Transcript Learning Which Verbs Allow Object Omission: Verb Semantic

Gradient Grammaticality of the
Indefinite Implicit Object Construction
in English
Tamara Nicol Medina
IRCS, University of Pennsylvania
Collaborators:
Barbara Landau 1, Géraldine Legendre 1, Paul Smolensky 1, Philip Resnik
Johns Hopkins University, Department of Cognitive Science
2 University of Maryland, Department of Linguistics, Department of
Computer Science
2
1
1
The (Indefinite) Implicit Object
Construction (in English)
John is eating
(something / some food).
John is reading (something / written material).
•
•
Verb selects for an object, but none is overtly
specified.
Verb Semantic
Selectivity
Interpretation
is of an indefinite
and nonspecific
object.
Aspect
(Telicity, Perfectivity)
* John is reading (War and Peace).
•
Grammaticality varies across verbs.
* John is pushing.
* John is opening.
2
Overview
1. Factors that Affect Grammaticality of an Implicit
Object
• Verb Semantic Selectivity
• Aspectual Properties (Telicity, Perfectivity)
2. Grammaticality Judgment Study
3. Linguistic Analysis (Optimality Theory)
4. Estimation of Constraint Ranking Probabilities
5. Implications for Acquisition
3
Verb Semantic Selectivity
•
The omitted object tends to be
recoverable from the verb.
John is eating (some food) / drinking (a beverage) /
singing (a song).
•
Verbs that select for a wide variety of
semantic complements, and therefore
there is no one recoverable
interpretation, tend to resist implicit
objects.
John is implicit
bringing *(something)
making *(something)
/
Indefinite
objects are /allowed
to the extent
*(something).
thathanging
they are
recoverable.
4
Selectional Preference Strength
(SPS) (Resnik, 1996)
An information-theoretic model of verbs’ strength of semantic
preferences. Calculates the strength of a verb’s selection for the
semantic argument classes from which its complements (or objects)
are drawn.
“eat”
“like”
SPSvi    Prc vi log
Don’t
push
yourgirl.
brother.
Eat
lunch.
Tonyyour
likes
that
Move
that
He’s
cereal.
I don’teating
like chair.
this
couch.
you
want
an apple?
She
always
eats
avocados.
IDo
really
like
bananas.
c
Prc vi 
Prc 
People
Furniture
Foods
For all argument classes (c),
PRIOR, Pr(c) – the overall distribution of argument classes
POSTERIOR, Pr(c|vi) – the distribution of argument classes, given a
particular verb
The greater the difference between Pr(c) and Pr(c|vi), the higher SPS will be.5
(Argument classes were those listed in WordNet.)
Selectional Preference Strength
(SPS) (Resnik, 1996)
• SPS correlated with experimental measures of recoverability
and ease of inference (Resnik, 1996).
– SPS corresponds to what people know about verbs’ selectional
preferences.
• SPS correlated with rate of object omission in Brown corpus
of American English (adult written English) (Resnik, 1996).
– SPS directly affects syntax.
6
SPS and Implicit Objects
Relative SPS is correlated with the
relative frequency of an implicit object.
Brown corpus of American English (Francis and Kučera, 1982 )
SPS
% Implicit
Objects
4.80
100%
90%
80%
70%
60%
50%
% Implicit Objects
40%
SPS
30%
20%
r = 0.48, p < 0.05
10%
0%
pour
drink
pack
sing
steal
eat
hang
wear
open
push
say
pull
like
write
play
hit
catch
expla
read
watc
do
hear
call
want
show
bring
put
see
find
take
get
give
make
0.72
Verb
7
Verb Semantic Selectivity
• High SPS is a necessary, but not sufficient
condition on object omissibility.
– Some verbs with high SPS do not occur with
implicit objects, e.g., hang.
– Not an inviolable rule.
• SPS is a continuous measure. How to
incorporate this into a formal grammar?
– As a statistical component to the grammar.
8
Telicity (Lexical Aspect)
TELIC
Existence of an inherent endpoint.
“The
Requires
ship sank.”
an overt object.
ATELIC
No inherent endpoint.
“The
Doesship
not floated.”
require an overt object.
A direct object serves to measure out the event.
[+ Telic]
“Kim is eating an apple.”
incremental THEME
(Once the apple is gone, the event is over.)
[+ Atelic]
“Kim is eating.”
[+Telic]
“Kim arrived.”
9
Telicity (Lexical Aspect)
• Atelicity is a necessary, but not sufficient
condition on object omissibility.
– Some atelic verbs do not occur with implicit
objects, e.g., push, pull.
– Not an inviolable rule.
10
Perfectivity (Grammatical Aspect)
PERFECTIVE
Perspective of event endpoint.
have + past participle
Requires an overt object.
“The ship has sunk.”
IMPERFECTIVE
Perspective of ongoing event.
be + “-ing”
Doesship
not is
require
an overt object.
“The
sinking.”
[+ Perfective]
“Kim had written */?(something).”
[+ Imperfective]
“Kim was writing.”
11
Perfectivity (Grammatical Aspect)
• Imperfectivity is a necessary, but not
sufficient condition on object omissibility.
– Perfectivity doesn’t render a sentence with an implicit object
completely ungrammatical, while Imperfectivity doesn’t
necessarily make it grammatical.
•Michelle had written ?(something).
•Michelle was hearing *(something).
PERFECTIVE
IMPERFECTIVE
– Not an inviolable rule.
12
Putting the Puzzle Together
No single factor completely distinguishes verbs that omit
objects from verbs that do not.
– SPS continuous measure which is related to the relative
frequency of an implicit object.
– Some Telic verbs do allow implicit objects, while some Atelic
verbs do not.
• Michelle packed.
• Michelle wanted *(something).
TELIC
ATELIC
– Perfectivity doesn’t render a sentence with an implicit object
completely ungrammatical, while Imperfectivity doesn’t
necessarily make it grammatical.
• Michelle had written ?(something).
• Michelle was hearing *(something).
PERFECTIVE
IMPERFECTIVE
13
Grammaticality Judgment Study
Method
Subjects
15 monolingual adult native speakers of English
Stimuli
30 verbs, 160 sentences
SPS (Resnik, 1996)
Telicity
Perfectivity
Verb-Argument
Structure
Two-Argument
Verbs (n = 30)
One-Argument
Verbs (n = 10)
Sentence
Type
Direct Object
Example Sentence
Target
Implicit Objects
Michael had brought.
Michael was bringing.
Control
Overt Objects
Sarah had brought a gift.
Sarah was bringing a gift.
No Objects
Emma had slept.
Emma was sleeping.
Overt Objects
Andrew had slept a blanket.
Andrew was sleeping a blanket.
Filler
14
put
get
like
make
bring
find
want
wear
take
say
open
show
give
catch
hang
hit
see
pour
pull
hear
push
drink
watch
write
call
read
sing
eat
play
pack
Average Grammaticality Judgment
.
Grammaticality Judgment Study
Results
5
4
3
2
1
Verb
15
Grammaticality Judgment Study
Verb Semantic Selectivity (SPS)
Average Grammaticality Judgment .
5
4
3
2
1
0.50
1.50
2.50
3.50
4.50
Selectivity
r = 0.66, p < 0.05
16
Grammaticality Judgment Study
Telicity
Average Grammaticality Judgment .
5
4
3
2
1
Telic
Atelic
F = 11.357, p < 0.05
17
Grammaticality Judgment Study
Perfectivity
Average Grammaticality Judgment .
5
4
3
2
1
Perfective
Imperfective
F = 3.63, p = 0.06
18
Grammaticality Judgment Study
Summary of Findings
• Gradient across verbs.
Effects of Verb Semantic Selectivity (SPS),
Telicity, and Perfectivity.
19
An Optimality Theoretic Analysis
Optimality Theory
(Prince and Smolensky, 1993/2004)
• Formulate conditions as violable constraints, not
inviolable rules.
• Take advantage of the component in OT called
"CON", in which constraints are ranked with
respect to one another.
– It is the evaluation of the output candidates against the
set of ranked constraints that determines the optimal
output.
– This will allow some constraints to have a greater effect
than others.
20
An Optimality Theoretic Analysis
Optimality Theory
(Prince and Smolensky, 1993/2004)
However…
• A strict ranking hierarchy (as in standard OT) will
be shown to be too strong.
• Take insights from partial ranking approaches.
• Furthermore, will incorporate a statistical
component to the ranking of constraints, which will
allow for the derivation of GRADIENT
grammaticality.
21
OT Framework
eat (x,y)
catch
(x,y)
x = David, y = unspecified
SPS=2.47
SPS=3.51
Telic, Perfective
Atelic,
Imperfective


F*AITH
INT
ARG
F*AITH
INT
ARG
TELIC
END
PERF
CODA
David was
had caught.
eating.




David was
had caught
eating something.
something.


* INTERNAL ARGUMENT (* INT ARG)
The output must not contain an overt internal argument (direct object).
FAITHFULNESS TO ARGUMENT STRUCTURE (FAITH ARG)
An internal argument in the input must be realized by an overt object.
TELIC ENDPOINT (TELIC END)
The internal argument must be overtly realized in the output, given Telic aspect.
PERFECTIVE CODA (PERF CODA)
The internal argument must be overtly realized in the output, given Perfective aspect.
22
Ranking of Constraints
catch (x,y)
x = David, y = unspecified
SPS=2.47
Telic, Perfective
Imperfective


* ARG
F*AITH
IHNT
OF
IGH
ARG
SPS
VERB
F*AITH
INT
ARG
TELIC
END
PERF
CODA
David had caught.




David had caught something.


p(*I
» F)
x p(*I
T)
p(*I
p(*I
»» P)
P)ranking
= p( *I »object
{F, T, P}is) optimal.
If
What
* INT
about
is
Aneeded
RG
SPS?
is »highest
is ax flexible
ranked,
then the
of constraints.
implicit
Problems
=overt
SetPof
•IfJoint
Partial
or
among
other
How
find
perfect
off
value?
p(*I
»Probabilities
F)to Ranking:
x RG
p(*I
T)One
xcut1[more
p(*I
» constraints
P) then
]
=
p(
»Rankings
*I » {F,is
T}optimal.
)
F
AITH
A
is» highest
ranked,
the“floats”
object
ranking of constraints)
 rise

 1to gradient
 partialgrammaticality.
 1(a
ranked
constraints.
Strictly
ranked
constraints
won’t
give
each pairwise
probability,
such
as
p(*I
»
F),

•For
Similar
for
TELIC
ENDp(*I
and
P
ERF
C
ODA
.



SPS

SPS
» F) =
i
min 

 1


SPS

SPS
Linear
Function:
given a total
probability
of 1,
• Current
Approach:
NO
ranked constraints,
a floating constraint.
max only min


the opposite probability, 1 - p(*I » F).
As there
SPSisincreases,


 2   2 

 SPSi  SPSmin    2
p(*I » T) =
soIncorporating
does the these gives rise to different partial
 different optimal
SPSmaxrankings
 SPSminwith
 outputs.
relative ranking of *


 3   3 




SPS

SPS
INT ARG.
p(*I » P) = 
i
min 
   3 23
 SPSmax  SPSmin 

Total Set of Possible Partial Rankings
NON-equiprobability
p(*I » F) = 0.75
p(*I » T) = 0.85
p(*I » P) = 0.55
Probability of Implicit Object
12.5%
35.1%
Telic
Perfective
63.8%
25%
Telic
Imperfective
41.2%
25%
Atelic
Perfective
50%
75%
Atelic
Imperfective
12.5% *I » {F, T, P}
35.1%
implicit
implicit
implicit
implicit
12.5% P » *I » {F, T}
28.7%
overt
implicit
overt
implicit
12.5%
6.2% T » *I » {F, P}
overt
overt
implicit
implicit
12.5%
5.1% {T, P} » *I » F
overt
overt
overt
implicit
12.5% F » *I » {T, P}
11.7%
overt
overt
overt
overt
12.5%
2.1% {F, T} » *I » P
overt
overt
overt
overt
12.5%
9.6% {F, P} » *I » T
overt
overt
overt
overt
12.5%
1.7% {F, T, P} » *I
overt
overt
overt
overt
Calculate the probability of an IMPLICIT object output as the total
proportion
of rankings
that give
rise to it.rankings can be captured by 8
The various
combinations
of pairwise
– This
is equivalent to the grammaticality of an implicit object output.
partial
rankings.
– If
1/8 = 12.5%.
– equiprobable:
Give rise to OVERT
or IMPLICIT object output depending on the
– Butaspectual
they are not
equiprobable,
since they depend on the joint pairwise
properties
of the input.
ranking probabilities that compose them, and these are tied to SPS.
24
Summary of OT Analysis
The grammaticality of an implicit object for a particular verb…
is equivalent to the probability of the implicit object output for that input,
which…
depends upon the probabilities of each of the possible partial rankings,
which…
depends on the probabilities of *I » F, *I » T, and *I » P,
which…
are a function of SPS.
25
Finding the Probabilities
So what are the pairwise probabilities of *I » F, *I » T, and *I » P in
English?
Can we even find probabilities that would work for all verbs?
Use grammaticality judgment data to estimate the probabilities.
26
Estimation of the Constraint Rankings for English
p(implicit)Telic Perfective = p(*I » {F, T, P})
= p(*I » F)  p(*I » T)  p(*I » P)
=   1   1   0.96  0.72   1 

 4.80  0.72

  2   2 





0
.
96

0
.
72




 2
x  4.80  0.72



  3   3 


 0.96  0.72   3 
x 

 4.80  0.72

1.93
.23 = grammaticality judgment
27
Estimated Probability Functions for English
.
.
.
• Taking the grammaticality judgments as a direct reflection of the
probabilities of an implicit object being generated by the grammar.
• Estimated what the pairwise rankings must be in order to produce
these results.
1.00
0.80
0.60
0.40
0.20
0.00
1.00
p (* INT ARG >> PERF CODA)
p (* INT ARG >> TELIC END)
p (* INT ARG >> FAITH ARG)
1.00
0.80
0.60
0.40
0.20
4.80
SPS
p(*I » F)
0.60
0.40
0.20
0.00
0.00
0.72
0.80
0.72
4.80
SPS
p(*I » T)
0.72
4.80
SPS
p(*I » P)
• The probability of * INT ARG ranked above each of the other three
constraints increased with SPS.
• Steepest function for the relative ranking of * INT ARG with TELIC
END.
28
.
Overall Predicted Grammaticality of An Implicit Object
Probability of Implicit Object Output
1.00
0.80
Telic Perfective
0.60
Telic Imperfective
Atelic Perfective
0.40
Atelic Imperfective
0.20
0.00
0
1
2
3
4
5
SPS
• Best for Atelic Imperfective, worst for Telic Perfective.
• Increase as a function of SPS, but differentially depending on aspect
type.
- Telic Imperfectives show greatest effect of SPS.
29
. ..
.
Correlations between Judgments and Model
Grammaticality
of Implicit
Implicit Object
Grammaticality of
Object
Grammaticality
Grammaticality of Implicit Object
..
.
5.00
5.00
5.00
4.00
4.00
4.00
Model
Model
Model
Judgments
Model
Judgments
Judgments
Judgments
3.00
3.00
2.00
2.00
2.00
1.00
1.00
1.00
0.72 1.2
1.7
2.2
2.7
3.2
0.72
3.2
0.72
1.2
1.7
2.2
2.7
3.2
1.2
1.7
2.7
SPS
SPS
SPS
3.7
3.7
3.7
4.2
4.2
4.2
4.7
4.7
4.7
TelicImperfective
Perfective
Telic
Atelic
Atelic
Imperfective
Perfective
0.84,
0.88,
<>0.05
r = 0.26,
-0.09,pp>
0.05
30
OT Analysis
What is the nature of the indefinite implicit object
construction in the adult grammar?
• The grammaticality of an implicit object across verbs is
– Gradient.
– Reduced in accordance with SPS, Telicity, and Perfectivity.
• For any verb, if you know SPS, Telicity, and Perfectivity, then the
grammar generates a relative grammaticality for the implicit object
output with that verb.
31
Linguistic Analysis
Turning to acquisition, we can now ask what the learner’s task must involve:
• Find p(*I » F), p(*I » T), and p(*I » P).
How?
• The model’s values were estimated from grammaticality judgments.
• But children don’t “hear” grammaticality judgments!
- Occurrence of implicit indefinite objects: increase ranking of * INT ARG.
- Occurrence of overt indefinite objects: reduce ranking of * INT ARG.
32
Implications for Acquisition
.
For example,
• Assign a grammaticality of 0 for any verb that never occurs with an implicit
object.
• Assign a grammaticality of 1 for any verb that occurs with an implicit object
at least 20% of the time.
• Assign a grammaticality of 0.50 for any verb that occurs with an implicit
object infrequently: 0 – 20% of the time.
Probability of Implicit Object Output
1.00
0.80
Telic Perfective
0.60
Telic Imperfective
Atelic Perfective
0.40
Atelic Imperfective
0.20
0.00
0
1
2
3
SPS
4
5
33
Conclusions
• The grammaticality of the indefinite implicit object construction is
– Gradient, as shown in the Grammaticality Judgment Study.
– Determined by a combination of factors, including Verb Semantic
Selectivity (SPS), Telicity, and Perfectivity.
• It is possible to derive gradient grammaticality, by allowing
constraints to "float" and assessing grammaticality over the total
set of possible rankings.
• Estimation of the constraint ranking probabilities for English
showed that it is, in fact, possible to find rankings that capture the
phenomenon with low error.
• Raises interesting questions for acquisition:
– What is the state of the child's early grammar?
– How does the learner adjust her grammar in accordance with what
she hears in the child-directed input (not grammaticality judgments)
in order to arrive at a grammar that displays gradient judgments?
34