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. Author manuscript; available in PMC: 2016 Jun 1.
Published in final edited form as: Lang Cogn Neurosci. 2014 Dec 24;30(5):620–634. doi: 10.1080/23273798.2014.981195

The Neural Computation of Scalar Implicature

Joshua K Hartshorne 1,1, Jesse Snedeker 2, Stephanie Yen-Mun Liem Azar 3, Albert E Kim 4
PMCID: PMC4406494  NIHMSID: NIHMS641680  PMID: 25914890

Abstract

Language comprehension involves not only constructing the literal meaning of a sentence but also going beyond the literal meaning to infer what was meant but not said. One widely-studied test case is scalar implicature: The inference that, e.g., Sally ate some of the cookies implies she did not eat all of them. Research is mixed on whether this is due to a rote, grammaticalized procedure or instead a complex, contextualized inference. We find that in sentences like If Sally ate some of the cookies, then the rest are on the counter, that the rest triggers a late, sustained positivity relative to Sally ate some of the cookies, and the rest are on the counter. This is consistent with behavioral results and linguistic theory suggesting that the former sentence does not trigger a scalar implicature. This motivates a view on which scalar implicature is contextualized but dependent on grammatical structure.

Understanding language is often divided into two types of processes: the derivation of the semantic meaning (those things entailed by the statement) and the calculation of pragmatic inferences that go beyond this literal meaning (Bach, 1999; Grice, 1989; Morris, 1938). For example, given sentence (1), the claim that Gabe is the agent of the drinking event is based on semantic decoding, while the inference that he is an inconsiderate lout who has annoyed the speaker is a pragmatic inference.

(1) Gabe drank all of the milk and put the carton back in the fridge.

Pragmatics may seem to be a peripheral phenomenon – the occasional minor inference that should not distract from the meat of language (syntax and semantics). In fact, pragmatic inferences are pervasive, affecting many if not all communicative acts, and often comprising core aspects of the linguistic message (Horn & Wald, 2004). For example, consider the inference in (1) that Gabe put the carton back in the fridge after drinking all the milk. Without a full account of pragmatic inference, our psychological and neuroscientific understanding of language will be severely limited.

In recent years, there has been an explosion of experimental and theoretical work in pragmatic inference (for review, see Noveck & Reboul, 2008). Scalar implicature -- the focus of our investigation below -- has emerged as a particularly important test case. In scalar implicatures, we infer from one statement that a stronger claim is false (Hirschberg, 1991; Horn, 1972). Consider:

(2) John ate some of the cookies.

The literal meaning of this statement is that John ate a quantity of cookies that is greater than zero, which leaves open the possibility that he ate all of the cookies. Nevertheless, most listeners infer from (2) that John did not eat all of the cookies.

This inference (John did not eat all of the cookies) has a different status from the literal meaning (John ate a non-zero quantity of cookies). If someone stated (2), but it turned out that John had in fact eaten all of the cookies, the speaker could be accused of being misleading or imprecise, but not of lying. However, if it turned out that John had not eaten any cookies, the speaker was lying.

What accounts for scalar implicature? Beginning with Grice (1989), most theories incorporate the intuition that if John had eaten all of the cookies and the speaker knew it, then s/he would have said so:

(3) John ate all of the cookies.

One can infer from the fact that the speaker did not say (3) that it is not true.1 Part of the explanation seems to lie in informativity: If John has eaten all of the cookies, (2) is true but less informative than (3). Informativity can be formalized in terms of asymmetric entailment: Whenever (3) is true, (2) must also be true, whereas the reverse is not the case (Table 1).

Table 1.

Informativity (Upward-Entailing Context)

Some P All P
T F
T T
F F
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Truth tables for (2) and (3).

Informativity: Lexical or Higher-Level?

An important open question is whether, for the purposes of scalar implicature, informativity is calculated at the lexical level (some) or at a higher level of representation, such as the entire utterance (John ate some of the cookies). A number of factors suggest a lexical account. One is that informativity accounts, without further constraints, can overgenerate. For instance, we do not normally infer from (2) that John does not like scuba diving, even though (4) is more informative than (2) (cf. Horn, 1972).

(4) John ate some of the cookies and likes scuba diving.

For this reason, many researchers, beginning with Horn (1972), have proposed that scalar implicatures derive from specific lexical scales, such as (some, all): Barring specific contextual support,2 the only alternative utterances considered are those involving other members of the entailment scale (cf. Chierchia, Fox, & Spector, 2012; Gazdar, 1979; Hirschberg, 1991; Levinson, 2000; Sauerland, 2004). In addition to (some, all), a number of other scales have been proposed, such as (or, and) and (warm, hot).

The introduction of lexical scales raises the possibility that scalar implicatures are calculated at the lexical level: On encountering the weak scalar term some, listeners could retrieve the more informative alternative all, negate it, and replace the original meaning with the enriched one (some-but-not-all). Below, we refer to this as the lexical informativity account, a position typically associated with Levinson (2000) (see discussion in Breheny, Katsos & Williams, 2006; Degen, 2013; Huang & Snedeker, 2009).3 This proposal gains some support from the relative robustness of scalar implicatures, which, unlike many other linguistic inferences, are typically derived without specific contextual support (see footnote 2).

However, other researchers have presented theoretical arguments that scalar implicature should not be calculated at the lexical level. Importantly, the relative informativity of items on these scales (some, all) interacts with the broader propositional content of the sentence. Consider sentences like the following:

(6) If John ate some of the cookies, then he cannot have dessert.

(7) If John ate all of the cookies, then he cannot have dessert.

In this case, the sentence with some (6) is more informative than the sentence with all (7): Whenever (6) is true, (7) is true, but there are cases where (7) is true but (6) is not (Table 2). Thus, the relative informativity of the utterances is reversed relative to the relative informativity of the lexical items. Grammatical contexts like this are called “downward entailing” contexts, in order to distinguish them from the typical “upward entailing” contexts, in which the relative informativity of the utterances and lexical items are matched.

Table 2.

Informativity (Downward-Entailing Context)

Some P All P Q If some P, Q If all P, Q
T F T T T
T F F F T
T T T T T
T T F F F
F F T T T
F F F T T
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Truth tables for (6) and (7).

If scalar implicature is calculated lexically, entailment context makes no difference and readers should get the some-but-not-all reading for (6). However, if scalar implicatures are calculated over higher-level structure, then no implicature for (6) is expected, since there is no more informative utterance to negate. Indeed, this is what some theorists predict (Chierchia, 2006; Chierchia, et al., 2012; Geurts, 2009; Geurts & Pouscoulous, 2009; Katsos, 2008; Sauerland, 2004).4 Note that some of these accounts (e.g., Chierchia et al., 2012) have alternative mechanisms allowing for scalar implicatures within downward-entailing contexts. However, for all these higher-level informativity accounts, scalar implicatures in downward-entailing contexts should be rare at best.

Although lexical-level processing is often assumed to be fast and automatic, in principle this distinction crosscuts the long-standing debate about whether scalar implicature is calculated by default or not (Bott & Noveck, 2004; Feeney, Scrafton, Duckworth, & Handley, 2004; Grodner, Klein, Carbary, & Tanenhaus, 2010; Huang & Snedeker, 2009a, 2009b, 2011; Levinson, 2000). There is now considerable evidence that scalar implicature machinery is deployed flexibly: Listeners are less likely to make scalar implicatures when they believe that the speaker is not motivated to be informative (Bonnefon, Feeney, & Villejoubert, 2009) or is unlikely to know whether the more informative statement is true (Bergen & Grodner, 2012). However, the machinery may be deployed flexibly but still operate over a lexical representation rather than over the proposition as a whole. In fact, the psycholinguistic studies suggesting rapid use of context are amendable to a purely lexical explanation. Specifically, in two reading studies that show immediate context sensitivity, the contexts that result in an implicature often (Bergen & Grodner, 2012) or always (Breheny, Katsos & William, 2006) include all or a near synonym (e.g., each) earlier in the discourse, while the contexts that do not support implicature never do. Thus the effects of context in these studies could result from the priming of the lexical scale.

Lexical or Higher-Level Informativity: Experimental Evidence

There is currently relatively little evidence to tell between the lexical and higher-level accounts, and none that speaks to the role of grammatical context in the neural processing of implicature. To date, evidence has primarily come from studies in which participants make explicit judgments about the interpretation of scalar terms. In the first of these studies (Noveck, Chierchia, Chevaux & Sylvestre, 2002), the critical utterances were part of an exercise in logical reasoning (11).

(11) If there is a P or a Q then there is an R.

There is a P.

There is a Q.

Is there an R?

If scalar implicatures are calculated over lexical scales ignoring higher-level structure, then given the lexical scale <or,and>, or should be interpreted exclusively (not both), and the answer should be “no”. On the higher-level informativity account, we should expect participants to answer “yes”. This is because “or” in the first sentence of (11) is in a downward entailing context, thus the implicature should be suspended, and or should be interpreted inclusively. The actual participants overwhelmingly answered “yes,” supporting the higher-level informativity account. Some subsequent judgment studies have confirmed this pattern (Chemla & Spector, 2011; Chierchia, Crain, Guasti, Gualmini, & Meroni, 2001), though not all have (Geurts & Pouscoulous, 2009).5

However, because these studies use explicit judgment tasks, in which participants consider the acceptability of the utterance or engage in explicit logical reasoning, they do not tell us how scalar inferences are made during every day, unreflective language comprehension. The present study explores the role of grammatical context during ordinary language comprehension, using measures that allow us to watch the process of implicature unfold in the brain over time.

Overview of the Experiments

In the present work, we compare processing of the scalar implicature trigger some in declarative (upward-entailing) and conditional (downward entailing) sentences, using ERP’s. As we noted above, higher-level informativity accounts predict that this manipulation should affect processing, whereas lexical informativity accounts do not.

This work expands and improves on previous research in several ways. First, as noted above, the experimental evidence thus far is limited to offline judgments, which can only tell us about final stage results. Moreover, most of these tasks have used highly repetitive abstract stimuli, which may have encouraged participants to treat the task as one of logical reasoning rather than linguistic communication, which could lead them to focus on logical entailment rather than lexical knowledge or communicative habits. Using an ERP paradigm allows us to assess interpretation without requesting explicit judgments about meaning. In addition, using a method that provides rich temporal information allows us to measure early interpretations that are less likely to be contaminated by explicit metalinguistic reasoning.

Second, despite an explosion of behavioral experiments on scalar implicature (Barner, Brooks, & Bale, 2010; Bonnefon et al., 2009; Bott & Noveck, 2004; Breheny, Ferguson, & Katsos, 2012; Chemla & Spector, 2011; Chevallier et al., 2008; Chevallier, Wilson, Happé, & Noveck, 2010; De Neys & Schaeken, 2007; Feeney, Scrafton, Duckworth, & Handley, 2004; Goodman & Stuhlmuller, 2013; Foppolo, Guasti, & Chierchia, 2012; Grodner et al., 2010; Huang & Snedeker, 2009a, 2009b, 2011; Marty, Chemla & Spector, 2013; Noveck, 2001; Papafragou & Musolino, 2003; Papafragou & Tantalou, 2004; Papafragou, 2006; Pouscoulous, Noveck, Politzer, & Bastide, 2007) relatively little is known about the neural computation of scalar implicature. Two studies have investigated the brain response produced when a scalar implicature conflicts with world knowledge. Nieuwland, Ditman and Kuperberg (2010) presented participants with sentences made felicitous or infelicitous by a prior scalar implicature (Some people have pets/?lungs…), finding a larger N400 to the infelicitous word (lungs). 6 Politzer-Ahles, Fiorentino, Jiang, and Zhou (2013) manipulated the felicity of the word some itself: participants were presented with sentences such as Some of the girls are sitting on blankets sun-tanning, after they had seen either a picture in which some-but-not-all of the girls are sitting on blankets sun-tanning (making the scalar implicature-enriched interpretation of the sentence felicitous) or a picture in which all of the girls are sitting on blankets sun-tanning (making the scalar implicature-enriched interpretation of the sentence infelicitous). This resulted in a sustained negativity to some in the infelicitous condition. Thus, these studies measure processing when a scalar implicature-enriched interpretation mismatches prior knowledge, rather than manipulating whether the scalar implicature itself was calculated, which is the focus of the present study.

Experiment 1

The present study contrasts lexical informativity and higher-level informativity accounts of scalar implicature by contrasting declarative sentences (12a) and conditional sentences (12b). As discussed above, if scalar implicatures are calculated based on higher-level informativity, then the some-but-not-all interpretation should be available in (12a) but not (12b).

(12) a. Addison ate some of the cookies before breakfast this morning, and the rest are on the counter. (DECLARATIVE SENTENCE)

b. If Addison ate some of the cookies before breakfast this morning, then the rest are on the counter. (CONDITIONAL SENTENCE)

Note that in both cases, the most likely referent for the rest is the remaining cookies that Addison did not eat. However, according to the higher-level informativity account, listeners do not normally calculate scalar implicatures in the antecedents of conditions. As such, interpreting the rest in (12b) – but not in (12a) – requires retroactive calculation of the scalar implicature. This method of probing interpretation was borrowed from Breheny, Katsos, & Williams (2006). Thus, interpreting the rest should be more difficult in (12b) than (12a). Associated ERPs may reflect the more involved search for the referent, the retroactive calculation of the scalar implicature, or both. In addition, by comparing ERPs at some, the word that triggers the scalar implicature, we may gain valuable information about the neural processes supporting scalar implicature calculation.

In contrast, the lexical informativity account predicts that the some-but-not-all interpretation is calculated regardless of entailment context, and thus the rest should be equally easy to interpret in both cases.

One methodological concern remains: Declarative and conditional sentences differ in numerous ways, not just in how they affect scalar implicature. The critical phrase the rest is preceded by different connectives – and in (12a) and then in (12b) – and thus differences seen in processing of the rest may merely reflect late components of the ERP to the different connectives. The two clauses in (12b) depend upon one another in a way that the two clauses in (12a) do not. Determining the truth of a declarative depends on states of the world, whereas determining the truth of a conditional depends on possible states: If Addison has not eaten any cookies, (12a) cannot be true but (12b) might be. Differences in the ERPs between our declarative and conditional sentences may reflect these or other implicature-irrelevant factors.

To address this issue, we conducted a control version of the experiment, where some was replaced everywhere by only some, a phrase that semantically forces the subset (“not all”) reading:

(13) a. Addison ate only some of the cookies before breakfast this morning, and the rest are on the counter. (DECLARATIVE SENTENCE)

b. If Addison ate only some of the cookies before breakfast this morning, then the rest are on the counter. (CONDITIONAL SENTENCE)

This allows us to control for differences between declarative and conditional sentences. Any differences between declarative and conditional sentences should affect both the experimental sentences (12) and the control sentences (13), whereas only the experimental sentences (12) manipulate scalar implicature processing. Thus, the crucial analyses are interactions: differences seen between the experimental declarative and conditional sentences (12) that are not seen between the control declarative and conditional sentences (13).

Method

Subjects

Forty-nine monolingual native English-speaking right-handed adults 18-38 years old participated. Two were excluded for equipment failure and ten for excessive artifact, leaving 35 participants (17 female, 18-38 y.o., M=21 y.o., SD=4): 19 in the experimental condition and 16 in the control condition. Participants were recruited from the broader Harvard University community and were compensated with either partial course credit or a small payment.

Materials and Procedure

We created 60 sentences, each of which could occur in four forms, as depicted in (12-13). Each participant saw 30 critical declarative sentences and 30 critical conditional sentences in either the experimental or the control conditions. Filler sentences consisted of 60 matched in structure – but not content – to the critical sentences but with continuations that did not mention “the rest” and 35 that additionally swapped the word some for all. These fillers prevented subjects from inferring that all sentences would refer to “the rest” of a previously-mentioned collection. An additional 42 filler sentences involved relative clauses and no quantifiers.

Four lists were created for the experimental condition. Within each list, 30 sentences appeared in the declarative version, and the other 30 in the conditional form. By counterbalancing the order of the stimuli (except the first four stimuli, which were always the same fillers) and counterbalancing which form the sentence appeared in (declarative or condition), we obtained the four lists. Four lists for the control condition were created as well, which were identical to the experimental lists, except that the word some was always preceded by only – both in the critical sentences and the filler sentences.

Sentences were presented in eight blocks, with breaks in between. Sixty-one of the sentences were followed by comprehension questions, which were not analyzed. Sentences were presented in displays of 1-2 words at a time. Wherever two short words appeared consecutively, we presented them together (e.g., Sally/saw/a cat/on the/table). This allowed us to present the critical phrase the rest as a single unit, rather than in two parts, which would potentially add noise to the ERP. Some was always presented singly. Stimuli were presented in the center of the screen for 350 ms with a 250 ms blank interval between words. Immediately prior to the beginning of the next trial, subjects saw a blank inter-trial screen whose duration varied randomly in a range 1600 to 2000 ms. The aim of the variable ISI was to reduce the degree to which oscillatory EEG activity would entrain to the regular frequency of the stimuli presented in the sentences.

Acquisition and Analysis

Ongoing EEG was recorded from 128 scalp locations using a geodesic sensor net (Electrical Geodesics, Eugene, OR) as subjects read the sentences silently. EEG was recorded relative to a vertex channel and later re-referenced to the average of the mastoid channels. Impedances were maintained below 75 Ω. Signals were recorded at 250 Hz and down-sampled to 200 Hz post-acquisition using the signal processing toolbox’s resample() function (Mathworks, 2012). We down-sampled to 200 Hz to facilitate comparison with other datasets that were already sampled at 200 Hz. A 0.1-30 Hz bandpass filter was applied. Epochs of 1500 ms were selected following the critical phrase (some or the rest) and were corrected with a 200 ms pre-stimulus baseline. Bad channels were replaced and epochs containing artifact (eye blink, eye movement, etc.) removed, both by computer algorithm. Bad channels were identified by hand, with an average of 1 (range: 0-5) replaced per participant. An additional automated screen of channels with spectral power more than 12.5 times the standard deviation did not identify any additional bad channels. Bad epochs were those with a maximal amplitude of ±125 uV from baseline on any channel. Only participants with at least 19 epochs per cell were included in analyses.

The Permutation Cluster Algorithm

The previous literature has focused on the role of the N400 in processing scalar implicature violations. Because no previous study has looked for components associated with scalar implicature generation, we needed a mechanism for selecting and analyzing exactly those electrodes in those time periods with the greatest differences between conditions without allowing multiple comparisons to inflate our Type I error rate (cf Vul, Harris, Winkielman, & Pashler, 2009). We adapted the permutation cluster analysis of Maris and Oostenveld (2007).

We calculated the context (declarative/conditional) by condition (experimental/control) interaction using a mixed effects model with maximal random effects for each electrode at each time point and recorded the t-value (to speed processing, we further down-sampled the data to 50 Hz, resulting in 20 ms windows). We then identified all clusters of data points with t-values greater than 1.96 or less than −1.96.7 Clustering crossed both time (consecutive super-threshold data points on the same electrode were placed in the same cluster) and space (super-threshold data points from the same time point and belonging to neighboring electrodes were placed in the same cluster). Clusters are assigned scores, which are the sum of their t-values; thus, clusters with larger statistical effects and/or which are extended in time and space are assigned larger scores.

Statistical significance was assessed through permutation analysis. The condition labels for the subjects (experimental/control) were shuffled, as were the context codes (declarative/conditional) for each subject’s average ERPs. The clustering algorithm was re-run, and the scores for the largest positive and negative clusters were recorded. This process was repeated 500 times. P-values for a given cluster in the actual data are estimated as the number of clusters of equal or greater size from the permuted data (calculated separately for positive and negative clusters).

Results and Discussion

At the rest, an interaction of condition and context was observed, frontally distributed and lasting from approximately 400 to 1300 ms post-stimulus (p=.048; see Figures 1 & 2). This is inconsistent with the lexical informativity account, on which no interaction was expected. The higher-level informativity account did predict an interaction, driven extra processing of the rest in the conditional sentences in the experimental condition (12b). This result is consistent with our norming studies (Hartshorne & Snedeker, submitted), in which the experimental conditional sentences (12b) were judged to be less felicitous than the other three types (an effect which disappeared if the sentences were truncated prior to the rest). Thus, we interpret the interaction at the rest to be due to a positive deflection for the experimental conditional sentences (12b), reflecting the added difficulty of interpreting the rest.

Figure 1.

Figure 1

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Permutation cluster analyses at the rest in Experiment 1. In each panel, electrodes are grouped into left-hemisphere, midline, and right-hemisphere, with more anterior electrodes placed higher. Panel A: t-values. Panel B: clusters (distinct color for each cluster). The significant cluster is in grey.

Figure 2.

Figure 2

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Difference waves (declarative – conditional) at the rest in Experiment 1. Topographical plots are shown at 600 ms post-stimulus. Four representative electrodes are depicted for the entire epoch. The relative negativity for the difference waves in the experimental sentences is driven by a positive deflection for the conditional sentences (see main text).

In contrast, the interaction at some was weak, and none of the resulting clusters were significant (ps>.47) (Figure 3). This finding is somewhat surprising: The results at the rest indicate that that the context manipulation did affect scalar implicature calculation, thus one might have expected to see a neural signature of that calculation at some in the experimental-declarative sentences (12a) as compared to the other sentences (where the implicature is not calculated). There are several possible interpretations of this null result, which we return to in the General Discussion. First, in Exp. 2, we confirm these findings through replication.

Figure 3.

Figure 3

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Permutation cluster analyses at some in Experiment 1. In each panel, electrodes are grouped into left-hemisphere, midline, and right-hemisphere, with more anterior electrodes placed higher. Panel A: t-values. Panel B: clusters (distinct color for each cluster).

Experiment 2

In Experiment 1, we found evidence that entailment context affected the ultimate interpretation of some (based on the results at the rest). However, we found no signature of the differential processing in the ERP signature at some itself. Given this, and given recent concern about replicability in the cognitive sciences (Open Science Collaboration, 2012; Hartshorne & Schachner, 2012; Pashler & Wagenmakers, 2012), we conducted a replication.

Method

Thirty-two monolingual native English-speaking right-handed adults participated, sixteen in each condition. Data for one participant in the control condition was corrupted and so excluded. Materials and ERP data analysis were identical to that of Experiment 1. EEG was recorded from 64 sintered Ag/AgCl electrodes embedded in an elastic cap (Neuroscan QuikCaps) following the extended 10-20 system (Nuwer et al., 1998). EEG data was sampled at 1000 Hz and later down-sampled to 200 Hz. Blink artifact was corrected through a subject-specific regression-based algorithm (Semlitsch, Anderer, Schuster, & Presslich, 1986). Reference location, filtering, and ERP epoching were as in Experiment 1. We also coded the stimuli so that the ERPs to some in the filler sentences – which up through some are indistinguishable from the critical sentences – could be included in analysis, doubling the number of trials for that analysis.

Results and Discussion

As in Experiment 1, permutation cluster analyses on the ERPs evoked by the rest detected a significant interaction (Figure 4). The single significant cluster (p=.008) begins somewhat later than in Experiment 1, starting at around 850 ms post-stimulus (as in Experiment 1, it extends to the end of the analyzed epoch). However, this cluster appears to be the extension of an effect beginning at around 600 ms (see Figure 4A). The distribution of the effect still appears skewed anterior but is more broadly distributed than in Experiment 1. As in Experiment 1, there were no significant effects at some (ps>.4).

Figure 4.

Figure 4

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Permutation cluster analyses at the rest in Experiment 2. In each panel, electrodes are grouped into left-hemisphere, midline, and right-hemisphere, with more anterior electrodes placed higher. Panel A: t-values. Panel B: clusters (distinct color for each cluster). The significant cluster is in grey.

Thus the results of Experiment 1 and 2 are quite similar, despite the differences in recording equipment and subject population. In both cases, we observed a widely distributed, sustained positivity beginning around half a second after onset of the rest. In neither case do the effects resemble any of the three other frequently observed ERP effects in language processing studies: N400, Left Anterior Negativity, or central-parietal P600 effects. In addition to resembling each other, both effect patterns bear some resemblance to recently reported anterior positivities, which have been elicited by plausible but unexpected words (e.g., Federmeier, Wlotko, De Ochoa-Dewald & Kutas, 2007), as discussed below. No significant effects were seen after some for either experiment.

General Discussion

A core issue in scalar implicature research is whether scalar implicatures are lexical inferences (e.g., some → not all) or are driven by broader informativity considerations. We found a robust difference in the ERPs triggered by the rest in declarative and conditional sentences, suggesting that scalar implicature calculation is modulated by the informational content of the sentence as a whole, rather than by lexical scales alone. Crucially, we controlled for implicature-irrelevant differences by replacing some with only some, forcing the subset interpretation of the quantifier. These results are consistent with several previous explicit judgment studies that had queried people’s intuitions about logical reasoning, similarly finding that participants were less likely to compute scalar implicatures within the antecedents of conditionals (see Introduction).

The present results demonstrate that scalar implicatures are calculated over propositional content rather than lexical items per se. Taken alone, however, this observation fails to explain why the terms on lexicalized scales seem to produce robust implicatures while other quantity implicatures require more support (see Introduction and Horn, 1989). As noted above, many theorists still make use of sets of lexical alternatives, positing that they are used to determine which sentences are considered as relevant alternatives. On some accounts, these sets of alternatives are lexicalized and included in the grammar (e.g., Chierchia et al., 2012), whereas on others they are a side effect of those terms frequently being used explicitly as alternatives to one another (e.g., Barner & Bachrach, 2010; Barner et al,, 2010). How this would play out during online processing is not yet well understood. Interestingly, the studies to date do not find any clear indication that there is a qualitative difference between the online processing of scalar implicatures that are based on sets of lexical alternatives and those based on contextual scales (see Breheny, Ferguson & Katsos, 2013; Zevakhina & Geurts, submitted).

There is an additional reason to doubt the viability of an account on which scalar implicatures are always calculated based on lexical alternatives, independent of proposition-level informativity. Considerable evidence has accumulated indicating that interpreting a scalar term pragmatically (e.g., some-but-not-all) takes longer and requires more cognitive resources than interpreting it semantically (e.g., at least some), which many researchers have argued is the opposite of what one would expect if implicatures are always calculated lexically and then cancelled as needed (Bott, Bailey, & Grodner, 2012; Bott & Noveck, 2004; De Neys & Schaeken, 2007; Dieussaert, Verkerk, Gillard & Schaeken, 2011; Feeney et al., 2004; Huang & Snedeker, 2009a, 2011; Marty, Chemla, & Spector, 2013; Noveck & Posada, 2003; but see Grodner et al., 2010). Whether this is a fatal argument depends on exactly what the underlying processing model looks like, and how the underlying processing gets transformed into the manifestations that we can measure (e.g., reaction time).

In the remainder of this section, we consider the implications of the ERP results in the context of our current understanding of ERPs and the neural bases of sentence comprehension.

Processing The Rest

Two previous scalar implicature EEG studies observed negativities in relation to scalar implicature processing (Nieuwland et al., 2010; Politzer-Ahles et al., 2013). Though the distribution and onset of the negativities was different across the two studies, that could be due to the differences in methodology: Politzer-Ahles and colleagues (2013) involved sentence-picture matching whereas Nieuwland and colleagues (2010) used reading-only paradigm. The authors of both studies interpreted their effects as reflecting pragmatic activity related to scalar implicature processing, in which case one might have expected a similar effect in our study. Instead, we observed a late, sustained positivity. Thus, across three studies, three different ERP effects have been observed.

One likely important difference between our study and the previous ones is that while the infelicitous sentences in the previous studies were infelicitous because the scalar implicature had been calculated (e.g., 14), our infelicitous sentences were infelicitous because the scalar implicature had not been calculated (12b, repeated below):

(14) Some people have lungs…

(12) If Addison ate some of the cookies before breakfast this morning, then the rest are on the counter.

It may be that the effects observed across the studies reflect integrating words that are made more or less felicitous/expected by the preceding context, rather than implicature processing per se. Nieuwland and colleagues (2010) observed an enhanced N400 on the critical infelicitous word (lungs), which typically indexes the overall degree of match between semantic features of an observed word and those that are predicted based on prior context (cf Kutas & Federmeier, 2011). The negativity observed by Politzer-Ahles and colleagues may be related. The difference between our findings and theirs could reflect a difference in the degree of infelicity of the continuation in the critical condition. Nieuwland’s infelicitous stimuli were quite infelicitous (14), and Politzer-Ahles’s involved reading sentences that did not match a previously viewed picture. In contrast, our manipulation was more subtle: The rest was difficult to interpret in the conditional sentences in the experimental condition, but the sentences are nonetheless relatively felicitous.

To verify this difference in felicity, we asked 40 native English speakers (23 female, 15 male, 2 no response; 23-67 y.o., M=42, SD=13) to rate the felicity (9-point Likert scale) of 40 randomly chosen stimuli from our study and 40 from Nieuwland’s. Critically, we turned those sentences into sentence fragments by truncating the sentence either before or after the critical word (e.g. lungs or the rest; Table 3). We counterbalanced felicity and where the truncation occurred across the participants using a Latin Squares design. The three-way interaction of experiment (Nieuwland vs. present) X truncation (pre-/post-critical word) X felicity (felicitous vs. infelicitous) was significant (t=4.4, p<.0001).8 The Nieuwland stimuli showed a large difference in acceptability post-critical word (felicitous: M=8.2, SE=0.1; infelicitous: M=6.3, SE=0.3) that was not present when the sentence was truncated prior to the critical word (felicitous: M=8.0, SE=0.3; infelicitous: M=8.1, SE=0.3), resulting in a significant interaction (t=11.4, p<.0001). For our stimuli, the analogous interaction was much smaller and not significant (pre-critical word, felicitous M=7.9, SE=0.2; infelicitous: M=7.3, SE=0.2; post-critical word, felicitous: M=8.1, SE=0.2; infelicitous: M=7.7, SE=0.2; t=1.5, p=.13). Note that while the conditional sentences appear to be slightly less acceptable than the declarative sentences–perhaps because of their greater complexity – any such issues are controlled for in the main experiments by the use of the “only some” control conditions.

Table 3.

Study Truncation Felicity Sentence
Nieuwland et al. Before Felicitous Some people have …
Nieuwland et al. Before Infelicitous Some people have …
Present Study Before Felicitous Addison ate some of the cookies before
breakfast this morning, and …
Present Study Before Infelicitous If Addison ate some of the cookies before
breakfast this morning, then …
Nieuwland et al. After Felicitous Some people have pets, …
Nieuwland et al. After Infelicitous Some people have lungs, …
Present Study After Felicitous Addison ate some of the cookies before
breakfast this morning, and the rest …
Present Study After Infelicitous If Addison ate some of the cookies before
breakfast this morning, then the rest …
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Stimuli from the sensibility judgment study.

Thus, the semantic felicity differences in our stimuli – in contrast to those of Nieuwland and colleagues – may have been too small to affect the N400 component. What can account for the sustained positivity we observed? One possibility is that it reflects retroactive calculation of the scalar implicature. If so, one might have expected to see a similar effect at some in the declarative sentences, which was not the case. However, as discussed in the next section, many researchers have argued that scalar implicature processing is slow and probabilistic. If so, ERPs related to scalar implicature processing at some may be spread out over time; after averaging across trials, they would be difficult to detect. It may be that by forcing retroactive calculation of the scalar implicature at the rest, we concentrated the ERP, making it more detectable.

Another possibility is suggested by several studies that found sustained frontal positivities not unlike our own, which typically appeared in cases where the critical word is unexpected but plausible (DeLong, Urbach, Groppe & Kutas, 2011; Federmeier, Wlotko, De Ochoa-Dewald & Kutas, 2007; Moreno et al., 2002). For instance, Federmeier and colleagues (2007) reported a sustained positivity starting at about 500 ms, triggered where a plausible word (look) appeared in a context where another word (play) was considerably more likely (The children went outside to…).

Intuitively, the rest is plausible but unexpected in our conditional sentences in the experimental condition (12b), and thus a similar explanation might apply to our results. It should be noted, however, that the analogy is not perfect. We modified the judgment study above to ask participants how likely the critical word (the rest) was in our upward- and downward-entailing contexts; while it was judged to be significantly more likely in the upward-entailing context, in neither case was it judged highly likely (upward-entailing: M=4.9, SE=0.4; downward-entailing: M=4.4, SE=0.3; difference: t=5.7, p<.001; judgments were made on a 7-point Likert scale). This could simply reflect the fact that all long sentences are unlikely, but if taken at face value, this contrasts with Federmeier and colleagues’ (2007) finding that their late positivity was specific to strongly constraining semantic contexts and did not appear for more weakly constraining contexts (Joy was too frightened to move/look). However, the comparison is complicated by the fact that we manipulated context whereas they manipulated the critical word. Further work will be needed to better characterize these sustained, late positivities and determine if they are indeed a single component.

In summary, it may be that the ERPs to infelicitous critical words in our study, the Nieuwland study, and the Politzer-Ahles study reflect general revision processes, rather than scalar implicature processes per se. While this is unfortunate news for those trying to uncover pragmatics-specific neural processes, it points in a profitable direction for uncovering the mechanisms by which pragmatic and semantic information is integrated online.

Processing Some

Perhaps the most intriguing finding was the absence of an effect at the scalar implicature trigger some. We found parallel results in five self-paced reading experiments involving similar stimuli (Hartshorne & Snedeker, submitted): some was read no slower (or faster) in contexts where the scalar implicature was calculated. Nonetheless, analyses at the rest – both here and in the self-paced reading experiments – show that our manipulation affected scalar implicature calculation.

The lack of an effect at some is made additionally surprising by a recent study by Bergen and Grodner (2012), in which they manipulated the speaker’s knowledge state: In typical scalar implicature theory, listeners should not infer from the utterance of a weaker statement (Addison ate some of the cookies) that a stronger one (Addison ate all of the cookies) is false if the speaker does not herself know whether the stronger statement is true or false. Essentially, this lack of knowledge provides an explanation for the fact that the speaker did not use the stronger statement, and no implicature is necessary. Using such a manipulation, Bergen and Grodner (2012) reported that reading time was longer for some in conditions where participants infer implicatures (speaker full-knowledge condition) relative to conditions where participants do not (speaker partial-knowledge condition) (for converging offline results, see Goodman & Stuhlmuller, 2013).

One possible, if unlikely, explanation is that the scalar implicature is always triggered by some, and thus the ERPs were identical across conditions. On this account the implicature must then be cancelled in the downward entailing conditions (in order to be consistent with our results at the rest). We have already discussed some of the difficulties with this prediction. Additionally, when we used longer analysis windows or analysis windows beginning with words subsequent to some, we saw no evidence of an ERP effect that could reflect this cancellation process. Finally, this theory fails to explain other recent findings (e.g., Bergen & Grodner, 2012).

A second possibility, which we also deem unlikely, is that scalar implicature is so fast and effortless that its computation is not detectable using EEG or self-paced reading. Not only does that suggestion hard to reconcile with Bergen and Grodner (2012), who found slower reading of some when scalar implicatures were calculated, it would require re-consideration of a large body of literature suggesting that scalar implicature calculation is slow (Bott, Bailey, & Grodner, 2012; Bott & Noveck, 2004; Feeney et al., 2004; Huang & Snedeker, 2009a, 2011; Noveck & Posada, 2003; but see Grodner et al., 2010) and requires considerable computational resources (De Neys & Schaeken, 2007; Dieussaert, Verkerk, Gillard, & Schaeken, 2011; Marty, Chemla, & Spector, 2013).

A third, more likely, reason why our EEG (and self-paced reading) experiments may be insensitive to scalar implicature calculation is that scalar implicature calculation is so spread out in time that any effect largely washes out after averaging across trials. Numerous studies have shown that scalar implicature calculation is relatively slow, taking approximately one second from the onset of some (Bott, Bailey, & Grodner, 2012; Bott & Noveck, 2004; Feeney et al., 2004; Huang & Snedeker, 2009a, 2011; Noveck & Posada, 2003; but see Grodner et al., 2010). If the cost of scalar implicature calculation is spread out across our analysis time window, that would diminish the effect size at any given point, rendering it difficult to detect without current analysis techniques and feasible sample sizes. One reason that Bergen and Grodner (2012) might nonetheless have detected this effect is that many of their implicature inducing contexts (speaker full-knowledge condition) – and none of their implicature-suppressing contexts (speaker partial-knowledge condition) – used the word all, potentially priming the scale and thus scalar implicature itself, speeding up the process and condensing it into a small enough time window to be detectable.

A final possibility is that while the outcome of scalar implicature processing in upward and downward entailing contexts is different, the processing is largely the same. On the Gricean account, scalar implicatures are calculated only when listener decides that some alternative would have been more informative. Presumably the listener must check the relative informativity of the alternatives before this decision can be made, and thus the overall processing may not be much different regardless of whether the ultimate interpretation does or does not include an implicature. Similarly, on Chierchia and colleagues’ (2012) Grammatical Theory, the parser entertains every possible insertion site for the exhaustivity operator, though whether the operator is retained in that position depends on several factors including its resulting in a more informative interpretation of the utterance (the authors consider two different algorithms which make different predictions; see Chierchia et al., 2012, Section 4.6). Presumably, the only way the grammar can know that these criteria have been met is to actually carry out the operations. Thus, if EEG and self-paced reading are sensitive primarily to processing and not the outcome of that processing, it may be difficult to distinguish our two conditions. This same reasoning need not apply to Bergen and Grodner’s (2012) study, because in their partial-knowledge condition, the speaker is assumed not to know whether all applies, and thus determining whether the same statement with all substituted for some is more informative is moot. As such, if the processor is reasonably efficient, implicature processing would only occur in their full-knowledge condition, resulting in an observable difference in processing cost across conditions.

Some headway might be made on determining exactly why Bergen & Grodner (2012) find effects of context at the word some, whereas we and Hartshorne & Snedeker (under review) do not, by investigating online processing of other contextual effects. For instance, listeners reportedly do not make scalar implicatures if they believe the speaker would be unlikely to use the more informative statement, even if it were true (Bonnefon et al., 2009).

Conclusion

We find that grammatical entailment context modulates online scalar implicature processing. In particular, encountering some of the X sets up a possible antecedent for a later anaphor, but only in contexts that support scalar implicature. If the scalar implicature was not calculated, resolution of the anaphor is more difficult, resulting in a sustained positivity. This finding strongly challenges lexical-based accounts.

Figure 5.

Figure 5

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Difference waves (declarative – conditional) for individual electrodes in Exp. 2. Panel A: F7. Panel B: F8. Panel C. Fz. Panel D. POz.

Figure 6.

Figure 6

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Permutation cluster analyses at some in Experiment 2. In each panel, electrodes are grouped into left-hemisphere, midline, and right-hemisphere, with more anterior electrodes placed higher. Panel A: t-values. Panel B: clusters (distinct color for each cluster).

Footnotes

1

This inference does not necessarily go through if the speaker does not know whether John ate every single one (maybe he was still eating when she left the room). While there is evidence that listeners are sensitive to the speaker’s knowledge state when calculating implicatures (Bergen & Grodner, 2012; Bonnefon, Feeney, & Villejoubert, 2009; Breheney, Ferguson & Katsos, 2013; Goodman & Stuhlmuller, 2013), it is not clear whether implicature processing involves explicit mental state reasoning or simply approximates it. That is, like gazelle stotting or communication between bees, the fact that the problem solved by scalar implicature is inherently social does not mean that the underlying mechanisms explicitly invoke mental state reasoning.

2

If a specific alternative statement has been made contextually relevant, other implicatures may apply:

(5) Alfred: Did John eat some of the cookies, and does he like scuba-diving?

Beatrice: John ate some of the cookies.

Note that regardless of what Alfred said, Beatrice’s statement implies that John did not eat all of the cookies. Additional inferences – e.g., about whether John likes scuba diving – may depend on what exactly Alfred asked.

3

Like the lexical alternatives account, the grammatical theory of implicature (Chierchia, Fox & Spector, 2012) operates over sub-propositional units and invokes lexical scales. However, on this proposal, the occurrence of a scalar implicature is sensitive to the grammatical context in which the scalar term appears.

4

Note that these accounts differ along a number of other dimensions, such as whether scalar implicature involves grammatical processing. The last two decade has witnessed an explosion of work on scalar implicature within theoretical linguistics, resulting in a rich literature and detailed theories. Many of these distinctions are beyond the scope of the present work. We refer the interested reader to Chierchia, Fox, & Spector (2012), Sauerland (2012), and Geurts (2010).

5

Panizza, Chierchia, and Clifton Jr. (2009) report an eyetracking-while-reading study that manipulates entailment context. But critically this work focuses on the interpretation of number words (“two” means two and not three). Whether number interpretation involves scalar implicature is controversial (Breheny, 2008), and a variety of behavioral paradigms have found categorical differences in how numbers and scalar quantifiers are interpreted (Huang & Snedeker, 2009a, 2009b, 2011; Huang, Spelke, & Snedeker, 2013; Marty, Chemla & Spector, 2013), suggesting that we cannot generalize from one to the other.

6

Note that this requires that the semantic relatedness to prior context be controlled (cf. Noveck & Posada, 2003; see also Kounios & Holcomb, 1992)

7

The choice of threshold (e.g., 1.96) affects the type of clusters found – low thresholds are better at detecting broadly extended but weak effects – but it does not affect robustness to multiple comparisons. Other threshold resulted in similar findings.

8

These and other analyses in this section utilized mixed effects models with subjects and items as random effects and with maximal random slopes design. P-values are derived from model comparison.

Contributor Information

Joshua K. Hartshorne, Department of Brain and Cognitive Sciences, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139 USA.

Jesse Snedeker, Department of Psychology, Harvard University, 33 Kirkland St., Cambridge, MA 02138 USA, snedeker@wjh.harvard.edu.

Stephanie Yen-Mun Liem Azar, Department of Psychology, Harvard University, 33 Kirkland St., Cambridge, MA 02138 USA.

Albert E. Kim, Institute of Cognitive Science, University of Colorado-Boulder, 594 UCB, Boulder, CO 80309 USA, albert.kim@colorado.edu

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