(AT e1 <EVERY r1 (ROADSTOP r1)>))

A few minor notatinal differences aside, this is the semantic
interpretation the parser would produce when given this sentence.
For this interpretation, however, notice that when the event
variable e1 appears in the prepositional phrase, it doesn't
seem to be within the scope of the predicate EAT, at least
according to Allen's description of the event-variable notation
on page 243.  In particular, the parser seems to be mixing the
event-variable notation using thematic roles, on the one hand,
with a predicate-argument notation in which arguments are
identified by their position (argument 1 is the eater, argument
2 is the thing eaten).  Expanding, you'd get something like the
following:

(& (EXISTS e1 (& (<PAST EAT> e1)
(ARG1 e1 (NAME g1 George))
(ARG2 e1  <A p1 (PIZZA p1)>)))
(AT e1 <EVERY r1 (ROADSTOP r1)>))

Even if you took the step, as I have, of expressing the
positional arguments as relations analogous to thematic roles,
this interpretation still seems to be ill formed from a
logical standpoint, since it has e1 appearing outside the
scope of the existential quantifier.

A better solution, even if it's not what the parser produces,
is something closer to the QLF for "John broke it with a
hammer" on p. 242, e.g.:

(EXISTS e1 (& (<PAST EAT> e1
(NAME g1 George)
<A p1 (PIZZA p1)>)
(IN e1 <EVERY r1 (ROADSTOP r1)>)))

where the existentially quantified event scopes over the
prepositional phrase also.  Or, if you want to go all the
way, you can reify all the arguments against the event
variable using thematic roles:

(EXISTS e1 (& (<PAST EAT> e1)
(AGENT e1 (NAME g1 George))
(THEME e1 <A p1 (PIZZA p1)>)
(IN e1 <EVERY r1 (ROADSTOP r1)>)))

Once you have thematic roles and everything is expressed with
respect to the event variable e1, the abbreviation convention
Allen uses on p. 243 makes sense, i.e. the above is
legitimately abbreviated as

(<PAST EAT> e1
(AGENT (NAME g1 George))
(THEME <A p1 (PIZZA p1)>)

(b)  Several employees from every company bought a pizza

<SEVERAL x1:(EMPLOYEE x1) (FROM x1 <EVERY c1 (COMPANY c1)>)>
<A p1 (PIZZA p1)>)

Here "several" is being treated as a quantifier; this QLF gives you
the following two readings given the exists/forall scope ambiguity:

there is a pizza p1 such that
for every company c1,
several employees from c1 bought p1

for every company c1,
there is a pizza p1 such that
several employees from c1 bought p1

There is also another ambiguity, namely whether "several employees
from every company" refers to (i) a set of groups of employees, one
group from each company, or to (ii) a set of individuals, each of
whom is an employee of every company.  (The latter reading could be
written as "several employees-from-every-company".)   So each of
the above two interpretations is itself ambiguous, since SEVERAL
can scope either over or under EVERY.  The QLF captures this as a
SEVERAL/EVERY scope ambiguity in just the same way as the EVERY/A
scope ambiguity.

(c)  We saw John in the park by the beach

(EXISTS e1
(& (SAW e1 (PRO w1 WE1) (NAME j1 John))
(IN e1 <THE p1 (PARK p1) (BY p1 <THE b1 (BEACH b1)>)>)))

(EXISTS e1
(& (SAW e1 (PRO w1 WE1) (NAME j1 John))
(IN e1 <THE p1 (PARK p1)>)
(BY e1 <THE b1 (BEACH b1)>)))

There are two readings here, one in which the event "seeing John" takes
place in a particular park, namely the park by the beach; and one
in which the seeing event "seeing John" takes place both in the
park and by the beach.  The parser output for these would be:

(& ((UNSCOPED PAST SEES1) V303 (PRO w1 We) (NAME V309 John))
(IN V303
(UNSCOPED THE V315
(& (PARK V315) (BY V315 (UNSCOPED THE V321 (BEACH V321)))))))

(&
(& ((UNSCOPED PAST SEES1) V303 (PRO w1 we) (NAME V309 John))
(IN V303 (UNSCOPED THE V315 (PARK V315))))
(BY V303 (UNSCOPED THE V321 (BEACH V321))))

I get another reading, in which we are standing on the beach, and from
there we observe that John is in the park (even though the park
is not by the beach, e.g. we do our observing through a telescope).
This reading is not as easily accommodated by the logical form, since
in effect the semantics would have to include not only the seeing
event, but also the state of John being in the park -- this would in
effect be a small clause reading of "John in the park".  My
approximation to that would be something like the following:

(EXISTS e1
(EXISTS s1
(&
(BE s1 (NAME j1 John) (IN e1 <THE p1 (PARK p1)>))
(SAW e1 (PRO w1 WE1) s1))))

Interestingly, Allen's parser/grammar for this chapter do not appear
to be able to generate this reading.

7.2

(a) We returned the ring to the store

AGENT:       we
THEME:       the ring
BENEFICIARY: the store    [could also be TO-LOC/RECIPIENT]

(b) We returned to the party

AGENT:       we
TO-LOC:      the party    [also known as DESTINATION]

(c) The owner received a ticket

THEME:       a ticket
TO-POSS:     the owner    [also known as RECIPIENT]

7.3  (a)  (P A)
(b)  (Q A)
(c)  (P A)

7.4  (a)  ((UNSCOPED PAST SEES1) V357
(NAME V355 JILL)
(UNSCOPED THE V365
(& (MAN1 V365) (IN V365 (UNSCOPED THE V371 (HOUSE1 V371))))))

(&
((UNSCOPED PAST SEES1) V357 (NAME V355 JILL)
(UNSCOPED THE V365 (MAN1 V365)))
(IN V357 (UNSCOPED THE V371 (HOUSE1 V371))))

(b)  This is explained by Allen in Section 9.3, pages 272-275.
Briefly, the interpretation without the lambda

(UNSCOPED THE V400 (HOUSE1 V400)))

is used when the prepositional phrase is used to indicate
the noun argument of a verb that subcategorizes for the PP with
the preposition acting as a particle.  For example, a case of
this would be the "decide on" use of "decide", where
"decide on the house" really is a verb/noun relationship in
just the same way that "choose the house" is.  There's no
lambda here because the PP is not modifying anything.

The interpretation with the lambda

(LAMBDA N1 (ON N1 (UNSCOPED THE V400 (HOUSE1 V400))))

is used when the PP is modifying something (an NP or a VP).

(c)  Sentences containing "decide on" will give you both readings,
but notice I wanted *distinct* sentences!  Examples:

Jill decided on the house

((UNSCOPED PAST DECIDES-ON1) V438
(NAME V436 JILL)
(UNSCOPED THE V448 (HOUSE1 V448)))

Jill saw the men on the house

((UNSCOPED PAST SEES1) V474
(NAME V472 JILL)
(UNSCOPED THE V482
(& ((PLUR MAN1) V482)
(ON V482 (UNSCOPED THE V488 (HOUSE1 V488))))))

7.5  (a)

S542:<S ((SEM
(PUTS1 V515
(NAME V513 JILL)
(UNSCOPED THE V521 (DOG1 V521))
(TO-LOC (UNSCOPED THE V527 (HOUSE1 V527)))))
(INV -) (AGR |3S|) (VFORM PAST) (1 NP529) (2 VP541))>
from 0 to 7 from rule -1>

(b) Adding the following VP rule is all that's needed for the
problem as I stated it:

((vp (var ?v)
(sem (LAMBDA ag3 (?semv ?v ag3 ?semnp (TO-LOC ?sempp)))))
-99>
(head (v (subcat _np_pp-loc) (sem ?semv)))
(np (sem ?semnp))
(pp (pred -) (sem ?sempp)))

It states that if you have a verb like 'put' that subcategorizes
for a locative PP complement, that complement should be interpreted
as a destination (TO-LOC).

You'll notice, however, that it is not a complete solution to the
more general problem, some verbs that subcategorize for NP's with
locative PP's give them other roles like RECIPIENT, etc., rather
than TO-LOC -- e.g. "give".  This raises the more general issue
of how to determine the correct thematic role to assign to a given
argument; approaches to this problem often involve more articulated
semantic representations of verbs than the ones we've seen here.

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