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Denis Hilton
Christophe Schmeltzer
Alice Delicourt
University of Toulouse
A cognitive consistency approach
to well-formedness in conditional
performatives
Birkbeck Workshop on Thinking
July 26th 2009
Why do we have to frame
communications about decisions?
• Actions can either be done or not done
• We have to decide
– To buy or not to buy a product
– To send or not to send a child to a school
– To hang or not hang out the washing
• There is no “middle ground” (Hilton, 2008)
– We have to argue for or against actions
Judgment vs. decision-making
• Judgments are constative
–
–
–
–
Describe an aspect of the world
E.g. “the candidate is highly skilled”
Can be true or false
Can be qualified & graded
• “e.g. this candidate is quite highly skilled”
• Decisions are performative
–
–
–
–
–
They make something happen
E.g. “this candidate is the one we want”
Can be wise or unwise
Bring about a change in the world
Cannot be qualified or graded
• “e.g. this candidate is the one we quite want”
Communication & planning in the face
of risk and uncertainty
• Communication expresses emotions and serves interests
• Linguistic communication overlays prior emotion
communication systems (Hilton, 2008; Hilton,
Villejoubert & Bonnefon, 2005)
– May incorporate their characteristics
– Even logical vocabulary is polarized & argumentative
– May “encourage” vs. “discourage” actions
Plan of present talk
• In the present talk, we apply a pragmatic analysis to
– Understanding how quantifiers are used to frame
conditional performatives, e.g.
• Advice
• Directives
– Use an application of cognitive balance theory to
show how frames exert consistency pressure on the
pragmatic formulation of conditionals
Part I
The communicational toolbox:
Polarity, logical expressions
and argumentation
A meta-frame:
Aristotle’s Square of Oppositions
• The toolbox we use to discuss and manage uncertainty
in everyday language is not disinterested
– It is impregnated with polarity
• Aristotle’s Square of Oppositions (Horn, 1989; Levinson,
2000) can be thought of as a meta-frame
– AffIrmo vs. nEgO
– N.B. the French word for frame - “cadre” - comes
from Latin quadra.
A
contraries
No S is /are P
contradictories
subalterne
subalterne
All S is / are P
E
subcontraries
Some S is /are P
Not all S is
/are P
A
contraries
Necessary
not
contradictories
subalterne
subalterne
Necessary
E
subcontraries
Possible
Possible
not
A
contraries
Certain not
contradictories
subalterne
subalterne
Certain
E
subcontraries
Possible
Possible
not
A
contraries
Must not
contradictories
subalterne
subalterne
Must
E
subcontraries
May
May(need)
not
Polarity & quantifiers
• Moxey & Sanford have shown that quantifiers
have polarity
– Some of the tourists went to the Blue Lagoon
because…
– Not all of the tourists went to the Blue Lagoon
because….
Polarity & quantifiers
• Moxey & Sanford have shown that quantifiers
have polarity
– Some of the tourists went to the Blue Lagoon
because…
reasons for…
– Not all of the tourists went to the Blue Lagoon
because….
reasons against…
Logical language & communicating
about uncertainty
• Logical vocabulary in natural language is
polarized
• Affects in the kinds of arguments (pro vs. con)
generated in communication
• Can serve as input into a consistency
propagation process that relies on “affective”
coding
Part II:
An affective balance model of
polarity in performative
conditionals
Cognitive equilibrium:
Heider’s 1958 balance theory
o
+
+
p
x
+
An incomplete triad
in attitude structure
Me
+
-
Nicolas
Carla
?
A balanced triad:
A positive product
Me
+
-
Nicolas
Carla
-
An imbalanced triad:
A negative product
Me
+
-
Nicolas
Carla
+
An re-balanced triad:
A positive product
Me
-
-
Nicolas
Carla
+
Affective balance & conditionals:
Consistency propagation
• Conditionals have two parts
– If antecedent then consequent
• There may be pressure for these to be
“balanced”
– The net polarity of the antecedent must be the same
as the net polarity of the consequent
• Similar to principles that govern the formation of
cognitive equilibrium in attitude structures?
Affective balance and polarity in
conditional performatives
• If the product of the condition p is positive
(positive argument)
– Then encouragement
• Do q
• If the product of the condition p is
negative (negative argument)
– Then discouragement
• Don’t do q
Balance model applied to
conditional performatives
• The product of condition p depends on three factors
Polarity of quantifier (+ vs. -)
Desirability of event (+ vs. -)
Absence/presence of explicit negation (+ vs. -)
• The product of the condition p is calculated by
multiplying these three factors
• The consequent (action q) should then take the same
value as the product of the antecedent (condition p)
-> Polarity “balance” between antecedent condition & consequent
action
« If the operation has few chances of failing,
then take it »
Sentence
elements
p Few
Nature
Negative
quantifier
Polarity
-
Chances of Undesirable
event
failing
-
Product
+
q Take it
Encourage
ment
+
Advice
« If the operation has some chances of failing,
then don’t take it »
Sentence
elements
p Some
Nature
Positive
quantifier
Polarity
+
Chances of Undesirable
event
failing
-
Product
-
Discourage
ment
-
q Don’t
take it
Advice
Directive
« If there are not many clouds,
then hang the washing outside »
Sentence
elements
p not
Nature
Polarity
Negation
-
many
Positive
quantifier
+
clouds
Undesirable
event
-
Prod
uct
q Hang
them outside
Encourage
ment
+
+
« If there is not a lot of sunshine,
Directive
then don’t hang the washing outside »
Sentence
elements
p not
Nature
Polarité
Negation
-
a lot of
Positive
quantifier
+
sunshine
Desirable
event
+
Prod
uct
q Hang
them outside
Discourage
ment
-
Plan of experiments to test model
• In Experiment 1
– We look at how participants generate antecedents (p) that are
appropriate to conclusions (q vs. not q; Encouragements vs.
Discouragements)
• In Experiment 2
– we give participants a positive or negative product antecedent
and ask them to generate appropriate conclusions
• In Experiment 3
– we give participants a positive or negative product antecedent
and ask them to select appropriate conclusions
Expt 1: Quantifier production task
– Participants (141 French undergraduate students)
completed a paper and pencil questionnaire
– Each questionnaire had six scenarios
• Three advice situations
• Three directive (instruction) situations
– Two experimental groups
• Encouragement conclusion given (Do q)
• Discouragement conclusion given (Don’t do q)
Four configurations presented in both
encouragement and discouragement conditions
– Have/Don’t have the operation if
– p = positive event
 the operation has ... chances to succeed
 Assertion of chances of positive outcome
– nn = linguistic negation + negative event
 the operation has not … chances of failing
 Denial of chances of negative outcome
– n = negative event
 the operation has … chances of failing
 Assertion of chances of negative outcome
– np = linguistic negation + positive event
 the operation has not … chances to succeed
 Denial of chances of positive outcome
All configurations can combine
with a positive quantifier:
– p = positive event
 the operation has a few chances to succeed
 Assertion of chances of positive outcome
– nn = negation + negative event
 the operation has not a few chances of failing
 Denial of chances of negative outcome
– n = negative event
 the operation has a few chances of failing
 Assertion of chances of negative outcome
– np = negation + positive event
 the operation has not a few chances to succeed
 Denial of chances of positive outcome
But in English (and French) explicit negations
cannot combine with negative quantifiers :
– p = positive event
 the operation has few chances to succeed
 Implicit denial of chances of positive outcome
– nn = negation + negative event
 the operation has not few chances of failing
 Impossible linguistic combination
– n = negative event
 the operation has few chances of failing
 Implicit denial of chances of negative outcome
– np = negation + positive event
 the operation has not few chances to succeed
 Impossible linguistic combination
Where is it impossible to insert
quantifiers?
• It seems to be impossible in natural language to negate
negative polarity quantifiers
– E.g. « not few », « not not many »,
• Thus participants in the present task will find it
impossible to achieve balance by combining negative
quantifiers with an explicit negation
• In these cases we predict they will say that the task is
impossible
Expt 1: Quantifier production task
– Experimental groups split
• In the first group q was positive (encouragement)
• In the second group q was negative (discouragement)
• Six tasks were presented
• Three advice situations, concerning whether to:
• have an operation
• buy a fridge
• take a shortcut
• Three instruction situations, concerning whether to:
• Buy strawberries
• Repair a car
• Hang out washing
Quantifier production task
instructions
« The questionnaire that follows has been produced for research on the
interpretation of utterances. It is composedof six scenarios which are each
followed by a series of four phrases from which a part is missing. Your task
is to complete (where you judge it possible) each of these phrases with the
help of a and appropriate quantifier
A quantifier is an expression which defines a quantity of some set. Here are
some examples : « too many (of) » « a few (of) », « some (of)», « enough
(of) », « several », « many (of) », « a lot of », « few (of) », « veru few
(of) », « not too many (of) », « certain », etc.
There are no right or wrong answers, and what is asked of you is to indicate
what your yourself think (while being paying particular attention to each
utterance). Thank you in advance for your participation. »
Task instructions (Operation
scenario)
• Jeanne is hesitating about whether to undergo a laser
operation to correct short-sightedness. Not being able to
wear contact lenses, she has been wearing glasses for
ten years. Finding the glasses to be inconvenient, the
operation could be a solutiion.
• Imagine that the following phrases have been uttered by
a friend of Jeanne who is trying to give her advice. What
would be the most natural way to complete each
phrase? Indicate your response with the help of the
quantifier of your choice, or put a cross if you think that
no quantifier is indeed possible.
Encouragement quantifier production
task (Operation scenario)
• « Have the operation…
p - …if the operation has _______________ chances of
succeeding
nn - …if the operation does not have _______________ chances
of failing
n - …if the operation has _______________ chances of failing
np - …if the operation does not have _______________ chances
of succeeding
Encouragement quantifier production
task (Operation scenario) Predictions
• « Have the operation…
p - …if the operation has positive quantifier (e.g. a few) chances
of succeeding
nn - …if the operation does not have positive quantifier (e.g. a
few) chances of failing
n - …if the operation has negative quantifier (e.g. few) chances of
failing
np - …if the operation does not have negative quantifier (e.g.
few) chances of succeeding -> impossible
Discouragement quantifier production
task (Operation scenario) Predictions
• « Do not have the operation…
p - …if the operation has negative quantifier (e.g. few) chances of
succeeding
nn - …if the operation does not have negative quantifier (e.g.
few) chances of failing -> impossible
n - …if the operation has positive quantifier (e.g. a few) chances
of failing
np - …if the operation does not have positive quantifier (e.g. a
few) chances of succeeding
Coding of data
Participants had to write their own quantifier
– Coded as positive or negative polarity
– Given option of saying impossible to insert a quantifier
Table 1. Global percent of quantifiers (positive, negative
or impossible case) for each of the configurations,
collapsed across the 6 scenarios
Encouragement
p
nn
Positive quantifier expected
Discouragement
n
np
p
nn
n
Negative
Quantifier
expected
Impossible
case expected
Negative
Quantifier
expected
Impossible
case expected
np
Positive quantifier expected
+
-
x
+
-
x
+
-
x
+
-
x
+
-
x
+
-
x
+
-
x
+
-
x
81
2
13
84
1
9
13
65
21
33
6
61
24
48
26
26
8
62
84
5
8
81
5
12
Content effects
• Overall, the model receives clear support
• Nevertheless, some scenarios produce
anomalous effects
– Closer analysis of these seems instructive
Table 2. Percent of quantifiers (positive, negative or impossible case)
as a function of the polarity of the conclusion (encouragement or
discouragement) for the group “If”
Encouragement conclusion
Positive
quantifier
expected
Negative
quantifier
expected
Discouragement conclusion
Impossible
case
expected
Positive
quantifier
expected
Negative
quantifier
expected
Impossible
case
expected
Scenario
+
-
x
+
-
x
+
-
x
+
-
x
+
-
x
+
-
x
Fridge (A1)
75
2
22
3
76
16
30
3
65
82
3
12
35
35
29
29
18
50
Operation (A2)
77
0
3
9
76
15
3
21
74
80
2
6
3
92
5
5
8
73
Itinerary (A3)
73
6
21
32
57
11
38
0
62
77
0
15
15
38
44
53
3
41
Strawberries (D1)
84
2
6
15
29
56
71
3
26
87
0
13
67
19
14
16
0
81
Car (D2)
88
0
10
0
76
22
27
0
68
91
6
2
15
24
59
21
9
65
Washing (D3)
79
0
6
20
71
9
21
9
68
67
6
17
11
70
11
24
8
59
79
2
11
13
64
22
32
6
61
81
3
11
24
46
27
25
8
62
Total
Table 2. Percent of quantifiers (positive, negative or impossible case)
as a function of the polarity of the conclusion (encouragement or
discouragement)
Encouragement conclusion
Positive
quantifier
expected
Negative
quantifier
expected
Discouragement conclusion
Impossible
case
expected
Positive
quantifier
expected
Negative
quantifier
expected
Impossible
case
expected
Scenario
+
-
x
+
-
x
+
-
x
+
-
x
+
-
x
+
-
x
Fridge (A1)
75
2
22
3
76
16
30
3
65
82
3
12
35
35
29
29
18
50
Operation (A2)
77
0
3
9
76
15
3
21
74
80
2
6
3
92
5
5
8
73
Itinerary (A3)
73
6
21
32
57
11
38
0
62
77
0
15
15
38
44
53
3
41
Strawberries (D1)
84
2
6
15
29
56
71
3
26
87
0
13
67
19
14
16
0
81
Car (D2)
88
0
10
0
76
22
27
0
68
91
6
2
15
24
59
21
9
65
Washing (D3)
79
0
6
20
71
9
21
9
68
67
6
17
11
70
11
24
8
59
79
2
11
13
64
22
32
6
61
81
3
11
24
46
27
25
8
62
Total
Predicted result for p in
discouragement case
• A cook has to prepare an important meal for a businessman. He
wants to make a strawberry tart for the dessert and decides to send
an apprentice to a fruitseller to buy the strawberries.
•
•
•
•
•
•
•
•
•
•
« Don’t buy the strawberries…
- …if they are negative quantifier (e.g. not enough/little) ripe
- …if they are not _______________ unripe (vertes/green)
- …if they are _______________ unripe (vertes/green)
- …if they are not _______________ ripe »
Actual modal result for p in
discouragement case
• A cook has to prepare an important meal for a businessman. He
wants to make a strawberry tart for the dessert and decides to send
an apprentice to a fruitseller to buy the strawberries.
•
•
•
•
•
•
•
•
•
•
« Don’t buy the strawberries…
- …if they are positive quantifier (e.g. too much/very) ripe
- …if they are not _______________ unripe (vertes/green)
- …if they are _______________ unripe (vertes/green)
- …if they are not _______________ ripe »
Too much of a good thing can
become negative..
• While it is good to eat fruit when it is ripe,
it can be come too ripe
In this context ripeness become negative
-> recoding of ripeness as negative
-> inversion of predicted quantifier in order to maintain consistency
Participants thus appear to be maintaining consistency in such cases
For the simple consistency model to work, consistent (monotonic)
coding of a characteristic as positive or negative is necessary
e.g. it is difficult to imagine how an eye operation to correct
myopia can be too successful
Summary of Expt 1:
Quantifier production task
• Clear overall support for consistency model
– 42 out of 48 scenarios (6 scenarios x 8 configurations) confirmed
the model
• Significantly differed from a random distribution of responses
• Modal response as predicted
• All cases of « impossible » judgments were as predicted
• In six cases the simple consistency model was not
confirmed
– Unpredicted responses
• Cases of significant non-random distributions of responses with unpredicted
•
•
•
modal response
However, closer analysis shows that these can still be interpreted as
indicating consistency resolution
Need to specify underlying assumptions of simple model, e.g. monotonicity
Usefulness of using multiple scearios to uncover these assumptions
Expt 2: Conclusion production task
– Participants (31 French undergraduate students)
completed a paper and pencil questionnaire
– Each questionnaire had same six scenarios
• Three advice situations
• Three directive (instruction) situations
– We only used the six “possible” configurations for the
antecedent
– Given each of the 6 configurations of the antecedent,
participants had to write a conclusion
Expt 2: Conclusion production task
– Experimental groups split
• Half the cases theoretical product of p was positive
– we expected encouragements as conclusions, e.g.
 If the operation has a lot of chances of succeeding,…
 If the operation has not a lot of chances of failing,…
 If the operation has few chances of failing,…
• Half the cases theoretical product of p was negative
– We expected discouragements as conclusions
 If the operation has a lot of chances of failing,…
 If the operation has not a lot of chances to succeeding,…
 Only if the operation has few chances of succeeding,…
• Participants had to write their own conclusion
– Coded as an encouragement or discouragement
Table 3. Global percent of conclusions (encouragement or
discouragement) for each of the configurations
If
Encouragement expected
Discouragement expected
pp
pn
nn
npn
np
npp
+
-
+
-
+
-
+
-
+
-
+
-
87
5
83
10
83
8
8
79
13
77
2
90
Table 4. Percent of conclusions (encouragement or discouragement)
for each of the scenarios
Encouragement expected
Discouragement expected
Scenario
+
-
+
-
Fridge (A1)
80
9
7
82
Operation (A2)
94
5
4
89
Itinerary (A3)
85
7
7
85
Strawberries (D1)
75
17
6
82
Car (D2)
85
3
6
83
Washing (D3)
85
6
17
71
84
8
8
82
Total
Expt 3: Selection of conclusions
• Design similar to Expt. 3, except that
instead of being asked to write their
conclusions, participants were asked to
select between conclusions
– Encouragement (do p, e.g. have the
operation)
– Discouragement (Don’t do p, don’t have the
operation)
Experiment on affective balance
performative conditionals
• We tested the model
– three situations involving conditional advice
– three situations involving conditional directives
– In each scenario, six combinations of
• Pos vs. neg quantifier
• Desirable vs. undesirable outcome
• Absence/presence of explicit negation
• 6 used, 2 of 8 logical combinations excluded as “bizarre”
– These involved explicit negations of negative polarity quantifiers
 E.g. “not few“, “not hardly”
• Participants were given a condition (p) constructed according to these rules
– Were asked to select either
• Do q
• Don’t do q
Results support balance model
Overall summary &
conclusions
Framing of conditionals,
Pragmatic well-formedness &
argumentation
Summary of findings
• “Encourage” vs. “discourage” frames
– Follows a logic of affective balance in performative conditionals
• Advice
• Instructions
– Even unpredicted responses can be interpreted in terms of
consistency resolution
• Assumption of monotonicity inappropriate in some cases
• Argumentative effects of polarity
– In Experiment 1, quantifiers chosen that transform the product
of antecedent p
• Into a positive argument in the case of encouragements
• Into a negative argument in the case of discouragements
Drawing and selecting conclusions
• Experiment 2 shows that
– given a positive product for p, encouragement conclusions are
drawn
– given a negative product for p, discouragement conclusions are
drawn
• Experiment 3 shows that
– given a positive product for p, encouragement conclusions are
selected
– given a negative product for p, discouragement conclusions are
selected
Pragmatic well-formedness
• These effects are overwhelmingly strong
•
– Suggest that people have very strong intuitions of
pragmatic well-formedness
– Perceptions of pragmatic ill-formedness are strong,
even when sentences are
• Syntactically well formed
• Semantically interpretable
Consistent with a gestalt approach
Argumentative
functions of polarity
• Polarity is a pragmatic phenomenon
– Does not describe the world, but
– Allows inferences about what the speaker thinks is
important & desirable
– Suggests reasons that “explain” pros & cons to hearer
– Calculated intuitively & automatically
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