The role of Alternatives in the interpretation of scalars and numbers: Insights from the inference task

What it is about

Numerical noun phrases ("three children") are ambiguous between "at least n" and "exactly n". The scalar-implicature view says the exact reading comes from excluding a higher alternative, as "some" gives "not all". The authors test this with an inference task, where participants judge whether a sentence licenses the negation of an alternative. They add a second probe. The standard "not Alt" probe asks whether one may conclude that the alternative is false. The new "could Alt" probe asks whether one may conclude that the speaker thinks it could be true, which makes the alternative look irrelevant. Forty adults were recruited and five removed for more than 20% wrong control answers, leaving 35. The items covered <some, all>, <possible, certain> and numerals three to five. Control accuracy was 92%. For "some" and "possible" the rate of implicature responses was higher under "not Alt" than under "could Alt", as the scalar view predicts. For numerals the pattern reversed: the could-Alt probe gave more target responses (beta 2.58, SE 0.66, p < .001). The authors conclude that the exact reading of numerals is strongly biased but not derived by scalar implicature.

Ideas

• I1. world/src/knowledge.rs: add a "could-alt" variant to school multiple-choice items where the higher number is marked as irrelevant. The SLM student's reading of a numeral ("at least" or "exactly") should not change under this manipulation. Measure agreement across the two variants.
• I2. prag/src/infer.rs: keep numerals as a two-reading entry, with the at-least reading as the default and the exact reading set by a flag, rather than by excluding an alternative. The scalar "some" should flip with the relevance cue, the numeral should not. Run both as a control.
• I3. Use the design as a deterministic test: for each item, record the rule that fired (exclusion or default) and check that the flip rate for "some" is above the numeral rate. Run twice and compare the outputs before any claim.
• I4. Report per-item counts with a plain binomial test, not a mixed model, since Mova has no random effects. Keep the 35-participant design as a reminder that small samples need counts shown in full.

For Mova

The chapters are 12. Pronouns, determiners and numerals (numerals and their readings) and 33. Implicature and presupposition (scalar terms). The code is prag/src/infer.rs for implicature rules and world/src/knowledge.rs for the school items. The measure is the rate of the exact reading on the two probe variants, as a difference between "some" and numerals, with a negative control in which the scalar term is replaced by a non-scalar one.

Topics: Implicature

Cite

The paper itself, not this card. BibTeX from the library's record of the work. DOI 10.3765/sp.15.8

@article{sun2022role,
  title = {{The role of Alternatives in the interpretation of scalars and numbers: Insights from the inference task}},
  author = {Sun, Chao and Breheny, Richard},
  journal = {Semantics and Pragmatics},
  year = {2022},
  doi = {10.3765/sp.15.8},
  url = {https://doi.org/10.3765/sp.15.8}
}

References

22 references, 0 of them with a card of ours. ↗ leads to the work, «find» searches for one we have no id for yet.

1. Barner, David & Asaf Bachrach. 2010. Inference and exact numerical representation in early language development. Cognitive Psychology 60(1). 40– 62. https://doi.org/10.1016/j.cogpsych.2009.06.002. ↗
2. Bates, Douglas, Martin Maechler, Ben Bolker & Steve Walker. 2015. Fitting linear mixed-effects models using lme4. Journal of Statistical Software 67(1). 1–48. https://doi.org/10.18637/jss.v067.i01. ↗
3. Breheny, Richard. 2008. A new look at the semantics and pragmatics of numerically quantified noun phrases. Journal of Semantics 25(2). 93–139. https://doi.org/10.1093/jos/ffm016. ↗
4. Buccola, Brian & Benjamin Spector. 2016. Modified numerals and maximality. Linguistics and Philosophy 39(3). 151–199. https://doi.org/10.1007/s1098 8-016-9187-2. ↗
5. De Neys, Wim & Walter Schaeken. 2007. When people are more logical under cognitive load: Dual task impact on scalar implicature. Experimental psychology (2). 128–133. https://doi.org/10.1027/1618-3169.54.2.128. ↗
6. Degen, Judith & Michael K. Tanenhaus. 2015. Processing scalar implicature: A constraint-based approach. Cognitive Science (4). 667–710. https://doi.org/10.1111/cogs.12171. ↗
7. Dieuleveut, Anouk, Emmanuel Chemla & Benjamin Spector. 2019. Distinctions between primary and secondary scalar implicatures. Journal of Memory and Language 106. 150–171. https://doi.org/10.1016/j.jml.2019.02.0 08. ↗
8. Fox, Danny & Roni Katzir. 2011. On the characterization of alternatives. Natural Language Semantics 19(1). 87–107. https://doi.org/10.1007/s11050-010-9065-3. ↗
9. Geurts, Bart. 2006. Take ‘five’: The meaning and use of a number word. In Svetlana Vogeleer & Liliane Tasmowski (eds.), Non-definiteness and plurality (Linguistics Today 95), 311–329. Amsterdam: John Benjamins. https://doi.org/10.1075/la.95.16geu. ↗
10. Geurts, Bart. 2010. Quantity implicatures. Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511975158. ↗
11. Chao Sun, Richard Breheny Geurts, Bart & Nausicaa Pouscoulous. 2009. Embedded implicatures?!? Semantics and Pragmatics 2(4). 1–34. https://doi.org/10.3765/sp.2.4. ↗
12. Horn, Laurence R. 1972. On the semantic properties of logical operators in English. University of California Los Angeles PhD dissertation. https://li nguistics.ucla.edu/images/stories/Horn.1972.pdf. ↗
13. Horn, Laurence R. 1992. The said and the unsaid. Semantics and Linguistic Theory 2. 163–192. https://doi.org/10.3765/salt.v2i0.3039. ↗
14. Huang, Yi Ting, Elizabeth Spelke & Jesse Snedeker. 2013. What exactly do numbers mean? Language Learning and Development 9(2). 105–129. https://doi.org/10.1080/15475441.2012.658731. ↗
15. Hurewitz, Felicia, Anna Papafragou, Lila Gleitman & Rochel Gelman. 2006. Asymmetries in the acquisition of numbers and quantifiers. Language Learning and Development 2(2). 77–96. https://doi.org/10.1207/s154733 41lld0202_1. ↗
16. Kennedy, Christopher. 2015. A “de-Fregean” semantics (and neo-Gricean pragmatics) for modified and unmodified numerals. Semantics and Pragmatics 8(10). 1–44. https://doi.org/10.3765/sp.8.10. ↗
17. Kuznetsova, Alexandra, Per B. Brockhoff & Rune H.B. Christensen. 2017. lmer-Test package: Tests in linear mixed effects models. Journal of Statistical Software (13). 1–26. https://doi.org/10.18637/jss.v082.i13. ↗
18. Marty, Paul, Emmanuel Chemla & Benjamin Spector. 2013. Interpreting numerals and scalar items under memory load. Lingua 133. 152–163. https://doi.org/10.1016/j.lingua.2013.03.006. ↗
19. Papafragou, Anna & Julien Musolino. 2003. Scalar implicatures: Experiments at the semantics–pragmatics interface. Cognition (3). 253–282. https://do i.org/10.1016/S0010-0277(02)00179-8. ↗
20. R Core Team. 2020. A Language and Environment for Statistical Computing. Vienna, Austria. https://www.r-project.org/. ↗
21. Rees, Alice & Lewis Bott. 2018. The role of alternative salience in the derivation of scalar implicatures. Cognition 176. 1–14. https://doi.org/10.1016/j.cognition.2018.02.024. ↗
22. Singh, Raj. 2019. Context, content, and the occasional costs of implicature computation. Frontiers in Psychology 10. 2214. https://doi.org/10.3389/f psyg.2019.02214. van Tiel, Bob, Emiel van Miltenburg, Natalia Zevakhina & Bart Geurts. 2016. Scalar diversity. Journal of Semantics 33(1). 137–175. https://doi.org/10.1 093/jos/ffu017. Scalars and numerals in inference tasks Chao Sun ZAS, Schützenstr. 18 10117, Berlin Peking University, Yiheyuan Road 5 100871, Beijing, China chaosun@pku.edu.cn Richard Breheny Chandler House, 2 Wakefield Street London WC1N 1PF r.breheny@ucl.ac.uk ↗

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