Marking and interpretation of negation: a bi-directional OT approach

Henriëtte de Swart

French/UiL-OTS, Utrecht

Expressing negation

Natural languages: ways to express negation/denial: not.

First-order propositional connective Natural languages: negative indefinites, nobody.

First-order quantifier x.

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.

DN and NC

Nobody said nothing. (Eng) xy

Niemand zei niets. (Dutch) xy

Nadie miraba a nadie. (Spa) xy

Nessuno ha parlato con nessuno. (Ital) xy

Personne n’a rien dit. (Fr)ambiguous

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.

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.

Approach: OTOT 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.

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.

Markedness of negation

*Neg: avoid negation in the output.

Markedness constraint

FaithNeg >> *Neg

Assumption: ranking fixed across languages

Negation is marked in form/meaning.

Propositional negation

meaning form FaithNeg *Neg

p S *

not S *

Negative sentences

John is not sick. [English]

No vino Pedro. [Spanish]

Not came Pedro.

Non piove. [Italian]

Not rains.

‘It doesn’t rain.’

Indefinites under negation

Production: how do languages express the meaning x1 x2 x3 P(x1, x2, x3)?

Three cases: o plain indefinites, o negative polarity items, o n-words.

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

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.

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 (x1 x2 x3).

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.

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.

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.

Constraint interaction

Relevant Rankings (OT syntax)

FaithNeg >> *Neg >> MaxNeg

[indefinites]

FaithNeg >> MaxNeg >> *Neg

[n-words]

Indefinites (production)

Meaning Form FNeg *Neg MaxNeg

x1x2 indef+indef * **

neg+indef * *

neg+neg **

N-word (production)

Meaning Form FNeg MaxNeg *Neg

x1x2 indef+indef * **

neg+indef * *

neg+neg **

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.

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]

DN (interpretation)

Form Meaning FNeg IntNeg *Neg

neg+neg x1x2 * **

x1x2 * *

x1x2 **

NC (Interpretation)

Form Meaning FNeg *Neg IntNeg

neg+neg x1x2 * **

x1x2 * *

x1x2 **

Bi-directional grammar

Negative concord:

MaxNeg >> *Neg >> IntNeg

‘Mark negative variables’

Double negation:

IntNeg >> *Neg >> MaxNeg

‘Fully compositional meaning’

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

Other rankings?

Three constraints allow 6 rankings:

MaxNeg >> *Neg >> IntNeg NC

MaxNeg >> IntNeg >> *Neg unstable

*Neg >> MaxNeg >> IntNeg unstable

IntNeg >> MaxNeg >> *Neg unstable

IntNeg >> *Neg >> MaxNeg DN

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..).

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.

Class III in OT

NegFirst: Negation is preverbal (Horn)

Preverbal n-word with SN.

meaning form NegFirst MaxNeg *Neg

Vx V neg * *

sn V neg **

Preverbal n-word

Relevant for production only!

meaning form NegFirst MaxNeg *Neg IntNeg

xV neg V *

neg sn V **

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

Class I in OT

MaxSN: a negative clause must bear a marker of sentential negation

Relevant for production only!

meaning form MaxSN MaxNeg *Neg

x1Vx2 neg V neg * **

neg sn V neg ***

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.

Postverbal n-word

NegFirst active: insertion of SN.

meaning form NegFirst MaxSN < >*Neg

Vx V neg * * *

sn V neg **

Pre-verbal n-word

MaxSN and *Neg equal in ranking.

meaning form NegFrst MaxSN< >*Neg

x1Vx2 neg V neg * **

neg sn V neg ***

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.

Written French

Preverbal ànd postverbal n-words require ne.

meaning form MaxSN *Neg

Vx V neg * *

ne V neg **

ne V pas neg ***

Spoken French

Neither preverbal nor postverbal n-word requires ne.

meaning form *Neg MaxSN

Vx V neg * *

ne V neg **

ne V pas neg ***

Negative clauses

Written French

meaning form FNeg MaxSN *Neg

P(a) NP ne V * *

NP V pas * * NP ne V pas **

Negative clauses

Spoken French

meaning form FaithNeg *Neg MaxSN

P(a) NP ne V * *

NP V pas * * NP ne V pas **

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

DN in French

Input [f,m]

f1: neg; f2: pas+neg

m1: xp; m2: xp

*Invent *Neg IntNeg

[neg, xp] **

[neg, xp] * ***

[pas+neg, xp] *** *

[pas+neg, xp] ****

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.

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.

Conflicts in interpretation

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