Overview of Grodner et al. (2010)

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1 Overview of Grodner et al. (21) Chris Potts, Ling 236: Context dependence in language and communication, Spring Background April 16 Central question of Grodner et al. (21) (henceforth G1): Is there a processing cost to interpreting some as some but not all? Like Huang and Snedeker (29) (HS9), G1 put subjects in an experimental situation in which the relevant scalar implicatures are highly relevant, in that they are crucial for fast object identification. Thus, neither paper addresses the question of whether generalized implicatures arise as defaults in other kinds of context. Rather, they address how quickly such inferences are made where they are relevant. (Compare with Breheny et al. (26), who sought to manipulate the contextual relevance of the target implicatures.) 2 Materials 46 D.J. Grodner et al. / Cognition 116 (21) 4 Table 1 Duration (in m G1 adapt the method of HS9. Using the visual-world eye-tracking paradigm, they analyze how quickly subjects fixate on the target item while listening to prerecorded audio sentences like (3). (3) Click on the girl who has a.... summa the balls. (Early-summa in fig A, Late-summa in fig. B) b.... alla the ballons (Alla) c.... nunna the items. (Nunna) 46 D.J. Grodner et al. / Cognition 116 (21) Table 1 Duration (in ms) of critical speech regions. Standard errors in parentheses. Quantifier to noun onset Noun onset to disambiguation Summa 348 (5.4) 257 (14.8) Alla 338 (5.1) 23 (13.6) Nunna 418 (2.8) N/A Table 2 Duration (in ms) between quantifier onset to determiner onset and for critical stimuli for this study and Huang and Snedeker. Standard errors in parentheses. Figure 1: G1 s visual scenes. Present study Huang and Snedeker Summa/some of 243 (33) 328 (78) Alla/all Fig. 1. of The displays for: 183 (A) (39) the Early-Summa, 267 Alla, (39) and Nunna conditions, and (B) the Late-Summa condition. Summa conditions revealed that the interval between the We constructed 32 stimulus items. Test stimuli were onset of the quantifier and noun was marginally shorter separated into four lists, where each condition was equally for the Alla commands (F(1, 31) = 3.1, p =.9) as was the represented, and each item appeared once. Across lists, interval between the noun onset and POD (F(1, 31) = 2.9, each item appeared in each condition an equal number of p =.1). Thus, if anything, the identifying acoustic informatimes. Test stimuli were presented in random order and Summa Alla Nunna Table 2 Duration (in m critical stimul parentheses. Summa/som Alla/all of Summa con onset of th for the Alla interval be p =.1). Th tion was de To deter of our item auditory st Three resea ses being te quantifier were highl fier lengths reliably sh MSE =.5, p <.1). T tion of the in the prese malized by of the verb

2 3 Central differences from Huang and Snedeker (29) (4) G1 use more complex displays with more figures and more objects. (5) G1 had a Nunna (none of) condition as a literal control in addition to Alla. (6) G1 s had 4 fillers (32 test items), whereas HS9 used no fillers. (7) G1 use reduced forms of the quantifiers to provide an earlier cue that the partitive is coming. (See p. 46, right, on what this did to the vowels and the length of the nominal.) a. The implicatures of some are robust only for the partitive. See Degen et al. s (29) gumball paradigm, in which gumballs drop from a higher chamber into a lower one. You got some gumballs was accepted in situations where all of the gumballs dropped, whereas You got some of the gumballs was rejected (p. 44, left). b. Appendix A study: aligns with Degen et al. s finding that the partitive is less natural than the bare form when picking out all (p. 51, right). c. Thus, it could be that people waited to compute implicatures until they heard of, whereas there is no need to wait for the other quantifiers. (8) G1 s instructions included a description of the domain of discourse that provided the counts of all the items in it (There are four balls, four planets, and four balloons; p. 45, right). This was to enhance the salience of the full set of each object type as a means of identifying a referential candidate. This potentially makes the contrast between full sets and sub-sets more prominent and could thus facilitate the comparison of alternatives that leads to the scalar inference. (p. 45, left). (9) G1 had no numerical conditions; the only numerical quantifiers people heard were in preliminary descriptions of the domain of discourse. a. Number terms are more natural than some where the number of objects is in the subitizing range. b. Appendix B study: including number terms reduced the naturalness of using some of. (1) G1 had a Late-summa condition in which even the enriched meaning was ambiguous until the descriptive content of the nominal (socks vs. soccer balls). Could further illuminate when people make pragmatic inferences (p. 45, right). Are they willing to do it even when the enriched meaning of the quantifier still underspecifies the referent? 2

3 4 Results.J. Grodner et al. / Cognition 116 (21) ere recorded ean response greater than cluded trials (.9%) and triandard devialish when the d the proporined fixations e Alla condie Summa tarct measure of ntly active to se in the ratio agmatic some depicts fixach of the critlyses, target ws: (1) from onset (gender er until POD er POD (posts were offset d for planning ff, 1993). The was whether r each condifore phonetic tification ocs were comuantifier, and were reliably, the Alla conkely reflects a cts. This trend tifier (Fig. 3), l three Huang ndingly, fixana conditions (1, 23) = 7.91, <.1; Nunna: = 4.75, MSE = t proportions Early-Summa:.15, MSE =.19, =.2, p <.5; 1, 23) = 11.53,.21, p <.1; res were submitgresti (22); see it transformation ve patterns were logit-transformed Looks to Target / Looks to Target + Competitor Looks to Target / Looks to Target + Competitor summa (early) alla nunna summa (late) chance = 5% Click on the girl who has the ball- -oons + 4ms summa (early) alla summa (late) nunna chance = 5% Time after quantifier onset (ms) Fig. 2. Fixations to the target as a proportion of combined fixations to the target and critical competitor. For Alla, the competitor was the Summa (a) G1, fig 2. target. For the other conditions the competitor was the Alla target. The top panel depicts target proportions over the gender interval, the quantifier interval, and the post-disambiguation interval. The lower panel depicts target proportions over each 1 ms window from the beginning of the quantifier. Nunna: F1(1, 23) = 39.28, MSE =.12, p <.1; F2(1, 31) = 45.69, MSE =.15, p <.1). Note that target proportions in the quantifier interval for Late-Summa were numerically slightly lower than for Early-Summa. This is expected because participants fixations were divided between the two targets consistent with pragmatic some; however, the target ratio for this analysis only included fixations to the correct target. To more precisely determine when the pragmatic interpretation emerged, we analyzed each 1 ms interval after the onset of the quantifier. Unlike the preceding analyses, intervals were not offset by 2 ms. A main effect of condition for the 2 ms before the quantifier was significant by items (F2(3, 93) = 2.81, MSE =.6, p <.5) but not by participants (F1(3, 69) = 2.15, MSE =.42, p =.1), reflecting more fixations to the Alla target than to Summa and Nunna targets. We compensated for differences in initial looking preference by using this 2 ms interval as the baseline rate of target fixations. Target convergence was defined as the first 1 ms interval for which the proportion of target fixations exceeded the baseline. For the Alla condition, target proportions were reliably higher than baseline 2 3 ms after quantifier onset in the participants analysis (F1(1, 23) = 5.73, MSE =.12, p < 5), but only marginally reliable by items (F2(1, 31) = 2.46, MSE =.33, p =.6). For Proportion of looks to target Y.T. Huang, J. Snedeker / Cognitive Psychology 58 (29) Two Some Three All BASELINE GENDER CUE QUANTIFIER DISAMBIGUATION END PHASE PHASE PHASE PHASE PHASE Point to the girl that has of the soc- -ks (end) Fig. 5. In Experiment 2, the time-course of looks to Target for the four trial types. In the coarse-gained time windows, there were no reliable effects of Quantifier Scale or Strength during the Baseline and Gender phases (all F s < 4., all p s >.5). This changed during the Quantifier phase where fixations to the Target character increased when participants heard two (66%), three (72%), and all (72%) but not when they heard some (45%). During this period, there were both main effects of Quantifier Scale (F1(1,16) = 5.16, p <.5; F2(1,15) = 6.39, p <.5) and Quantifier Strength (F1(1,16) = 16.86, p <.1; F2(1,15) = 18.29, p <.1). Critically, there was also the predicted significant interaction between these variables (F1(1,16) = 6.58, p <.5; F2(1,15) = 5.25, p <.5). Planned comparisons within the levels of Quantifier Strength revealed that looks to the Target in the some trials were significantly lower than in the two trials (t1(19) = 3.22, p <.1; t2(15) = 3.11, p <.1) but there was no reliable difference between the all and three trials (t1(19) =.1, p >.5; t2(15) =.4, p >.5). Comparisons within the Quantifier Scales revealed that there was no difference between two and three trials (t1(19) = 1.8, p >.2; t2(15) =.98, p >.3) but a reliable difference between the some and all trials (t1(19) = 3.93, p <.1; t2(15) = 4.15, p <.1). However, unlike Experiment 1, this pattern quickly disappeared after the onset of the final phoneme (see Fig. 6). Fixations to the Target character during the Disambiguation phase increased for all trial types (82% for the two trials, 91% for the three trials, 86% for the all trials, and 71% for the some trials). In this region there was a significant effect of Quantifier Strength (F1(1,16) = 15.65, p <.1; F2(1,15) = 23.66, p <.1) but no effect of Quantifier Scale (F1(1,16) = 3.19 p >.5; F2(1,15) = 3.2, p >.5) and no interaction (F1(1,16) =.73, p >.1; F2(1,15) =.63, p >.1). Finally, during the End phase, total fixations closed in unsurprisingly on the Target leading to no effect of Quantifier Scale (F1(1,16) =.24, p >.1; F2(1,15) =.7, p >.1) and Strength (F1(1,16) =.78, p >.1; F2(1,15) =.48, p >.1), and no interaction between them (F1(1,16) =.32, p >.1; F2(1,15) =.29, p >.1). Additional analyses of 2 ms intervals following the quantifier onset confirmed the difference in time it took participants to reliably fixate on the Target character across the four terms. Table 3 displays the proportion of looks to the Target for each quantifier type during each of these time windows. There was a significant Quantifier Scale by Strength interaction that began approximately 4 ms after the onset of the quantifier (F1(1,16) (b) = 6.78, HS9, p <.5; F2(1,15) fig. = , p <.5) and continued into the 6 ms time window (F1(1,16) = 11.9, p <.1; F2(1,15) = 14.19, p <.1). During this period, the proportion of looks to the Target on the two (t1(19) = 4.77, p <.1; t2(15) = 3.62, p <.1), three (t1(19) = 4.2, p <.1; t2(15) = 4.76, p <.1), and all (t1(19) = 2.82, p <.5; t2(15) = 3.22, p <.1) tri- Figure 2: G1 central timing result compared with those of HS9, experiment 2. (11) Prior to the quantifier, there is a bias for looking at the Alla target. This is due to a bias in the visual system for looking at more complex images; HS9 saw these effects as well. (12) Thus, the denominator in the y-axis measurement in fig 2, top (given above), combines looks to the target with looks to the Alla target. For Alla, the denominator includes Summa targets. (For discussion of this, see p. 51, right, and fn. 7 on how HS9 addressed this.) (13) In the Quantifier interval, looks to the target are above chance for all determiners (p. 47, left). This is a central contrast with HS9. Late-summa shows the least gain, due to the fact that it remains ambiguous in this region even if enriched. (14) Fig 2, bottom, looks at the 1ms after the quantificational determiner (p. 47, right). The baseline corrects for the bias for Alla targets. Convergence in this region is reliable for all conditions except Late-Summa (which is only fully disambiguated later). (15) For Late-summa trials, subjects reliably shifted to one of the two Summa targets within the 1ms interval after the determiner (p. 48). 3

4 p Ling 236, Stanford (Potts) Items analysis Main effect of condition (early-summa vs. alla) F(1, 31) p * * * * * * * Main effect of interval (baseline vs. current) F(1, 31) p.6.7 ** * ** *** *** Interaction F(1, 31) p (16) Is convergence reliably more robust for the Alla condition? If so, that would be in line with HS9 s findings. * p <.5 To find support for accepting the null hypothesis that Alla and Summa do ** p <.1 *** p<.1. not differ, G1 use a Bayesian method (p.49): convergence was faster in the Alla condition. To this end, we employed the Bayesian method outlined by Gallistel (29) for comparing the likelihood of the null hypothesis to a reasonably specified alternative hypothesis. To compensate for visual biases, target convergence was defined as the difference between target proportions during the baseline interval and target proportions during the interval 2 3 ms after quantifier onset where convergence was first observed. To license modeling hypotheses using a normal distribution, proportions were submitted to a log odds transform prior to calculating target convergence values. These values were calculated for each subject in the Alla Null hypothesis: the mean target convergence values for All and Early-summa are identical. (Null prior = normal distribution based on the log-odds proportions for Early-summa.) Alternative hypothesis: the mean target convergence values for All and Earlysumma are maximally dissimilar in that Alla conditions lead to perfect convergence in this 1ms interval and Earlysumma conditions lead to convergence in this interval. and Early-Summa conditions. We evaluated whether the mean target convergence values for Alla and Early-Summa were the same or whether the mean for the Alla condition was larger for each interval. The method requires determining a plausible range of effect sizes for the alternative hypothesis. At the lower bound, it might be that there is no difference between target convergence in the Alla and Early-Summa conditions. At the higher bound, the alternative hypothesis might predict that target proportions could increase from chance levels in the baseline interval (1/2) to complete convergence on the target for the Alla condition (1, which was converted to.99 in this analysis to avoid division by zero), but zero target convergence for Early- Finding: the null hypothesis is vastly more likely given the likelihood function of the Alla data than is the alternative hypothesis within the range of possible effect sizes. Summa. The maximally vague alternative hypothesis is one in which any effect size in between these bounds is equally likely. Fig. 4A depicts the prior probability density functions for the null hypothesis and maximally vague alternative hypothesis. These were derived from the target convergence data from the Early-Summa condition and can be thought of as predictions for the data in the Alla condition. Fig. 4A also depicts the likelihood function of the Fig. 4. Panel A: the prior probability density functions of the null hypothesis and the maximally vague alternative hypothesis along with the likelihood function of the Alla data. The high degree of overlap between the null and likelihood functions indicate that it does a superior job of predicting the data. Panel B: the odds in favor of the null as a function of the upper limit on the possible size of the effect. The dotted line indicates where the odds ratio reverses (from favoring the null to favoring the alternative). For all effect sizes greater than zero, the odds ratio favors the null hypothesis. Figure 4: Baysian modeling for accepting the null hypothesis that Alla and Early-summa do not differ in the 1ms after hearing the determiner. 5 Questions and responses (17) Did subjects develop a nonce association between Summa utterances and one of the two summa targets? (This would have been detected in HS9 s experiment since two of also described those images.) Response: a. Such associations would need to be developed during the experiment, but there was no effect of order on the core results (p. 5, right). b. Such associations would have led people astray during fillers involving the. c. Such associations would have needed to be sensitive to the gender of the person in the target picture. d. Summa items were associated with both two- and three-object displays, making encoding without pragmatic comparison even harder. (18) The Nunna conditions used items, which is much more taxonomically abstract than the other objects. Could this have confused subjects? Response: not impossible, but this won t explain the response patterns (p. 5, right). 4

5 References Breheny, Richard; Napoleon Katsos; and John Williams. 26. Are generalised scalar implicatures generated by default? an on-line investigation into the role of context in generating pragmatic inferences. Cognition 1: Degen, Judith; Patricia A. Reeder; Katie Carbary; and Michael K. Tanenhaus. 29. Using a novel experimental paradigm to investigate the processing of scalar implicatures. Slides from Experimental Pragmatics 29. Grodner, Daniel J.; Natalie M. Klein; Kathleen M. Carbary; and Michael K. Tanenhaus. 21. some, and possibly all, scalar inferences are not delayed: Evidence for immediate pragmatic enrichment. Cognition 116(1): Huang, Ti Ting and Jesse Snedeker. 29. Online interpretation of scalar quantifiers: Insight into the semantics pragmatics interface. Cognitive Psychology 58(3):