Expression and
interpretation of negation:
a bidirectional OT typology
Henriëtte de Swart
Utrecht University
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.
Quanta Costa?
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
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.
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.
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.
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).
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, ..).
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?
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.
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.
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
Ranking fixed across
languages
Negation is marked in
form/meaning (opposed
to affirmation).
Propositional negation
Meaning form

It is raining

It is not raining
FaithNeg *Neg
*
*
Negative sentences
It is not raining.
No vino Pedro.
Not came Pedro.
Ni fydd Sioned yna.
Not be.fut Sioned there.
[English]
[Spanish]
[Welsh]
Interpretation
F\form
meaning FaithNeg *Neg
It is not raining
*



*
Bi-directional optimization
f: it is raining
f’: it is not raining
m:  m’: 
<raining, >
FNeg
*Neg
<raining, >
*
*
<not raining, >
*
*
<not raining, >


**
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.
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: Nada
A: What did you see? B: nothing.
No vino nadie.
Not came nobody.
Nadie miraba a nadie
Nobody looked at nobody.
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 antiadditive contexts, many 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: faithfulness constraint MaxNeg.
MaxNeg: Mark an argument under negation
as negative (use negative indefinites in the
scope of an anti-additive operator).
Constraint interaction
Relevant Rankings (OT syntax)
FaithNeg >> *Neg >> MaxNeg
[produce indefinites]
FaithNeg >> MaxNeg >> *Neg
[produce n-words]
Indefinites (production)
Meaning
x1x2
Form
indef+indef

FNeg
*Neg MaxNeg
*
**
neg+indef
*
neg+neg
**
Dutch, German, Turkish,..
*
N-word (production)
Meaning
x1x2
Form
indef+indef
neg+indef

FNeg
*
MaxNeg *Neg
**
*
neg+neg
Romance, Slavic, Greek, Hungarian..
*
**
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.
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]
DN (interpretation)
Form
neg+neg
Meaning
x1x2
x1x2

x1x2
FNeg
*
IntNeg *Neg
**
*
*
**
NC (Interpretation)
Form
neg+neg
Meaning
x1x2

FNeg
*Neg
*
IntNeg
**
x1x2
*
x1x2
**
*
Bi-directional grammar
Negative concord:
MaxNeg >> *Neg >> IntNeg
‘Mark negative variables’
Double negation:
IntNeg >> *Neg >> MaxNeg
‘First-order 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 (uniformly ).
Constraints are universal, ranking is
language-specific (NC vs. DN).
Reranking = typology in OT
Other rankings?
Three constraints allow 6 rankings:
MaxNeg >> *Neg >> IntNeg
NC
MaxNeg >> IntNeg >> *Neg
unstable
*Neg >> MaxNeg >> IntNeg
unstable
*Neg >> IntNeg >> MaxNeg
unstable
IntNeg >> MaxNeg >> *Neg
unstable
IntNeg >> *Neg >> MaxNeg
DN
Recoverability problem
meaning form

neg+indef
MaxNeg IntNeg
*
*
 neg+neg
form
meaning
neg+neg

 
*Neg
**
*
**
**
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)
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.
Non-strict NC in OT
 NegFirst: Negation is preverbal (Horn)
Postverbal n-word with SN (Ladusaw
1992: clausal scope).
meaning
Vx
form
V neg
 sn V neg
NegFirst MaxNeg *Neg
*
*
**
Preverbal n-word
meaning form
xV
 neg V
NegFirst MaxNeg *Neg IntNeg
neg sn V
Relevant for production only!
*
**
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
Strict NC in OT
 MaxSN: a negative clause must bear a
marker of sentential negation (sn)
Meaning
x1Vx2
form
neg V neg
MaxSN MaxNeg
*
 neg sn V neg
Relevant for production only!
*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 nword, optional for preverbal n-word.
Postverbal n-word
NegFirst active: insertion of SN.
meaning form
Vx
V neg
 sn V neg
NegFirst MaxSN < >*Neg
*
*
*
**
Pre-verbal n-word
MaxSN and *Neg equal in ranking.
meaning
form
x1Vx2  neg V neg
NegFrst MaxSN< >*Neg
*
 neg sn V neg
Language change in progress: Spanish
influence leads to demotion MaxSN.
**
***
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 SN
He says nothing
Written French
Preverbal ànd postverbal n-words
require ne: Il ne dit rien.
meaning
form
Vx
V neg

MaxSN *Neg
*
*
ne V neg
**
ne V pas neg
***
Spoken French
Neither preverbal nor postverbal n-word requires ne:
Il dit rien.
meaning
Vx
form
 V neg
*Neg
*
ne V neg
**
V pas neg
**
MaxSN
*
*
Language change in progress: demotion of MaxSN.
Negative clauses
Written French: Il ne vient pas
Meaning form
P(a)
NP ne V
NP V pas
 NP ne V pas
FNeg MaxSN *Neg
*
*
*
*
**
Negative clauses
Spoken French: Il vient pas.
Meaning form
P(a)
NP ne V
 NP V pas
NP ne V pas
FaithNeg *Neg MaxSN
*
*
*
**
*
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.
Weak bi-directional
optimality
Weak bi-directional optimality:
‘superoptimality’ (Blutner)
Unmarked forms-unmarked meanings;
marked forms-marked meanings.
<f1,m1>  <f1,m2>


<f2,m1>  <f2,m2>
DN in French
Input [f,m]
*Neg IntNeg
f1: neg; f2: pas+neg
m1: xp; m2: xp
[neg, xp]
 **
[neg, xp]
***
[pas+neg, xp]
***
[pas+neg, xp]
 ****
*
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]
DN in Italian
Non-strict NC languages: block
sentential negation with preverbal nwords.
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]
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]
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.
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.
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.