I provide experimental evidence that quantifier semantics guides visual verification processes (Lidz et al. 2011). I tested the processing of two majority quantifiers in Bulgarian and Polish: the proportional Most1, the counterpart of English most, and the superlative/relative Most2. Three obtained notable results have been obtained: (i) Most1 is verified by a Subtraction strategy, directly replicating the findings of Lidz et al. for Slavic; (ii) Most2 is verified by a Selection strategy in accordance with its lexical semantics; (iii) each verification strategy is consistently used even in cases where either strategy would yield the correct truth value.
Lidz et al. (2011) argue that the verification of truth/falsity a declarative sentence is
biased towards those procedures that are transparently associated with the semantic
representation of that sentence. They show that sentences containing the quantifier most such as
(
2. |Dot(x) & Yellow(x)| > |Dot(x)| – |Dot(x) & Yellow(x)| 3. |Dot(x) & Yellow(x)| > |Dot(x) & Red(x)| + |Dot(x) & Blue(x)| + |…|
I provide further experimental evidence that quantifier semantics guides the verification process. My evidence is based on the comparison of the verification patterns of two minimally distinct quantifiers and suggests that the properties of the linguistic input directly influence the unconscious visual processes.
The meaning of most intuitively refers to a comparison of quantities, where one of the quantities is greater than others. For countable objects what is compared are cardinalities. Visual perception of numerical information has been studied extensively and it is known in psychology that the visual selection of a target "can be influenced by expectations and strategies" (Trick, 2008). Manipulating a linguistic stimulus affects the patterns of the visual search for obtaining a cardinality (or its estimation), however, at the same time the choice of the visual verification strategy is also constrained by the psychophysics of visual cognition. We can both formulate hypotheses and interpret the visual response pattern on the basis of the findings about human perception in visual numerical judgment tasks. Under time pressure, when precise counting becomes impossible, people switch to the Approximate Number System (ANS) that generates a representation of magnitude and is governed by Weber’s law, i.e. the greater the distance between two numbers the better discriminability (Dehaene, 1997). Numbers can be represented as 'noisy magnitudes' even for the purposes of basic arithmetic operations like addition and subtraction. Quantifiers can be verified against a visual display even when counting is blocked.1 Psychophysical constraints, however, affect the accuracy of judgment.
Lidz et al. (2011) hypothesize that the procedure in (
I argue, however, that the choice of the procedure (
I tested the processing of two majority quantifiers in Bulgarian and Polish: the
counterpart of English proportional majority quantifier most (povečeto in Bg, większość in Pl,
henceforth Most1) and a superlative/relative majority quantifier (naj-mnogo in Bg,
najwięcej in Pl, henceforth Most2). I obtained three notable results:
1 Also Halberda, Taing and Lidz (2008) have shown that children who have not yet learned to count
are perfectly able to understand sentences containing most.
• Most1 is verified by a Subtraction strategy as in (
The results have some immediate implications for the semantics of quantifiers and the interface of semantics with visual cognition. We can argue for the contribution of the individual morphemes not only to the meaning of Most1 vs Most2 but also to the interface with the visual cognition. The combined Bulgarian and Polish results further strengthen the conclusions I presented in Tomaszewicz (2011) that quantifier semantics provides a set of instructions to visual verification processes, since each of the two Polish Most1 and Most2 biases a distinct verification strategy.
. 2
Pietroski et al. (2008), Lidz et al. (2011) devised experimental paradigms to look
“beyond” the truth conditions of (
(b) OneToOnePlus({Dot(x)&Yellow(x)},{Dot(x)&~Yellow(x)})
Pietroski et al. (2008) obtained evidence that even when the arrangement of dots favors
the verification by strategy in (5b) (i.e. paired vs. unpaired arrangements of dots in two
colors), this strategy is not used. Using the same experimental paradigm requiring visual
verification under time pressure (screens displayed for 150 ms), Lidz et al. (2011)
investigated how the cardinality of the non-yellow set in (5a) is estimated when this set contains
dots in 1-4 different colors. They tested which of the two specifications in (
|{Dot(x)&Red(x)} ∪{Dot(x)&Blue(x)} ∪ {Dot(x)&Green(x)} ∪…| 7. Subtraction strategy |Dot(x)| – |Dot(x)&Yellow(x)|
Their proposed Subtraction strategy is based on the psychological evidence that a
heterogeneous set is not automatically selectable (i.e. red, green, blue dots are not
automatically processed as one set unless it is the total set of dots), as well as on the findings of
Halberda et al. (2006) that humans can automatically (i.e. without a prompt) compute the
total number of dots and two color subsets but no more. Thus, Subtraction in (
In the experiment of Lidz et al. (2011) screens with dots in up to 5 colors in varying
ratios (yellow to non-yellow dots) were flashed for 150ms. Twelve participants evaluated
whether the sentence in (
Yet, even on the two-color condition Subtraction appeared to be used, since the accuracy was not higher than on the multi-color screens, i.e. the verification procedure failed to make use of the automatically obtained information, the cardinality of the two subsets that could be compared directly (Halberda et al. 2006). Thus, Lidz et al. conclude that Subtraction is the default procedure for verifying most under time pressure. On the basis of this finding they formulate the Interface Transparency Thesis: “the verification procedures that speakers employ, when evaluating sentences they understand, are biased towards algorithms that directly compute the relations and operations encoded by the relevant logical forms” (Pietroski et al. 2011).2 2 What is crucial when comparing different strategies is evidence that a more advantageous strategy is failed to be used in favor of one that can be directly linked to semantics. Pietroski et al. (2011) “take it as given that speakers use various strategies in various situations. For us, the question is whether available procedures are neglected—in circumstances where they could be used to good effect—in favor of a strategy that reflects a candidate logical form for the sentence being evaluated.” A strategy may be abandoned in favor of one that is unrelated to a semantic representation, but that cannot be taken as evidence against a particular semantic specification.
Bulgarian and Polish have “two” versions of the English majority quantifier most.
Most1 in both languages has the same proportional reading as the English most has, so
that (8a) and (9a) are equivalent to (
8.
(a) Povečeto točki sa žəәlti.
Most1 dots are yellow 'Most dots are yellow.' (b) Naj-mnogo točki sa žəәlti.
Most2 dots are yellow 'Yellow dots form the largest subset.’ (a) Większość kropek jestżółta.
Most1 dots is yellow 'Most dots are yellow.' (b) Najwięcej jestkropek żółtych.
Most2 is dots yellow 'Yellow dots form the largest subset.'
Most2 in Bulgarian (8b) and Polish (9b) contains superlative morphology in contrast to Most1 as illustrated in (11). In accordance with the standard meaning of the superlative morpheme (the relative reading), Most2 modifying a noun says that what the noun denotes is the most numerous thing among other things of the same type, in our case, the set of yellow dots is more numerous than any other color set.
I predicted that Most1, being equivalent to the English most, should be compatible with the Subtraction strategy. Thus, the number of color sets was expected to not affect the accuracy of judgments with Most1 (it should only be affected by the ratio of yellow to non-yellow dots). Since the semantics of Most2 can be specified as in (10), which I call Stepwise Selection, I expected to find both an effect of ratio and of number of colors in contrast to Most1. 10. Stepwise Selection strategy |Dot(x) & Yellow(x)| > |Dot(x) & Red(x)|, & |Dot(x) & Yellow (x)| > |Dot(x) & Blue(x)|, & |Dot(x) & Yellow (x)| > |Dot(x) & Green(x)|, & …
Both of the predictions were met. The results of the Experiment 1 (on Bulgarian) and of the Experiment 2 (on Polish) contain exactly the same main effects in the two conditions. 3.1
Experiments 1 and 2: Materials and methods
I conducted two on-line visual-display verification studies designed along the lines of the experiment of Lidz et al. (2011). A group of 39 native speakers of Bulgarian participated in Experiment 1 and 20 native speakers of Polish participated in Experiment 2. The Polish experiment is reported in Tomaszewicz (2011).
The procedure was identical in both experiments. The participants evaluated the truth
of the sentences in (
As the schema in Fig. 8 in the Appendix shows, 360 displays were presented in 2 blocks (180 for Most1 and 180 Most2, half of each requiring a yes response and half a no response). Participants had 380ms to indicate their response by a button press. The experiment was performed using Presentation® software (Version 14.2, www.neurobs.com). 3.2
Experiments 1 and 2: Results
For Most1 accuracy rates were significantly affected only by ratio, and not by number of color sets (Table 3, rows (a),(c)). For Most2 accuracy rates were significantly affected both by ratio and by number of color sets (Table 3, rows (b),(d)). I analyzed each quantifier with a 3x3x2 Repeated Measures ANOVA crossing the 3 levels of the ratio variable, 3 levels of distractor, and the truth/falsity of screens: .871 .866
The accuracy rates with Most1 in Bulgarian and Polish are significantly affected only
by ratio3 and not by number of color sets. These results are the same as for the English
most in Lidz et al. (2011) and are entirely consistent with the prediction that Most1 is
verified by Subtraction. The graphs in Fig. 2 and Fig. 3 clearly show the lack of a main
effect of number (Bulgarian: F(
The results for Most2 are entirely compatible with the view that it is verified by
Selection. In both Bulgarian (Fig. 4) and Polish (Fig. 5) the accuracy rates are significantly
affected both by ratio (Bulgarian: F(
It is also evident in the graphs in Fig. 5 and Fig. 6 that the accuracy with Most2 is affected by the truth/falsity of screens. The present design does not allow us to determine the reason for this, however, with Selection correct estimation of both the target set and each color set is expected to be affected by a higher number of factors than Subtraction.
Crucially, the significant effect of number of colors in addition to the effect of ratio indicate that both the yellow set and the other color sets are selected for the verification of Most2 in conformity with its semantics.6
Importantly, on screens with 2 color sets (identical for both quantifiers) both Bulgarian and Polish participants were significantly less accurate and slower confirming the truth of Most1 than of Most2. This indicates that Subtraction continues to be used with Most1 and Selection with Most2 even on the condition, where switching between the two procedures would provide more accurate results.
Participants could have used whichever strategy is computationally less costly/more accurate under time pressure, since both strategies are otherwise used by the speakers of Bulgarian and Polish. If the semantic representation guides verification, then with Most2 the non-yellow set should be selected directly – the accuracy should be greater than with Most1 where the non-yellow set is computed (cf. Lidz et al. 2011), which is exactly what we find on true screens.
6 Note that successful selection and comparison of 3-4 color sets in 200ms is not inconsistent with the findings of Halberda et al. (2006). The three set limit is on the automatically obtained information without a stimulus that creates expectations and directs attention to some specific aspect of the display. The superlative morphology clearly contributes an expectation that multiple sets should be compared.
Both Bulgarian and Polish participants were significantly better with Most2 than
Most1 on true screens (Bulgarian: (F(
Notably, the two languages also behave exactly the same with respect to the reaction
times. The accuracy is higher despite faster RTs and lower despite slower RTs (Table 4).
On true screens Most2 is faster (Bulgarian: F(
Crucially, the accuracy patterns together with RTs consistent in both languages indicate that participants do not switch to the more advantageous strategy, e.g. they don’t use Selection to more accurately confirm the truth of Most1. This is the more interesting given the findings of Halberda et al. (2006) that the cardinality of two color sets is automatically computed. Yet the semantics of Most1 apparently precludes the use of this automatically available information.
Different behavior with each quantifier on the very same screens indicates that participants do not switch between the procedures and that the way those procedures differ is specified by the semantics. Computation for both Most1 and Most2 involves the comparison between the yellow and the non-yellow set. The components provided by the visual system are exactly the same: yellow set, non-yellow set, superset. However, the algorithms must be different. To verify Most2 one has to (i) estimate target, (ii) estimate competitor, (iii) compare. To verify Most1 one needs to (i) estimate target, (ii) estimate total, (iii) subtract target from total. The lexical meaning of the functional morphemes that build up Most1 and Most2 and their logical syntax are interfacing with the visual system during the verification process. 4
In conclusion, our experiments indicate that semantics provides a direct set of instructions to the visual cognition processes, and that these instructions are followed even when computationally more advantageous strategies are available.
We have met the prediction that Bulgarian and Polish proportional majority quantifier Most1, just like English most, is verified using Subtraction strategy (we found a main effect of ratio and no effect of number of colors). The superlative/relative majority quantifier Most2 requires the Stepwise Selection strategy (as evidenced by the effect of ratio together with the effect of number of colors)7. Importantly, in a within-subject design the same group of participants behaves differently depending on the quantifier. The overall patters of accuracy are exactly the same in Bulgarian and Polish. 7 As one of the reviewers observes, my evidence for the different verification processes for Most1 and Most2 is based on the use of the ANS representation of magnitude for the comparisons required by the semantics. If the superlative Most2 incurs a larger processing cost, it would be interesting to see if we find evidence for it also in experiments where counting is not precluded. Note, however, we cannot just “switch off” ANS, e.g. the effects of ratio-dependency characteristic of ANS are present also with judgments involving Arabic numerals,s although the quantities evoked by Arabic numerals may be more precise than those evoked by sets of dots (Dehaene 1997).
On two color screens (where Most1 and Most2 are either both true or both false) the verification procedure depends on the lexical item used. The patterns of accuracy for Most1 and Most2 were conspicuously different (but had the same direction in both Bulgarian and Polish) indicating that computationally Most1 and Most2 are different.
My results confirm and extend the findings of Pietroski et al. (2008) and Lidz et al. (2011) and indicate that semantics provides inviolable instructions to visual cognition processes.
I would like to thank Roumi Pancheva as well as Elsi Kaiser, Barry Schein and Toby Mintz, for their invaluable comments and/or help with the experiments. Thanks are also due to Hagit Borer, Jeff Lidz, Martin Hackl, Victor Ferreira, Jon Gajewski, Robin Clark, Tom Buscher, Katy McKinney-Bock, Mary Byram, Ed Holsinger, Krzysztof Migdalski, Dorota Klimek-Jankowska, Grzegorz Jakubiszyn, Ewa Tomaszewicz, Marcin Suszczyński, Patrycja Jabłońska, Petya Osenova, Halina Krystewa, Petya Bambova, Ewa Panewa, Bilian Marinov, Marieta and the students of IFA at Wroclaw University and WSF Wroclaw and Polish Institute in Sofia. My work was partially supported by an Advancing Scholarship in the Humanities and Social Sciences Grant from USC awarded to R. Pancheva. no. of screens ratio distractors Fig. 8. A schema of the experimental procedure.