Polarity Items in Questions Manfred Krifka Humboldt Universität zu Berlin Zentrum für Allgemeine...

Polarity Itemsin Questions

Manfred KrifkaHumboldt Universität zu Berlin

Zentrum für Allgemeine Sprachwissenschaft, Berlin

Korean Society of Language and Information ConferenceInha UniversityIncheon, KoreaJune 28, 2003

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.

Negative Polarity Items in Questions

Syntactic Accounts of NPIs in QuestionsSyntactic account of NPIs:

E. Klima 1964, “Negation in English”, C. L. Baker 1970, “Double negatives”M. C. Linebarger 1980, The grammar of negative polarityL. 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 Qwhich is just 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.

This 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!

Derivative Licensing of NPIs in Questions

NPIs might also be licensed by way of entailments (C. L. Baker 1970).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 NPIsB. Ladusaw 1979, Polarity sensitivity 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 yearEvery student who has been to China last month enjoyed it.hence: Every student who has ever been to China enjoyed it.

NPIs in questions?Ladusaw assumes derivative licensing in rhetorical questionsthat entail a negated answer.

Problem:No treatment of NPIs in information-seeking questions.

Problems with NPIs in Questions: FauconnierG. Fauconnier 1975, “Polarity and the scale principle”:

NPIs are associated with ordered alternatives (“scales”) and denote the minimal elements of the scales.

a drop: associated with amounts of liquid, ordered by size < denotes the minimal amount of liquid.

Negated proposition concerning a minimal element of a scalewill negate proposition concerning non-minimal elements:

John didn’t drink a drop of alcohol ==> John didn’t drink a quantity x of alcohol(for any quantities of alcohol x).

NPIs in questions:Fauconnier 1980, Pragmatic entailment and question.Did John drink a drop of alcohol?‘Speaker wonders, whether John drank a drop of alcohol.’

Roughly: If Speaker has disbelief whether John drank a minimal quantity, he also has disbelief whether John drank more substantial quantities.

Problem:Again, this only explains NPIs in rhetorical questions.

A Semantic / Pragmatic Account for NPIs in Questions

Elaboration on:Krifka 1995, “The semantics and pragmatics of polarity items”

Following Fauconnier:NPIs introduce ordered alternativesand denote the minimal alternative.

Alternatives don’t have to be ordered linearly.

Different types of alternative sets and polarity items:

a drop: (cf. Fauconnier)- denotes the set of minimal liquid entities,

- is associated with the set of quantities of liquid (sets of liquid of the same size), - this set is ordered by size of quantities.

ever: - denotes the set of all (relevant) times T,- is associated with subsets of T: {T’ | T’ T}, ordered by subset relation .

The Principle of Motivated Introduction of Alternatives (MIA):If an assertion [… …] is made,

where comes with an alternative set A,and hence [… …] comes with alternative assertions [… ’ …], with ’ A(cf. alternative semantics: Hamblin 1973, Rooth 1985)

then the speaker must have reasons-- to introduce the alternative assertions [… ’ …]-- not to assert any alternative assertion [… ’ …].

Example: Focus, John gave MARY the necklace.

Alternatives:John gave Sue the necklace, John gave Jill the necklace...

Reason of introducing these alternative assertions:Coherence with explicit or implicit question, Who did John give the necklace?

Reason not to assert these alternative assertions:Speaker knows that they are false.

Principles for dealing with alternatives in assertions

Example: Scalar Implicature

John ate three eggs.

Alternatives (as number words form a Horn scale):... John ate two eggs, John ate three eggs, John ate four eggs, ...

Alternatives stand in logical relationship to each other:

John ate four eggs ==> John ate three eggs ==> John ate two eggs

Why are alternative assertions introduced?Speaker indicates he is aware of being able to make stronger or weaker claims.

Why are alternative assertions not made?-- For weaker assertions: They are not the strongest defendable claims (Grice’s first submaxim of Quantity)-- For stronger assertions: Speaker lacks evidence for their truth (Grice’s maxim of Quality)

Implicature of Negating Stronger Alternatives (NSA): If a speaker introduces stronger claims as alternativesbut explicity doesn’t assert them,it can be assumed that he considers them to be false.

NSA implicature in our example: John ate four eggs, John ate five eggs, John ate six eggs, ...

Principles for dealing with alternatives in assertions

The MIA and NSA principles and Negative Polarity Items

NPIs in downward entailing contexts:Mary hasn’t ever been to China.

Alternatives:Mary hasn’t been to China last year.Mary hasn’t been to China the year before last year.Mary hasn’t been to China in the last five years....

Alternatives stand in logical relationship to (at least) the assertion made:

Mary hasn’t been to China at any time==> Mary hasn’t been to China last year

Mary hasn’t been to China the year before last year, ...

Why are alternative assertions introduced?Speaker indicates being aware of being able to make stronger or weaker claims.

Why are alternatives not asserted?As they are all weaker: They are not the strongest defendable claims.

No NSA implicature, as there are no stronger alternative assertions.

NPIs in upward entailing contexts:*Mary has ever been to China.

Alternatives:Mary has been to China last year.Mary has been to China the year before last year.Mary has been to China in the last five years....

Alternatives stand in logical relationship to (at least) the assertion made:Mary has been to China last yearMary has been to China the year before last year, ==> Mary has been to China some time.

Why are alternative assertions introduced?Speaker indicates being aware of being able to make stronger or weaker claims.

Why are alternatives not asserted?As they are all stronger: Standardly, because speaker considers them false.

NSA implicature systematically contradicts the assertion made:Assertion made: Mary has been to China some time.NSA implicature: Mary has been to China last year,

Mary has been to China the year before last year, ...

The MIA and NSA principles and Negative Polarity Items

The MIA principle in QuestionsWe apply the same general interpretation principle as with assertions:

If an question Q[… …] is asked, where comes with an alternative set A,and hence Q[… …] comes with alternative questions Q[… ’ …], with ’ A

then the speaker must have reasons

-- to introduce the alternative questions Q[… ’ …]-- not to ask any alternative assertion Q[… ’ …].

Example: Focus in questions.

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.

Why are these alternative questions introduced?Speaker indicates he is aware that these questions are also potentially relevant, e.g. as questions under discussion (Roberts 1995, Büring 1998).

Why are these alternatives not asked?The speaker might know the answer already, or might indicate that he considers this question more important.

NPIs in Rhetorical QuestionsDid John drink a drop of liquor?

Meaning: Did John drink a minimal quantity of liquor?

Alternatives: ...Did John drink a glass of liquor?,Did John drink 2 grams of liquor?...

Why are the alternative questions introduced?Speaker indicates being aware of being able to ask more or less inquisitive questions.

Why are the alternatives not asked?

Possible answers:

-- Borkin 1971: Because their answers are already known (and negative).

The question presupposes that John didn’t drink any substantial quantity of liquorand just asks whether he drank a minimal amount.

-- Because the speaker is so sure that the answer is negativethat he asks a question that has very low a-priori chances to be answered positively.

NPIs in Rhetorical Questions

According to this theory, the speaker asks a risky question:Speaker wants to claim: ‘John didn’t drink any liquor’, and makes it as easy as possible to the hearer to say: ‘John drank some liquor.’

The Handicap Principle Zahawi & Zahawi (1997): The handicap principle. Oxford University Press.

Examples of handicap principle in animal communication:

• Gazelles jumping up and down in sight of predatorsto prove that they are strong enough to outrun them

• Male dominance features like antlers, showy feathers.

Examples in non-linguistic human communication:

• Conspicuous consumption

Examples in linguistic communication:

• Rhetorical questions

• Elaborate text and speech genres

• Politeness phenomena

NPIs in Information-Seeking Questions

Has Bill ever smoked marihuana?

Meaning: Is there a time t T such that Bill smoked marihuana at t?i.e. Is there a time at which Bill smoked marihuana?

Alternatives: Is there a time t T’ such that Bill smoked marihuana at t?where T’ ranges over (relevant) subsets of T, i.e. Has Bill smoked marihuana last year?

Has Bill smoked marihuana the year before last year?...

Why are the alternative questions introduced?Speaker indicates he is aware of being ableto ask more specific questions.

Why are the alternative questions not asked?Because they don’t fit the informational needs of the speakeras well as the question that is asked.

By this, speaker indicates that he does not know, for any time t, whether Bill smoked marihuana at t.

NPIs in Information-Seeking Questions

More systematically (cf. Krifka 1995):the speaker doesn’t ask the more specific questionsbecause they don’t satisfy the current informational needas well as the question that is actually asked:Speaker optimizes the potential utility of the question.

One way of optimizing question utility:Utility is greatest if every possible answer to the question yields a similar amount of information

(We call this equilibrium of the question).

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.)

Robert van Rooy 2002, “Negative Polarity Items in questions: Strength as relevance”

makes these ideas precise within a general framework for scalar implicaturesthat replaces logical entailment by the more general notion of increased likelihood.

Probability of propositions: P(q) [0 ... 1]

Probability and information value:The greater the probability of a proposition,the lower its information value.

A convenient measure of information,cf. Carnap & Bar-Hillel (1952), ‘An outline of a theory of semantic information’

The information of a proposition q`;

inf(q) = – log2(P(q)),

i.e. the information of q is the negative logarithm with base 2 of the probability of q.

NPIs in Information-Seeking Questions: van Rooy’s Implementation

Inf(q)

y = -log2 x

If P(q) = 1,then inf(q) = 0

If P(q) = 1/2,then inf(q) = 1

If P(q) = 1/4, then inf(q) = 2if P(q) 0

then inf(q)

P(q)

inf(A) = -log2 P(A)

The smaller the probability,

the greater the information.

If p, q are independent of each other, then: inf(pq) = inf(p) + inf(q),

Example: P(p) = P(q) = 1/2, inf(p) = inf(q) = 1, P(p q) = 1/4, inf(p q) = 2

Equilibrium of a question:

Assume that a question meaning is a set of mutually exclusive propositionsthat cover all possible states of affairs(the potential answers of the question; cf. Groenendijk & Stohkhof’s theory).

The equilibrium of the question increasesif the “average utility” of the potential answers increases.

For particular potential answers, this means:If the answer is unlikely, then at least its information should be high.

One possible way of implementing equilibrium of a questionis by (Shannon’s) Entropy:

E(Q) = P(q) * inf(q)

q Q

The entropy/equilibrium of a question Qis the sum of the probability times the informationof all possible answers to Q.


Equilibrium / Entropie of Question:

E(Q) = P(q) * inf(q)

q Q

Example: Q = {q, q} (typical for yes/no-questions)We have: P(q) = 1 – P(q).


P(q)

E(Q)

P(q)

0,10,20,30,40,50,60,70,80,91

P(–q)

0,90,80,70,60,50,40,30,20,10

inf(q)

3,3222,3221,7371,322

10,7370,5150,3220,152

0

inf(-q)

0,1520,3220,5150,737

11,3221,7372,3223,322#NUM!

P(q)*inf(q)

0,3320,4640,5210,529

0,50,4420,3610,2580,137

0

P(–q)*inf(–q)

0,1370,2580,3610,442

0,50,5290,5210,4640,332#NUM!

E({q,-q}) =

P(q)*inf(q)+P(–q)*inf(–q)

0,4690,7220,8820,971

10,9710,8820,7220,469#NUM!

Maximal entropy:

P(q) = P(q) = 0,5

entropy 0if P(q) 1 or P(q) 0

Basic idea of the function of NPIs in questions:

The presence of an NPI indicatesthat the question with the NPI meaningis less biased,is more balanced, has a greater equilibrium between the potential answers, than any alternative induced by the NPI.


Example:Did Bill ever smoke marihuana?Did Bill smoke marihuana last year?

Assume for the sake of illustration:

-- We restrict our attention to the last ten years.

-- A-priori-likelihood that you smoked marihuana in any given year: 0,1 it follows: a-priori likelihood for the last 10 years: 0,65

NPIs in Information-Seeking Questions: Examples

CumulativeYear Probability

1 0,1002 0,1903 0,2714 0,3445 0,4106 0,4697 0,5228 0,5709 0,613

10 0,651

0,00,10,20,30,40,50,60,70,80,91,0

1 2 3 4 5 6 7 8 9 10

Years

Cumulative Probability






Scenario 1: No additional assumption.

Then P(Bill “ever” (= in the last 10 years) smoked marihuana) = 0,65,hence E(Did Bill ever smoke marihuana?) = 0,93.

And P(Bill smoked marihuana last year) = 0,1,hence E(Did Bill smoke marihuana last year?) = 0,496.

Hence: Did Bill smoke marihuana last year? is less balanced, and Did Bill ever smoke marihuana? is felicitous.





Scenario 2: P(Bill smoked marihuana before last year) = 1,i.e. it is known that Bill smoked Marihuana before last year.

Then P(Bill “ever” (= in the last 10 years) smoked marihuana) = 1,hence E(Did Bill ever smoke marihuana?) = 0.


Hence: Did Bill smoke marihuana last year? is more balanced, and Did Bill ever smoke marihuana? is infelicitous.





-- A-priori-likelihood that you smoked marihuana in a given year: 0,1 it follows: a-priori likelihood for the last 10 years: 0,65

Scenario 3: P(Bill smoked marihuana before last year) = 0,i.e. it is known that Bill didn’t smoke marihuana before last year.

Then P(Bill “ever” (= in the last 10 years) smoked marihuana) = 0,1,hence E(Did Bill ever smoke marihuana?) = 0,496.


Hence: Did Bill smoke marihuana last year? is equally balanced, and Did Bill ever smoke marihuana? is mildly infelicitous,as it doesn’t increase equilibrium.


Prediction: Usage of NPIs in information-seeking questionsdepends on a-priori likelihood.

(a) Did you ever have tuberculosis?

(b) #Did you ever have the common cold?

Assume: a-priori probability of getting tuberculosis in a year is 0,01,a-priori probability of getting the common cold in a year is 0,5


0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1 2 3 4 5 6 7 8 9 10

Years

Cumulative probability tuberculosis

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1 2 3 4 5 6 7 8 9 10

Years

Cumulative probability common cold

Prediction: Usage of NPIs in information-seeking questionsdepends on a-priori likelihood.

(a) Did you ever have tuberculosis?

(b) #Did you ever have the common cold?

Assume: a-priori probability of getting tuberculosis in a year is 0,01,a-priori probability of getting the common cold in a year is 0,5,you are 10 years old.


P(you “ever” (in the last 10 years) had tuberculosis) = 0,0956, hence E(Did you ever have tuberculosis?) = 0,4549P(you had tuberculosis last year) = 0,01, hence E(Did you have tuberculosis last year?) = 0,0808: dispreferred!

P(you “ever” (in the last 10 years) had the common cold) = 0,9990, hence E(Did you ever have the common cold?) = 0,0114P(you had the common cold last year) = 0,5, hence E(Did you have the common cold last year?) = 1: preferred!

NPIs in Biased Questions

• Positively biased questions do not allow for NPIs.Cf. “declarative” questions without Subj/Aux inversion, Did you have the common cold? (unbiased) You had the common cold? (biased towards positive answer)(Gunlogson 2001, True to form: Rising and falling declaratives as questions in English).

Observation: No NPIs in such questions,especially in the presence of question tags.

??You ever had the common cold?*You ever had the common cold, didn’t you?

• Negatively biased questions do allow for NPIsCf. questions in German with particle denn:Haben Sie denn jemals Tuberkulose gehabt?‘Did you DENN ever have tuberculosis?”

NPIs used to accommodate equilibrium assumptions

We assume:Assumptions about probablities of potential answersis crucial for the understanding of questions.

But:Context and background knowledgeoften does not determine probablities of potential answers.

Hence:The speaker may suggest a range for probabilities of potential answersby using a NPI in the question(accomodation of a range for probabilities of potential answers).

Example:A doctor examins a person, who appears extremely healthy.Doctor: Did you ever have the common cold?

Use of the NPI ever suggests a relatively low likelihoodthat addressee had the common cold.

NPIs in Constituent Questions

Which student has ever been to China?

Assume: There are two students, John, Mary

To compute entropy, we have to work with partitions as question meanings:-- Theory of Groenendijk / Stokhof-- or intersection of Hamblin style meanings of questions

John wentto China

Mary wentto China

Hamblin style question meaning:

2 propositions

Only John wentto China

Only Mary wentto China

Nobody went to China

John and Marywent to China

Groenendjik/Stokhof style

question meaning:4 propositions

NPIs in Constituent Questions

Assume: A-priori-likelihood of a student being in China in a given year: 0,01

For any given year x:P(John and Mary have been to China in x) = 0,0001P(Only John has been to China in x) = 0,0099P(Only Mary has been to China in x) = 0,0099P(Neither John nor Mary have been to China in x) = 0,9801

For 10 years:P(John and Mary have been to China in the last 10 years) = 0,0091P(Only John has been to China in the last 10 years) = 0,0086P(Only Mary has been to China in the last 10 years) = 0,0086P(Neither John nor Mary have been to China in the last 10 years) = 0,8179

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

Years

P(J&M)

P(only J),P(only M)

P(-J & -M)

Rhetorical Questions, Once More

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 Kadmon & 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 Mary drink a drop of alcohol?

Indicates (cf. also Borkin 1971): -- The question Did Mary drink a quantity x of alcohol? 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 quantities of alcohol.

Rhetorical Questions, Once More

A slightly different view:

Assume that the information state assigns to the propositionMary drank a quantity x of alcoholvery small probabilities, for all substantial quantities of alcohol x.

We then have:E({Mary drank a quantity x of alcohol,

Mary drank a quantity x of alcohol}) 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:{Mary drank a minimal quantity x of alcohol, Mary drank a minimal quantity x of alcohol}

While the entropy of this question is still very small, it is greater than with all of the alternatives.

Cf. the previous argumentation that the speaker makes it as easy for the hearerto give a positive answer as possible.

Polarity Items in Questions

Slides can soon be downloaded at:

www.amor.hu-berlin.de/~h2816i3x

(“Talks”)

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