Priming reveals similarities and differences between three purported cases of implicature: Some, number and free choice disjunctions

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Highlights

  • Implicature consists in a series of sub-computations, but these can be computed online or stored.

  • Evidence from priming suggests the quantifier some and number words involve a shared computation.

  • The most likely candidate for this shared computation is the negation of alternatives.

  • Alternatives for number are lexically stored, but the alternatives for some are computed online.

  • Free Choice disjunctions do not show evidence for a shared computation with either some or number .

Abstract

Across a wide variety of semantically ambiguous sentences, implicature has been proposed as a single mechanism which can derive one reading from another in a systematic way. While a single formal mechanism for computing implicatures across disparate cases has an appealing parsimony, differences in behavioral and processing signatures between cases have created a debate about whether the same computation really is so widely shared. Building on previous work by Bott and Chemla (2016), three experiments use structural priming to test for shared computations across three purported cases of implicature: the quantifier some, number words, and Free Choice disjunctions. While we find evidence of a shared computation between the enriched readings of some and number words, we find no evidence that Free Choice readings involve any shared computation with either some or number. Along with evidence of a shared mechanism between some and number implicatures, we also find substantial differences between these two cases. We propose a way to reconcile these findings, as well as seemingly contradictory prior evidence, by understanding implicature as a sequence of separable sub-computations. This implies a spectrum of possibilities for which sub-computations might be shared or distinct between cases, instead of a single implicature mechanism that can only be either present or absent.

Introduction

Since Grice first suggested that even unspoken sentences can contribute to the meaning of an utterance, half a century of research on implicatures has formalized and substantiated the idea in different frameworks. A significant body of work in this area has focused on showing how implicature can be extended to a diverse set of phenomena, far exceeding the scope of Grice’s original proposal. But just because a formal mechanism can be designed by the theorist to derive certain phenomena, does not mean that human minds actually use this mechanism in the course of language comprehension, especially when alternative explanations for the same phenomena are readily available.

In this paper, we apply psycholinguistic tools to examine which – if any – components of a hypothesized general implicature mechanism might be shared across different categories of utterances. We start by noting that implicature consists of several sub-computations. Focusing on these sub-computations will allow us to develop a finer-grained view of implicature: Rather than asking whether or not implicature as a whole is applied across different categories, we can ask which of the sub-computations are shared across categories. Indeed, as our experimental results reveal, the sub-computations are not all equally likely to be applied in different categories, necessitating a finer-grained theoretical notion of implicature, which we will develop in this paper.

Using the structural priming method, we study three different domains: the quantifier some, number words, and Free Choice disjunctions. In each case, two readings are available; for some and number these are shown below:

We refer to the reading that is hypothesized to be the input to the implicature mechanism as the basic reading, and to the reading that is hypothesized to be the output of the implicature mechanism as the enriched reading, following Bott and Chemla (2016), among many others. While this terminology transparently reflects the hypothesis we set out to test, it does not reflect any prior commitment to the truth of that hypothesis.

Theories of implicature posit a general mechanism that takes the basic, lexically encoded reading of a sentence as input and yields its enriched reading as output. We home in on the following two sub-computations, assumed by all accounts of implicature:

The alternatives are sentences which were not asserted, but would have been equally relevant and more informative in the given context. The generation of alternatives is that computation which yields those alternatives; it can itself be broken down into several components (Katzir, 2007). For Some of the houses have a fence, it involves retrieving specific lexical material (the quantifier all) and replacing the lexical item some in the original sentence, generating the alternative sentence All of the houses have a fence. The alternatives are then negated; for our example, conjoining the negation with the original sentence yields Some of the houses have a fence & not all of the houses have a fence as the final output – the enriched reading of the sentence.

The enriched reading of sentences like There are four dogs has been argued to be derived in much the same way (e.g. Gazdar, 1979, Horn, 1989, van Rooij and Schulz, 2006). According to this implicature-based view of numerals, the basic, lexically stored reading of four can be paraphrased as at least four or four or more. On this reading, There are four dogs would be true in a scenario in which there are in fact six dogs. But a more natural reading is of course the exactly- reading, on which the sentence is judged false in this scenario. By hypothesis, this reading is derived through the same implicature mechanism as in the case of some. First, generating the alternative will again involve retrieving a specific lexical alternative, in this case the number word five, followed by appropriate replacement in the original sentence, yielding the alternative sentence There are five dogs. Next, this alternative is negated. When conjoined with the original sentence, the enriched exactly- reading is obtained: There are (at least) four dogs & it’s not the case that there are (at least) five dogs. In this way, the hypothesized mechanism underlying the enriched readings of number and some sentences differs only in the specific alternatives that are generated and then negated.

The hypothesis that the enriched readings of different sentences are derived by a general implicature mechanism has the strong appeal of parsimony, extending far beyond the domain of quantifiers and number words. Implicature has been invoked to explain other cases of seeming ambiguities in logical connectives, as in John bought apples or oranges (enriched: John bought apples or oranges, but not both), gradable adjectives, as in The soup is warm (enriched: The soup is warm, but not hot), modal expressions, as in John may come (enriched: John may come, but doesn’t have to), and even attitude verbs, as in John believes/thinks that it’s ok (enriched: John thinks, but doesn’t know, that it’s ok; see Hirschberg, 1991, van Tiel et al., 2014 for an overview).

Importantly, the question of whether a shared implicature mechanism is responsible for these disparate phenomena is independent of many active debates concerning the nature of implicature. (Neo-)Gricean (Gazdar, 1979, Geurts, 2010, Grice, 1989, Grice, 1975, Hirschberg, 1991, Horn, 1972, van Rooij and Schulz, 2004), grammatical (Chierchia, 2004, Fox, 2007, Meyer, 2013, van Kuppevelt, 1996, van Rooij and Schulz, 2006), relevance-theoretic (Carston, 1998, Merin, 1999, Sperber and Wilson, 1986, van Kuppevelt, 1996, van Rooy, 2002), game-theoretic (Benz, 2006, Franke, 2011, Parikh, 2001), and Bayesian (Bergen et al., 2016, Goodman and Frank, 2016, Potts et al., 2015) theories disagree on whether or not implicatures are computed as part of the grammar or as a pragmatic inference. They also differ on the question of what causes implicatures to be computed in the first place: Gricean maxims of cooperative conversation, domain-general principles of rational behavior, or something else still. What matters for our present purpose is that, with the exception of probabilistic theories,1 all of these theories share the core assumption that when implicatures are computed, the mechanism involves the two sub-computations outlined in (3) above (see also Bott & Chemla, 2016, for discussion). It is this shared assumption which we will be investigating in this paper.

Along with the quantifier some and number words, we investigate the case of Free Choice disjunctions (for review see Meyer, 2020). Alonso-Ovalle (2006) and Fox (2007) first showed how to extend the implicature mechanism to account for the ambiguity of disjunctions like the following:

Under one reading, which we will call the uncertainty reading, the sentence is used as a report on John’s options from a speaker who has incomplete knowledge of what these options are. The uncertainty reading is derived by the standard assumption that the lexical meaning of or can be modeled by the logical connective . This predicts (4) to be true in three scenarios: (i) if John can take the red umbrella, but not the yellow one, (ii) if John can take the yellow umbrella, but not the red one, and (iii) if John can take both umbrellas.2

The Free Choice (FC) reading, on the other hand, conveys that John has both the option of taking the red umbrella and the option of taking the yellow one, though he may not necessarily have the option of taking two umbrellas at once. Under this FC reading, the speaker has full knowledge of all options, and might even be the one granting permission to choose between them (as in a parent saying, You may have cake or ice-cream for dessert).

How could an implicature mechanism derive the FC reading of (4) from its hypothesized basic uncertainty reading? In the cases of some and number, the hypothesized implicature mechanism involves the negation of the basic reading of alternatives. To derive FC readings, it has instead been proposed that the alternatives are first themselves enriched, and it is the enriched readings of the alternatives which are then negated (Alonso-Ovalle, 2006, Fox, 2007, Kratzer and Shimoyama, 2002). This is schematically illustrated below (the parts that differ from (3) are underlined):

For FC sentences like (4), the proposal is that the alternatives in question are the disjuncts, John can take the red umbrella and John can take the yellow umbrella. The enriched meanings of these two alternatives are derived by conjoining each of them with the negation of the other (which means they are alternatives to each other). This yields their enriched meaning: John can take the red umbrella & not the yellow umbrella and John can take the yellow umbrella & not the red umbrella. This concludes the sub-computation in step 2 above. In a last step, these enriched alternatives are negated, and conjoining them with the basic uncertainty reading yields the FC reading of the whole disjunction:

Because the alternatives hypothesized to be negated in the derivation of the FC meaning are themselves enriched, the mechanism can be characterized as recursive: it takes the output of an implicature computation as its input.

The mechanism may be ornate, but the resulting parsimony is appealing, as the enriched readings of sentences with quite disparate content – number words, some, and disjunctions combined with modals – can all be derived by the application of one core mechanism, a procedure for generating and negating alternatives. Positing a category-general implicature mechanism also makes a clear, testable prediction. If, whenever the enriched meaning is accessed, an implicature computation consisting of the sub-computations in (3) above is performed, then any processing signature of these computations should be shared across otherwise very distinct categories of enriched meanings.

This prediction has been tested extensively, but the results have not been conclusive. Many findings show that the different cases for which implicature-based accounts have been proposed exhibit substantial differences. Before we go on to the present study, we briefly review the most relevant prior results.

The evidence that implicature is used to derive the enriched meaning of some has been mixed. On the one hand, several studies of online sentence processing with adults have found that the basic reading of some is accessed earlier, and verified faster, than the enriched reading in comprehension. This is consistent with the enriched reading being the output of an additional implicature computation that is not involved in accessing the basic reading (e.g. Bott and Noveck, 2004, De Neys and Schaeken, 2007, Huang and Snedeker, 2018, Huang and Snedeker, 2011, Huang and Snedeker, 2009, Tomlinson et al., 2013).

But other experimental studies have produced contradictory results. For example, Degen and Tanenhaus (2015) replicate the finding of higher reaction times for the enriched vs. basic reading of some, but show that these results might be due to decreased acceptability of some in the relevant experimental conditions. In a similar vein, Grodner, Klein, Carbary, and Tanenhaus (2010) and Feeney, Scafton, Duckworth, and Handley (2004) argue that increased processing times for enriched readings are due to independent factors rather than implicature computations. Foppolo and Marelli (2017) show that when the confound identified by Degen and Tanenhaus (2015) is controlled for, processing times of the enriched vs. basic reading do not differ (see also Breheny, Ferguson, & Katsos, 2013). These findings do not support the hypothesis that the enriched reading is derived from the basic one via a cognitively costly implicature computation, but are more consistent with accounts in which the enriched reading is stored directly as part of a lexical ambiguity of the quantifier some. Still, the debate continues, with Huang and Snedeker (2018) challenging these conclusions and reporting further evidence consistent with multi-step processing of the enriched meaning of some.

The empirical evidence on whether implicature generates exactly- readings of number words is likewise mixed, with more evidence against this hypothesis than in the case of some. First, not only can the enriched readings of number words be accessed as quickly as their basic readings, Huang and Snedeker, 2011, Huang and Snedeker, 2009 also find that in the very same contexts in which hearers are slow to access the enriched reading of some, they access the enriched reading of two as quickly as both the basic reading of some and the meaning of all, which is not derived via implicature on any account (Huang & Snedeker, 2011). Huang, Spelke, and Snedeker (2013) also show that hearers access the basic reading of some more often than the basic reading of number when given the choice (see also Marty, Chemla, & Spector, 2013). Lastly, Marty et al. (2013) and De Neys and Schaeken (2007) found that, while increased cognitive load made the basic reading of some more accessible, it instead made it harder to access the basic, at least reading of number words. These results are consistent with the possibility that implicature underlies the enriched reading of some, but not of number words.

Weighing on the other side, there is also evidence of a multi-step implicature mechanism generating the enriched reading of number words. Results from Panizza, Chierchia, and Clifton (2009) suggest that the choice between the enriched and the basic reading correlates with logical properties of the linguistic environment for both some and numbers. The enriched meaning is preferred for both items in upward-entailing environments, where it would make the whole sentence more informative overall, and dispreferred in downward-entailing environments, where it would make the whole sentence less informative. Taken alone, the significance of this type of evidence is limited by its correlational nature, and the relative preference of basic vs. enriched readings of two different items in the same environment can be explained by a general preference for an overall more informative statement, regardless of whether or not the enriched readings are generated by the same mechanism in both items. The stronger evidence from Panizza et al. is that in upward-entailing contexts in which enriched readings are more informative, reading times for number words were higher than in downward-entailing contexts, in which basic readings would be more informative and therefore expected to be preferred. This shows that the two readings are not equivalent when controlling for informativity, and more strongly suggests that the exactly- reading of numbers involves an additional computation (see also Chierchia et al., 2001, Gualmini et al., 2001, Guasti et al., 2005, Noveck et al., 2002).

The strongest evidence in favor of implicatures generating the enriched exactly- readings of number words comes from structural priming. Bott and Chemla (2016) show that when participants access the exactly- reading of number words, they are subsequently more likely to access the enriched reading of some than its basic reading, suggesting a shared mechanism responsible for generating both enriched meanings. This test has not previously been extended to FC disjunctions, one of the primary targets of our investigation below.

For FC disjunctions, experimental studies in general are sparse so far, and the most relevant study is inconclusive. If it is indeed a recursive implicature computation which derives the FC reading, accessing the FC reading should take longer compared to the uncertainty reading, analogously to the logic of studies comparing basic vs. enriched readings of both some and number words.3 In the only experimental test of this hypothesis so far, Chemla and Bott (2014) instead found faster response times for FC compared to uncertainty readings. On this basis they argue that the FC reading cannot stem from an implicature computation requiring additional processing steps. There is, however, a plausible alternative explanation for this finding. Recall that the uncertainty reading of a FC sentence like John can have the red bottle or the yellow bottle states that he can have (at least) one of the two, but the speaker is uncertain as to which one. In a scenario in which the speaker already knows that John can have the red bottle, the whole disjunction would be infelicitous, presumably because the assumption of speaker uncertainty is violated. The items used by Chemla and Bott (2014) do not satisfy this uncertainty condition, and the basic reading is therefore infelicitous in their scenarios, though it is true in a strictly logical or semantic sense. The increased processing times compared to the FC reading could be due to participants trying to accommodate the infelicitous reading.

In sum, there is mixed evidence that both the enriched reading of some and number words are derived by an implicature mechanism, as proposed in the theoretical literature. The two cases also differ, with the enriched meaning of number words being relatively easier to access. Whether implicature is involved in generating FC readings is currently unclear.

To test whether there is a shared implicature computation, we will look for a causal link: does deriving an enriched reading for one sentence (e.g., a FC sentence) increase the likelihood of deriving an enriched reading for a subsequent sentence from a different category (e.g., a number sentence)? As Bott and Chemla (2016) pointed out, the majority of studies on whether different types of enriched readings involve a shared implicature mechanism are correlational, comparing independent patterns of distributional or processing data from each category. Structural priming is a method that can provide stronger, causal evidence in this ongoing debate. The underlying rationale is that if a computation or representation is involved in the processing of one sentence, it will be easier to reuse in the processing of another sentence in which it is also involved (see Branigan & Pickering, 2017 for an overview).

For the cases we are interested in, this translates into the following prediction. If a general implicature mechanism underlies the enriched readings of some, number, and FC sentences, then accessing this reading in one sentence should increase the likelihood of accessing the enriched reading again in a subsequent sentence. Importantly, this prediction holds regardless of whether the two sentences are from the same (within-category effect) or a different category (between-category effect). This is because the assumed mechanism, which involves generating and negating alternatives, is category-general.

The only previous study that uses structural priming to investigate implicature is Bott and Chemla (2016), which serves as our starting point. Our experiments have a similar design to theirs. On both prime and target trials, participants see two pictures presented below a sentence, and are asked to choose the picture that best matches the sentence. The “priming effect” is measured by how participants’ choice on a given target trial changes depending on the kind of prime trial that preceded it. The prime trials were meant to elicit either a basic or an enriched reading, for sentences from each of the three categories of interest. The target trials following each prime trial then assessed whether participants opt for an enriched or a basic reading when given the choice. A given combination of prime and target items can be either within-category, where both prime and target are from the same category (e.g., number), or between-category, where the categories are different (e.g., FC for prime, some for target). Since the enriched reading is typically preferred, target items did not simply present a choice between the two, but rather a choice to accept or reject the basic reading. In keeping with the picture-matching design, this was implemented as a choice between a picture that matched the basic reading, and a picture only containing the words Better Picture, which allows participants to indicate that they would prefer an unspecified different picture to the depicted basic reading, following Bott and Chemla (2016) and Huang et al. (2013).

In Experiment 1, we investigate both within-category priming effects and between-category effects to establish whether, and in which cases, implicature computations might be shared. A control experiment, reported in Supplementary Materials, rules out the possibility that within-category priming in this design is due to greater similarity between pictures depicting the same readings than different readings.

Experiment 2 controls for the possibility that the prime trials that were meant to elicit basic readings actually primed participants to accept dispreferred readings more generally, independently of an implicature mechanism.

Experiment 3 replicates Experiment 1 using different picture stimuli that provide another control. These pictures were designed to be category-neutral, so that a single picture could exemplify the basic reading of a some, number, and FC sentence simultaneously (and likewise for the enriched readings). This ensures that differences in the priming effects between within-category and between-category trials are due to the processing of the sentences involved, rather than to e.g., basic some pictures being more similar to basic number pictures than to basic FC pictures.

Section snippets

Experiment 1

This experiment had two aims. The first was to replicate Bott and Chemla’s results for both within- and between-category priming with some and number, using experimental items that substantially differed from Bott and Chemla’s (see Fig. 1). The second goal was to test the hypothesis that FC readings arise through recursive implicatures, by testing for priming effects between some and number sentences on the one hand, and FC sentences on the other. Experiment 1 thus included all three categories

Experiment 2

Experiment 1 showed that given the choice between the enriched and the basic interpretation of a sentence on enriched prime trials, participants preferred the enriched reading across all three categories. This raises the possibility that the basic primes, which forced participants to choose between a strongly dis-preferred basic picture and an outright false one, might be priming a general permissiveness towards semantic slop (as when a teacher with 19 or 21 students in their class might say

Experiment 3

In Experiment 1, we found no between-category priming involving FC sentences, together with significant priming between some and number sentences. A deflationary interpretation is that this priming pattern reflects patterns of picture similarity. The pictures for some and number items involve many of the same entities (houses, dogs, ponds, etc.), while the FC items show a figure, two roads, and black boxes, which the participant is told are covered trucks. Moreover, the basic pictures for both

Summary of results

We set out to test the hypothesis that enriched readings of some and number, together with FC readings, are derived through the computation of an implicature using a shared, category-general mechanism. We observed between-category priming effects from some to number and vice versa, such that accessing the enriched reading for one category increased the likelihood of accessing the enriched reading for the other category. We also found evidence that these effects are not reducible to either

CRediT authorship contribution statement

Marie-Christine Meyer: Conceptualization, Methodology, Investigation, Writing - original draft, Project administration, Resources. Roman Feiman: Conceptualization, Methodology, Investigation, Writing - review & editing, Formal analysis, Visualization.

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    For comments and discussion, we would like to thank audiences at SALT30, UCSD, Leibniz-ZAS Berlin, the Crete Summer School of Linguistics, the Syntax-Semantics Seminar at the University of Nantes, and three anonymous reviewers. We would also like to thank Marlena Jakobs for help with the experimental stimuli. Part of this work has been supported by DFG grant SA 925/11-2 within the XPrag.de priority program (SPP 1727).

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