Negative Polarity Items
in Questions
Manfred Krifka
Humboldt Universität zu Berlin
&
Zentrum für Allgemeine Sprachwissenschaft, Berlin
Polarity Items in Questions
Ann Borkin 1971, “Polarity Items in Questions”, CLS 7
Did Mary ever lift a finger to help you?
Who ever lifted a finger to help you?
==> Rhetorical questions, expected answer: No. / Noone.
Have you ever been to China?
Which student has ever been to China?
==> Information-seeking questions.
Problems with NPIs in Questions: Syntactic Accounts
Syntactic account of NPIs:
E. Klima 1964, “Negation in English”, C. L. Baker 1970, “Double negatives”
M. C. Linebarger 1980, The grammar of negative polarity
L. Progovac 1987, A binding-theoretic approach to polarity sensitivity
NPIs have to stand in construction with (be c-commanded by) a trigger,
the classical trigger is negation.
*Mary lifted a finger to help you.
Mary didn’t [lift a finger to help you].
NPIs in questions can be explained by question morpheme Q
as another trigger (Progovac):
Did Mary lift a finger to help you?
Q [did Mary lift a finger to help you?]
Q triggers Subj/Aux-inversion in English,
may be realized as a particle or a morpheme in other languages.
May explain why we don’t find NPIs in non-inverted questions
(they lack a question morpheme), R. Huddlestone 1994.
*Mary lifted a finger to help you?
??You have ever been to China?
But: Why is the question morpheme a trigger? Why not, e.g., the imperative?
*Lift a finger to help me!
Problems with NPIs in Questions: Syntactic Accounts
Another way of motivating NPIs in questions:
NPIs might also be licensed by way of entailments (C. L. Baker).
John was surprised that Mary said anything.
==> John expected that Mary did not say anything.
This can explain why we find NPIs in rhetorical questions:
They expect a negative answer, which may be an entailment.
Did Mary ever lift a finger to help you?
==> I believe that Mary did not [ever lift a finger to help you].
Who ever lifted a finger to help you?
==> I believe that no-one [ever lifted a finger to help you].
The NPI might serve an indication that a negative answer is expected,
hence be a marker for rhetorical questions.
But: no explanation why NPIs also occur in information-seeking questions:
Have you ever been to China?
=/=> I believe that you have not [ever been to China].
Which student has ever been to China?
=/=> I believe that no student [has ever been to China].
Problems with NPIs in Questions: Semantic Accounts
Semantic Accounts of NPIs
B. Ladusaw 1979, Polarity sensitivty as inherent scope relations
NPIs occur in downward-entailing contexts:
Mary hasn’t [been to China last year]
last month  last year
==> Mary hasn’t [been to China last month].
hence: Mary hasn’t [been to China ever].
Every student who has been to China last year enjoyed it.
last month  last year
Every student who has been to China last month enjoyed it.
hence: Every student who has ever been to China enjoyed it.
Problem: Has Mary ever been to China?
How can a question be downward-entailing?
Perhaps (Groenendijk & Stokhof 1984):
Q entails Q’ iff every complete answer to Q is a complete answer to Q’.
But: Has Mary been to China last year? <=/=> Has Mary been to China last month?
Yes. >>> No or Yes.
No or Yes. <<< No.
Problems with NPIs in Questions: Fauconnier
G. Fauconnier 1975, “Polarity and the scale principle”, CLS:
NPIs are associated with ordered alternatives (“scales”)
and denote the minimal elements of the scales.
lift a finger: associated with [sets of] acts of labor,
ordered by amount of labor involved,
denotes the [set of] minimal acts of labor.
a drop:
associated with amounts of liquid,
ordered by size <
denotes the minimal amount of liquid.
Implicational relationship
in upward-entailing contexts:
Mary drank x,
y<x
==> Mary drank y.
Implicational relationship
in downward-entailing contexts:
Mary did not drink x,
x<y
==> Mary did not drink y.
Quantificational interpretation
No use of alternatives
in upward-entailing contexts: with NPI in downward-ent. context:
Mary did not drink a drop,
Mary drank a drop.
==> Mary drank nothing.
Not good,
presumably because alternatives are not used.
2 liters
x
x
1 liter
a drop
Problems with NPIs in Questions: Fauconnier
Semantic account for questions with polarity items:
G. Fauconnier 1980, “Pragmatic entailment and questions”,
in Searle / Kiefer / Bierwisch (eds.), Speech Act Theory and Pragmatics.
Treatment of questions embedded by verbs like wonder:
I wonder if Mary has ever lifted a finger to help John.
Notice: Not with “extensional” question-embedding verbs:
*I know if Mary has ever lifted a finger to help John.
Initial observation: wonder does not create downward-entailing contexts:
Harry lives in California
==> Harry gets plenty of sunshine.
But:
I wonder if Harry gets plenty of sunshine
=/=> I wonder if Harry lives in California.
So, why do such sentences support NPIs after all?
Problems with NPIs in Questions: Fauconnier
Ordered propositions in a linguistic context, asymmetric entailment:
… P7 => P6 => P5 => P4 => P3 => P2 => P1 ...
–– P9
–– P8
Logical entailment of propositions is upward-entailing:
P5 => P4, P3, P2, P1, P0, P-1, ...
Logical entailment of believes (K) is also upward-entailing,
under assumption that believes are closed under logical entailment.
KP5 => KP4, KP3, KP2, KP1, KP0, KP-1, ...
Relation between wonder and believe: WP => KP KP
–– P7
P6
KP––
6
P
WPKP
5––
5P
5KP5 5
–– P4
Cut-off-point P:
[WP  KP]  P’[[P’=>P]  KP’]  P”[[P=>P”]  WP”  KP”]
Consider only the part where WP  KP
WP is downward-entailing in this part: WP  [P’ => P]  WP’
Explains NPIs: I wonder if Mary even drank a drop (of alcohol).
Speaker does not know, for any amount x, whether Mary drank x.
General rule: No evidence for P is evidence against P,
hence: Speaker knows that Mary did not drink any amount x.
–– P3
WP–– P2
2
–– P1
–– P0
–– P-1
Problems with NPIs in Questions: Fauconnier
Main Problem of Fauconnier’s account:
Explains the rhetorical use of questions with NPIs:
I wonder if Mary even drank a drop of alcohol.
‘I don’t know, for any amount x of alcohol, if Mary drank x’
No evidence for is evidence against:
‘I know that Mary didn’t drink any amount x of alcohol.’
Does not explain the information-seeking use of questions with NPIs:
I wonder if Mary has ever been to China.
NOT: ‘I know that Mary has never been to China.’
A Semantic Account for NPIs in Questions: Krifka 95
Krifka 1995, “The semantics and pragmatics of polarity items”
Following Fauconnier:
NPIs introduce ordered alternatives and denote the minimal alternative.
Alternatives don’t have to be ordered linearly.
Different types of alternative sets and polarity items:
a drop: associated with sets of liquid entities of the same size,
ordered by size <: L < L’ iff for all x, y: If L(x)  L’(y), then x is smaller than y.
denotes the set of minimal liquid entities.
ever:
denotes the set of all times T,
associated with all subsets of T: {T’ | T’  T},
ordered by subset relation .
A Semantic Account for NPIs in Questions: Krifka 95
Explanation of distribution of polarity items in assertions:
If an assertion […  …] is made,
where  comes with an alternative set A,
then the speaker must have reasons to assert […  …] and not [… ’ …],
for any ’  A.
Scalar implicature with alternatives that are related by implication:
If [… ’ …] ==> […  …], i.e. [… ’ …] is stronger,
the typical reason is that speaker lacks evidence for [… ’ …].
If […  …] ==> [… ’ …], i.e. [… ’ …] is weaker,
the typical reason is that [… ’ …] would be less informative.
If John has eaten exactly three eggs for breakfast,
and the speaker knows that:
John has eaten four eggs avoided because there is no evidence (it is, in fact, false),
John has eaten two eggs avoided because it is less informative than
John has eaten three eggs, which is optimal.
A Semantic Account for NPIs in Questions: Krifka 95
Distribution of NPIs in assertions:
If […  …] is an assertion with  an NPI in a downward-entailing context,
this will be the strongest assertion,
this situation is o.k.:
speaker indicates that he wanted to make a strong assertion.
Mary hasn’t ever been to China is stronger than, e.g.,
Mary hasn’t been to China last year.
If […  …] is an assertion with  an NPI in an upward-entailing context,
this will be the weakest assertion,
this situation is not o.k.:
Unclear, why the alternatives have been introduced in the first place.
*Mary has ever been to China.
Why introduce alternatives?
Why not just say, e.g., Mary has been to China?
A Semantic Account for NPIs in Questions: Krifka 95
Explanation of distribution of polarity items in questions, in a similar manner:
If a question Q[…  …] is asked,
where  comes with an alternative set A,
then the speaker must have reasons to ask Q[…  …] and not Q[… ’ …],
for any ’  A.
Example:
What did John give to MARYF as a birthday present?
Alternative questions:
What did John give to Sue as a birthday present?
What did John give to Bill as a birthday present? etc.
these alternative questions are not asked because their answer might be known
or be otherwise irrelevant at the current point of discourse.
The alternatives may be introduced by regular focus [fall]
or by contrastive topic [fall-rise].
A Semantic Account for NPIs in Questions: Krifka 95
Rhetorical Questions:
Have you lifted a finger to help me?
Meaning: Have you performed a minimal act of labor to help me?
Alternatives: Have you performed X to help me?
where X ranges over types of acts of labor.
Notice: You have performed X to help me. ==>
You have performed a minimal act of labor to help me.
Pragmatic setting of rhetorical question:
Speaker is so certain that the answer will be negative
that he increases the a-priori possibility for a positive answer
as much as possible.
By this, speaker shows how certain he is of a negative answer.
[General background: Handicap principle, Zahawi & Zahawi 1998:
Serious signals should involve risks (a handicap).]
A Semantic Account for NPIs in Questions: Krifka 95
Information-seeking question:
Have you ever smoked marihuana?
Meaning: Is there a time t  T such that you smoked marihuana at t?
Alternatives: Is there a time t  T’ such that you smoked marihuana at t?
where T’ ranges over (relevant) subsets of T.
Reason for speaker to ask the more general question:
Indicate the current informational need,
optimize the potential benefit of the question.
Benefit is greatest if every answer to the question yields the same amount of information.
Example:
S1 draws a card from a deck of cards,
S2 has to find out with yes/no questions which card it is,
using as few questions as possible.
An uneconomical question: Is it the seven of diamonds?
• A yes would be highly informative,
• but a no would be much more likely, and be highly uninformative.
A more economical question: Is it a diamonds?
A most economical question: Is it a diamonds or a heart?
The two possible answers are equally likely and yield the same amount of information.
A Semantic Account for NPIs in Questions: Krifka 95
Implementation of yes/no-questions based on a proposition p with alternative set A,
in a model of context-change semantics,
where c: the information state, the common ground.
c + Q(p,A) = {c + p, c + p}
(intention: Adressee should identify one element of the set,
this element becomes the new common ground.)
where for all p’  A: Speaker has reasons not to ask c + Q(p’,A).
A typical reason:
The probabilties of c+p and c+ p are more similar
than the probabilities of c+p’ and c+ p’.
Example:
Have you ever smoked marihuana?
The current information state is such that
the probabilities of
(a) there is a time t  T such that you smoked marihuana at t and
(b) there is no time t  T such that you smoked marihuana at t
are more similar to each other than the probabilites of
(c) there is a time t  T’ such that you smoked marihuana at t and
(d) there is no time t  T’ such that you smoked marihuana at t, with T’  T.
Hence: NPIs in question reduce bias of questions.
NPIs in Questions: van Rooy 2002
Robert van Rooy 2002, “Negative Polarity Items in questions: Strength as relevance”
makes these ideas precise within a general framework for scalar implicatures
that replaces logical entailment by the more general notion of increased likelihood.
Probability of propositions: P()  [0 ... 1]
Probability and information value:
The greater the probability of a proposition,
the greater its information value.
Measures of information,
cf. Carnap & Bar-Hillel (1952), ‘An outline of a theory of semantic information’
1. The content,
cont() = P() = 1 – P(),
i.e. the content of  is the inverse of the probability of .
Problem, among others:
P() = 1, i.e. contradictions are maximally informative.
2. The information,
inf() = – log2(P()),
i.e. the information of  is the negative logarithm with base 2 of the probability of .
Inf(A)
if P()  0
then inf()  
The smaller the probability,
the greater the information.
If P() = 1/4,
then inf() = 2
=2-log
yinf(A)
= -log
x 2 P(A)
If P() = 1/2,
then inf() = 1
If P() = 1,
then inf() = 0
P()
If ,  are independent of each other, then: inf() = inf() + inf(),
Example: P() = P() = 1/2, inf() = inf() = 1, P(  ) = 1/4, inf(  ) = 2
NPIs in Questions: van Rooy 2002
Informativity of a question:
If the meaning of a question is the set of possible answers (Hamblin),
then the informativity of a question should be a function
of the informativity of the possible answers
and the probability that these answers are given.
This is the Entropy measure E:
E(Q) =

P(q) * inf(q)
qQ
The informativity of a question Q
is the sum of all the probability times the information
of all possible answers to Q.
A potential answer contributes more to the informativity of a question
-- if it is more probable, and
-- if it is more informative.
E(Q)
NPIs in Questions: van
Rooy 2002
E(Q) =

P(q) * inf(q)
qQ
Example:
Let Q = {q, q},
which is typical for yes/no-questions.
We have: P(q) = 1 – P(q).
p(q)
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
p(–q)
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
inf(q)
3,322
2,322
1,737
1,322
1
0,737
0,515
0,322
0,152
0
inf(-q)
0,152
0,322
0,515
0,737
1
1,322
1,737
2,322
3,322
#NUM!
p(q)*inf(q)
0,332
0,464
0,521
0,529
0,5
0,442
0,361
0,258
0,137
0
P(q)
p(–q)*inf(–q)
0,137
0,258
0,361
0,442
0,5
0,529
0,521
0,464
0,332
#NUM!
p(q)*inf(q) + p(–q)*inf(–q)
0,469
0,722
Maximal
0,882
entropy:
0,971
p(q)=p(q)
1
= 0,5
0,971
0,882
0,722
No value
0,469
if p(q)=0
#NUM!
or p(q)=0
NPIs in Questions: van Rooy
Basic idea of the function of NPIs in questions:
The presence of an NPI indicates
that the question with the NPI meaning
has a greater equilibrium between the potential answers,
is less biased,
then any alternative induced by the NPI.
Prediction: With biased questions we shouldn’t find NPIs.
Evidence:
Questions without Subject/Aux-Inversion are biased questions.
Do you have a car? vs. You have a car?
(cf. C. Gunlogson 2001,
True to form: Rising and falling declaratives as questions in English).
NPIs are restricted in questions with declarative syntax:
??You have ever been to China?
*You have ever been to China, haven’t you?
NPIs in Questions: van Rooy
Van Rooy distinguishes:
-- information-seeking questions with NPIs
(explanation: optimizing questions by de-biasing)
-- rhetorical questions,
for which he proposes a theory along the lines
of N. Kadmon & F. Landman 1993, “Any”.
Basic assumption: any widens the domain of a noun.
A: I don’t have potatoes.
B: Do you perhaps have just a few that I could fry in my room?
A: I’m sorry, I don’t have ANY potatoes.
NPIs in rhetorical questions:
Did she ever lift a finger to help you?
Indicates:
-- The question Did she perform an action x to help you?
is already settled for the standard values of x,
i.e. the alternatives of x.
-- The domain is now broadened so to include even minimal acts
of labor.
NPIs in Questions: Rhetorical Questions
Do we need a special treatment for rhetorical questions?
No!
Assume that the information state assigns to the proposition
she performed an action x to help you
very small probabilities, for all substantial acts of labor x.
We then have:
E({she performed an action x to help you,
she performed an action x to help you})  0,
that is, the entropy is very small, for substantial acts of labor x.
To increase the entropy of the question,
the speaker asks the extreme question:
{she performed a minimal action x to help you,
she performed a minimal action x to help you}
The entropy of even this question might be small,
but it is still better than with all of the alternatives.
Cf. the previous argumentation that the speaker makes it as easy for the hearer
to give a positive answer as possible.