Processing Degree Operator Movement : Implications for the Semantics of Differentials

1. 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/

2. 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

3. Scope Ambiguities Processing Degree Operator Movement - Salt 2011 Theoretical background

4. 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

5. 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

6. - Narrow Scope - Basic Case Heim’s LFs Processing Degree Operator Movement - Salt 2011

7. 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)

8. - Narrow Scope - Basic Case Oda / Beck LFs Processing Degree Operator Movement - Salt 2011

9. Oda / Beck LFs – 2 Wide Scopes High -er Low -er Processing Degree Operator Movement - Salt 2011

10. 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

11. 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

12. Experimental Design and Analysis of Results Processing Degree Operator Movement - Salt 2011 Real time processing

13. … 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

14. 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

15. 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)

16. 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

17. 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

18. 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

19. 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

20. Predicted Interaction - Heim Processing Degree Operator Movement - Salt 2011

21. 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

22. 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

23. Residual Reading Times Processing Degree Operator Movement - Salt 2011

24. Interaction after ACE site Processing Degree Operator Movement - Salt 2011

25. 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

26. 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

27. Semantics Processing Degree Operator Movement - Salt 2011 Comparatives WITH differentials

28. 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

29. 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

30. 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

31. 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

32. Thank You! Processing Degree Operator Movement - Salt 2011

33. Appendix Main Effect on Differential Processing Degree Operator Movement - Salt 2011

34. Residual Reading Times Processing Degree Operator Movement - Salt 2011

35. 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