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Processing Degree Operator Movement : Implications for the Semantics of Differentials. Micha Y. Breakstone*, Alexandre Cremers † , Danny Fox ‡ and Martin Hackl ‡. *HUJI and MIT; † SIGMA – ENS; ‡ MIT Contact: michab@mit.edu; alexandre.cremers@gmail.com

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processing degree operator movement implications for the semantics of differentials

Processing Degree Operator Movement:Implications for the Semantics of Differentials

Micha Y. Breakstone*, AlexandreCremers†, Danny Fox‡ and Martin Hackl‡

*HUJI and MIT; †SIGMA – ENS; ‡MIT

Contact: michab@mit.edu; alexandre.cremers@gmail.com

Experimental Syntax and Semantics Lab: http://web.mit.edu/hackl/www/lab/

roadmap
Roadmap
  • Theoretical background: scope ambiguities with differentials
  • Two competing theories
  • A sentence processing study
  • Semantics of differentials in comparatives

Processing Degree Operator Movement - Salt 2011

theoretical background
Scope Ambiguities

Processing Degree Operator Movement - Salt 2011

Theoretical background
heim s a mbiguity
Heim’s Ambiguity
  • exactly differentials give rise to scope ambiguities (Heim*):

John is required to be exactly 2" inches taller than Mary is.

    • exactly reading: If Mary is 5 feet tall, the requirements will be met only if John is 5’2’’ tall. (“Narrow Scope”)
    • at least reading: If Mary is 5 feet tall, the requirements will be met if John is at least 5’2’’ tall.(“Wide Scope”)

*Heim, Irene (2000): ‘Degree Operators and Scope’, Proceedings of SALT X, 40–64.

Processing Degree Operator Movement - Salt 2011

two competing theories
Two Competing Theories
  • Two competing theories of this ambiguity, that differ in what takes scope:
    • [exactly 5 pages -er than…] Heim (2000)
    • [exactly 5 pages] Oda (2008)1, Beck (2010)2

1 Oda, Toshiko (2008) ‘Degree constructions in Japanese’. Dissertations Collection for University of Connecticut.

2 Beck, Sigrid (2010) ‘DegPScope Revisited’. Ms., UniversitätTübingen.

Processing Degree Operator Movement - Salt 2011

heim s lfs

- Narrow Scope

- Basic Case

Heim’s LFs

Processing Degree Operator Movement - Salt 2011

heim s lfs wide scope
Heim’s LFs - Wide Scope

Processing Degree Operator Movement - Salt 2011

If Mary is 5’ tall, John must be at least 5’2’’ tall (at least reading)

oda beck lfs

- Narrow Scope

- Basic Case

Oda / Beck LFs

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oda beck lfs 2 wide scopes
Oda / Beck LFs – 2 Wide Scopes

High -er

Low -er

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distinguishing oda beck from heim
Distinguishing Oda/Beck from Heim
  • Under Heim only one LF for wide scope reading
  • Under Oda/Beck two possible LFs for wide scope reading
  • Assume we had a method of fixing wide scope for exactly and asking what the syntactic position of the than-clause is:
    • If the location of DegP (er… than-clause) is always high  Heim
    • If the location of DegPis ambiguous  Oda/Beck

One might hope that the position of the DegP could have consequences for truth conditions. Based on Heim 2000 the differences would be subtle (pertaining to de dicto/ de re). We will use a different strategy to distinguish the 2 theories but will return to the semantic distinction later

Processing Degree Operator Movement - Salt 2011

our goals for this talk
Our Goals for this Talk
  • Present a real time sentence processing experiment designed to tease apart these two structural analyses for exactly differentials
    • The results support Heim’s structure
  • Propose a semantics for comparatives with exactly differentials that explains why Oda/Beck structures are not available

Processing Degree Operator Movement - Salt 2011

real time processing
Experimental Design and Analysis of Results

Processing Degree Operator Movement - Salt 2011

Real time processing
in a nutshell
… in a Nutshell
  • Use real time sentence processing
  • Fix wide scope for exactly (by context)
  • Probe for location of than-clause (by ACE; following the logic of HK&V*)
  • The key result:

exactly takes wide scope  than clause is high

predicted by Heim’s LFs, left unexplained by Oda/Beck

*Hackl M., Koster-Moeller, J. & Varvoutis, J. (submitted): ‘Quantification and ACD: Evidence from Real Time Sentence Processing’.

Processing Degree Operator Movement - Salt 2011

forcing w ide scope
Forcing Wide Scope
  • How do we fix the scope for exactly? By context:

To become the all time champion, John was required to win exactly 3 more matches than Bill

  • This context strongly disfavors an exactly reading
    • If you happen to win more than required, you’ll still be the all time champion
  • Wide scope is fixed for exactly

Processing Degree Operator Movement - Salt 2011

fixing the location of the than clause
Fixing the Location of the than-clause

John is required to be exactly 2" inches taller than Mary is d-tall / required to be d-tall

Oda/Beck: 2 options for wide scope Heim

Processing Degree Operator Movement - Salt 2011

  • For Heim wide scope determines location of than-clause
  • For Oda/Beck wide scope gives 2 options. One can fix the location of the than-clause in wide scope using non-local ACE
  • For both theories, a than-clause containing non local ACE could only be in 1 place (to resolve antecedent containment)
probing for location of than in real time
Probing for Location of [than…] in Real Time

To become the all time champion, John was required to win exactly 3 more matches than Bill was <required to win>

  • Heim: wide scope of exactly  high attached than-clause
    • When ACE site is reached, there is only one available structure (which also happens to license non-local ACE)
    • ACE site doesn’t trigger reanalysis  no additional cost due to reanalysis
  • Oda/Beck: wide scope doesn’t determine than-clause height
    • Two structures are still possible, only one of which licenses ACE
    • ACE site may trigger reanalysis  possible increased processing cost at ACE site
  • Furthermore, HK&V observe that ACE will incur increased processing cost on the ACE site, unless a structure licensing ACE was previously established

Processing Degree Operator Movement - Salt 2011

experimental paradigm
Experimental Paradigm

In order to become the all-time champion, the American athlete was required to win…

a. exactly 3 more matches than the British athlete did

b.exactly 3 more matches than the British athlete was

c. a fewmore matches than the British athlete did

d. a few more matches than the British athlete was

… and so practiced arduously for several months.

Processing Degree Operator Movement - Salt 2011

the base line a few
The Base Line: A few
  • a fewintuitively is not ambiguous (always ‘at least’ reading)

John was required to be a few inches taller than Mary

  • Assume non-local QR is more costly than local QR, then even with an at least reading a few prefers narrow scope
  • Formally:
    • [[a few –er]](P)(Q) = 1 iff max(Q)  max(P)+
    • John is required [[a few -er than Mary is <d-tall>]i [VP to be ti tall]]
    • w[w  Accw0 [max(d. J. d-tall in w) max(d. M. is d-tall) + ]

Processing Degree Operator Movement - Salt 2011

predictions
Predictions

To become the all-time champion, the American athlete was required to win…

  • exactly 3 more matches than the British athlete did
  • exactly 3 more matches than the British athlete was
  • a fewmore matches than the British athlete did
  • a few more matches than the British athlete was
  • Predictions for Heim: Resolution of non-local ACE in (b) should incur less of a processing cost than in (d)
    • exactly, in this context, triggers non-local movement facilitating ACE
    • a few yields semantically equivalent LFs so reanalysis is triggered only at ACE site (local QR preferred)
  • Prediction for Oda/Beck: exactlycan move over requirew/o pied-piping the than-clause, so there is no reason to predict a difference in processing cost
  • Resolution of local ACE (a),(c) should incur the same difficulty (baseline)

Processing Degree Operator Movement - Salt 2011

predicted interaction heim
Predicted Interaction - Heim

Processing Degree Operator Movement - Salt 2011

methods and materials
Methods and Materials
  • 37 subjects from MIT BRL subject pool, native English speakers
  • Single word, self-paced reading, “moving window” paradigm
  • Response Times (RTs) measured between button presses for each word
  • 4 conditions:
    • 2 equal-length differentials [“a few”/”exactly n”] x (non-)local ACE
  • 44 target items (11 x 4 conditions) in a Latin square setup
  • 109 filler items
  • Each sentence followed by a comprehension question

Processing Degree Operator Movement - Salt 2011

analysis
Analysis
  • Residual RTs (RRTs) calculated as difference between RT and a linear model of average RT per subject per word length
  • Outliers trimmed: under 18 ms; over 2s; outside 2 SDs
  • Removed measurements for erroneous answers, and for last word of each sentence
  • Removed subjects with total precision below 75% (only 1 of the 37 subjects)
  • Effects analyzed using a contrast coded linear mixed effects model

Processing Degree Operator Movement - Salt 2011

residual reading times
Residual Reading Times

Processing Degree Operator Movement - Salt 2011

interaction after ace site
Interaction after ACE site

Processing Degree Operator Movement - Salt 2011

results
Results
    • Mixed effects analysis (# of obs: 1336, groups: Item, 44; Subject, 36)
  • Interaction of differential x ACE:
    • Mean over 3 words following ACE site: p=0.0279 (pMCMC)
    • 3rd word following ACE p=0.001 (pMCMC)
    • RRTs for [Exactly/Non-local] are lower than [A Few/Non-local]
    • RRTs for [Exactly/Local] are higher than [A Few/Local]
  • We find that with local ACE, “a few” is easier than “exactly”, possibly due to the following preference (see: Romeo & Hardt*):

Scope should match size of ACE – wide scope is hard with small ACE

Ellipsis and the Structure of Discourse. Daniel Hardt and Maribel Romero. Proceedings of Sinn und BedeutungVI, 2002.

Processing Degree Operator Movement - Salt 2011

conclusions
Conclusions
    • “exactly” differentials, but not “a few” differentials facilitate wide scope ACE
    • This shows that the at least reading is not generated by the following LF (otherwise we wouldn’t get facilitation):
      • [[exactly 2’’] … [require [… er-than]]]
    • This is in line with Heim’s structure
    • Not predicted by Oda/Beck’s approach without some kind of locality restriction, e.g.:
    • An exactly quantifier over degrees must receive narrowest possible scope. The sister of exactly 2'' cannot dominate a distinct constituent of type t that dominates the trace of exactly 2''.
  • Instead, we will pursue a compositional analysis of exactly differentials that predicts Heim’s structures

Processing Degree Operator Movement - Salt 2011

comparatives with differentials
Semantics

Processing Degree Operator Movement - Salt 2011

Comparatives WITH differentials
theory of exactly differentials
Theory of exactlydifferentials
  • ] is a quantifier over degrees, if it raises alone out of a comparative it leaves behind a trace of type <dt,t>, hence the interpretation would still be narrow scope:
  • [[exactly 2'']j [John is required [t<dt,t>,j-er than Mary is <d-tall>]i [VP to be td,itall]]]
  • Hence, the only way to receive wide scope under this spell-out of Heim’s theory is for the DegP+than-clause to pied-pipe

Processing Degree Operator Movement - Salt 2011

two consequences
Two Consequences
    • Exactly phrases are not scopally inert:
      • Since all we did is change Oda/Beck’s semantics of the comparative from <d,<dt,<dt,t>>> to <dtt,<dt,<dt,t>>>, we predict there should be environments in which exactly phrases are not scopally inert. Specifically: any environment where the exactly phrase leaves a d-type trace and moves across an operator with which it is not scopally commutative. Evidence is mixed:
      • Scopally active (at most reading): You’re allowed to miss exactly 3 classes
      • Scopally inert (unambiguous): In order to join the NBA, John is required to be exactly 6 feet tall
  • De dicto unavailable for wide scope readings
    • In our analysis the modal is always below than clause for at least reading  de dicto for than-clause is ruled out
    • Evidence seems to support this prediction but is quite involved

Processing Degree Operator Movement - Salt 2011

de dicto de re
De Dicto / De Re
  • For wide scope reading (ignoring ACE)
    • Heim: modal always below than clause  de dicto for than-clause is ruled out
    • Oda/Beck: modal may be above than clause  optional de dicto for than-clause
  • Forcing wide scope + de re (ok according to both)
    • Base line: forcing wide scope for 'exactly' without controlling for de-dicto/de-reSpeaker A: What do I need to do in order to pay no taxes at all? Do I have to earn less than 20K?Speaker B: Not quite. You are allowed to earn exactly $300 more than that.
    • Now Speaker A: What do I need to do in order to pay no taxes at all? Do I have to earn less than last year's average?Speaker B: Not quite. You are allowed to earn exactly $300 more than last year's average.
  • Forcing wide scope + de dicto (ruled out by Heim)
    • Base line: forcing de-dicto (without thinking about the scope of the degree phrase)Speaker A: What do I need to do in order to pay no taxes at all? Do I have to earn less than average?Speaker B: Not quite. You are required to earn less than average plus $300.
    • Speaker A: What do I need to do in order to pay no taxes at all. Do I have to earn less than average??? Speaker B: Not quite. You are allowed to earn exactly $300 more than average.

Processing Degree Operator Movement - Salt 2011

summary
Summary
  • Can differentials take semantically detectible scope independently of the comparative? NO!
  • We investigated this question in a specific environment with ‘at least’ contexts combined with ACE, using real time processing
  • Our results show that an at least reading is not generated by the following LF:
    • [[exactly 2’’] … [require [… er-than]]]
  • The question is why?
    • Our answer: we devised a compositional semantics that does not give this LF an at least reading

Processing Degree Operator Movement - Salt 2011

slide32

Thank You!

Processing Degree Operator Movement - Salt 2011

appendix
Appendix

Main Effect on Differential

Processing Degree Operator Movement - Salt 2011

residual reading times1
Residual Reading Times

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main effect on diff exactly harder
Main Effect on diff: exactly harder

Processing Degree Operator Movement - Salt 2011

  • Main effect of differential (2 words after “a”/“exactly”):
    • p =0.001 (pMCM) ; “Exactly” condition harder