Competition during the processing of relative quantifier scope

1
Competition during the processing of relative
quantifier scope
Ruth Filik, University of Glasgow Kevin Paterson,
University of Leicester Simon Liversedge,
University of Durham
2
When we read a sentence, it is necessary to form
a mental representation containing

• people, objects, events
• relationships between them
• how many of these there are

Quantifiers specify how many acts or participants
were involved in the situation.
3
Sentences often are ambiguous when containing two
or more different quantifiers. E.g., this
sentence containing a and every Kelly showed
a photo to every critic. There could be

• one photo
• more than one photo

4

• Disambiguation occurs by determining the relative
  scope of the quantifiers, with one quantifier
  taking scope over the other.
• Kelly showed a photo to every critic.
• If a takes wide scope there is only one photo.
• If every takes wide scope there can be more
  than one photo.

5
Competition vs reanalysis
Reanalysis based accounts (e.g., Fodor, 1982)

• - Surface linear order of quantifiers provides a
  structural cue to initial scope assignment.
• Readers initially assign wide scope to the first
  quantifier.
• Reading difficulty occurs as a result of
  reanalysis.

6
Fodor (1982)
Readers assign wide scope to every when it
appears first in the sentence, and instantiate
multiple photos and critics in their discourse
model. Kelly showed every photo to a critic
photo critic photo critic
photo critic
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Fodor (1982)
Readers initially assign wide scope to a when
it appears first in the sentence, but must
reanalyse on encountering every, incurring a
cost. Kelly showed a photo to every
critic photo critic critic REANALYSE
critic photo critic photo critic p
hoto critic
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Competition vs reanalysis
Competition based accounts (e.g., Kurtzman
MacDonald, 1993)

• Multiple factors influence quantifier scope
  resolution, including processing principles
  identified by Ioup (1975).
• Reading difficulty occurs due to conflict between
  processing principles.

9
Ioup (1975)
Proposed two hierarchies of scope-taking
preferences.
Quantifier Hierarchy eachgteverygtagtallgtmostgtmanygts
everalgtsomegta few
Grammatical Hierarchy
topicgtdeep and surface subjectgtdeep subject or
surface subjectgtprepositional objectgtindirect
object gtdirect object
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Dative sentences

• Direct object precedes the indirect object.
• Kelly showed a photo to every critic.
• DIRECT INDIRECT
• OBJECT OBJECT
• Linear order and grammatical hierarchy predict
  different scope preferences.
• Linear order a takes wide scope.
• Grammatical hierarchy every takes wide scope.

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Double object sentences

• Indirect object precedes direct object.
• Kelly showed every critic a photo.
• INDIRECT DIRECT
• OBJECT OBJECT
• Linear order and grammatical hierarchy make same
  predictions for double object sentences.
• Linear order every takes wide scope
• Grammatical hierarchy every takes wide scope

12
Previous studies

• Most previous studies used off-line number
  judgement tasks, or on-line grammaticality
  judgements, and therefore may not be informative
  about normal on-line sentence processing
• (Catlin Micham, 1975 Micham, Catlin, Van
  Derven Loveland, 1980 van Lehn, 1978 Ioup,
  1975 Johnson-Laird, 1969 Kurtzman MacDonald,
  1993 Tunstall, 1996).

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Experiment 1 from Filik, Paterson Liversedge
(in press)

• 56 participants from the University of Durham
• 48 experimental items, 70 filler items
• 3 independent variables
• Quantifier order a or every first
• Syntactic constituent order direct object
  (dative) or indirect object first (double object)
  
• Continuation singular or plural
• Examined reading times for quantified region and
  for continuation region.

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Materials Datives The celebrity gave1? an in
depth interview to every reporter from the
newspaper, but2? the interview(s) was/were3? not
very4? interesting.5 The celebrity gave1? every
in depth interview to a reporter from the
newspaper, but2? the reporter(s) was/were3? not
very4? interested.5 Double Objects The celebrity
gave1? a reporter from the newspaper every in
depth interview, but2? the reporter(s) was/were3?
not very4? interested.5 The celebrity gave1?
every reporter from the newspaper an in depth
interview, but2? the interview(s) was/were3? not
very4? interesting.5
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Predictions Quantified region Fodor would
predict a processing cost when a precedes
every. Kurtzman MacDonald would predict a
processing cost when grammatical and quantifier
hierarchies are in conflict. Continuation region
Reading times will be shorter for singulars if
a takes wide scope, and shorter for plurals if
every takes wide scope.
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First pass reading time Sum of duration of
fixations in region prior to eye leaving region
to either left or right. Measures early
processing decisions.
Measures of reading time
2
1
3
4
7
5
6
Measures of reading time
Total reading time Sum of duration of fixations
in region of interest. Overall reading time
measure.
7
4
3
2
1
6
5
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First pass reading times for quantified region

• Quantifier order not significant (Fslt2.4)
• Interaction of quantifier order and constituent
  order (Fsgt13)
• Longer RTs for datives with every first (Fsgt11)
• No reliable differences for double objects

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Total reading times for quantified region

• Longer RTs with a first (Fsgt5)
• Interaction of quantifier order and constituent
  order (Fsgt57)
• Longer RTs for datives with every first (Fsgt11)
• Longer RTs for double objects with a first
  (Fsgt50)

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Quantified region - summary

• Reading difficulty when processing hierarchies
  were in conflict.
• Total times consistent with interactive effects
  of quantifier and grammatical hierarchies.
• First pass effects not reliable for both sentence
  constructions.
• Additional effect of linear order in total times.

20
Reading times at the continuation region The
photo was/the photos were

• First pass and total times longer for plural than
  singular continuations.
• No evidence that computation of relative
  quantifier scope affected anaphoric processing.
• Evidence for on-line scope processing at the
  quantified region but none at the continuation.

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Experiment 2 Substituted each for every

• Each has stronger scope taking properties than
  every (e.g., Beghelli Stowell, 1997 Frazier,
  1999 Vendler, 1967).
• Ioup placed each higher than every in her
  Quantifier Hierarchy.
• Enables us to investigate the influence of a
  quantifier with stronger scope taking properties.
• Might obtain quantifier scope processing effects
  at the continuation.

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Experiment 2

• 48 participants from University of Derby
• 48 experimental items, 70 filler items
• 3 independent variables
• Quantifier order a or each first
• Syntactic constituent order direct object
  (datives) or indirect object first (double
  objects)
• Continuation singular or plural

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Experiment 2 - materials
Datives The celebrity gave1? an in depth
interview to each reporter from the newspaper,
but2? the interview(s) was/were3? not very4?
interesting.5 The celebrity gave1? each in depth
interview to a reporter from the newspaper, but2?
the reporter(s) was/were3? not very4?
interested.5 Double Objects The celebrity gave1?
a reporter from the newspaper each in depth
interview, but2? the reporter(s) was/were3? not
very4? interested.5 The celebrity gave1? each
reporter from the newspaper an in depth
interview, but2? the interview(s) was/were3? not
very4? interesting.5
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First pass reading times for quantified region

• Quantifier order not significant (Fslt1.8)
• Interaction of quantifier constituent order
  (Fsgt5)
• Longer RTs for double objects with a first
  (Fsgt5)
• No effect for datives (Fslt1)

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Total reading times for quantified region

• Longer RTs with a first (Fsgt14)
• Interaction of quantifier order constituent
  order (Fsgt38)
• Longer RTs for double objects with a first
  (Fsgt43), 575ms diff
• Longer RTs for datives with each first (Fsgt4),
  157ms diff
• So, larger effects for double objects than datives

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Reading times for quantified region -summary

• Total time effects consistent with interactive
  effects of quantifier and grammatical
  hierarchies.
• First pass effect was not reliable for both
  sentence constructions.
• Evidence in total reading times that linear order
  contributed to scope processing, in addition to
  the influence of the hierarchies.

27
First pass reading times at continuation the
photo was/the photos were

• Longer RTs for plurals than singulars (Fsgt13).
• No evidence that computation of relative
  quantifier scope affected anaphoric processing.

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Total reading times at continuation

• Spillover effects from quantified region
• Longer RTs with a first (Fsgt5)
• Longer RTs for double objects (Fsgt4)
• Interaction of quantifier order and constituent
  order (Fsgt5)
• Longer RTs for double objects with indefinite
  first (Fsgt12)
• No effect for datives (Fslt1)

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Reading times at continuation - summary

• Preference for singular continuations, despite
  strong scope-taking properties of each.
• Processing of definite NP anaphors is impervious
  to relative quantifier scope.
• Evidence for spillover effects of relative scope
  computation at previous region.

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Experiments 1 and 2 combined analyses Reasons

• Increased statistical power potentially yielding
  more robust first pass effects.
• Enabled us to compare the influence of each and
  every on ambiguity processing.

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Combined analyses of the quantified region

• 4 independent variables
• Form of universal quantification each or
  every
• Quantifier order a or universal first
• Syntactic constituent order direct object
  (datives) or indirect object first (double
  objects)
• Continuation singular or plural

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First pass reading times for quantified region

• No main effect of quantifier order (Fslt1.3)
• Interaction of quantifier order and constituent
  order (Fsgt17)
• Longer RTs for double objects with a first
  (Fsgt7)
• Longer RTs for datives with universal quantifier
  first (Fsgt8)
• Same size effect for datives and double objects

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Total reading times for the quantified region

• Main effect of quantifier order (Fsgt20)
• Interaction of quantifier order and constituent
  order (Fsgt92)
• Longer RTs for double objects with a first
  (Fsgt94)
• Longer RTs for datives with universal quantifier
  first (Fsgt14)
• Larger effect for double objects than datives

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Why are there larger effects for double object
sentences?
Balance of factors when hierarchies in
conflict Double objects
Linear Order Grammatical Hierarchy
Vs Quantifier Hierarchy
Datives
Linear Order Quantifier Hierarchy
Vs Grammatical Hierarchy
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Combined analyses summary

• First pass reading times showed interactive
  effects of Quantifier and Grammatical
  Hierarchies.
• Same magnitude of reading difficulty for datives
  and double objects when hierarchies conflicted.
• No linear order effect.
• Total times showed interactive effects of linear
  order, and Quantifier and Grammatical
  Hierarchies.
• Larger penalty for double objects than datives
  when hierarchies conflicted.
• Delayed effect of linear order modulated
  interaction between hierarchies.
• Form of universal quantification does not
  modulate scope processing effects

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General conclusions

• Quantifier scope is computed on-line in normal
  reading.
• Multiple factors contribute to on-line scope
  processing.
• Interactive effects of the Quantifier and
  Grammatical Hierarchies
• Reading time penalty when hierarchies favour
  rival analyses.
• Consistent with Kurtzman MacDonald (1993).
• However
• Linear order effects are also observed (e.g.,
  Fodor, 1982).
• This indicates that both linear order and
  grammatical hierarchies provide structural cues
  to relative quantifier scope.

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Need to test other sentence constructions to see
if findings generalise
The social worker spotted an addict in every
alleyway. The social worker spotted every addict
in an alleyway. addict direct object alleyway
prepositional phrase object
Longer first pass (Fsgt8) and total times (Fsgt13)
when every is first. Consistent with processing
cost when Quantifier and Grammatical Hierarchies
are in conflict. Support for grammatical function
being principle determinant of scope processing.
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Pre-tests

• No difference in plausibility of there being many
  photos compared to many critics (4.1 vs. 4.0, on
  7-point scale, t(47)lt1)
• Kelly showed a different photo to every critic.
• Kelly showed every photo to a different critic.
• No difference in frequency of usage of singular
  and plural versions of nouns (t(47)lt1).
• Singular 81.8 words/million (sd 132.3)
• Plural 67.2 words/million (sd 125.2)

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Offline number judgement task
How many photos are there? Kelly showed a photo
to every critic. Definitely one 1 2 3 4
5 definitely more than one
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Offline number judgement task

• Higher plurality ratings when every was first
  (Fsgt8)
• Interaction of quantifier constituent order
  (Fsgt60)
• Higher ratings for double objects with every
  first (Fsgt62)
• Higher ratings for datives with a first (Fsgt37)
• Larger effects for double objects than datives

42
Pre-tests

• No difference in plausibility of their being many
  photos compared to many critics(3.4 vs. 3.5, on
  7-point scale, t(47)lt1.3)
• Kelly showed a different photo to each critic.
• Kelly showed each photo to a different critic.
• No difference in frequency of usage of singular
  and plural versions of nouns (t(47)lt1).
• Singular 81.8 words/million (sd 132.3)
• Plural 67.2 words/million (sd 125.2)

43
Offline number judgement task

• Higher plurality ratings when each was first
  (Fsgt15)
• Interaction of quantifier constituent order
  (Fsgt17)
• Higher ratings for double objects with each
  first (Fsgt28)
• No difference for datives (Fslt1.8)
• So, larger effects for double objects than datives