1. Expression and interpretation of negation: a bidirectional OT typology Henriëtte de Swart Utrecht University

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. Quanta Costa?

5. 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

6. 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.

7. De Swart & Sag (2002) Lexical claim: n-words denote negative quantifiers, just like negative indefinites. Syntax-semantics interface (HPSG): N-store collects all negative quantifiers; interpretation upon retrieval. Semantic claim: polyadic quantification. Iteration  double negation. Resumption  negative concord.

8. Main insights Polyadic quantification/HPSG grammar: defines space of possible meanings in language. No lexical difference between negative quantifiers and n-words. No ‘hidden’ negations in syntax. Retrieval determines meaning at the syntax-semantics interface.

9. Grammar and typology Grammar does not predict when iteration or resumption arises. Cross-linguistic variation: typology. Two main classes: negative concord languages (NC) and double negation languages (DN).

10. Modeling typology? Richter and Sailer (2006): complement general rules of grammar with language specific constraints. NC languages: Negation Complexity constraint (Romance, Slavic..). DN languages: Negation Faithfulness constraint (English, German,..).

11. Evaluation Why do languages ‘bother’ to develop these additional constraints? Relation between constraints? Typological theory? How to account for language change in the system of negation?

12. Typology in OT All constraints are universal. Constraints are soft (violable). Ranking of constraints determined by language-specific grammar. Typology by reranking. Diachronic change: (gradual) process of promotion/demotion of constraints.

13. Syntax-semantics interface 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.

14. 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.

15. Markedness of negation  *Neg: avoid negation in the output. Markedness constraint FaithNeg >> *Neg Ranking fixed across languages Negation is marked in form/meaning (opposed to affirmation).

16. Propositional negation  Meaning   formFaithNeg*Neg It is raining * It is not raining *

17. Negative sentences It is not raining.[English] No vino Pedro.[Spanish] Not came Pedro. Ni fydd Sioned yna.[Welsh] Not be.fut Sioned there.

18. Interpretation  F\form It is not raining meaningFaithNeg*Neg  *  *

19. Bi-directional optimization f: it is raining f’: it is not raining m:  m’:   FNeg*Neg  * * * *  **

20. 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.

21. 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.

22. 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.

23. 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 ).

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

25. NPIs and n-words N-words denote  x in isolation, NPIs (n particular minimizers) denote  x. NPIs have to be licensed, n-words are ‘self-licensing’ (preverbal, fragment answers). Negative concord is limited to anti- additive contexts, many NPIs occur in decreasing or non-veridical contexts.

26. N-words in OT N-words mark ‘negative’ variables (Corblin and Tovena 2003). Functional motivation: mark focus of negation (Haspelmath 1997). In OT terms: faithfulness constraint MaxNeg. MaxNeg: Mark an argument under negation as negative (use negative indefinites in the scope of an anti-additive operator).

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

28. Indefinites (production)  Meaning  x 1  x 2 FormFNeg*NegMaxNeg indef+indef * ** neg+indef * * neg+neg ** Dutch, German, Turkish,..

29. N-word (production)  Meaning  x 1  x 2 FormFNegMaxNeg*Neg indef+indef * ** neg+indef * * neg+neg ** Romance, Slavic, Greek, Hungarian..

30. Interpretation Issue: Does a sequence of neg 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.

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

32. DN (interpretation)  Form neg+neg MeaningFNegIntNeg*Neg x1x2x1x2 * **  x 1  x 2 * *  x 1  x 2 **

33. NC (Interpretation)  Form neg+neg MeaningFNeg*NegIntNeg x1x2x1x2 * **  x 1  x 2 * *  x 1  x 2 **

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

35. 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 (uniformly  ). Constraints are universal, ranking is language-specific (NC vs. DN). Reranking = typology in OT

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

37. Recoverability problem meaning  formMaxNegIntNeg*Neg neg+indef * *  neg+neg ** form neg+neg meaning  * **   **

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

39. Non-strict NC: asymmetry Preverbal versus postverbal n-words, e.g. Spanish, Portuguese, Italian,.. Maria non ha parlato con nessuno. Maria sn has talked to nobody. Nessuno ha parlato con nessuno. *Maria ha parlato di niente con nessuno *Nessuno non ha parlato con nessuno.

40. Non-strict NC in OT  NegFirst: Negation is preverbal (Horn) Postverbal n-word with SN (Ladusaw 1992: clausal scope). meaning  V  x formNegFirstMaxNeg*Neg V neg * *  sn V neg **

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

42. Strict NC: 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

43. Strict NC in OT  MaxSN: a negative clause must bear a marker of sentential negation (sn) Relevant for production only! Meaning  x 1 V  x 2 form MaxSNMaxNeg * Neg neg V neg * **  neg sn V neg ***

44. 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.

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

46. Pre-verbal n-word MaxSN and *Neg equal in ranking. Language change in progress: Spanish influence leads to demotion MaxSN. meaningform NegFrstMaxSN<>*Neg x1Vx2x1Vx2 neg V neg * ** neg sn V neg ***  

47. Special case: French Written French: type I language, preverbal ne always required. Il ne vient pas. Il ne dit rien. He SN comes SN. He SN says nothing. Spoken French: demotion of MaxSN. Il vient pas.Il dit rien. He comes SNHe says nothing

48. Written French Preverbal ànd postverbal n-words require ne: Il ne dit rien. meaningformMaxSN*Neg VxVx V neg * *  ne V neg ** ne V pas neg ***

49. Spoken French Neither preverbal nor postverbal n-word requires ne: Il dit rien. Language change in progress: demotion of MaxSN. meaning  V  x form*NegMaxSN  V neg * * ne V neg ** V pas neg ** *

50. Negative clauses Written French: Il ne vient pas Meaning  P(a) formFNegMaxSN*Neg NP ne V * * NP V pas * *  NP ne V pas **

51. Negative clauses Spoken French: Il vient pas. Meaning  P(a) formFaithNeg*NegMaxSN NP ne V * *  NP V pas * * NP ne V pas **

52. Double negation DN in French: (ne..) pas + n-word. Il n’est pas venu pour rien. He SN has not come for nothing. ‘He has not come for nothing.’ [DN] Unexpected: combination pas + n-word does not come out as optimal form in tableaux so far.

53. Weak bi-directional optimality Weak bi-directional optimality: ‘superoptimality’ (Blutner) Unmarked forms-unmarked meanings; marked forms-marked meanings.    

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

55. DN in Afrikaans Hy het nie haar verjaarsdag vergeet nie. He has sn her birthday forgotten sn ‘Her sister didn’t forget her birthday.’ Hulle het nooit gesing nie. They have never sung sn ‘They have never sung.’ [NC] Hy kon nie niemand gesien het nie. He could sn nobody saw has sn ‘He could not have seen nobody’ [DN]

56. DN in Italian Non-strict NC 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 sn is come. ‘None of the students hasn’t come’ [DN]

57. DN in Welsh Fuo’ fo *(ddim) yn gweithio erioed. be.past.3sg he SN prog work never. ‘He has never worked.’[NC] Dydy hi erioed ddim wedi helpu. neg.be3sg she never SN perf help ‘She has never not helped.’[DN]

58. Lexicon or grammar? Pas always incompatible with n-words, so lexical account de Swart & Sag OK. Afrikaans nie, Italian non and Welsh ddim not incompatible with n-words, but DN readings in certain configurations. OT analysis predicts DN readings in cases in which presence of SN is not required by OT syntax.

59. Conclusions of the day I DN languages first-order compositional, NC languages require resumptive quantification, because they mark ‘negative variables’,. Bi-directional OT grammar leads to typology of negation in terms of ranking of three constraints: MaxNeg, IntNeg and *Neg.

60. Conclusions of the day II Marker of SN gets absorbed in resumptive polyadic quantifier, and plays no role in semantics of NC. Role of marker of SN: purely syntactic (scope marker: strict vs. non-strict NC). Weak bi-directional optimality: DN readings in configurations where SN is not required to express NC.