Optimal Reasoning About Referential Expressions Judith Degen1
Michael Franke2
1 Department
of Brain and Cognitive Sciences University of Rochester
2 Institute
for Logic, Language and Computation Universiteit van Amsterdam
September 19, 2012
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Reference to objects
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Reference to objects
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Reference to objects
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A hard problem
Production (audience design) Clark & Murphy, 1982; Horton & Keysar, 1996; Brown-Schmidt et al., 2008
Choose a message to convey a given intended meaning with sufficiently high probability.
Comprehension (perspective-taking) Keysar et al., 2000; Hanna et al., 2003; Heller et al., 2008
Infer the most likely intended interpretation upon observing an utterance.
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Today
Questions 1
How much strategic back-and-forth reasoning is involved in the production and comprehension of referential expressions?
2
How well do current game-theoretic models based on rational back-and-forth reasoning about interlocutors (Franke, 2009) account for behavioral data?
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Outline
1
Game-theoretic pragmatics & IBR
2
Experiment 1 - comprehension
3
Experiment 2 - production
4
Discussion
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An example
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An example
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An example
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An example
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An example
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An example Intended meanings / Interpretations
Messages
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Signaling games
sequential game: 1
2 3 4
the sender/speaker S wants to convey an intended meaning t out of a set of possible meanings T according to a certain probability distribution p ∗ S chooses a message m out of a set of possible messages M S transmits m to the receiver/hearer R R guesses an interpretation/type t 0 , based on the sent message
if t = t 0 , both players score a point, otherwise not
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Exogeneous meaning
we assume messages have conventional or iconic meaning
[[ [[ [[ [[
]] ]] ]] ]]
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= = = =
{ { { {
} } } ,
}
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Literal receiver
R0
1
0
0
0
0
1
0
1/2
1/2
1
0
0
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Literal sender
S0 1/2
0
0
1/2
0
0
1
0
0
1/2
1/2
0
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The Iterated Best Response sequence sends any true message
S0
R0
interprets messages literally
best response to S0
R1
S1
best response to R0
S2
R2
best response to S1 .. .
.. .
.. .
best response to R1 .. .
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Computing best responses
Sender: choose only messages that maximize the expected utility of Sk , given Rk−1 Receiver: choose only messages that maximize the expected utility of Rk , given Sk−1 expected utility is a function of outcome utility the players’ probabilistic beliefs about interlocutor behavior
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Iterated Best Response
S1
R1
1
0
0
0
0
1
0
1
0
1
0
0
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1/2
0
0
1/2
0
0
1
0
0
1
0
0
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Experiment 1 - comprehension
test participants’ behavior in a comprehension task implementing previously described signaling games 30 participants on Amazon’s Mechanical Turk initially 4 trials as senders 36 experimental trials 6 simple (one-step) implicature trials 6 complex (two-step) implicature trials 24 filler trials (entirely unambiguous/ entirely ambiguous target)
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Simple implicature trial
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Simple implicature trial - predictions
IBR predictions for distribution of responses over target and competitor: 100
Proportion of choices
80
Response
60
target competitor
40
20
0 k=0
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k>0
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Complex implicature trial
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Complex implicature trial - predictions
IBR predictions for distribution of responses over target and competitor: 100
Proportion of choices
80
Response
60
target competitor
40
20
0 k <= 1
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Unambiguous filler
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Ambiguous filler
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Results - proportion of responses by condition
Proportion of choices
1.0 0.8 Response 0.6
target distractor
0.4 competitor
0.2 0.0
r ille
sf
u uo
big
am
m co
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e tur
a plic im x ple
e
tur
a plic
ple
sim
im
r
ille
sf
u uo
big
am
un
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Results - proportion of responses by condition
Proportion of choices
1.0 0.8 Response 0.6
target distractor
0.4 competitor
0.2 0.0
r ille
sf
u uo
big
am
m co
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e tur
a plic im x ple
e
tur
a plic
ple
sim
im
r
ille
sf
u uo
big
am
un
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Results - proportion of responses by condition
Proportion of choices
1.0 0.8 Response 0.6
target distractor
0.4 competitor
0.2 0.0
r ille
sf
u uo
big
am
m co
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e tur
a plic im x ple
e
tur
a plic
ple
sim
im
r
ille
sf
u uo
big
am
un
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Results - distribution of subjects over target choices
Number of subjects (out of 28)
20
15 Implicature complex
10
simple 5
0 0
1 2 3 4 5 6 Number of target choices (out of 6 possible)
→ not predicted by standard IBR Degen & Franke
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Experiment 2 - production
test participants’ behavior in the analogous production task 30 participants on Amazon’s Mechanical Turk 36 experimental trials 6 simple (one-step) implicature trials 6 complex (two-step) implicature trials 24 filler trials (entirely unambiguous/ entirely ambiguous target)
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Simple implicature trial
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Simple implicature trial
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Complex implicature trial
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Complex implicature trial
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Proportion of choices
Results - proportion of responses by condition 1.0 0.8 Response 0.6
target distractors
0.4 competitor
0.2 0.0
us uo
r fille im lex p m
big
am
co
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e tur
a plic
ple sim
e
tur
a plic
im
r
ille
sf
u uo
big
am
un
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Results - proportion of responses by condition
Experiment 2 (production)
Proportion of choices
1.0 0.8 Response 0.6
target distractor
0.4 competitor
0.2 0.0
Proportion of choices
Experiment 1 (comprehension) 1.0 0.8
Response 0.6
target distractors
0.4 competitor
0.2 0.0
f us
o igu
b am
r
ille
im lex mp co
e
tur
a plic
a plic
ple
e tur o
igu
im
sim
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un
r ille
r
ille
b am
f us
sf ou igu
b am
e
r atu plic
im lex mp
co
Reasoning About Referential Expressions
plic
sim
ple
im
re atu
s ou
r fille
igu
b am un
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Results - distribution of subjects over target choices
Experiment 1 (comprehension)
Experiment 2 (production) 20
15 Implicature complex
10
simple 5
0
Number of subjects (out of 28)
Number of subjects (out of 28)
20
15 Implicature complex
10
simple 5
0 0
1 2 3 4 5 6 Number of target choices (out of 6 possible)
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1 2 3 4 5 6 Number of target choices (out of 6 possible)
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Interim summary
asymmetry in production and comprehension: simple implicatures easier in production than comprehension and vice versa for complex implicatures not predicted by standard IBR
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Towards an explanation
Success expectations are given in order for R: target, competitor, distractor object S: target, competitor, distractor1 , distractor2 message simple level
complex
R
S
R
S
1
h2/3, 1/3, 0i
h1, 1/2, 0, 0i
h1/2, 1/2, 0i
h1/2, 1/2, 0, 1/3i
2
h1, 0, 0i
h1, 0, 0, 0i
h1, 0, 0i
h1/2, 0, 0, 1/3i
3
h1, 0, 0i
h1, 0, 0, 0i
h1, 0, 0i
h1, 0, 0, 1/3i
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Conclusion
interlocutors do take perspective and simulate each others’ beliefs but not always optimally and less so as the number of required reasoning steps increases
IBR requires updating to allow for probabilistic rather than categorical choice rule
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Future directions
moving into the realm of actual language: manipulating message costs manipulating utility of communicative success / failure interactive experiments with feedback
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?
learning
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Thanks to EURO-XPRAG Tanenhaus lab Mike Tanenhaus & the NIH Gerhard J¨ager Florian Jaeger
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Results - Exp. 1 learning effects simple implicature
complex implicature
Proportion of choices
1.0 0.8 Response 0.6
target distractor
0.4 competitor 0.2 0.0 1
2
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4
5 6 1 2 3 Relative trial number
4
5
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References I Brown-Schmidt, S., Gunlogson, C., & Tanenhaus, M. K. (2008, June). Addressees distinguish shared from private information when interpreting questions during interactive conversation. Cognition, 107(3), 1122–34. Clark, H., & Murphy, G. L. (1982). Audience design in meaning and reference. In J. LeNy & W. Kintsch (Eds.), Language and comprehension. Amsterdam: North-Holland. Hanna, J., Tanenhaus, M. K., & Trueswell, J. C. (2003). The effects of common ground and perspective on domains of referential interpretation. Journal of Memory and Language, 49, 43-61. Heller, D., Grodner, D., & Tanenhaus, M. K. (2008). The role of perspective in identifying domains of reference. Cognition, 108, 831-836. Horton, W., & Keysar, B. (1996). When do speakers take into account common ground? Cognition, 59, 91–117. Degen & Franke
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References II
Keysar, B., Barr, D. J., & Brauner, J. S. (2000). Taking perspective in conversation: The role of mutual knowledge in comprehension. Psychological Science, 11, 32-37.
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