1. Marking and interpretation of negation: a bi-directional OT approach Henriëtte de Swart French/UiL-OTS, Utrecht

2. Expressing negation Natural languages: ways to express negation/denial: not. First-order propositional connective  Natural languages: negative indefinites, nobody. First-order quantifier  x.

3. Negation and cognition Assumption: something like or something equivalent to first-order logic part of general human cognition. Prediction: negation and negative quantifiers behave alike across languages. Prediction falsified by data.

4. DN and NC Nobody said nothing. (Eng)  x  y Niemand zei niets. (Dutch)  x  y Nadie miraba a nadie. (Spa)  x  y Nessuno ha parlato con nessuno. (Ital)  x  y Personne n’a rien dit. (Fr)ambiguous

5. Negation in context Double negation versus negative concord negative quantifiers versus n-words. In isolation: same form, same meaning. In a sequence: same forms, different meanings.

6. What to do? Many theories about negation/negative quantifiers in language. Key: languages make use of the same underlying mechanisms, but exploit the relation between form and meaning in different ways.

7. Approach: OT OT syntax: choose the optimal form for a given meaning. OT semantics: choose the optimal interpretation for a given form. Bi-directional OT: evaluate pairs of form and meaning.

8. Propositional negation Production issue: how does a language express the meaning  p?  FaithNeg: reflect non-affirmativity of the input in the output. Faithfulness constraint ‘double-edged’ constraint: both in OT syntax, and in OT semantics.

9. Markedness of negation  *Neg: avoid negation in the output. Markedness constraint FaithNeg >> *Neg Assumption: ranking fixed across languages Negation is marked in form/meaning.

10. Propositional negation  meaningformFaithNeg*Neg pp S * not S *

11. Negative sentences John is not sick.[English] No vino Pedro.[Spanish] Not came Pedro. Non piove.[Italian] Not rains. ‘It doesn’t rain.’

12. Indefinites under negation Production: how do languages express the meaning  x 1  x 2  x 3 P(x 1, x 2, x 3 )? Three cases: o plain indefinites, o negative polarity items, o n-words.

13. indefinites Example: Dutch, Turkish,.. Ik heb niet onmiddellijk iets gekocht. I have not immediately something bought. Niemand heeft iets aan iemand gezegd. No one has something to someone said. Negation/negative quantifier

14. Negative polarity items Languages in which plain indefinites are positive polarity items may use negative polarity items. Example: English, Basque,.. *I did not buy something I did not buy anything. Nobody said anything to anyone.

15. N-words Languages in which plain indefinites are positive polarity items may use n-words. N-words denote  x in isolation, but express a single negative statement together with sentential negation or other n-words (  x 1  x 2  x 3 ).

16. Example: Spanish A: Qué viste?B: Nade A: What did you see? B: nothing. No vino nadie. Not came nobody. Nadie maraba a nadie Nobody looked at nobody.

17. NPIs and n-words N-words denote  x in isolation, NPIs denote  x. NPIs have to be licensed, n-words are ‘self-licensing’. Negative concord is limited to anti- additive contexts, NPIs occur in decreasing or non-veridical contexts.

18. N-words in OT N-words mark ‘negative’ variables (Corblin and Tovena 2003). Functional motivation: mark focus of negation (Haspelmath 1997). In OT terms: constraint MaxNeg  MaxNeg: Mark the argument of a negative chain.

19. Constraint interaction Relevant Rankings (OT syntax) FaithNeg >> *Neg >> MaxNeg [indefinites] FaithNeg >> MaxNeg >> *Neg [n-words]

20. Indefinites (production)  MeaningFormFNeg*NegMaxNeg  x 1  x 2 indef+indef * ** neg+indef * * neg+neg **

21. N-word (production)  MeaningFormFNegMaxNeg*Neg  x 1  x 2 indef+indef * ** neg+indef * * neg+neg **

22. Interpretation Issue: Does a sequence of items that express  x in isolation express a single or a double (multiple) negation.  InterpretNeg (IntNeg): Interpret all neg expressions in the input as contributing a negative meaning in the output.

23. Ranking MaxNeg and IntNeg: mirror images of each other (syntax/semantics). Relevant rankings to consider for interpretation: FaithNeg >> *Neg >> IntNeg [NC] FaithNeg >> IntNeg >> *Neg [DN]

24. DN (interpretation)  FormMeaningFNegIntNeg*Neg neg+neg x1x2x1x2 * **  x 1  x 2 * *  x 1  x 2 **

25. NC (Interpretation)  FormMeaningFNeg*NegIntNeg neg+neg x1x2x1x2 * **  x 1  x 2 * *  x 1  x 2 **

26. Bi-directional grammar Negative concord: MaxNeg >> *Neg >> IntNeg ‘Mark negative variables’ Double negation: IntNeg >> *Neg >> MaxNeg ‘Fully compositional meaning’

27. Results so far Whether a neg expression is interpreted as a negative quantifier or as an n-word depends on bi-directional grammar, not on lexical meaning. Constraints are universal, ranking is language-specific. Reranking = typology in OT

28. Other rankings? Three constraints allow 6 rankings: MaxNeg >> *Neg >> IntNegNC MaxNeg >> IntNeg >> *Neg unstable *Neg >> MaxNeg >> IntNeg unstable IntNeg >> MaxNeg >> *Neg unstable IntNeg >> *Neg >> MaxNeg DN

29. Sentential negation Haspelmath (1997): subtypes of negative indefinites, depending on relation to marker of negation. o Class I: SN mandatory (Rumanian, Greek, Afrikaans, Polish,..) o Class II: SN impossible (Dutch, English) o Class III: SN with postverbal n-words only (Italian, Spanish, Portuguese..).

30. Class III: asymmetry Preverbal versus postverbal n-words, e.g. Spanish, Portuguese, Italian,.. Maria non ha parlato con nessuno. Maria not has talked to nobody. Nessuno ha parlato con nessuno. *Maria ha parlato di niente con nessuno *Nessuno non ha parlato con nessuno.

31. Class III in OT  NegFirst: Negation is preverbal (Horn) Preverbal n-word with SN. meaningformNegFirstMaxNeg*Neg VxVx V neg * *  sn V neg **

32. Preverbal n-word Relevant for production only! meaningform NegFirstMaxNeg * Neg IntNeg  xV  neg V * neg sn V **

33. Class I: mandatory SN Negative indefinites always co-occur with SN: Rumanian, Greek, Polish,.. Nikt nie przyszekl[Polish] Nobody SN came. Nie widzialam nikogo. SN saw nobody

34. Class I in OT  MaxSN: a negative clause must bear a marker of sentential negation Relevant for production only! meaningform MaxSNMaxNeg * Neg  x 1 V  x 2 neg V neg * **  neg sn V neg ***

35. Special Case: Catalan En Pere no ha fet res. The Peter SN has done nothing. *En Pere ha fet res. Ningú (no) ha vist en Joan. Nobody (SN) has seen John. Preverbal SN required for postverbal n- word, optional for preverbal n-word.

36. Postverbal n-word NegFirst active: insertion of SN. meaningformNegFirstMaxSN <>*Neg VxVx V neg * * *  sn V neg **

37. Pre-verbal n-word MaxSN and *Neg equal in ranking. meaningform NegFrstMaxSN<>*Neg x1Vx2x1Vx2 neg V neg * ** neg sn V neg ***  

38. Special case: French Written French: type I language, preverbal ne always required. Il ne vient pas. Il ne dit rien. He NE comes not. He NE says nothing. Spoken French: demotion of MaxSN.. Il vient pas.Il dit rien.

39. Written French Preverbal ànd postverbal n-words require ne. meaningformMaxSN*Neg VxVx V neg * *  ne V neg ** ne V pas neg ***

40. Spoken French Neither preverbal nor postverbal n-word requires ne. meaningform*NegMaxSN  V  x  V neg * * ne V neg ** ne V pas neg ***

41. Negative clauses Written French meaningformFNegMaxSN*Neg  P(a) NP ne V * * NP V pas * *  NP ne V pas **

42. Negative clauses Spoken French meaningformFaithNeg*NegMaxSN  P(a) NP ne V * *  NP V pas * * NP ne V pas **

43. Double negation Double negation: pas + n-word. Il n’est pas venu pour rien. He NE has not come for nothing. Weak bi-directional optimality: ‘superoptimality’. Unmarked forms-unmarked meanings; marked forms-marked meanings

44. DN in French Input [f,m] f 1 : neg; f 2 : pas+neg m 1 :  xp; m 2 :  xp *Invent*NegIntNeg [neg,  xp] ** [neg,  xp] * *** [pas+neg,  xp] *** * [pas+neg,  xp] ****  

45. DN in Italian Class III languages: block sentential negation with preverbal n-words. Marginal DN readings, e.g. Italian (Zanuttini 1991). Nessuno degli studenti non è venuto. None of the students not is come. = None of the students hasn’t come.

46. Conclusions DN languages fully compositional, NC languages mark ‘negative variables’. Bi-directional OT grammar leads to typology of negation in terms of ranking. Role of marker of SN: purely syntactic! Weak bi-directional optimality explains DN readings in certain NC languages.

47. Conflicts in interpretation Research team: Petra Hendriks, Gerlof Bouma (Groningen), Helen de Hoop, Irene Krämer (Nijmegen), Henriëtte de Swart, Joost Zwarts (Utrecht)