Negative Polarity Items in Questions

1. Negative Polarity Itemsin Questions Manfred KrifkaHumboldt Universität zu Berlin & Zentrum für Allgemeine Sprachwissenschaft, Berlin

2. 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.

3. 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 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 Qas 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!

4. 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 everlift a finger to help you?==> I believe that Mary did not [ever lift a finger to help you]. • Who everlifted 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].

5. Problems with NPIs in Questions: Semantic Accounts • Semantic Accounts of NPIsB. 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 yearEvery 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.

6. 2 liters x 1 liter x a drop 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 interpretationwith NPI in downward-ent. context:Mary did not drink a drop, ==> Mary drank nothing. No use of alternatives in upward-entailing contexts:Mary drank a drop. Not good, presumably because alternatives are not used.

7. 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?

8. –– P9 –– P8 –– P7 –– P6 –– P5 –– P4 –– P3 –– P2 –– P1 –– P0 –– P-1 KP5 P5 WP2 KP6 Problems with NPIs in Questions: Fauconnier Ordered propositions in a linguistic context, asymmetric entailment:… P7=> P6=> P5=> P4=> P3=> P2=> P1 ... 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, ... WP5 KP5 Relation between wonder and believe: WP => KP KP 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.

9. 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.’

10. 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 .

11. 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.

12. 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?

13. 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 knownor be otherwise irrelevant at the current point of discourse. • The alternatives may be introduced by regular focus [fall] or by contrastive topic [fall-rise].

14. 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 negativethat he increases the a-priori possibility for a positive answeras 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).]

15. 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.

16. 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 similarthan 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 tare 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.

17. 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 implicaturesthat 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 .

18. P() Inf(A) If P() = 1/4, then inf() = 2 if P()  0then inf()   inf(A) = -log2 P(A) y = -log2 x If P() = 1/2,then inf() = 1 The smaller the probability, the greater the information. If P() = 1,then inf() = 0 If ,  are independent of each other, then: inf() = inf() + inf(), Example: P() = P() = 1/2, inf() = inf() = 1, P(  ) = 1/4, inf(  ) = 2

19. 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 answersand 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 Qis the sum of all the probability times the informationof 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.

20. E(Q) P(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). Maximal entropy:p(q)=p(q) = 0,5 No valueif p(q)=0or p(q)=0

21. NPIs in Questions: van Rooy • Basic idea of the function of NPIs in questions: • The presence of an NPI indicatesthat 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?

22. 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.

23. NPIs in Questions: Rhetorical Questions • Do we need a special treatment for rhetorical questions? • No! • Assume that the information state assigns to the propositionshe performed an action x to help youvery 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 hearerto give a positive answer as possible.