Transcript Slide 1

Probabilistically Ranked Constraints: Derivation of the Gradient Grammaticality of Implicit Objects
Tamara Nicol Medina
Institute for Research in Cognitive Science (IRCS), University of Pennsylvania
Control Sentences: Overt objects.
Sarah was bringing a gift. / Sarah had brought a gift.
 20 sentences containing 10 two-argument verbs (5 telic, 5 atelic)
Emma was sleeping. / Emma had slept.
Andrew was sleeping a blanket. / Andrew had slept a blanket.
5. Atelic: John sang (something).
6. Telic: John brought *(something).
Perfectivity
Since perfective aspect targets the endpoint of an event, the
grammaticality of an indefinite implicit object will be lower given
perfective than imperfective aspect.
 Denotes the point along the temporal constituency of an event from
the speaker’s perspective (Comrie, 1976; Olsen, 1997): perfective
indicates an event at its endpoint, while imperfective construes an
event in progression.
 Informal grammaticality judgments suggest that indefinite implicit
objects are preferred with imperfective aspect (7) than with perfective
aspect (8).
7. Imperfective: John was writing (something).
8. Perfective: John had written ?(something).
.

Probabilistic Ranking of Constraints:
Follows partial ranking (Reynolds, 1994; Nagy & Reynolds, 1997; Anttila, 1997; Legendre
et al., 2002; Davidson & Goldrick, 2003) and stochastic ranking (Boersma, 1997, 1998,
2004; Hayes & MacEachern, 1998; Boersma & Hayes, 2001) approaches.
 * INT ARG is the only constraint which is violated by the overt object
output candidate; thus, what matters is the relative ranking of this
constraint to each of the other three: p(* INT ARG » FAITH ARG), p(*
INT ARG » TELIC END), and p(* INT ARG » PERF CODA).
 If FAITH ARG, TELIC END, and PERF CODA are unranked with respect
to each other, then there are eight possible orderings of the constraints.
Telic
Perfective
*I » {F,T,P}
Results: Grammaticality judgments are gradient across verbs for the
Test Sentences (shown here collapsing Perfective/Imperfective).
implicit
P » *I » {F,T}
T » *I » {F,P}
{T,P} » *I » F
Telic
Imperfective
implicit
Atelic
Perfective
implicit
implicit
Atelic
Imperfective
0.80
AI
0.60
AP
TI
0.40
TP
0.20
0.00
0
1
2
3
4
5
Correlations between Model and Judgments:
5.00
5.00
4.00
Model
Judgments
3.00
2.00
1.00
0.72
1.2
1.7
2.2
2.7
3.2
3.7
4.2
4.00
Model
Judgments
3.00
2.00
1.00
2.02
4.7
SPS
SPS
Telic Perfective
r = 0.84, p < 0.05
implicit
implicit
1.00
SPS
implicit
implicit
implicit
F » *I » {T,P}
{F,T} » *I » P
4
{F,P} » *I » T
{F,P,T} » *I
3
Telic Imperfective
r = 0.88, p < 0.05
5.00
5.00
4.00
Model
Judgments
3.00
2.00
1.00
0.72
1.2
1.7
2.2
2.7
3.2
3.7
4.2
4.7
4.00
Model
Judgments
3.00
2.00
1.00
SPS
SPS
2
1
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
 Refers to the existence of a natural end or result of an event: a telic
event entails an endpoint, while an atelic verb does not.
 Indefinite object omission is preferred with atelic (5) rather than telic
verbs (6) (Tenny (1994), van Hout (1996), Olsen and Resnik (1997), and others).
Jack had caught
something.
Procedure: Rate the goodness of sentences on a scale of 1 (very bad) to
5 (very good).
Average Rating
Telicity
Since a direct object often specifies what constitutes the endpoint of a
telic event, the grammaticality of an indefinite implicit object will be
lower for telic verbs than for atelic verbs.

Aspectual Features in the Input
5
3. Highly Selective Verb: John read (something).
4. Low Selective Verb: John wanted *(something).

.
 Selectional Preference Strength (SPS) (Resnik, 1996): Model calculates
relative entropy between a “baseline” distribution of the semantic
argument classes of the direct objects in a corpus, and the distribution
of the argument classes of direct objects given a particular verb. SPS
will be greater, the greater the difference between the two probability
distributions.
 Verbs with higher SPS (stronger semantic selectional preferences)
were more likely to occur without an overt object (Resnik, 1996).
Filler Sentences: With and without overt objects.

Jack had caught.
.
Verb Semantic Selectivity
The grammaticality of an indefinite implicit object will be lower for
verbs with weaker semantic selectional preferences.
PERF CODA
.
Michael was bringing. / Michael had brought.
TELIC END
Grammaticality of Implicit Object
.
Test Sentences: Implicit objects.
FAITH ARG
Grammaticality of Implicit Object
.
1. John ate (something).
2. John found *(something).
Stimuli and Design:
Grammaticality of an Implicit Object:
Increases gradiently as a function of SPS, differently for each of the four
aspectual types of inputs.
Probability of Implicit Object Output
In English, indefinite object omission is preferred with certain verbs
but not others:
Input: catch (x,y), x = Jack, y = unspecified
SPS = 2.47, [+ Past], [+ Telic], [+ Perfective]
* INT ARG
 140 sentences containing 30 two-argument verbs for which:
− SPS had been calculated by Resnik (1996) using the Brown corpus
of American English (Francis & Kučera, 1982).
− Telicity was assessed: 14 telic, 16 atelic.
− Each verb was used once in a sentence with perfective aspect and
once in a sentence with imperfective aspect.
An Optimality-Theoretic Analysis, cont.
. .
The Indefinite Implicit Object
Construction
Participants: 15 monolingual native speakers of English at Johns
Hopkins University.
An Optimality-Theoretic Analysis, cont.
Grammaticality of Implicit Object
.
The grammaticality of an indefinite implicit object is gradient across
verbs, varying in accordance with the Semantic Selectivity of the verb,
Telicity, and Perfectivity. The gradient grammaticality can be derived
using probabilistically ranked constraints within the framework of
Optimality Theory (Prince and Smolensky, 1993/2004).
Gradient Grammaticality
Grammaticality of Implicit Object
Proposal
Verb
A multiple linear regression was found to be significant (F = 9.68, p <
0.05), with each of the three factors making small but significant
contributions: SPS accounted for 12% of the variance, Telicity
accounted for 7% and Perfectivity accounted for 6%.
An Optimality-Theoretic Analysis
 Within this probability space of the eight partial orderings, the
probability of each individual partial ordering, e.g., p(* I » F), is equal
to the joint probabilities of the independent pairwise orderings that
comprise it.
 The probability (= grammaticality) of an implicit object is equal to the
sum of the probabilities of each of the constraint orderings that give
rise to the implicit object output candidate for an input according to its
aspectual features:
p(implicit)Telic Perfective =
p(implicit)Telic Imperfective =
p(implicit)Atelic Perfective =
p(implicit)Atelic Imperfective =
Constraints:
* INT ARG (* OVERT INTERNAL ARGUMENT)
The output must not contain an overt internal argument (direct object).
FAITH ARG (FAITHFULNESS TO ARGUMENT STRUCTURE)
All arguments present in the input must be present in the output.
TELIC END (TELIC ENDPOINT)
The endpoint of a Telic event must be bounded by the presence of an
overt internal argument in the output.
PERF CODA (PERFECTIVE CODA)
The coda (endpoint) targeted by perfective aspect must be indicated
by the presence of an overt internal argument in the output.
p(*I » {F, T, P})
p(*I » {F, T, P}) + p(P » *I » {F, T})
p(*I » {F, T, P}) + p(T » *I » {F, P})
p(*I » {F, T, P}) + p(T » *I » {F, P})
+ p(P » *I » {F, T}) + p({T, P} » *I » F)
 The probability of * INT ARG ranked above each of the other three
constraints is defined by separate linear functions:
p(* INT ARG » FAITH ARG) =
p(* INT ARG » TELIC END) =
p(* INT ARG » PERF CODA) =



1   1 

 SPSi  SPSmin    1
 SPSmax  SPSmin 



 2   2 

 SPSi  SPSmin    2
 SPSmax  SPSmin 



 3   3 

 SPSi  SPSmin    3
 SPSmax  SPSmin 

Atelic Perfective
r = 0.26, p > 0.05
Atelic Imperfective
r = -0.09, p > 0.05
Acknowledgements
This research was conducted at Johns Hopkins University under the
guidance of Géraldine Legendre, Paul Smolensky, Barbara Landau, and
Philip Resnik, as part of the PhD dissertation, and was supported by an
Integrative Graduate Education & Research Training (IGERT)
Fellowship.
References
Anttila, A. (1997). Variation in Finnish phonology and morphology. Unpublished Ph.D. Dissertation, Stanford University, Stanford, CA.
Boersma, P. (1997). How we learn variation, optionality, and probability. Proceedings of the Institute of Phonetic Sciences of the University of
Amsterdam, 21, 43-58.
Boersma, P. (1998). Functional phonology: Formalizing the interactions between articulatory and perceptual drives. Unpublished Dissertation,
University of Amsterdam, The Hague: Holland Academic Graphics.
Boersma, P., & Hayes, B. P. (2001). Empirical tests of the gradual learning algorithm. Linguistic Inquiry, 32(1), 45-86.
Boersma, P. (2004). A stochastic OT account of paralinguistic tasks such as grammaticality and prototypicality judgments.
Comrie, B. (1976). Aspect: An introduction to the study of verbal aspect and related problems. Cambridge, UK: Cambridge University Press.
Davidson, L., & Goldrick, M. (2003). Tense, agreement, and defaults in child Catalan: An optimality theoretic analysis. In S. Montrul & F.
Ordonez (Eds.), Linguistic theory and language development in Hispanic languages. Cambridge, MA: Cascadilla Press.
Francis, W., & Kučera, H. (1982). Frequency analysis of English usage. New York, NY: Houghton Mifflin.
Hayes, B. P., & MacEachern, M. (1998). Quatrain form in English folk verse. Language, 74, 473-507.
Legendre, G., Hagstrom, P., Vainikka, A., & Todorova, M. (2002). Partial constraint ordering in child French syntax. Language Acquisition,
10(3), 189-227.
Nagy, N., & Reynolds, B. (1997). Optimality theory and variable word-final deletion in Faeter. Language Variation and Change, 9(1), 37-56.
Olsen, M. B. (1997). A semantic and pragmatic model of lexical and grammatical aspect. New York, NY: Garland Publishing, Inc.
Olsen, M. B., & Resnik, P. (April, 1997). Implicit object constructions and the (in)transitivity continuum. Paper presented at the 33rd Regional
Meeting of the Chicago Linguistics Society, Chicago, IL.
Prince, A., & Smolensky, P. (1993). Optimality theory: Constraint interaction in generative grammar: Rutgers University Center for Cognitive
Science Technical Report 2.
Prince, A., & Smolensky, P. (2004). Optimality theory: Constraint interaction in generative grammar. Oxford: Blackwell Publishing.
Resnik, P. (1996). Selectional constraints: An information-theoretic model and its computational realization. Cognition, 61(1), 127-159.
Reynolds, W. (1994). Variation and phonological theory., University of Pennsylvania, Philadelphia.
Tenny, C. (1994). Aspectual roles and the syntax-semantics interface. Dordrecht: Kluwer Academic Publishers.
van Hout, A. (1996). Event semantics of verb frame alternations: A case study of Dutch and its acquisition. Tilburg University.