Polarity Items in Questions

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Polarity Itemsin Questions

• Manfred KrifkaHumboldt Universität zu Berlin
• Zentrum für Allgemeine Sprachwissenschaft, Berlin
• Korean Society of Language and Information
  ConferenceInha UniversityIncheon, KoreaJune
  28, 2003

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Negative 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?
• gt Rhetorical questions, expected answer No. /
  Noone.
• Have you ever been to China?
• Which student has ever been to China?
• gt Information-seeking questions.

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Syntactic Accounts of NPIs in Questions

• Syntactic account of NPIsE. Klima 1964,
  Negation in English, C. L. Baker 1970, Double
  negativesM. 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 didnt 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 dont 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!

4
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.gt John expected that Mary did
  not say anything.
• This can explain why we find NPIs in rhetorical
  questionsThey expect a negative answer, which
  may be an entailment.
• Did Mary ever lift a finger to help you?gt I
  believe that Mary did not ever lift a finger to
  help you.
• Who ever lifted a finger to help you?gt 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?/gt I believe that
  you have not ever been to China.
• Which student has ever been to China?/gt I
  believe that no student has ever been to China.

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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 hasnt been to China last year
• last month ? last year
• gt Mary hasnt been to China last month.
• hence Mary hasnt 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.
• ProblemNo treatment of NPIs in
  information-seeking questions.

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Problems with NPIs in Questions Fauconnier

• G. Fauconnier 1975, Polarity and the scale
  principleNPIs are associated with ordered
  alternatives (scales) and denote the minimal
  elements of the scales.
• a drop associated with amounts of liquid,
  ordered by size lt denotes the minimal amount
  of liquid.
• Negated proposition concerning a minimal element
  of a scalewill negate proposition concerning
  non-minimal elements
• John didnt drink a drop of alcohol gt John
  didnt drink a quantity x of alcohol(for any
  quantities of alcohol x).
• NPIs in questionsFauconnier 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.
• ProblemAgain, this only explains NPIs in
  rhetorical questions.

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A Semantic / Pragmatic Account for NPIs in
Questions

• Elaboration onKrifka 1995, The semantics and
  pragmatics of polarity items
• Following FauconnierNPIs introduce ordered
  alternativesand denote the minimal alternative.
• Alternatives dont 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 ?.

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Principles for dealing with alternatives in
assertions

• 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
  assertionsCoherence with explicit or implicit
  question, Who did John give the necklace?
• Reason not to assert these alternative
  assertionsSpeaker knows that they are false.

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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 gt John ate three eggs gt
  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 (Grices first submaxim of
  Quantity)-- For stronger assertions Speaker
  lacks evidence for their truth (Grices maxim
  of Quality)
• Implicature of Negating Stronger Alternatives
  (NSA) If a speaker introduces stronger claims
  as alternativesbut explicity doesnt 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,
  ...

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The MIA and NSA principles and Negative Polarity
Items

• NPIs in downward entailing contextsMary hasnt
  ever been to China.
• AlternativesMary hasnt been to China last
  year.Mary hasnt been to China the year before
  last year.Mary hasnt been to China in the last
  five years....
• Alternatives stand in logical relationship to (at
  least) the assertion made
• Mary hasnt been to China at any timegt Mary
  hasnt been to China last year Mary hasnt 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.

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The MIA and NSA principles and Negative Polarity
Items

• NPIs in upward entailing contextsMary has ever
  been to China.
• AlternativesMary 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 madeMary has been to China
  last yearMary has been to China the year before
  last year, gt 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 madeAssertion 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, ...

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The MIA principle in Questions

• We 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.

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NPIs in Rhetorical Questions

• Did 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 didnt
  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.

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NPIs in Rhetorical Questions

• According to this theory, the speaker asks a
  risky questionSpeaker wants to claim John
  didnt 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

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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 dont 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.

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NPIs in Information-Seeking Questions

• More systematically (cf. Krifka 1995)the
  speaker doesnt ask the more specific
  questionsbecause they dont satisfy the current
  informational needas well as the question that
  is actually askedSpeaker optimizes the
  potential utility of the question.
• One way of optimizing question utilityUtility
  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.)

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NPIs in Information-Seeking Questions van Rooys
Implementation

• 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 valueThe 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 informationThe 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.

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Inf(q)
If P(q) 1/4, then inf(q) 2
if P(q) ? 0then inf(q) ? ?
y -log2 x
inf(A) -log2 P(A)
If P(q) 1/2,then inf(q) 1
The smaller the probability, the greater the
information.
If P(q) 1,then inf(q) 0
If p, q are independent of each other, then
inf(p?q) 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
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NPIs in Information-Seeking Questions van Rooys
Implementation

• 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 Stohkhofs
  theory).
• The equilibrium of the question increasesif the
  average utility of the potential answers
  increases.
• For particular potential answers, this meansIf
  the answer is unlikely, then at least its
  information should be high.
• One possible way of implementing equilibrium of a
  questionis by (Shannons) EntropyE(Q) ?
  P(q) inf(q) q ? QThe
  entropy/equilibrium of a question Qis the sum of
  the probability times the informationof all
  possible answers to Q.

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NPIs in Information-Seeking Questions van Rooys
Implementation

• Equilibrium / Entropie of QuestionE(Q) ?
  P(q) inf(q) q ? Q
• Example Q q, ?q (typical for
  yes/no-questions)
• We have P(?q) 1 P(q).

Maximal entropyP(q) P(?q) 0,5
entropy ? 0if P(q) ? 1 or P(q) ? 0
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NPIs in Information-Seeking Questions van Rooys
Implementation

• 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.

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NPIs in Information-Seeking Questions Examples

• ExampleDid 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

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NPIs in Information-Seeking Questions Examples

• ExampleDid 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

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.
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NPIs in Information-Seeking Questions Examples

• ExampleDid 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

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. 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 more balanced, and Did Bill ever smoke
marihuana? is infelicitous.
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NPIs in Information-Seeking Questions Examples

• ExampleDid 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 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 didnt
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. 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 equally balanced, and Did Bill ever
smoke marihuana? is mildly infelicitous,as it
doesnt increase equilibrium.
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NPIs in Information-Seeking Questions Examples

• 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

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NPIs in Information-Seeking Questions Examples

• 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?) 0,4549 P(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?)
0,0114 P(you had the common cold last year)
0,5, hence E(Did you have the common
cold last year?) 1 preferred!
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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,especiall
  y in the presence of question tags. ??You ever
  had the common cold? You ever had the common
  cold, didnt you?
• Negatively biased questions do allow for NPIsCf.
  questions in German with particle dennHaben Sie
  denn jemals Tuberkulose gehabt?Did you DENN
  ever have tuberculosis?

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NPIs used to accommodate equilibrium assumptions

• We assumeAssumptions about probablities of
  potential answersis crucial for the
  understanding of questions.
• ButContext and background knowledgeoften does
  not determine probablities of potential answers.
• HenceThe 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).
• ExampleA 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.

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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

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NPIs in Constituent Questions

• Assume A-priori-likelihood of a student being in
  China in a given year 0,01
• For any given year xP(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 yearsP(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

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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 dont have potatoes.B Do you perhaps have
  just a few that I could fry in my room?A Im
  sorry, I dont 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.

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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 haveE(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 questionMary 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.

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Polarity Items in Questions

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