Resolving
Quantity and Informativeness Implicature
in Indefinite Reference
Till Poppels and Roger Levy
July 18
XPRAG 2015
The Phenomenon
OWN
The man injured his child.
The man injured someone else’s child.
The man injured a child.
OTHER’S
Till Poppels & Roger Levy (UCSD)
Q/I Resolution in Indefinite Reference
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The Phenomenon
OWN
The man injured his child.
The man injured someone else’s child.
The man injured a child.
OTHER’S
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Q/I Resolution in Indefinite Reference
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The Phenomenon…
…and the research question
OWN
The man injured his child.
The man broke a finger.
The man broke a nose.
The man injured a child.
The man injured a son.
OTHER’S
The X V-ed a Y.
What determines this
variation in the
directionality and strength
of inferences about
utterance meaning?
The man injured someone else’s child.
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Q/I Resolution in Indefinite Reference
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Gricean inferences
Quantity
John ate some of the cookies
+> but not all of them
Be brief.
speaker behavior
Be informative.
listener inferences
Informativeness
I’ll give you $5 if you mow the lawn
+> but only if you do
The X V-ed a Y.
Grice (1967, 1975); Zipf (1949);
Grice (1967,
Levinson
1975);
& Atlas
Grice
Zipf(1987);
(1949);
(1967,Levinson
Levinson
1975); Zipf
(2000);
& Atlas
(1949);
Horn
(1987);
Levinson
(1984,
Levinson
2004);
&Grice
Atlas
(2000);
Frank
(1967,
(1987);
&
Horn
1975);
Goodman
Levinson
(1984,
Zipf (2000);
(1949);
2004);
(2012)
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Q/I Resolution in Indefinite Reference
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The Rational Speech Act (RSA) model
Assumption 1:
The “Lexicon”
OWN
OTHER’S
The man injured a child.
1
1
The man injured his child.
1
0
The man injured someone else’s child.
0
1
Frank & Goodman (2012)
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Q/I Resolution in Indefinite Reference
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The Rational Speech Act (RSA) model
Assumption 1:
The “Lexicon”
Assumption 2:
Utterance costs
OWN
OTHER’S
The man injured a child.
1
1
The man injured his child.
1
0
The man injured someone else’s child.
0
1
𝐷 𝑎 =
1
𝐷 ℎ𝑖𝑠 =
1
𝐷 𝑠𝑜𝑚𝑒𝑜𝑛𝑒 𝑒𝑙𝑠𝑒 ′ 𝑠 =
4
Frank & Goodman (2012)
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Q/I Resolution in Indefinite Reference
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The Rational Speech Act (RSA) model
Utterance Cost
L0
L0
OTHER’S
The1man injured a child.
1
1
The1man injured his child.
1
0
The4man injured someone else’s child.
0
1
S1
Literal Listener
~ lexicon * prior
Gricean Speaker
S1 ~ exp(log(L
exp(λ*(log(L
0)-cost)
0)-cost))
OTHER’S
0
OWN
Prior
OTHER’S
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Interpretation
Interpretation
OWN
L1
Pragmatic Listener
L1 ~ prior * S1
1
𝑝(𝑎|𝑂𝑇𝐻𝐸𝑅′ 𝑆)
𝑝(𝑎)
OTHER’S
OWN
OWN
OWN
Prior OTHER’S
Q/I Resolution in Indefinite Reference
OWN
OTHER’S (2012)
Frank
Prior& Goodman
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Predictions
Interpretation
OTHER’S
(Prior only)
The X V-ed a Y.
X V-ed Y.
The X V-ed a Y.
(X’s Y unique)
OWN
1.Interpretations track priors
2.Baseline Q-implicature
towards OTHER’S
3.Reduced Q-implicature in
“headlines”
4.Strengthened
Q-implicature
The
man broke
a nose.
Utterance
The X V-ed
a Y.
X V-ed Y.
where
Y is unique
0
# aX’s
brightest
student
ambiguous
1
1
# ahisUS president
someone else’s
OWN
Prior
OTHER’S
1
4
D(a,OWN) > D(a,OTHER’S)
4
Frank & Goodman
Frank(2012);
& Goodman
Hawkins
Frank
(2012);
(1991);
& Goodman
Hawkins
Jäger (1991)
(2012)
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Q/I Resolution in Indefinite Reference
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Methodology
The man broke a finger.
Man broke finger.
The man broke a nose.
Man broke nose.
The man injured
a child.
Father injured son.
Experiment
1: Interpretations
The father injured a son.
Nurse broke finger.
The nurse broke a finger.
Man shaved leg.
The man shaved a leg.
Man shaved upper lip.
Norming
experiment: Priors
The man shaved an upper lip.
Woman shaved leg.
The woman shaved a leg.
Woman shaved upper lip.
The woman shaved an upper lip.
Man entered house.
The man entered a house.
Man broke neck.
The man broke a neck.
Tiger broke nose.
The tiger broke a nose.
Python broke nose.
The python broke a nose.
Python broke neck.
The python broke a neck.
Tiger broke neck.
The tiger broke a neck.
Man broke leg.
The man broke a leg.
Man broke back.
The man broke a back.
Man broke promise.
The man broke a promise.
Man broke cup.
response ~ prior + XYuniqueness + relatability + headline + (1 + headline | item)
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Q/I Resolution in Indefinite Reference
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man saving family
teacher injuring student
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Q/I Resolution in Indefinite Reference
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Results
Model Predictions
OTHER’S
Regression Results
(Prior only)
The X V-ed a Y.
X V-ed Y.
The X V-ed a Y.
(X’s Y unique)
OWN
OWN
Till Poppels & Roger Levy (UCSD)
Prior
OTHER’S
***
***
Model Coefficients
Posterior
OTHER’S
OWN
ns
***
Q/I Resolution in Indefinite Reference
***
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Discussion point 1 of 3:
No effect of the prior?
OTHER’S
OWN
Till Poppels & Roger Levy (UCSD)
Q/I Resolution in Indefinite Reference
***
***
Model Coefficients
3 possibilities:
1. Noisy measures
2. MaybeNorming
RSA gotexperiment:
it wrong? Priors
3. Event priors vs. “Intention priors”
ns
***
***
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Discussion point 2 of 3:
Support for RSA
OTHER’S
OWN
Till Poppels & Roger Levy (UCSD)
Q/I Resolution in Indefinite Reference
***
***
Model Coefficients
RSA excels at predicting Q-implicatures:
1. Overall OTHER’S skew
2. Opposing trend in headline versions
3. Enhanced Q-implicature where X’s Y is unique
ns
***
***
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Discussion point 3 of 3:
Relatability – Q or I (or neither?)
The X V-ed a Y.
OTHER’S
2 possible reasons:
• Ad hoc Q-implicature about referring expressions
(e.g. man vs. father)
• I-driven inference from real-world knowledge
about the event participants
(cf. I almost bought a car today but the engine
was too noisy.)
***
***
Model Coefficients
The man injured a child.
The father injured a child.
OWN
ns
***
***
Hirschberg (1985); Clark (1975); Prince & Cole (1981); see also Cohen & Kehler (in prep)
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Q/I Resolution in Indefinite Reference
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Conclusion
What we have learned
• Forced-choice experiments and
mixed-logit models: great for
studying interpretational preferences
Where to go from here
• Cross-linguistic validation of RSA
• More research on I-driven
inferences
• Q/I resolution is determined by
multiple interacting factors
• RSA captures the essence of
Q-implicature
• We don’t understand
Informativeness nearly as well
• Inference taxonomies may become
explanatorily obsolete
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Q/I Resolution in Indefinite Reference
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Thank you.
References
Atlas, J., & Levinson, S. (1981). It-clefts, informativeness
and logical form: radical pragmatics (revised
standard version). Radical Pragmatics.
Clark, H. (1975). Bridging. In Proceedings of the 1975
workshop on Theoretical issues in natural language
processing. Stroudsburg, PA, USA: Association for
Computational Linguistics.
Frank, M. C., & Goodman, N. D. (2012). Predicting
pragmatic reasoning in language games. Science,
336(6084), 998–998.
Grice, H. P. (1957). Meaning. The Philosophical Review,
377–388.
Grice, H. P. (1975). Logic and conversation. 1975, 41–58.
Hawkins, J. A. (1991). On (in)definite articles: implicatures
and (un)grammaticality prediction. Journal of
Linguistics, 27(02), 405.
Hirschberg, J. (1985). A Theory of Scalar Implicature
(Natural Languages, Pragmatics, Inference).
Dissertations Available from ProQuest.
Till Poppels & Roger Levy (UCSD)
Horn, L. R. (1984). Toward a New Taxonomy for Pragmatic
Inference: Q-based and R-based Implicatures. In D.
Schiffrin (Ed.), Meaning, Form, and Use in Context
(pp. 11–42). Georgetown University Press.
Horn, L. R. (2004). Implicature. In L. R. Horn & G. Ward
(Eds.), Handbook of pragmatics (pp. 3–28).
Blackwell Publishing Ltd.
Jäger, G. (2012). Game theory in semantics and
pragmatics, in C. Maienborn, P. Portner & K. von
Heusinger (eds.), Semantics. An International
Handbook of Natural Language Meaning, Vol. 3,
Berlin: de Gruyter, 2487-2516.
Kehler, A., & Cohen, J. (in prep). Conversational Elicitures.
Levinson, S. C. (2000). Presumptive meanings: The theory
of generalized conversational implicature. MIT
Press.
Prince, E. F., & Cole, P. (1981). Toward a taxonomy of
given-new information (pp. 223–255).
Zipf, G. (1949). Human behavior and the principle of least
effort.
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RSA predictions by disambiguation costs
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Q/I Resolution in Indefinite Reference
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Comparing RSA implementations
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Q/I Resolution in Indefinite Reference
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Regression results
Prior
(p = .13)
Intercept
(p < .001)
+Relatable
(p < .001)
+X's Y unique
(p < .001)
+HEADLINE
(p < .001)
-2
<< OTHER'S
-1
0
1
2
OWN >>
Model Coefficients
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Q/I Resolution in Indefinite Reference
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Logit transform
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Q/I Resolution in Indefinite Reference
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