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Introduction Being Complete Being True Conclusions
Complete and True:
A Uniform Analysis for Mention-Some and Mention-All
Yimei Xiang
Harvard University
[email protected]
October 23, 2014
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Introduction Being Complete Being True Conclusions
1
Introduction
2
Being Complete
Exp1-2: Comp-Sensitivity
Exp3-4: Comp-projection
Formalization
3
Being True
FA-Sensitivity
Intermediate Mention-Some
Formalization
4
Conclusions
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Introduction Being Complete Being True Conclusions
I NTRODUCTION
Mention-All (MA) Questions vs. Mention-Some (MS) Questions
In a natural conversation, (1) needs to be answered by specifying all the true answers.
(1)
Where did you get gas today?
(Context: Today I went to both station A and B for gas.)
a. ? Station A./ ? Station B.
b. Station A and station B.
MA -Q
partial answer
complete answer
In contrast, question (2) can be naturally answered simply by specifying some true answer.
(2)
Where can I get gas?
a. From station A./ From station B.
b. From station A and/or B.
MS -Q
MS-Qs are not just questions admitting partial answers: (MS 6= partial)
(3)
Who can serve on the committee?
(Context: exclusively speaking, Gennaro+Danny can, Gennaro+Martin can)
a. ? Gennaro can.
partial MS answer
b. Gennaro and Danny can.
complete MS answer
A wh-Q takes an MS reading if it contains a weak modal like can and to do. (George 2011)
(4)
a. Where can I get gas?
b. Tell me where to get gas.
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Introduction Being Complete Being True Conclusions
Direct Questions vs. Indirect Questions
Karttunen (1977): the problem of how direct questions are interpreted can be reduced to
the problem of how indirect questions are interpreted.
(5)
a. I ask you (to tell me) where you got gas.
b. I ask you (to tell me) where I can get gas.
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Introduction Being Complete Being True Conclusions
Types of MA readings classified by the strength of exhaustivity:
(6)
John told who came.
Weakly exhaustive (WE):
What John told affirmed all the true answers.
Intermediately exhaustive (IE):
What John told affirmed all the true answers and didn’t affirm any false answers.
(7)
John knows who came.
Strongly exhaustive (SE):
John’s belief affirms all the true answers and denies all the false answers.
The distributions and relations among MA readings are under debate. For instance:
Indirect-Q (7) admits only SE;
G&S (1982, 1984), K&R (2011)
Indirect-Q (7) admits both SE and IE.
Spector & Egré (2014)
Cremers & Chemla (to appear) supports the latter view. If questions admitting SE also admit IE,
then SE should be a variant of IE. (Uegaki 2014, cf. K&R 2011)
⇒ MA readings can be firstly grouped based on the sensitivity to false answers (FAs):
IE and SE are FA-sensitive, while WE is FA-insensitive.
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Introduction Being Complete Being True Conclusions
Questions for Experiments
1
Are indirect MA-questions equally sensitive to completeness?
MA -Qs
2
under know are more sensitive to completeness than MA-Qs under tell.
Are FAs (over-affirming and over-denying) equally unacceptable?
No. Over-affirming is more acceptable than over-denying in MA-Qs, while over-denying is
more acceptable than MS-Qs.
3
Is there any FA-sensitive MS reading?
Yes. There is an intermediate mention-some (IMS) reading, in parallel to IE.
Questions for Formalizations
1
Derive complete answers to MA-Qs and MS-Qs (WE & WMS)
2
Explain the contrast between over-denying and over-affirming wrt acceptability
3
Derive FA-sensitive readings of MA-Qs and MS-Qs (IE & IMS)
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Introduction Being Complete Being True Conclusions
Exp1-2: Comp-Sensitivity Exp3-4: Comp-projection Formalization
E XPERIMENT 1-2: S ENSITIVITY TO C OMPLETENESS
1. Are indirect MA-questions equally sensitive to completeness?
M1: sensitive only
QMA
Comp
Part ∨ Comp
M2: insensitive only
QMA
Comp
M3: sensitive + insensitive
Comp
QMA
Part ∨ Comp
Part ∨ Comp
Design & Participants
Each experiment showed participants 16 context-sentence pairs (8 targets and 8 fillers) and
asked them to judge the truth value of each sentence under the context.
The Q-embedding verb used in Exp 1/2 was know/tell.
The target items were manipulated based on the Q TYPE: MA or MS.
In all the target items, the agent knows or told only part of the full true answer.
Each experiment recruited 40 participants on AMT and selected 33 participants based on
filler accuracy and native language.
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Introduction Being Complete Being True Conclusions
Exp1-2: Comp-Sensitivity Exp3-4: Comp-projection Formalization
MA
questions
Context: Alice, Bill and Celine are the only three people who pass the math exam. John
knows (/told Mary) that Alice and Bill passed the math exam, but he doesn’t know (/didn’t
tell her that) Celine also did.
Mary says: “John knows (/told me) who passed the math exam.”
Is Mary right or wrong?
Right.
Wrong.
MS
questions
Context: There are three places in total selling pre-paid envelopes near the train station,
including USPS, UPS, and Fedex. Marek knows that he can (/told Mary that she) buy
pre-paid envelops at USPS and UPS, but he doesn’t know that he (didn’t tell her that she)
can also do that at Fedex.
Mary says: “Marek knows (/told me) where to buy pre-paid envelops.”
Is Mary right or wrong?
Right.
Wrong.
Predictions
For MA-targets:
1
Sensitive only → most responses would be “wrong” (W);
2
Insensitive only → most responses would be “right” (R);
3
Sensitive+insensitive → half R and half W
For MS-targets, most responses would be R.
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Introduction Being Complete Being True Conclusions
Exp1-2: Comp-Sensitivity Exp3-4: Comp-projection Formalization
By Qtype*Verb
1
Combine the data of Exp 1&2 and fit a logistic mixed
effects model.
Estimate
0.5215
2.4788
-0.8498
Verb
Qtype
Verb:Qtype
SE
0.4180
0.3482
0.2360
Pr(>|z|)
0.212159
1.09e-12 ***
0.000317 ***
(Verb = -1/1 for know/tell. Qtype = -1/1 for MA/MS.)
⇒ MS-Qs were significantly more likely to get R answers
than MA-Qs.
2 Split the data into two sets based on Q TYPE .
Qtype
MA
By Item
MS
Verb
Verb
Estimate
2.3720
-0.3260
SE
0.8257
0.9285
Pr(>|z|)
0.00407 **
0.726
⇒ MA-Qs under tell were significantly more likely to get R
answers than those under know.
know
QMA
tell
Comp
Part ∨ Comp
QMA
Comp
Part ∨ Comp
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Introduction Being Complete Being True Conclusions
Exp1-2: Comp-Sensitivity Exp3-4: Comp-projection Formalization
E XPERIMENT 3-4: P ROJECTION OF C OMPLETENESS
Do the Q-models concluded from Exp 1-2 apply to negative contexts?
MA -Qs
under know
MA -Qs
Comp
QMA
Part ∨ Comp
QMA
under tell
Comp
Part ∨ Comp
Projection of Completeness
(8)
John doesn’t know who came.
= “John doesn’t know any true answers as to who came”
6= “It is not the case that John knows all the true answers as to who came.”
(9)
John didn’t tell who came.
= “John didn’t tell me any true answers as to who came”
6= “It is not the case that John told me all the true answers as to who came.”
Design & Participants
Exp 3-4 were designed in the same way as Exp 1-2 but with negation.
Exp 3 and 4 kept 37 (out of 40) and 33 (out of 48) participants, respectively.
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Introduction Being Complete Being True Conclusions
MA
Exp1-2: Comp-Sensitivity Exp3-4: Comp-projection Formalization
questions
Context: Alice, Bill and Celine are the only three people who pass the math exam. John
knows (/told Mary) that Alice and Bill passed the math exam, but he doesn’t know (/didn’t
tell her that) Celine also did.
Mary says: “John doesn’t know (didn’t tell me) who passed the math exam.”
Is Mary right or wrong?
MS
Right.
Wrong.
questions
Context: There are three places in total selling pre-paid envelopes near the train station,
including USPS, UPS, and Fedex. Marek knows that he can (/told Mary that she) buy
pre-paid envelops at USPS and UPS, but he doesn’t know that he (didn’t tell her that she)
can also do that at Fedex.
Mary says: “Marek doesn’t know (didn’t tell me) where to buy pre-paid envelops.”
Is Mary right or wrong?
Right.
Wrong.
Predictions
Participants would accept Mary’s claim iff
(i) the indirect question in Mary’s claim was sensitive to completeness, and
(ii) the completeness didn’t project up.
∀
¬∀
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Introduction Being Complete Being True Conclusions
Exp1-2: Comp-Sensitivity Exp3-4: Comp-projection Formalization
By Qtype*Verb
1
Fit the full data with a logistic mixed effect model.
Verb
Qtype
Verb:Qtype
Estimate
-0.5952
-2.0293
0.7121
SE
0.3889
0.3288
0.2254
Pr(>|z|)
0.12589
6.73e-10 ***
0.00158 **
⇒ MS-Qs were significantly less likely to get R responses
than MA-Qs.
By Item
2
Split the data into two sets based on Qtype.
Qtype
MA
MS
Verb
Verb
Estimate
-1.6848
-0.04102
SE
0.5573
1.20650
Pr(>|z|)
0.0025 **
0.973
(The model for MS-targets failed to converge.)
⇒ MA-Qs under tell were significantly less likely to get R
responses than those under know.
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Introduction Being Complete Being True Conclusions
Exp 1-2 (positive contexts)
Exp1-2: Comp-Sensitivity Exp3-4: Comp-projection Formalization
Exp 3-4 (negative contexts)
If completeness projected mandatorily, then ideally P(R34 ) = P(R12 )
If completeness didn’t project at all, then ideally P(R34 ) = P(W12 )
If completeness projected optionally, then ideally P(R34 ) = 1/2 * P(W12 )
√
⇒ Completeness of MA-Qs under both verbs projected optionally.
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Introduction Being Complete Being True Conclusions
(1) know-pos
Exp1-2: Comp-Sensitivity Exp3-4: Comp-projection Formalization
(3) know-neg
R
50%
W
50%
R
25%
W
75%
[−projection]
Comp
QMA
W
100%
Comp
[+projection]
(4) tell-neg
(2) tell-pos
Comp
QMA
QMA
W
50%
QMA
Comp
[−projection]
[+projection]
Part∨Comp
R
50%
Part∨Comp
The proportion of R responses to an MA-Q is reduced to the variations on:
1
Sensitivity to completeness
MA -Qs
MA -Qs
2
under know are comp-sensitive only, while
under tell can be either comp-sensitive or comp-insensitive.
Projection of completeness
Completeness projects optionally.
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Introduction Being Complete Being True Conclusions
Exp1-2: Comp-Sensitivity Exp3-4: Comp-projection Formalization
C OMPLETE ANSWERS OF MA -Q S
Dayal (1996):
(10)
A NS(Q)(w) = ιp[w ∈ p ∈ Q & ∀p0 ∈ Q[w ∈ p0 → p ⊆ p0 ]]
(the unique true proposition in Q that entails all the true propositions in Q)
Fox (2013):
A NS(Q)(w) returns the set of maximally informative true (MIT) answers of Q in w.
(11)
(12)
A NS(Q)(w) = {p : w ∈ p ∈ Q & ∀p0 ∈ Q[w ∈ p0 → p0 6⊂ p]}
{p: p is a true answer to Q(w), and p isn’t asymmetrically entailed by any true
answer to Q(w)}
Who came to the party yesterday? (Context: Only John and Mary came.)
a. A NS [Who came to the party yesterday]
= A NS{John did, Mary did, John and Mary did}
= {John and Mary did}
comp-sensitive
b. [Who came to the party yesterday]
= {John did, Mary did, John and Mary did}
comp-insensitive
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Introduction Being Complete Being True Conclusions
Exp1-2: Comp-Sensitivity Exp3-4: Comp-projection Formalization
Answer space of MA-Q
→ Maximally informative
f (a + b + c)
f (a + b)
f (a + c)
f (b + c)
→ Not maximally informative
f (a)
f (b)
f (c)
→ Not maximally informative
Comp-sensitive readings of MA-Qs are derived by applying an A NS.
Comp-insensitive readings of MA-Qs are derived on absence of A NS.
Since we haven’t found a predicate below which an MA-Q takes only comp-insensitive
readings, we can assume that A NS is applied by default.
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Introduction Being Complete Being True Conclusions
Exp1-2: Comp-Sensitivity Exp3-4: Comp-projection Formalization
C OMPLETE A NSWERS FOR MS -Q S
(13)
Where can I fill my tank?
(Context: station A has enough gas to fill my tank, but station B doesn’t.)
a. From station A.
b. From station A and B together.
? 3w f (b)
? 3w f (a + b)
On the one hand, under the canonical analysis, (13) isn’t maximally informative, and hence
applying A NS to (13) will incorrectly exclude (13a). On the other hand, it’s also odd to assume
that A NS is present by default in MA-Qs while absent by default in MS-Qs. I offer an
explanation with the prediction that an MS answer is maximally informative.: insert an
EXH -operator under the weak modal.
(14)
A NS [can EXH [where I fill my tank] ]
(15)
EXH (p) = p ∧ ∀q ∈ A lt(p)[p 6⊆ q → ¬q]
(the prejacent p is true, and any alternative of p not entailed by p is false.)
(16)
A NS{3w EXH f (a), 3w EXH f (a + b)} = {3w EXH f (a), 3w EXH f (a + b)}
1
The use of EXH captures the scalar implicature of (13a) that “... from station A alone”
2
The non-monotonicity of EXH prevents (13b) from entailing (13a).
3
EXH creates a non-monotonic context to the wh-item, making all answers maximally
informative.
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Introduction Being Complete Being True Conclusions
Exp1-2: Comp-Sensitivity Exp3-4: Comp-projection Formalization
Answer space of MA-Q
→ Maximally informative
f (a + b + c)
f (a + b)
f (a + c)
f (b + c)
→ Not maximally informative
f (a)
f (b)
f (c)
→ Not maximally informative
Answer space of MS-Qs
3EXH f (a + b + c)
→ Maximally informative
3EXH f (a + b)
3EXH f (a + c)
3EXH f (b + c)
→ Maximally informative
3EXH f (a)
3EXH f (b)
3EXH f (c)
→ Maximally informative
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Introduction Being Complete Being True Conclusions
FA-Sensitivity Intermediate Mention-Some Formalization
T RUE : FA- SENSITIVE
MA readings are firstly grouped in terms of the sensitivity to false answers (FAs):
IE and SE are FA-sensitive, while WE is not.
WE: The prediction affirmed all the true answers.
IE: The prediction affirmed all the true answers and didn’t affirm any false answers.
SE The prediction affirms all the true answers and denies all the false answers.
2. Are false answers equally unacceptable?
MA -Qs:
Reanalyze Klinedinst & Rothschild (2011)
MS -Qs:
Experiment 5
3. Is there any MS reading sensitive to FAs?
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Introduction Being Complete Being True Conclusions
MA -Q:
FA-Sensitivity Intermediate Mention-Some Formalization
Klinedinst & Rothschild (2011)
Four individuals a, b, c and d trying out for the swimming team: a and d made the swimming
team and b and c failed to. Identify whether or not a set of predictions (A1 to A4) correctly
predicted who made the swimming team.
A1
A2
A3
A4
MA -Qs
A
No
?
Yes
Yes
b
?
No
?
Yes
c
No
No
No
?
D
Yes
Yes
Yes
Yes
SE
×
×
×
×
IE
×
×
√
×
WE
×
×
√
√
embedded under predict support all types of MA readings.
K&R didn’t consider comp-insensitive readings and excluded subjects who accepted A1/A2.
Hence I reanalyzed their raw data and kept 107 subjects (out of 193) based on:
1
excluding non-native speakers (-79);
2
excluding workers rejected by MTurk (-4);
3
excluding subjects with missing responses (-3).
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Introduction Being Complete Being True Conclusions
MS -Q:
FA-Sensitivity Intermediate Mention-Some Formalization
Experiment 5
Four places (a, b, c, d) at the Central Square selling alcohol, among which only a and d sold red
wine. Susan asked where she could buy a bottle of red wine at the Central Square. Identify
whether an answer (A1 to A4) correctly answered Susan’s question.
A1
A2
A3
A4
A
No
?
Yes
Yes
b
?
No
?
Yes
c
No
No
No
?
D
Yes
Yes
Yes
Yes
SE
×
×
×
×
IE
×
×
√
×
WE
×
×
√
√
WMS
√
√
√
√
Example
A1: Bob told Susan that she could buy one from d, but not from a or c.
Did Bob tell Susan where to buy a bottle of red wine at the Central Square?
Yes
No
The four target items (A1 to A4) and two fillers were randomized into 10 lists. I recruited 100
participants on Mturk and kept 88 in the analysis (filler accuracy 100%).
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Introduction Being Complete Being True Conclusions
FA-Sensitivity Intermediate Mention-Some Formalization
By Answer in K&R (2011): MA-Q
2. Are FAs equally unacceptable?
A1
A2
A3
A4
A
No
?
Yes
Yes
b
?
No
?
Yes
c
No
No
No
?
D
Yes
Yes
Yes
Yes
FA-type
over-denying
over-affirming
(i) Are MS-Qs and MA-Qs the same wrt FA-sensitivity?
By Answer in Exp 5: MS-Q
Fit each data with a logistic effect model and found a
significant effect for A NSWER (A1 = -1 vs A4 = 1):
K&R (2011)
Experiment 5
βˆ = 1.0952, p < .001
βˆ = -0.7324, p < .005
Compared with over-affirming (A4), over-denying (A1) is
significantly less acceptable in an MA-Q
significantly more acceptable in an MS-Q.
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Introduction Being Complete Being True Conclusions
FA-Sensitivity Intermediate Mention-Some Formalization
By Answer in K&R (2011): MA-Q
A1
A2
A3
A4
A
No
?
Yes
Yes
b
?
No
?
Yes
c
No
No
No
?
D
Yes
Yes
Yes
Yes
FA-type
over-denying
over-affirming
(ii) For MA-Qs, are their comp-sensitive and comp-insensitive
readings consistent wrt FA-sensitivity?
In K&R, among 28 subjects who coded A2-3 as
By Answer in Exp 5: MS-Q
A1
×
√
×
√
A2
√
√
√
√
A3
√
√
√
√
A4
×
×
√
√
ˆ
N(N)
11 (4.05)
1 (2.16)
8 (9.44)
8 (2.03)
√
:
Reading
X
Y
N(Y) was significantly higher than N(X).
(Binomial test: 89%, p < .05)
Among comp-insensitive readings, over-affirming is also
significantly more acceptable than over-denying.
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Introduction Being Complete Being True Conclusions
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
A1
×
√
×
×
×
√
√
√
×
×
×
√
√
√
×
√
A2
×
×
√
×
×
√
×
×
√
√
×
√
√
×
√
√
A3
×
×
×
√
×
×
√
×
√
×
√
√
×
√
√
√
A4
×
×
×
×
√
×
×
√
×
√
√
×
√
√
√
√
FA-Sensitivity Intermediate Mention-Some Formalization
K&R (MA-Q)
19 (8.29)
0
1
21 (23.41)
3
0
2
2
11 (4.05)
0
25 (22.13)
1 (2.16)
3
3
8 (9.44)
8 (2.03)
Exp 5 (MS-Q)
0
0
0
2
0
2
0
0
11 (7.24)
0
0
23 (28.86)
0
0
5 (9.78)
45 (37.98)
Reading
SE
IE
IMS
WE
X
Y
WMS
3. Is there any FA-sensitive MS reading? Consider:
What the agent told/predicted affirmed some true answer, and
... didn’t overly affirm or overly deny.
IMS
... didn’t overly affirm.
X
... didn’t overly deny.
Y
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Introduction Being Complete Being True Conclusions
6
7
8
9
10
11
12
13
14
15
16
A1
√
√
√
A2
√
×
×
×
√
√
√
√
×
√
×
×
√
×
√
√
×
√
√
A3
×
√
×
√
×
√
√
×
√
√
√
A4
×
×
√
×
√
√
×
√
√
√
√
Exp 5 (MS-Q)
2
0
0
11 (7.24)
0
0
23 (28.86)
0
0
5 (9.78)
45 (37.98)
FA-Sensitivity Intermediate Mention-Some Formalization
Reading
IMS
not over-affirming/denying
WE
X
not over-affirming
Y
WMS
not over-denying
IMS exists!
In Exp 5, the observed N of IMS was
ˆ
1 higher than the estimated N;
2
significantly higher than the observed Ns of its group-mates (viz. response sets with 2
(binomial test: 85%, p < .001).
√
).
The existence of X/Y is hard to tell.
1
ˆ
Their observed Ns were lower than their estimated Ns.
2
N(X) was significantly higher than N(Y) in Exp 5 (binomial test: 82%, p < .001)
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Introduction Being Complete Being True Conclusions
FA-Sensitivity Intermediate Mention-Some Formalization
FA- SENSITIVITY
FAs are not equally unacceptable
Over affirming is more acceptable than over denying in MA-Qs;
Over denying is more acceptable than over affirming in MS-Qs.
My proposal
An FA is strictly unacceptable iff it yields an MI answer that doesn’t entail any MIT answers.
MS -Q
MA -Q
3EXH f (b + c)
f (a + b + c)
f (a + b)
f (a + c)
f (b + c)
f (a)
f (b)
f (c)
3EXH f (a)
√
3EXH f (b)
3EXH f (c)
Over affirming p is not acceptable iff an MI answer resulted of adding p to the true answer
space doesn’t entail any MIT answers.
MA -Q:
f (a + b + c) entails f (b + c)
× MS-Q: 3EXH f (a) doesn’t entail any MIT answer.
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Introduction Being Complete Being True Conclusions
FA-Sensitivity Intermediate Mention-Some Formalization
FA- SENSITIVITY
FAs are not equally unacceptable
Over affirming is more acceptable than over denying in MA-Qs;
Over denying is more acceptable than over affirming in MS-Qs.
My proposal
An FA is strictly unacceptable iff it yields an MI answer that doesn’t entail any MIT answers.
MS -Q
MA -Q
3EXH f (b + c)
f (a + b + c)
f (a + b)
f (a + c)
f (b + c)
f (a)
f (b)
f (c)
3EXH f (a)
3EXH f (b)
3EXH f (c)
Over denying p is not acceptable iff an MI answer resulted of removing p from the true
answer space doesn’t entail any MIT answers.
× MA-Q: f (b + c) doesn’t entail f (a + b + c)
√
MS -Q: Every remained MIT answer entails itself.
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Introduction Being Complete Being True Conclusions
FA-Sensitivity Intermediate Mention-Some Formalization
FA- SENSITIVE READINGS : IE & IMS
K&R (2011)
IE is derived from WE by applying an EXH-operator over the matrix clause.
(17)
a. John told who came
b. EXH [John told who came] V
= JJohn told who cameK ∧ ( p∈JJohn told who cameKF+ ¬p)
“John told the WE answer ∧ he didn’t say any answers not entailed by this answer.”
WE
IE
K&R’s analysis, however, cannot extend to IMS:
“# John told some true answer ∧ he didn’t say any answers not entailed by this answer.”
IMS: What the agent told affirmed some true answer, and
didn’t affirm any false answers or deny any true answers.
IE: What the agent told affirmed all the true answers, and
didn’t affirm any false answers or deny and true answers.
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Introduction Being Complete Being True Conclusions
FA-Sensitivity Intermediate Mention-Some Formalization
FA- SENSITIVE READINGS : IE & IMS
My Proposal: Weak and Intermediate A NS-operators
(18)
A NSW (Q)(w) = {p : w ∈ p ∈ Q & ∀p0 ∈ Q[w ∈ p0 → p0 6⊂ p]}
{p : p is an MIT answer to Q(w)}
(19)
A NSI (Q)(w) = {p : p(w) ∧ p J Q ∧ ∃p0 ∈ A NSW (Q)(w)[p ⊆ p0 ]}
{p : p is true in w, Q-relevant, and entails an MIT answer to Q(w)}
(20)
A recursive definition of Q-relevance:
a. If ∃w[p ∈ Q(w)], then p and ¬p are Q-relevant
b. If p and q are Q-relevant, then p ∩ q and p ∪ q are Q-relevant
Fox (2013)
c. Nothing else is Q-relevant.
IMS
IE
A NSI
QMA
A NSW
A NSI
WE
QMS
∅/A NSW
WMS
-EXH; ∅
∅
Part
Part
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Introduction Being Complete Being True Conclusions
C ONCLUSIONS
Experiments
1
Sensitivity to completeness varies by the Q-embedding predicate:
An MA-Q under know is comp-sensitive;
An MA-Q under tell can be either sensitive or insensitive, depending on the speaker.
2
False answers are not equally bad, in particular:
in MA-Qs, (for both comp-sensitive and comp-insensitive readings), over-affirming is more
acceptable than over-denying;
in MS-Qs, over-denying is more acceptable than over-affirming.
3
In parallel to IE, there is an IMS reading sensitive to false answers.
Formalizations
1
Complete and FA-(in)sensitive readings of MA-Qs and MS-Qs are derived uniformly:
A NSW (Q)(w) returns a WE/WMS answer;
A NSI (Q)(w) returns an IE/IMS answer.
2
By virtue of a local EXH-operator, MS-Qs take MS answers as complete/ MI answers.
3
An FA is more unacceptable iff it yields an MI answer that doesn’t entail any MIT answers.
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Introduction Being Complete Being True Conclusions
THANK YOU!
I thank Gennaro Chierchia, Martin Hackl, Daniel Lassiter, Jesse Snedeker, and Wataru Uegaki
for general comments and discussions! I also thank Michael Yoshitaka Erlewine, Zuzanna
Fuchs, Amy Geojo, Hadas Kotek, and Eun-Kyung Lee for suggestions on experimental settings
and statistical analyses. All errors are mine!
Cremers, A. and E. Chemla. to appear. A psycholinguistic study of the different readings
for embedded questions. Journal of Semantics.
Egré, P. and B. Spector. to appear. A uniform semantics for embedded interrogatives: an
answer, not necessarily the answer. Synthese.
Fox, D. 2013. Mention-some readings of questions, class notes, MIT seminars.
Groenendijk, J. and Stokhof, M. 1982. Semantic analysis of wh-complements. L&P,
5:175-233.
Groenendijk, J. and M. Stokhof. 1984. Studies in the semantics of questions and the
pragmatics of answers. Amsterdam: University of Amsterdam dissertation.
Karttunen, L. 1977. Syntax and semantics of questions. L&P 1:3-44.
Klinedinst, N. and D. Rothschild. 2011. Exhaustivity in questions with non-factives.
Semantics and Pragmatics 4:1-23.
Uegaki, W. 2014. Predicting the variations in the exhaustivity of embedded interrogatives.
Handout for Sinn und Bedeutung 19.
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