Gradient Grammaticality of the Indefinite Implicit Object Construction in English

1
Gradient Grammaticality of theIndefinite
Implicit Object Constructionin 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
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The (Indefinite) Implicit Object Construction (in
English)

• John is eating
• John is reading

(something / some food).
(something / written
material).
Verb Semantic Selectivity Aspect (Telicity,
Perfectivity)

• Verb selects for an object, but none is overtly
  specified.
• Interpretation is of an indefinite and
  non-specific object.

John is reading (War and Peace).

• Grammaticality varies across verbs.

John is pushing. John is opening.
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
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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.

Indefinite implicit objects are allowed to the
extent that they are recoverable.
John is bringing (something) / making
(something) / hanging (something).
5
Selectional Preference Strength (SPS) (Resnik,
1996)
An information-theoretic model of verbs strength
of semantic preferences. Calculates the strength
of a verbs selection for the semantic argument
classes from which its complements (or objects)
are drawn.
eatEat your lunch.Hes eating cereal.She
always eats avocados.
likeTony likes that girl.I dont like this
couch.I really like bananas.
Dont push your brother.Move that chair.Do you
want an apple?
For all argument classes (c), PRIOR, Pr(c)
the overall distribution of argument classes
POSTERIOR, Pr(cvi) the distribution of
argument classes, given a
particular verb
The greater the difference between Pr(c) and
Pr(cvi), the higher SPS will be.
(Argument classes were those listed in WordNet.)
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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.

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SPS and Implicit Objects
Relative SPS is correlated with the relative
frequency of an implicit object. Brown corpus of
American English (Francis and Kucera, 1982 )
Implicit Objects
SPS
4.80
SPS
r 0.48, p lt 0.05
0.72
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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.

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Telicity (Lexical Aspect)
TELICExistence of an inherent endpoint.ATELICN
o inherent endpoint.
The ship sank.
Requires an overt object.
The ship floated.
Does not require an overt object.
A direct object serves to measure out the
event. TelicKim is eating an apple.
incremental THEME(Once the apple
is gone, the event is over.) AtelicKim is
eating.TelicKim arrived.
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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.

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Perfectivity (Grammatical Aspect)
PERFECTIVEPerspective of event
endpoint.IMPERFECTIVEPerspective of ongoing
event.
have past participle The ship has sunk.
Requires an overt object.
be -ingThe ship is sinking.
Does not require an overt object.
PerfectiveKim had written
/?(something). ImperfectiveKim was
writing.
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Perfectivity (Grammatical Aspect)

• Imperfectivity is a necessary, but not sufficient
  condition on object omissibility.
• Perfectivity doesnt render a sentence with an
  implicit object completely ungrammatical, while
  Imperfectivity doesnt necessarily make it
  grammatical.
• Michelle had written ?(something). PERFECTIVE
• Michelle was hearing (something). IMPERFECTIVE
• Not an inviolable rule.

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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 doesnt render a sentence with an
  implicit object completely ungrammatical, while
  Imperfectivity doesnt necessarily make it
  grammatical.
• Michelle had written ?(something). PERFECTIVE
• Michelle was hearing (something). IMPERFECTIVE

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Method
Grammaticality Judgment Study
Subjects 15 monolingual adult native
speakers of English
Stimuli 30 verbs, 160 sentences SPS
(Resnik, 1996) Telicity Perfectivity
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Results
Grammaticality Judgment Study
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Verb Semantic Selectivity (SPS)
Grammaticality Judgment Study
r 0.66, p lt 0.05
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Telicity
Grammaticality Judgment Study
F 11.357, p lt 0.05
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Perfectivity
Grammaticality Judgment Study
F 3.63, p 0.06
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Summary of Findings
Grammaticality Judgment Study

• Gradient across verbs.Effects of Verb Semantic
  Selectivity (SPS), Telicity, and Perfectivity.

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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.

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Optimality Theory(Prince and Smolensky,
1993/2004)
An Optimality Theoretic Analysis
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.

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OT Framework
catch (x,y) x David, y unspecified
SPS2.47 Telic, Perfective
eat (x,y) x David, y unspecified
SPS3.51 Atelic, Imperfective
INT ARG
FAITH ARG
INT ARG
FAITH ARG
TELIC END
PERF CODA
?
?
?
?
?
David had caught. David had caught something.
David was eating. David was eating 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.
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Ranking of Constraints
catch (x,y) x David, y unspecified
SPS2.47 Telic, Perfective
catch (x,y) x David, y unspecified
SPS2.47 Telic, Imperfective
ARG OF HIGH SPS VERB
INT ARG
FAITH ARG
TELIC END
PERF CODA
INT ARG
FAITH ARG
?
?
?
?
?
David had caught. David had caught something.
?
?
?

• Problems
• How to find perfect cut off value?
• Strictly ranked constraints wont 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.
p(I F) p(I T) p(I P)
p(I F) x p(I T) x p(I P)
p( I F, T, P )
Joint Probabilities
Set of Rankings (a
partial ranking of constraints)

• If FAITH ARG is highest ranked, then the overt
  object is optimal.
• Similar for TELIC END and PERF CODA.

p(I F) x p(I T) x 1- p(I P)
p( P I F, T )
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.
p(I F)
Linear Function As SPS increases, so does the
relative ranking of INT ARG.
p(I T)
p(I P)
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Total Set of Possible Partial Rankings
Probability of Implicit Object
NON-equiprobability p(I F) 0.75 p(I
T) 0.85 p(I P) 0.55
12.5
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25
50
35.1
63.8
41.2
75
12.5
35.1
12.5
28.7
12.5
6.2
12.5
5.1
12.5
11.7
12.5
2.1
12.5
9.6
12.5
1.7

• 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.

• 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.

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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.
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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.
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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)

x
x
grammaticality
judgment
1.93
.23
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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.

p(I F)
p(I T)
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.

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Overall Predicted Grammaticality of An Implicit
Object

• 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.

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Correlations between Judgments and Model
Telic Perfectiver 0.84, p lt 0.05
Telic Imperfectiver 0.88, p lt 0.05
Atelic Imperfectiver -0.09, p gt 0.05
Atelic Perfectiver 0.26, p gt 0.05
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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.

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Linguistic Analysis

• Turning to acquisition, we can now ask what the
  learners task must involve
• Find p(I F), p(I T), and p(I P).

• How?
• The models values were estimated from
  grammaticality judgments.
• But children dont hear grammaticality
  judgments!
• Occurrence of implicit indefinite objects
  increase ranking of INT ARG.
• Occurrence of overt indefinite objects reduce
  ranking of INT ARG.

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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.

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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?