Conference on Optimal Interpretations of Words and Constituents
31 August - 1 September, 2000 — Utrecht University
Negative Strengthening and Blocking
Description of the phenomena
1.1
Levinson's typology of implicatures
♦ The Q-heuristics: (For the relevant salient alternates) What
isn’t said is not the case.
Reinhard Blutner & Bart Geurts
0
1
Introduction
-
♦ The Tradition of Radical Pragmatics
Division of labour between semantics and pragmatics
“Radical pragmatics is the hypothesis that many linguistic phenomena which had previously been viewed as belonging to the
semantic subsystem, in fact belong to the pragmatic subsystem.”
-
Neo-Gricean account (Atlas & Levinson, Horn, ...)
-
Relevance Theory (Sperber & Wilson, Carston, ...)
♦ Bidirectional OT and the Revival of Radical Pragmatics
- (can be made) formal precise
- reformulates, clarifies and relates the earlier approaches
Scalar implicatures
some of the boys came => not all of the boys came
-
Clausal implicatures
If John comes, I'll go => maybe he will, may be he won't
♦ The I-heuristics: What is expressed simply is stereotypically
exemplified
Conditional perfection (if => iff)
Bridging inferences
-
Negative strengthening
The effect of “neg-raising”
♦ The M-heuristics: What is said in an abnormal way isn’t
normal
♦ Negative strengthening & Neg-Raising
-
0
1
Introduction ............................................................................................0
Description of the phenomena...............................................................1
1.1
Levinson's typology of implicatures ................................................1
1.2
Gradable antonyms and negative strengthening..............................2
1.3
Verbs of mental attitudes and “neg-raising”....................................5
2
Bidirectional Optimality Theory ...........................................................7
3
Negative Strengthening........................................................................12
4
Neg-Raising ..........................................................................................13
5
Conclusions ..........................................................................................15
-
Pragmatic effects of double negatives
Periphrastic alternatives to simple causatives
Remark: Levinson tries to turn this heuristic classification
scheme into a general theory by stipulating a ranking Q > M > I.
We accept the classification schema but not the theory. (Instead,
we consider M as an epiphenomenon that results from the
interaction of Zipf’s two “economy principles”).
1
1.2
Gradable antonyms and negative strengthening
Consider gradable antonyms like {good, bad}, {large, small},
{happy, unhappy}. Semantically, they are contraries.
Sometimes, the weather is neither good nor bad.
This house is neither large nor small.
Sometimes I’m neither happy nor unhappy.
What are the effects of negating gradable adjectives?
(1)
(
I'm not happy
;
a.
b.
Entailment: It isn’t the case that I’m happy
Implicature: I'm unhappy
c.
defeasibility: I'm not happy and not unhappy
HAPPY
|
INDIFFERENT |
UNHAPPY
coded range of happy
coded range of not happy
implicated range
Figure 1: Contradictories implicating contraries
The described effect of strengthening is restricted to the positive
(unmarked) elements of antonym pairs!
2
Grüne Harmonie. Glücklich (ganz links): Fraktionschefin Kerstin
Müller. Glücklich (darunter): Fraktionschef Rezzo Schlauch.
Glücklich (rechts daneben): Gesundheitsministerin Andrea
Fischer. Glücklich (darüber): Schleswig-Holsteins Umweltminister Klaus Müller. Glücklich (verdeckt): Umweltminister
Jürgen Trittin. Nicht unglücklich (vor Trittin): Außenminister
Joschka Fischer. Überglücklich: die neue Parteichefin Renate
Künast. (TAZ 26.6.2000)
3
(2)
(
I'm not unhappy
a.
b.
;
1.3
Entailment: It isn’t the case that I’m unhappy
Implicature: I'm rather happy (but not quite as happy as
(3)
defeasibility: I'm not unhappy, in fact I’m happy
|
UNHAPPY
INDIFFERENT
|
I don't believe it is raining.
a.
b.
using the expression “happy” would suggest)
c.
Verbs of mental attitudes and “neg-raising”
Entailment: It isn't the case that I believe it is raining.
Implicature: I believe it isn't raining.
c. Defeasibility: I neither believe that it is raining nor that
it is not raining
HAPPY
Horn / Levinson account
coded range of unhappy
♦ The effect of “neg-raising” is attributable to the I/R-
coded range of not unhappy
principle.
The central problem for understanding the phenomenon is
implicated range
understanding why just some predicates show the “neg-raising”
effect. For example, the effect disappears with stronger
predicates:
Figure 2: Litotes: when two negatives don't make a positive
Levinson’s account
♦ the typical effect of negative strengthening is attributable to
(4)
the I-principle (R-based strengthening in Horn's theory)
It isn't evident that it is raining.
No Implicature: It is evident that it isn't raining.
♦ Double negatives (litotes) fall under the M-principle
(5)
I didn't realize that it was raining.
No Implicature: I realized that it wasn't raining.
Problems
♦ It’s not easy to see why the interpretation
should be less
informative than the interpretation ; (intuitively
is less
interesting than ; ; a case for relevance? Cf. Carston 1998)
The corresponding generalization can best be stated in Horn’s
arithmetic scalar model:
♦ What is the precise content of the M-principle?
♦ The M-principle destroys the elegance of the original theory.
4
5
We realize Horn’s “arithmetic square” within a probabilistic
account (prob(p|e) = probability for p in light of evidence e)
prob(p|e) $ "
know
realize
be certain
be evident/clear/sure
believe
suppose/think
be likely/probable
appear
1
2
prob(p|e)#1!"
0 know not
.
.
.
disbelieve
.
.
.
0.5
0.5
1 not certain
0
Horn’s not exceptionless generalization:
Weak intolerant predicates (near the midline, minimizing the
difference between Neg-V and V-Neg) invite the neg-raising
interpretation, but stronger intolerant predicates do not.
Exception: must is a strong predicates and shows the neg-raising
effect! It can be argued that we have a structural ambiguity in
this case. Preferences for structural analyses. (cf. Bresnan 1999)
(6)
He must not be at home
a. He must [not be at home]
b. He [must not] be at home
6
Gen: (very general) relation between form and interpretation
♦ Version 1 (Classical semantics)
J is a state (description) that makes A true.
♦ Version 2 (Update semantics, with underspecification)
J is a potential result of updating the context F with A
Con: set of ranked violable constraints on form-interpretation
pairs
.
.
.
possible
Bidirectional Optimality Theory
♦ markedness
(forms, interpretations)
♦ faithfulness
(forms × interpretations)
Eval: the elements of the generator are evaluated by the
constraints they violate.
♦ The constraint ranking defines a preference relation “™”
(more harmonic) between form-interpretation pairs.
♦ Determination of an optimal input-output pairs among a
given competition set.
♦ In bidirectional optimization we compare
(i) different forms for the same meaning (expressive or
speaker’s perspective) and
(ii) different interpretations for the same form (interpretive or
hearer’s perspective) .
♦ One system of constraints for both modes of optimization.
(see Zeevat for an alternative account)
7
The Neo-Gricean account and bidirectional OT
Definition 1 (Optimality)
<A,J> is optimal iff
I-principle
Q-principle
(termed R by Horn)
Quantity 2, Relation
Quantity 1
Say no more than you must
Say as much as you can (given
(given Q) (Horn 1984: 13).
I) (Horn 1984: 13).
Read as much into an utterance as is
Do not provide a statement that is
consistent with what you know about
the world (bearing the Q-principle in
mind) (Levinson 1983: 146f.)
informationally weaker than your
knowledge of the world allows,
unless providing a stronger
statement would contravene the I-
(Gen)
<A,J> 0 Gen F
(Q)
there is no +A',J, 0 Gen F such that <A',J> ™ <A,J>
(I)
there is no +A,J', 0 Gen F such that <A,J'> ™ <A,J>
McCawley’s example
Standard diagram
F C
M A1
A1
A2 *
principle (Levinson 1987: 401).
Conditional perfection, “negraising”, bridging inferences, ...
F
Dekker/van Rooy diagram
C
A1
M
*
A2
*
direct
*
A2
indirect
direct
indirect
M = Nash-equilibrium
Scalar implicatures
A1. Black Bill killed the sheriff
A2. Black Bill caused the sheriff to die
+A,J, satisfies I iff J is an
+A,J, satisfies Q iff A is
optimal interpretation of A
an optimal expression for
[bearing I in mind]
J [bearing Q in mind]
Seeks to select the most typical /
coherent interpretation
Comments
•
This version accounts for total blocking!
• Conforms to the OT learning algorithm (Tesar /
Smolensky)
Can be considered as a
•
It doesn’t account for partial blocking.
blocking mechanism
•
It doesn’t account for Levinson’s M-principle and Horn’s
division of pragmatic labour: Unmarked forms tend to be
used for unmarked situations and marked forms for marked
In OT, the principles I and Q are parameterised for constraint systems. The constraints determine what is informative or relevant!
situations.
8
9
Definition 2 (Super-Optimality)
3
<A,J> is super-optimal iff
Negative Strengthening
Version A
(Gen)
<A,J> 0 Gen F
(Q)
there is no super-optimal <A',J> ™ <A,J>
(I)
there is no super-optimal <A,J'> ™ <A,J>
•
happy
•a a
not unhappy
not happy
•
unhappy
•
h
f
McCawley’s example again
J1 J2 J3 ... Ji
A1
M
M
A2
direct
(
A1 M
M
A2
A3
M
...
Ai
indirect
;
Version B
M
Iconicity
Levinson’s M-principle and Horn’s division of pragmatic labour
are resulting from the solution concept of super-optimality!
Theorems (Jäger, Dekker & van Rooy)
Let’s assume that „™" is transitive and well-founded. Then
• There is a unique super-optimality relation.
• Optimal solutions are super-optimal (but not vice versa).
• If the set of super-optimal solutions is a one-to-one relation
between forms A and interpretations J, then the preference
relation between pairs <A,J> can be equivalently stated by
happy
•
•
not unhappy
not happy
•
unhappy
•
(
;
♦ Morphosyntactic ordering
♦ Ordering of states. Cognitive effort /salience
♦ We need a continuous scale & stochastic evaluation!
(Boersma 1998, Boersma & Hayes 1999)
means of a linear order of forms A and interpretations J.
11
12
4
Neg-Raising
♦ Propositions are evaluated on a scale of confirmation / refutation
♦ The salience of elements increases towards the ends of the scale.
♦ Semantically, epistemic predicates realize intervals on this scale.
realize: prob(p|e) $ 80 %
believe: prob(p|e) $ 60 %
believe not: prob(p|e) # 20 %
realize not: prob(p|e) # 40 %
Version A: believe (without blocking)
believe
•
a
Version B (including blocking)
•
realize
believe
•a
possiblybel
possiblyreal
not realize
•
•
possiblebel
not believe
•
not believe
believe not
•
believe not
prob(p|e) 80-100
60-80
40-60
20-40
0-20
Version A: realize (without blocking)
•
realize
•
•
•
60-80
40-60
20-40
0-20
Horn’s generalization results from the fact hat the negation of
stronger predicates covers a broader area near the middle of the
scale
60-80
40-60
20-40
0-20
♦ The effect of blocking doesn’t disturb Horn’s generalization
♦ Simplification: “categorial scale” instead of a continuous
one.
♦ In order to give a less artificial account we need
o gradient acceptability
o continuous scales
o stochastic evaluation procedures
(cf. Boersma 1998, Boersma & Hayes 1999)
13
5
•
♦ The effect of blocking leads to scalar implicatures.
realize not
prob(p|e) 80-100
•
realize not
prob(p|e) 80-100
possiblereal
not realize
•
14
References
Conclusions
♦ Bidirectional OT helps to put in concrete terms what are the
requisites for explaining the peculiarities of negative
strengthening and “neg-raising”
o Morpho-syntactic complexities
o Scales of cognitive states
♦ The M-heuristics can be deduced from (weak) bidirectional
OT. It takes the general form of Iconicity.
J1 J2 J3
If more than one interpretations is
A1 M
not normal, then the least
abnormal one is selected!
A2
M
♦ Why salience is an important notion
♦ What is the nature of salience?
♦ For more realistic applications of OT in the domain of natural
language interpretation it requires
o gradient acceptability
o continuous scales
o stochastic evaluation procedures
15
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and logical form’. In Peter Cole (ed.), Radical Pragmatics. Academic
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16