Negative Polarity Items
and Downward Entailment
Alexis Dimitriadis
Negative polarity items I
•
Expressions like any, ever, a red cent or give a damn are
“restricted in their distribution”:
(1) a. * I’ve seen anything.
b.
I haven’t seen anything.
(2) a. * John has ever been to Paris.
b.
John hasn’t ever been to Paris.
(3) a. * Mary has a red cent.
b.
Mary doesn’t have a red cent.
(4) a. * Tina gives a damn about your problems.
b. Tina doesn’t give a damn about your problems.
Negative polarity items II
•
In Dutch: hoeven, kunnen uitstaan, ook maar iets, voor de
poes zijn, etc.
(5) a. * Je hoeft deze opgave te maken.
b. Je hoeft deze opgave niet te maken.
(6) a. * Mijn moeder is voor de poes.
b. Mijn moeder is niet voor de poes.
(7) a. * De zeug kan de boer uitstaan.
b. De zeug kan de boer niet uitstaan.
•
Roughly: NPIs are somehow “licensed” by negation.
Is it negation? I
(8) a. De zeug kan de boer niet uitstaan.
...but also:
b. De zeug kan maar weinig mensen uitstaan.
c. De zeug kan de boer zelden uitstaan.
d. * De zeug kan de boer (vaak/meestal) uitstaan.
(9) a. Mijn moeder is niet voor de poes.
b. * Mijn moeder is zelden voor de poes.
c. * Niemand is voor de poes.
d. * Weinig mensen zijn voor de poes.
Is it negation? II
(10) a. Nobody has seen anything.
b.
My mother seldom sees anything.
c. * My mother has seen anything.
d.
e.
Everyone who saw anything should call the police.
* Everyone who saw him should say anything.
Is it negation? II
(10) a. Nobody has seen anything.
b.
My mother seldom sees anything.
c. * My mother has seen anything.
d.
e.
•
Everyone who saw anything should call the police.
* Everyone who saw him should say anything.
Other environments also license NPIs:
everyone, weinig, zelden, ...
Is it negation? II
(10) a. Nobody has seen anything.
b.
My mother seldom sees anything.
c. * My mother has seen anything.
d.
e.
•
Everyone who saw anything should call the police.
* Everyone who saw him should say anything.
Other environments also license NPIs:
everyone, weinig, zelden, ...
•
NPIs must be in the scope of a licenser.
[ Everyone who saw anything ] should call the police.
Downward entailment I
•
Ladusaw / Fauconnier: NPIs are licensed in downward
entailing (downward monotonic) environments.
•
Regular (“upward” entailment):
If P ⊆ S (as sets), P(x) =⇒ S(x)
(11)
•
John is Dutch =⇒ John is European.
Negation reverses the implication: “downward” entailment.
(12) a. John is not Dutch =⇒
6
John is not European.
b. John is not European =⇒ John is not Dutch.
Downward entailment II
Formal definition
•
A function f is upward entailing iff for every X , Y : if
X ≤ Y , then f (X ) ≤ f (Y ).
•
A function f is downward entailing iff for every X , Y : if
X ≤ Y , then f (Y ) ≤ f (X ).
•
Note that some environments block such entailments:
(13)
John thinks that Mary is Greek. =⇒
6
John thinks that Mary is European.
(Maybe John thinks that Greece is in Asia.)
Testing downward entailment
(14)
Negation:
I did not walk =⇒ I did not walk quickly
(15)
Conditional sentence antecedent:
[ If you talk ], you should leave =⇒
[ If you talk loud ], you should leave.
(16)
Comparative of inequality:
Obelix is stronger than [ a soldier can be ] =⇒
Obelix is stronger than [ a Roman soldier can be ]
Which of these are DE?
1
Comparatives of equality
Obelix is as strong as [ a soldier can be. ]
2
Conditional sentence consequent (right side)
If you talk, [ you should leave ]
3
Restriction of universal (every, each, all the, any)
Every [ student who came to the party ] danced.
4
Complement (“nuclear scope”) of universal
Every student who came to the party [ danced. ]
5
Restriction of few
Few [ students ] enjoyed the exam.
Complications I
•
NPIs can also occur in environments that are not DE
(17) Questions
a. Do you know anything about this?
b. Heb je ook maar iets gezien?
•
Similar constructions can show different licensing behavior
(18) a.
Every student who saw anything reported it.
b. ?* Each student who saw anything reported it.
Complications II
•
NPIs differ from each other in their licensers
(19) a. Few people saw anything.
b. * Weinig mensen hebben ook maar iets gezien.
(20) a. Only John noticed anything
b. * Only John has seen him in weeks
c.
I am sorry I ever met you.
d. * I am sorry I recognized you until it was too late.
•
(Example (a) involves Strawson entailment: To get DE, we
must rely on the presupposition “John noticed X”)
Alternatives
•
The Zwarts hierarchy adds a number of stronger licensing
environments to DE:
1
F is downward entailing iff for all x, y such that
x =⇒ y , F (y ) =⇒ F (x). (Ladusaw 1979)
2
F is anti-additive iff for all x, y : F (x ∨ y ) = F (x) ∧ F (y ).
(Zwarts 1981)
3
F is anti-multiplicative iff F (x ∧ y ) = F (x) ∨ F (y ). (Zwarts
1998)
4
F is anti-morphic iff F is anti-additive and
anti-multiplicative.
5
F is nonveridical iff F (p) does not entail p. (Giannakidou
1997)
The “Zwarts hierarchy”
Summary: What we want to know
•
Which syntactic environments (constructions) license each
particular NPI? (Descriptive)
•
What property/properties of the licensers is responsible for
licensing? (Theoretical)
•
How do we test for downward entailment and the other
properties? (Practical)