Constraints on quantifiers · Hearers perspective 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0 50...
Transcript of Constraints on quantifiers · Hearers perspective 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0 50...
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Constraints on quantifiers
Chris Cummins DTAL, University of Cambridge
PUQOL workshop at ESSLLI, 8-12 August 2011
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The luxury of choice…
Bååth, Sauerland, and Sikstrøm (in preparation)
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Speaker’s perspective
Bååth, Sauerland, and Sikstrøm (in preparation)
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Speaker’s perspective (200 dots)
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Speaker’s perspective (200 dots)
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Hearer’s perspective
Bååth, Sauerland, and Sikstrøm (in preparation)
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Hearer’s perspective
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Hearer’s perspective
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Usage and interpretation…
• Speakers are not choosing arbitrarily among possible semantically correct utterances
– Why?
– What are they doing?
• This information could enable hearers to adjust their interpretation of utterances
– How?
– Are they doing this?
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Numerical quantification
(Perhaps infinitely) many semantically truthful options are available for the speaker’s use in a given situation
More than 20/19/18…
Fewer than 25/26/27…
Between 20 and 25/19 and 26...
…boats are in the harbour
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Determining the optimal utterance
• Considering the ‘competitor’ utterances
“more than 22” “more than 20” “between 20 and 30”…
• Arguments for and against each
• No intuitively clear winner
• Relevance appears only to offer post hoc explanation
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Soft constraints?
• Idea: model speaker’s decision procedure as a problem of multiple constraint satisfaction
• Advantages:
– Theoretical frameworks exist to do this
– Can yield quantifiable, testable predictions
– Constraints have (accidentally) been studied…
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Example: time reporting
• Van der Henst and colleagues
– Precise vs. imprecise elicitation contexts
– Analogue vs. digital watches
• Predictable trends analysed in RT terms
• However, individual factors touched upon:
– Informativeness
– Communicative preference for roundness
– (implicitly) Numeral priming from watch-face
– (implicitly) Granularity requirement
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Proposed constraints
• Informativeness (e.g. Van der Henst, Carles and Sperber 2002)
• Numeral salience (e.g. Jansen and Pollmann 2001)
• Quantifier simplicity (e.g. Cummins and Katsos 2010)
• Granularity (e.g. Krifka 2009)
• Numeral / quantifier priming
• Functionally motivated/empirically validated
• Cross-disciplinary (cf. Musolino 2004)
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Constraint-based model of speaker’s choice
Two main components: (Individually) ranked list of relevant constraints
Selection procedure to determine optimal utterance
Classical Optimality Theory account Speaker-referring
Unidirectional
Constraints are: Preferably observed
Non-obligatory
Defined such that their violations can be quantified
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Example 1: ‘more than n’
• Problem:
– ‘more than n’ seems to resist implicature
– yet ‘more than 100’ seems to convey two bounds
• Constraint-based account
– Consider ‘more than n’ vs. ‘more than m’
– If m > n, and speaker knows ‘more than m’ holds, m preferred unless (potentially)
• m is less salient numeral than n
• m is not a scale point at relevant granularity level
• n is primed and m is not
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Prediction
• ‘more than n’ +> ‘not more than m’…
– strongly if ‘more than m’ is a good candidate with respect to the relevant constraints
• More specifically, if ‘more than m’ harmonically bounds ‘more than n’
– weakly if not
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Experimental verification
Information: A newspaper reported the following.
“[Numerical expression] people attended the public meeting about the new highway construction project.”
Question: Based on reading this, how many people do you think attended the meeting?
Between ______ and ______ people attended [range condition]
______ people attended [single number condition].
Cummins, Sauerland and Solt (submitted)
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Experimental verification
Fielded on MTurk: 100 participants per condition
ANOVAs show significant effects in both conditions (p < 0.05)
Comments reflect explicit awareness of this reasoning
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Effect of priming
Less obvious prediction: Prior mention of numeral attenuates implicature
A: We need to sell (n) tickets to break even.
B: We’ve already sold more than n tickets.
No prior mention Hearer reasons as before
Prior mention Speaker could have said ‘more than m’ for some m > n…
…but maybe chose ‘more than n’ to satisfy numeral priming…
…so implicature not available.
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Experimental verification (2)
Please read the following short dialogues, and answer the questions by filling in a value for each blank space, according to your opinion. Consider each dialogue separately. Assume that participant B is well-informed, telling the truth, and being co-operative in each case.
A: We need to sell (60) tickets to cover our costs. How are the ticket sales going?
B: So far, we’ve sold fewer than 60 tickets.
How many tickets have been sold? From …… to ……, most likely …….
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Experimental verification (2)
40 participants: “more than” and “fewer than” conditions. 3x2x2 ANOVA shows main effects of quantifier (F(1,41)= 8.66, p<0.01) roundness (F(2,80)=44.83, p<0.001) priming (F(1,40)=10.78, p<0.01).
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Example 2: ‘more than’ vs. ‘at least’
• Problem:
– ‘at least n’ seems to convey sense of modality that ‘more than n-1’ lacks (Geurts and Nouwen 2007)
– Expressions such as ‘up to’, ‘maximally’, etc. do likewise (Nouwen 2010)
– This disappears in antecedent of conditional and certain other contexts (Cummins and Katsos 2010)
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Example 2: ‘more than’ vs. ‘at least’
Constraint-based account:
• Comparing ‘more than n’ with ‘at least n’:
– Former harmonically bounds latter unless possible that ‘exactly n’ holds, so ‘at least n’ should convey this
• Reason to believe that ‘at least’ is more complex than ‘more than’, so violates quantifier simplicity
• Comparing ‘more than n-1’ with ‘at least n’:
– Former harmonically bounds latter unless n is a more salient number than n-1
– This appears to predict major usage trends
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Example 3: bare numeral approximations
• Problem:
– Round numbers have (preferentially?) round interpretations (Krifka 2002, 2009 i.a.)
• Constraint-based model:
– If all numbers approximative on semantics…
– …then e.g. ‘49’, ‘50’ compete as expressions…
– …but ‘50’ harmonically bounds ‘49’
• Similar in spirit to Krifka (2009)’s bidirectional model
• Might predict differentiation over time between round/non-round numeral semantics
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Summary
• Constraint-based account is
– Constituted of functionally motivated components
– Useful as a source of (sometimes non-obvious) predictions
– Applicable to some open questions on the semantics/pragmatics interface
– Potentially psychologically plausible
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Possible future directions
• Constraint-based account is
– Constituted of functionally motivated components
– Useful as a source of (sometimes non-obvious) predictions
– Applicable to some open questions on the semantics/pragmatics interface
– Potentially psychologically plausible
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Possible future directions
• Constraint-based account is
– Open to introduction of further functionally motivated constraints (QUD?)
– Useful as a source of (sometimes non-obvious) predictions
– Applicable to some open questions on the semantics/pragmatics interface
– Potentially psychologically plausible
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Possible future directions
• Constraint-based account is
– Open to introduction of further functionally motivated constraints (QUD?)
– Able to generate further testable predictions, some of which might be illuminating
– Applicable to some open questions on the semantics/pragmatics interface
– Potentially psychologically plausible
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Possible future directions
• Constraint-based account is
– Open to introduction of further functionally motivated constraints (QUD?)
– Able to generate further testable predictions, some of which might be illuminating
– Potentially applicable to other open questions in quantification (e.g. isomorphism)
– Potentially psychologically plausible
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Possible future directions
• Constraint-based account is
– Open to introduction of further functionally motivated constraints (QUD?)
– Able to generate further testable predictions, some of which might be illuminating
– Potentially applicable to other open questions in quantification (e.g. isomorphism)
– Amenable to testing as a performance model for individual speakers