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Polarity Items in Questions Manfred Krifka Humboldt Universität zu Berlin Zentrum für Allgemeine Sprachwissenschaft, Berlin Korean Society of Language.

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Presentation on theme: "Polarity Items in Questions Manfred Krifka Humboldt Universität zu Berlin Zentrum für Allgemeine Sprachwissenschaft, Berlin Korean Society of Language."— Presentation transcript:

1 Polarity Items in Questions Manfred Krifka Humboldt Universität zu Berlin Zentrum für Allgemeine Sprachwissenschaft, Berlin Korean Society of Language and Information Conference Inha University Incheon, Korea June 28, 2003

2 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

3 Syntactic Accounts of NPIs in Questions 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 didnt [lift a finger to help you]. NPIs in questions can be explained by question morpheme Q which 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. ==> 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].

5 Problems with NPIs in Questions: Semantic Accounts Semantic Accounts of NPIs B. 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 ==> 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 year Every 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 questions that entail a negated answer. Problem: No treatment of NPIs in information-seeking questions.

6 Problems with NPIs in Questions: Fauconnier G. 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 scale will negate proposition concerning non-minimal elements: John didnt drink a drop of alcohol ==> John didnt 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.

7 A Semantic / Pragmatic Account for NPIs in Questions Elaboration on: Krifka 1995, The semantics and pragmatics of polarity items Following Fauconnier: NPIs introduce ordered alternatives and 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.

8 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

9 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 (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 alternatives but 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,... Principles for dealing with alternatives in assertions

10 The MIA and NSA principles and Negative Polarity Items NPIs in downward entailing contexts: Mary hasnt ever been to China. Alternatives: Mary 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 time ==> 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.

11 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 year Mary 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

12 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 MARY F 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.

13 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 liquor and just asks whether he drank a minimal amount. -- Because the speaker is so sure that the answer is negative that he asks a question that has very low a-priori chances to be answered positively.

14 NPIs in Rhetorical Questions According to this theory, the speaker asks a risky question: Speaker 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 predators to 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

15 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 able to ask more specific questions. Why are the alternative questions not asked? Because they dont fit the informational needs of the speaker as 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.

16 NPIs in Information-Seeking Questions More systematically (cf. Krifka 1995): the speaker doesnt ask the more specific questions because they dont satisfy the current informational need as 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.)

17 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(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) = – log 2 (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 Rooys Implementation

18 Inf(q) y = -log 2 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) = 2 if P(q) 0 then inf(q) P(q) inf(A) = -log 2 P(A) The smaller the probability, the greater the information. 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

19 Equilibrium of a question: Assume that a question meaning is a set of mutually exclusive propositions that cover all possible states of affairs (the potential answers of the question; cf. Groenendijk & Stohkhofs theory). The equilibrium of the question increases if 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 question is by (Shannons) Entropy: E(Q) = P(q) * inf(q) q Q The entropy/equilibrium of a question Q is the sum of the probability times the information of all possible answers to Q. NPIs in Information-Seeking Questions: van Rooys Implementation

20 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). NPIs in Information-Seeking Questions: van Rooys Implementation P(q) E(Q) Maximal entropy: P(q) = P( q) = 0,5 entropy 0 if P(q) 1 or P(q) 0

21 Basic idea of the function of NPIs in questions: The presence of an NPI indicates that the question with the NPI meaning is less biased, is more balanced, has a greater equilibrium between the potential answers, than any alternative induced by the NPI. NPIs in Information-Seeking Questions: van Rooys Implementation

22 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

23 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 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.

24 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 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. NPIs in Information-Seeking Questions: Examples

25 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 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. NPIs in Information-Seeking Questions: Examples

26 Prediction: Usage of NPIs in information-seeking questions depends 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 NPIs in Information-Seeking Questions: Examples Cumulative probability tuberculosisCumulative probability common cold

27 Prediction: Usage of NPIs in information-seeking questions depends 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. NPIs in Information-Seeking Questions: Examples 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!

28 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, didnt you? Negatively biased questions do allow for NPIs Cf. questions in German with particle denn: Haben Sie denn jemals Tuberkulose gehabt? Did you DENN ever have tuberculosis?

29 NPIs used to accommodate equilibrium assumptions We assume: Assumptions about probablities of potential answers is crucial for the understanding of questions. But: Context and background knowledge often does not determine probablities of potential answers. Hence: The speaker may suggest a range for probabilities of potential answers by 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 likelihood that addressee had the common cold.

30 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 went to China Mary went to China Hamblin style question meaning: 2 propositions Only John went to China Only Mary went to China Nobody went to China John and Mary went to China Groenendjik/Stokhof style question meaning: 4 propositions

31 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) = 0,0001 P(Only John has been to China in x) = 0,0099 P(Only Mary has been to China in x) = 0,0099 P(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) = 0,0091 P(Only John has been to China in the last 10 years) = 0,0086 P(Only Mary has been to China in the last 10 years) = 0,0086 P(Neither John nor Mary have been to China in the last 10 years) = 0,8179

32 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.

33 Rhetorical Questions, Once More A slightly different view: Assume that the information state assigns to the proposition Mary drank a quantity x of alcohol very 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 hearer to give a positive answer as possible.

34 Polarity Items in Questions Slides can soon be downloaded at: www.amor.hu-berlin.de/~h2816i3x (Talks)


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