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1
Gradient Grammaticality of theIndefinite Implicit Object Construction
in English
Tamara Nicol Medina
IRCS, University of Pennsylvania
Collaborators:Barbara Landau 1, Géraldine Legendre 1, Paul Smolensky 1, Philip Resnik 2
1 Johns Hopkins University, Department of Cognitive Science
2 University of Maryland, Department of Linguistics, Department of Computer Science
2
The (Indefinite) Implicit Object Construction (in English)
John is eatingJohn is reading
• Verb selects for an object, but none is overtly specified.
• Interpretation is of an indefinite and non-specific object.
(something / some food). (something / written material).
* John is reading (War and Peace).
• Grammaticality varies across verbs.
* John is pushing.* John is opening.
Verb Semantic SelectivityAspect (Telicity, Perfectivity)
3
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
4
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 bringing *(something) / making *(something) / hanging *(something).
Indefinite implicit objects are allowed to the extent that they are recoverable.
5
Selectional Preference Strength (SPS) (Resnik, 1996)
Don’t push your brother.Move that chair.Do you want an apple?
“like”
Tony likes that girl.I don’t like this couch.I really like bananas.
People Furniture FoodsPeople Furniture Foods
“eat”
Eat your lunch.He’s eating cereal.She always eats avocados.
People Furniture Foods
c
vcvcvSPS i
cii Pr
PrlogPr
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.
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 verbThe greater the difference between Pr(c) and Pr(c|vi), the higher SPS will be.(Argument classes were those listed in WordNet.)
6
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.
7
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 )
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
po
ur
dri
nk
pa
cksi
ng
ste
al
ea
th
an
gw
ea
ro
pe
np
ush
say
pu
lllik
ew
rite
pla
yh
itca
tch
exp
lare
ad
wa
tc do
he
ar
call
wa
nt
sho
wb
rin
gp
ut
see
find
take ge
tg
ive
ma
keVerb
% Implicit Objects
4.80
0.72
SPS% Implicit Objects
SPS
r = 0.48, p < 0.05
8
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.
9
TELICExistence of an inherent endpoint.
ATELICNo inherent endpoint.
“The ship sank.”
Telicity (Lexical Aspect)
“The ship floated.”
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.”
Requires an overt object.
Does not require an overt object.
10
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.
11
Perfectivity (Grammatical Aspect)
[+ Perfective]“Kim had written */?(something).”
[+ Imperfective]“Kim was writing.”
Requires an overt object.
Does not require an overt object.
PERFECTIVEPerspective of event endpoint.
IMPERFECTIVEPerspective of ongoing event.
have + past participle “The ship has sunk.”
be + “-ing”“The ship is sinking.”
12
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). PERFECTIVE•Michelle was hearing *(something). IMPERFECTIVE
– Not an inviolable rule.
13
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. TELIC• Michelle wanted *(something).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). PERFECTIVE• Michelle was hearing *(something). IMPERFECTIVE
14
Method
Grammaticality Judgment Study
Subjects 15 monolingual adult native speakers of English
Stimuli 30 verbs, 160 sentences
SPS (Resnik, 1996)TelicityPerfectivity
Verb-Argument Structure
Sentence Type
Direct Object Example Sentence
Two-Argument Verbs (n = 30)
Target Implicit ObjectsMichael had brought.Michael was bringing.
Control Overt ObjectsSarah had brought a gift.Sarah was bringing a gift.
One-Argument Verbs (n = 10)
Filler
No ObjectsEmma had slept.Emma was sleeping.
Overt ObjectsAndrew had slept a blanket.Andrew was sleeping a blanket.
15
Results
Grammaticality Judgment Study
1
2
3
4
5
put
get
like
mak
ebr
ing
find
want
wear
take say
open
show give
catc
hha
ng hit
see
pour pull
hear
push
drin
kwa
tch
write ca
llre
adsi
ng eat
play
pack
Verb
Aver
age
Gra
mm
atic
ality
Jud
gmen
t
.
16
Verb Semantic Selectivity (SPS)
Grammaticality Judgment Study
1
2
3
4
5
0.50 1.50 2.50 3.50 4.50
Selectivity
Ave
rage
Gra
mm
atic
ality
Judg
men
t
.
r = 0.66, p < 0.05
17
Telicity
Grammaticality Judgment Study
F = 11.357, p < 0.05
1
2
3
4
5
Telic Atelic
Ave
rage
Gra
mm
atic
ality
Judg
men
t
.
18
Perfectivity
Grammaticality Judgment Study
F = 3.63, p = 0.06
1
2
3
4
5
Perfective Imperfective
Ave
rage
Gra
mm
atic
ality
Judg
men
t
.
19
Summary of Findings
Grammaticality Judgment Study
• Gradient across verbs.Effects of Verb Semantic Selectivity (SPS), Telicity, and Perfectivity.
20
Optimality Theory(Prince and Smolensky, 1993/2004)
An Optimality Theoretic Analysis
• 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.
21
Optimality Theory(Prince and Smolensky, 1993/2004)
An Optimality Theoretic Analysis
• 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.
However…
22
OT Framework
catch (x,y)x = David, y = unspecified SPS=2.47Telic, PerfectiveDavid had caught.
David had caught something.
* INTERNAL ARGUMENT (* INT ARG) The output must not contain an overt internal argument (direct object).
* INT ARG
FAITHFULNESS TO ARGUMENT STRUCTURE (FAITH ARG) An internal argument in the input must be realized by an overt object.
FAITH ARG
* INT ARG
FAITH ARG
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.
TELIC END
PERF CODA
eat (x,y)x = David, y = unspecified SPS=3.51Atelic, ImperfectiveDavid was eating.
David was eating something.
23
Ranking of Constraints
catch (x,y)x = David, y = unspecified SPS=2.47Telic, PerfectiveDavid had caught.
David had caught something.
* INT ARG
FAITH ARG
TELIC END
PERF CODA
* INT ARG
FAITH ARG
p(*I » F) p(*I » T) p(*I » P)
* ARG OF HIGH
SPS VERB
p(*I » F) x p(*I » T) x p(*I » P) = p( *I » {F, T, P} )
1min
minmax
11
SPSSPSSPSSPS ip(*I » F) =
2min
minmax
22
SPSSPSSPSSPS i
3min
minmax
33
SPSSPSSPSSPS i
p(*I » T) =
p(*I » P) =
p(*I » F) x p(*I » T) x 1- [ p(*I » P) ] = p( P » *I » {F, T} )
Problems• How to find perfect cut off value?
• Strictly ranked constraints won’t give rise to gradient grammaticality.
What about SPS?What is needed is a flexible ranking of constraints.• Partial Ranking: One or more constraints “floats” among other
ranked constraints.
• Current Approach: NO ranked constraints, only a floating constraint.
If * INT ARG is highest ranked, then the implicit object is optimal.
If FAITH ARG is highest ranked, then the overt object is optimal.• Similar for TELIC END and PERF CODA.
Linear Function:
As SPS increases, so does the relative ranking of * INT ARG.
Joint Probabilities = Set of Rankings (a partial ranking of constraints)
For each pairwise probability, such as p(*I » F), given a total probability of 1, there is the opposite probability, 1 - p(*I » F).
Incorporating these gives rise to different partial rankings with different optimal outputs.
catch (x,y)x = David, y = unspecified SPS=2.47Telic, Imperfective
24
Total Set of Possible Partial Rankings
Telic Perfective
Telic Imperfective
Atelic Perfective
Atelic Imperfective
*I » {F, T, P} implicit implicit implicit implicit
P » *I » {F, T} overt implicit overt implicit
T » *I » {F, P} overt overt implicit implicit
{T, P} » *I » F overt overt overt implicit
F » *I » {T, P} overt overt overt overt
{F, T} » *I » P overt overt overt overt
{F, P} » *I » T overt overt overt overt
{F, T, P} » *I overt overt overt overt
12.5%
12.5%
12.5%
12.5%
12.5%
12.5%
12.5%
12.5%
The various combinations of pairwise rankings can be captured by 8 partial rankings.
– Give rise to OVERT or IMPLICIT object output depending on the aspectual properties of the input.
12.5% 25% 25% 50%NON-equiprobability p(*I » F) = 0.75 p(*I » T) = 0.85 p(*I » P) = 0.55
35.1% 63.8% 41.2% 75%
35.1%
28.7%
6.2%
5.1%
11.7%
2.1%
9.6%
1.7%
Probability of Implicit Object
Calculate the probability of an IMPLICIT object output as the total proportion of rankings that give rise to it.
– This is equivalent to the grammaticality of an implicit object output. – If equiprobable: 1/8 = 12.5%.
Calculate the probability of an IMPLICIT object output as the total proportion of rankings that give rise to it.
– This is equivalent to the grammaticality of an implicit object output.– If equiprobable: 1/8 = 12.5%.– But they are not equiprobable, since they depend on the joint pairwise
ranking probabilities that compose them, and these are tied to SPS.
25
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.
26
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.
27
Estimation of the Constraint Rankings for English
= p(*I » F) p(*I » T) p(*I » P)
p(implicit)Telic Perfective = p(*I » {F, T, P})
= grammaticality judgment
111 72.096.072.080.4
222 72.096.072.080.4
333 72.096.072.080.4
1.93
=
x
x
.23
28
Estimated Probability Functions for English
p(*I » F) p(*I » T) p(*I » P)
0.00
0.20
0.40
0.60
0.80
1.00
0.72 4.80
SPS
p (*
INT A
RG
>>
TELI
C E
ND
)
.
0.00
0.20
0.40
0.60
0.80
1.00
0.72 4.80
SPS
p (*
INT A
RG
>>
PER
F C
OD
A)
.
0.00
0.20
0.40
0.60
0.80
1.00
0.72 4.80
SPS
p (*
INT A
RG
>>
FAIT
H A
RG
)
.
• 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.
• 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.
29
Overall Predicted Grammaticality of An Implicit Object
0.00
0.20
0.40
0.60
0.80
1.00
0 1 2 3 4 5
SPS
Pro
babi
lity
of Im
plic
it O
bjec
t Out
put
.
Telic Perfective
Telic Imperfective
Atelic Perfective
Atelic Imperfective
• 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.
30
Correlations between Judgments and Model
Telic Perfectiver = 0.84, p < 0.05
Telic Imperfectiver = 0.88, p < 0.05
1.00
2.00
3.00
4.00
5.00
0.72 1.2 1.7 2.2 2.7 3.2 3.7 4.2 4.7
SPS
Gra
mm
atic
ality
of I
mpl
icit
Obj
ect
.
.
Model
Judgments
1.00
2.00
3.00
4.00
5.00
0.72 1.2 1.7 2.2 2.7 3.2 3.7 4.2 4.7
SPS
Gra
mm
atic
ality
of Im
plic
it O
bject
.
.
Model
Judgments
Atelic Imperfectiver = -0.09, p > 0.05
1.00
2.00
3.00
4.00
5.00
0.72 1.2 1.7 2.2 2.7 3.2 3.7 4.2 4.7
SPS
Gra
mm
atic
alit
y o
f Im
plic
it O
bje
ct . .
Model
Judgments
Atelic Perfectiver = 0.26, p > 0.05
1.00
2.00
3.00
4.00
5.00
0.72 1.2 1.7 2.2 2.7 3.2 3.7 4.2 4.7
SPS
Gra
mm
atic
ality o
f Im
plic
it O
bje
ct . .
Model
Judgments
31
What is the nature of the indefinite implicit object construction in the adult grammar?
OT Analysis
• 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.
32
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.
33
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.
0.00
0.20
0.40
0.60
0.80
1.00
0 1 2 3 4 5
SPS
Pro
babi
lity
of Im
plic
it O
bjec
t Out
put
.
Telic Perfective
Telic Imperfective
Atelic Perfective
Atelic Imperfective
34
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?