Priming scalar and ad hoc enrichment in children

Sentences can be enriched by considering what the speaker does not say but could have done. Children, however, struggle to derive one type of such enrichments, scalar implicatures. A popular explanation for this, the lexical alternatives account , is that they do not have lexical knowledge of the appropriate alternatives to generate the implicature. Namely, children are unaware of the scalar relationship between some and all . We conducted a priming study with N = 72 children, aged 5;1 years, and an adult sample, N = 51, to test this hypothesis. Participants were exposed to prime trials of strong, alternative, or weak sentences involving scalar or ad hoc expressions, and then saw a target trial that could be interpreted in either way. Consistent with previous studies, children were reluctant to derive scalar implicatures. However, there were two novel findings. (1) Children responded with twice the rate of ad hoc implicature responses than adults, suggesting that the implicature was the developmentally prior interpretation for ad hoc expressions. (2) Children showed robust priming effects, suggesting that children are aware of the scalar relationship between some and all , even if they choose not to derive the implicature. This suggests that the root cause of the scalar implicature deficit is not due to the absence of lexical knowledge of the relationship between some and all .

Priming enrichment in children Children's acquisition of language is not as straightforward as learning words and how to combine them. Children also need to learn how to enrich what they hear to infer the speaker's intended meaning (Grice, 1989). Consider the following interactions: (1) A: John ate some of the cookies.
⇨ John did not eat all of the cookies (2) A: I hear Helen's husband is rich and intelligent. B: Well, he's rich.
⇨ Helen's husband is not intelligent.
In (1), a listener might infer that John did not eat all of the cookies. Likewise, in (2), they might infer that Helen's husband is not intelligent. According to Grice (1989) and many others (Geurts, 2010;Goodman & Frank, 2016;Horn, 1972;Levinson, 2000), such inferences, or implicatures, are derived using the alternative to what was said. On hearing, "John ate some of the cookies" in (1), the listener recognises that the speaker could have been more informative, for example by saying, "John ate all of the cookies". Since the speaker did not use this more informative alternative, and assuming that they are knowledgeable (e.g. they were present when John consumed the cookies), the listener infers that the alternative is not true i.e. not all. Similarly, in (2), because Speaker B did not say that Helen's husband was rich and intelligent, which would have been more informative than simply saying he was rich, the listener can infer that Helen's husband is not rich and intelligent.
Implicatures can be classified according to how the alternatives are derived. For our purposes we consider two groups. In the first, scalar implicatures (Horn, 1972), implicatures arise due to the scalar ordering of lexical items based on informativity, such as <warm, hot > and < some, all>. In these scales, stronger terms in the lexicon give rise to sentences that are more informative than sentences with weaker terms. Use of the weaker term in the sentence implicates the negation of the stronger sentence, as in (1). Scalar implicatures are said to be context independent because the same implicatures arise irrespective of the context. For the second group, in contrast, the alternatives can only be derived from context, as in (2) (see Hirschberg, 1985). The resulting implicatures are said to be derived on an ad hoc basis since the content of the implicature is not fixed. For example, the inference that Helen's husband is not intelligent depends on the previous statement about Helen's husband being rich and intelligent. Had Speaker A selected other qualities, such as being rich and kind, a different inference would arise; namely, that Helen's husband is not kind.
In this study, we compare children's ability to derive scalar and ad hoc implicatures. We used a priming task based on Bott and Chemla (2016) and Rees and Bott (2018) to test whether the difficulty children experience with scalar implicatures (e.g. Noveck, 2001) is due to limited lexical knowledge of the scalar relationship between some and all, an explanation we refer to as the lexical alternatives hypothesis.

Scalar implicatures in children
There is abundant evidence that children between two-and tenyears-old have difficulty deriving scalar implicatures (e.g. Foppolo, Guasti, & Chierchia, 2012;Huang & Snedeker, 2009;Noveck, 2001;Papafragou & Musolino, 2003;Papafragou & Tantalou, 2004;Pouscoulous, Noveck, Politzer, & Bastide, 2007). For example, Papafragou and Musolino (2003) showed four-and five-year-old children pictures where all horses had jumped over the fence. When asked if it was true that some of the horses jumped over the fence, children agreed, whereas adults did not. Similarly, Noveck (2001) found that when evaluating statements such as "some giraffes have long necks", children did not display adult-like understanding even at age 10.
According to this view, which we call the lexical alternatives account, children's difficulties with scalar implicatures are rooted in their knowledge of the scale. It is not the case that children are never able to compute scalar implicatures, as seen in their success at computing implicatures with other scales (e.g. ad hoc: Horowitz et al., 2018;Stiller et al., 2015;numbers: Barner & Bachrach, 2010;Barner et al., 2011;Papafragou & Musolino, 2003;Sarnecka & Gelman, 2004); rather, there is a specific difficulty associated with the quantifiers some and all. Namely, children lack knowledge about the scalar relation between some and all that prevents all from being considered an alternative. Children demonstrate knowledge of the core meaning of some and all early in childhood and are aware that they denote different set meanings (Barner, Chow, & Yang, 2009;Barner, Libenson, Cheung, & Takasaki, 2009). However, it is not until later in development that they link them together as being on the same semantic scale. In other words, early lexical entries contain knowledge of what some and all mean, but not that all is an alternative to some i.e. their knowledge of lexical alternatives is lacking.
Evidence supporting the lexical alternatives account comes from Barner et al. (2011), who presented four and five-year-old children with scalar sentences in simple form, e.g. "some of the animals are sleeping", and in a form modified with the focus operator, only, e.g. "Only some of the animals are sleeping." The sentences were made underinformative by pairing them with pictures in which all the subjects obeyed the predicate. If children were not aware that all and some were scale mates, then they would fail to correctly reject underinformative sentences with only. Consistent with this hypothesis, children failed to reject underinformative descriptions with or without the modifier only (in contrast to adults). Crucially, in a condition with contextually determined alternatives (ad hoc items), e.g. "Only the dog and cat are sleeping," when the dog, the cat, and the cow were sleeping, children rejected the only sentences just as adults did. This confirmed that children understood the focus operator only and that their difficulties with alternatives were constrained to lexical scalemates. Thus, while the alternatives used to derive ad hoc implicatures were easily accessible, the alternatives used to derive scalar implicatures (stored lexically) were not.
Further support for the lexical alternatives account stems from studies showing that while children are impaired on scalar implicatures, they derive ad hoc implicatures based on the same materials with ease (Foppolo et al., 2021;Gotzner et al., 2020;Horowitz et al., 2018). For example, Horowitz et al. showed children three book covers with pictures of animals on each. One picture had animals all of the same type (dogs), another had animals all of a different type (cats), and a third had pictures of two animals of one type (cats) and two of a different type (rabbits). In the quantity condition, children were asked which book corresponded to "some of the animals are cats" and in the ad hoc condition, "there are cats". Implicature answers corresponded to the book with the partial set and the book with only cats respectively. In Experiment 1, they found that four-and five-year-old children responded with the implicature option at ceiling for the ad hoc implicature questions but around 40% for the quantity implicature questions. Foppolo et al. (2021) found similar results in children aged three-to six-years-old. Children derived ad hoc implicatures at a higher rate than scalar implicatures (78% vs 57%). Because the two sorts of implicature involve the same communicative processes and differ only on lexical content, Horowitz et al. (2018) and Foppolo et al. (2021) argued that children's difficulties with quantity implicatures must have a semantic basis (e.g. the link between some and all), consistent with the lexical alternatives account.
The lexical alternatives account has experimental support from studies that have tested ad hoc implicatures. Nonetheless, studies demonstrating that children derive scalar implicatures to adult-like levels when pre-exposed to alternatives (e.g., Guasti et al., 2005;Pouscoulous et al., 2007;Skordos & Papafragou, 2016) raise questions about the generality of the lexical alternatives account. For example, Skordos and Papafragou gave children a sentence-picture matching task with underinformative some sentences (e.g. "Some of the blickets have an X" when in fact all did) and manipulated when they were exposed to all sentences ("All of the blickets have X"). When children processed all sentences before underinformative sentences, rejection of the underinformative sentences was higher than when they heard them after. The difficulty for the lexical alternatives account is how to explain why children were able to derive scalar implicatures in the pre-exposure condition. If children had no knowledge that all is an alternative to some, as the lexical alternatives account maintains, why would making all more salient elevate implicature rates? All should be no different to other expressions unconnected with some, yet children appear to recognise that when all is more salient, it should be used to derive an implicature.
One way of reconciling the pre-exposure results with the lexical alternatives account is to argue that children had partial knowledge of the relationship between scale mates but not complete knowledge. In other words, children were able to access the lexical alternatives to some extent, but only at low probability relative to adults. The results of Barner et al. (2011) and others require that scalar alternatives are less accessible than those of ad hoc alternatives, but not that they are completely inaccessible. A definitive test of the lexical alternatives account would therefore require a control condition involving ad hoc implicatures. If the probability of retrieving all from some was lower than the probability of retrieving ad hoc alternatives from their triggers, the effects of pre-exposing the alternative on scalar expressions should be smaller than on ad hoc expressions.
Another approach to explaining the pre-exposure results is to allow that children are able to derive scalar implicatures as ad hoc implicatures when they do not have appropriate lexical knowledge. For example, Barner et al. (2011) suggested that when children were trained to derive implicatures (e.g. Guasti et al., 2005), they did so by applying ad hoc reasoning; namely, they derived more informative sentences from the general context and negated them as appropriate (see Sullivan, Davidson, Shirlene, & Barner, 2019, for a similar suggestion). This extends the lexical alternatives account because it assumes children can still derive scalar implicatures with non-lexical alternatives (with prompting). Moreover, the difficulty with this explanation is why an ad hoc strategy is successful for ad hoc implicatures but not for scalar implicatures (outside of pre-exposure conditions). Why do children fail to derive scalar implicatures in experimental contexts when they could apply an ad hoc strategy?
One answer is that scalar alternatives might be more difficult to retrieve from the context than ad hoc alternatives. If children cannot easily retrieve the alternative, they would fail to derive scalar implicatures, even if they were using an ad hoc strategy. However, it is unclear why children would find scalar alternatives more difficult to retrieve. In experimental contexts, all trials typically occur as often as ad hoc alternative trials, and indeed, all trials are often used as control trials to ensure that children understand the basic task and semantic terms (e.g. Barner et al., 2011;Katsos & Bishop, 2011;Noveck, 2001). Frequency of exposure to the respective alternatives does not seem to be the reason why scalar alternatives are less salient than ad hoc alternatives. Nor does the experimental stimuli makes it easier to access ad hoc alternatives than scalar alternatives. For example, in Barner et al. (2011), the sleeping cow, dog, and cat are in the picture so a child can easily see that the ad hoc alternative sentence ("the cow, the dog and the cat are sleeping") is true, but then again, the child can also easily see that the scalar alternative ("all the animals are sleeping") is true. Moreover, the lexical alternatives account maintains that children have an adult understanding of all and someit is the link between them that is underdevelopedhence there is no reason why children would have difficulty accessing the meaning of all.
While the ad hoc extension of the lexical alternatives account leaves some questions unanswered, it nonetheless remains a possibility. It also makes predictions about pre-exposure of the alternative, however. If scalar alternatives are more difficult to access than ad hoc alternatives, priming with the alternative should have less of an effect on scalar expressions than on ad hoc expressions. To see why, consider a model in which alternatives have varying degrees of activation, and an activity threshold must be exceeded to trigger an implicature (Rees & Bott, 2018). Assume further that when an alternative is less accessible, it has a lower baseline activation, and that an alternative prime increases the activation level of the alternative. Under this model, alternatives with lower baseline activation levels (all) will see less of an increase in implicatures following an alternative prime than those with higher baseline activation levels (ad hoc alternatives). This is because activation levels will exceed the implicature threshold in a lower proportion of trials in low baseline alternative conditions than in high baseline alternative conditions.
In this study, we test the hypothesis that scalar alternatives are less accessible than ad hoc alternatives in children. If they are, this provides support for the lexical alternatives theory. If not, another explanation would be required for why children fail to derive scalar implicatures on some occasions but not others. We used a form of pre-exposurestructural priming (Branigan & Pickering, 2018;Raffray & Pickering, 2010) -and tested whether there was equal priming between some and all and ad hoc triggers and their respective alternatives.

Experiment overview
Participants completed a sentence-picture matching task where they had to decide which of two pictures best matched the meaning of a sentence. There were prime trials and target trials (see Fig. 1). In prime trials, the interpretation of the sentence was guided by the configuration of the pictures such that one picture (interpretation) provided a much better fit to the sentences. In target trials, the configuration of the pictures allowed either interpretation. Participants therefore had a choice of interpretations in target trials but not prime trials. There were three types of prime trial: strong, weak, and alternative. Target trials immediately followed prime trials.
Strong and weak prime trials used sentences containing an implicature trigger, e.g., "Some of the animals are dogs", whereas alternative prime trials used sentences that were more informative, "All of the animals are dogs". In strong prime trials, the sentence picture combination encouraged participants to make an implicature interpretation (a strong interpretation), some but not all of the animals are dogs. In weak prime trials, the sentence picture combination encouraged participants to make a literal interpretation (a weak interpretation), some and possibly all of the animals are dogs. In the alternative prime trials, one picture matched the alternative interpretation of the sentence, all of the animals are dogs. Thus the alternative prime trial made the alternative salient.
In target trials, the sentence used an implicature trigger, e.g. "Some of the animals are dogs". One picture was consistent with a weak interpretation of the sentence and the other card was a "better picture" option ( Fig. 1). Participants were instructed to select the "better picture" option if they thought there was a different, better picture that would match the sentence (as in Bott & Chemla, 2016; see also Bill, Romoli, Schwarz, &Huang, Spelke, &Snedeker, 2013, for hidden box implementations with children aged two-and three-yearsold). The logic was that if participants derived an implicature then the picture consistent with the weak interpretation would not be an acceptable choice and they would select the "better picture" option.
We tested four-and five-year-old children, and adults, using scalar expressions (some, all) and ad hoc expressions ("There is an X", "There is an X and a Y"). Adult responses should follow patterns reported in previous literature (Bott & Chemla, 2016;Rees & Bott, 2018), namely higher rates of strong responses (implicature interpretations) after strong primes than after weak primes, and higher rates of strong responses after alternative primes than weak primes. The logic of the task was that the strong prime and the alternative prime both made the alternative more salient, explicitly so for the alternative prime, implicitly so for the strong prime. Since more salient alternatives increases the likelihood of deriving an implicature (Bott & Frisson, 2022;Chierchia, Fox, & Spector, 2012;Skordos & Papafragou, 2016;Van Tiel & Schaeken, 2016), higher rates of strong responses should be observed after strong and alternatives primes than after weak primes.
Uncontroversial predictions for children's responses can also be made from previous literature. Following Barner et al. (2011), Stiller et al. (2015 and others, we expected children to derive ad hoc implicatures without difficulty and to choose the strong interpretation on the strong prime trials. We also expected a lower rate of strong responses on the strong scalar prime in children compared to adults, consistent with the classic finding of a low rate of implicatures with quantifiers in children (e.g. Noveck, 2001).
The crucial test of our hypothesis was behaviour on the target trials. If children have only a weak connection between scalar trigger and alternative, there should be less priming after the alternative prime in scalar expressions than in ad hoc expressions (relative to the weak prime) i.e. an interaction between prime type (strong, weak, alternative) and expression type (scalar quantifier, ad hoc) on the rate of implicatures in the target trials.

Participants
72 children aged 4;2 to 5;11 (mean 5;1 years; 40 male) were recruited from primary schools in Rugby and Warwickshire. They were given a sticker for their participation. Data were excluded from two children who did not pass the familiarisation trials. 51 adult controls were recruited from Cardiff University (N = 21) and Prolific Academic, an online recruitment website (N = 30). All adult participants completed the study online and received either course credit or payment for their participation.

Design and materials
For children, the sentence picture-matching task was conducted in person using a set of physical A6 printed cards. The cards showed two pictures consisting of rectangles containing either cartoon images of animals or the text "Better Picture?" (See Fig. 1). There were two implicature categories: quantifier and ad hoc, and three prime types: strong, weak, and alternative. For each category-prime combination there were four examples resulting in 48 experimental trials (24 primetarget pairs) that were randomly presented within-participants. Table 1 shows the scalar terms used together with plausible alternatives and the subsequent implicature.

Quantifier trials
For quantifier trials, sentences were of the form "[Quantifier] of the animals are [animal]." Strong prime trials had two pictures, one with 9 of the same animal and another containing 6 of that same animal and 3 new animals. The sentence predicate was the animal seen in the both pictures. For example, in Fig. 1, the sentence for the strong prime is, "Some of the animals are dogs," and there is one picture with 9 dogs and another picture with 6 dogs and 3 cats. Thus the partial set picture is consistent with the strong interpretation, some but not all of the animals are dogs. Thus, in strong prime trials, participants should select the partial set picture and derive the strong interpretation.
Weak trials had two pictures, each consisting of a set of 9 animals. The animals were different in both pictures. The sentence predicate was the animal seen in one of the pictures. Since neither picture involved a partial set of animals, participants were obliged to select a picture corresponding to a weak interpretation. In Fig. 1, the weak prime used the sentence, "Some of the animals are cats," and included one picture with 9 rhinoceroses and another with 9 cats. Participants should therefore select the picture with 9 cats, consistent with the weak interpretation of the sentence.
Alternative trials had the same picture configuration as the weak trials but were accompanied by a sentence that used the alternative quantifier, all. The sentence therefore unambiguously identified one picture and made the alternative salient without requiring an implicature. In Fig. 1, the alternative sentence is, "All of the animals are sharks," and one picture contains 9 sharks and the other 9 meerkats. Participants would therefore select the shark picture.
Target trials contained one picture with a full set of 9 animals (the weak picture), and one "better picture" option. The accompanying sentence used the less informative quantifier (some) and referred to the animals in the picture. Thus if participants derived the weak interpretation, they should select the full set picture, but if they derived the strong interpretation, they should select the "better picture" option. In Fig. 1, the sentence is "Some of the animals are pigs", and the full set picture contains 9 pigs. Thus, the selection consistent with the weak interpretation, some and possibly all of the animals are pigs, is the picture with pigs, but the selection consistent with the strong interpretation, some but not all of the animals are pigs, is the "better picture" option.

Ad hoc trials
For ad hoc trials there were two sentence forms, either, "There is an [animal]," for strong, weak, or target trials, or the conjunction, "There is an [animal 1 ] and an [animal 2 ]," for alternative trials.
Strong prime trials had one picture with two animals and another picture with one animal. The single animal picture contained the same animal as one of the animals on the other picture. The sentence referred to the animal that appeared in both pictures. Participants could therefore reason that if the sentence had meant to refer to the picture with two animals, it would have included both animals, and consequently the sentence must refer to the picture with only one animal. For example in Fig. 1. Example prime and target trials. Left to right: quantifier and ad hoc. Primes top to bottom: strong, weak, and alternative. Each trial consisted of a sentence and two pictures. Participants selected the picture that best matched the sentence. E.g. for the quantifier alternative prime (bottom left), "All of the animals are sharks", participants should select the right hand picture. There is an X X and Y There is an X and nothing more A. Rees et al. Fig. 1, the strong prime trial contains the sentence, "There is a fox," with one picture of a fox only and one with a fox and a bee. Participants can reason that since the sentence mentioned only the fox, and not the fox and the bee, the sentence must refer to the picture with only the fox. Strong primes encourage strong interpretations of the sentence, e.g. there is a fox and nothing else. Thus, in strong prime trials, participants should select the card with only one animal. Weak trials had two unique animals in each picture. The sentence referred to one of the animals in the pictures. In Fig. 1, the weak sentence is, "There is a chicken," and has one picture with a sheep and a chicken, and another with penguin and a lion. Here, the sentence-picture combination forces a weak interpretation of the sentence, there is a chicken and possibly something else.
Alternative trials had the same configuration as strong trials but used the more informative conjunction sentence. For example, in Fig. 1, the alternative sentence is, "There is a bat and a caterpillar," and there is one picture with a bat and a caterpillar, and another with a caterpillar. The sentence unambiguously identifies one of the pictures but without invoking an implicature.
Target trials had one picture with two different animals (the weak picture), and one "better picture" option. The sentence referred to one of the animals in the picture. Thus a weak interpretation of the sentence was shown by selection of the animal picture, and the strong interpretation by the "better picture" option. In Fig. 1, the sentence is, "There is an octopus," and the animal picture contains an octopus and a duck. Thus, the selection consistent with the weak interpretation, there is an octopus and possibly something else, is the octopus and duck picture, but the selection consistent with the strong interpretation, there is an octopus and nothing else, is the "better picture" option.

Procedure
For the child participants, testing took place in a quiet room at the participants' school. Before the main experiment, children had a familiarisation task where they were shown example cards with animals and asked to identify the animal. This was to ensure children were able to name all the animals in the experimental items and were comfortable interacting with the experimenter. Children were then shown five examples of "better picture" trials to get them comfortable with selecting that option. Children were instructed to select the "better picture" option if they thought that a different picture would match the sentence better. In these example trials, the spoken sentence did not match the items in the picture to try an encourage children to select the "better picture" option. If children failed to understand the "better picture" paradigm twice during familiarisation the experimenter ended the testing session, two participants were excluded for this reason. The main experimental session involved showing participants one card (two sets of pictures) and a corresponding spoken sentence. Children indicated which picture they thought matched by pointing and the experimenter took note of their responses.
For adults, the study was run as an online survey (via Qualtrics). The structure was the same as the main experimental session for children.

Analysis procedure
We fitted a logistic mixed effects model in R (R Development Core Team, 2020) using lme4 (Bates, Maechler, Bolker, & Walker, 2015) and afex (Singmann, Bolker, Westfall, Aust, & Ben-Shachar, 2020). The model predicted participant's correct response as an interaction of prime (alternative, strong, or weak) and expression (quantifier or ad hoc) with random effects for participants. Like many developmental studies (e.g. Barner et al., 2011;Gotzner et al., 2020;Skordos & Papafragou, 2016), we had insufficient numbers of items (only 4 per cell) to include items as a random effect. To obtain convergence, we began with the maximal random effects structure supported by the design (Barr, Levy, Scheepers, & Tily, 2013;Gelman & Hill, 2006) and then simplified until convergence was obtained. Correlations between slopes and intercepts were set to 1 in all cases. Treatment coding was used throughout. Quantifier expression and weak prime type were reference levels for expression and prime respectively.
Main effects and overall interactions were established with likelihood ratio tests between complex and simplified models. Simple effects p-values were computed with the Kenward-Roger and Satterthwaite approximations to degrees of freedom (lmerTest(), Kuznetsova, Brockhoff, & Christensen, 2017).
We use Bayes Factors to interpret non-significant findings. Bayes factors indicate how strongly the data supports a hypothesis and can be used in the case of non-significant results to determine whether this is merely due to a lack of power (Dienes, 2011). We used the default JZS prior (0.707) for all analyses (Rouder, Speckman, Sun, Morey, & Iverson, 2009). The JZ prior minimises assumptions regarding expected effect sizes. Bayes factors were calculated using JASP (JASP Team, 2020). Bayes factors > 3 suggest 'substantial' evidence for the alternative hypothesis and Bayes factors < 0.33 indicate 'substantial' evidence for the null hypothesis (Dienes, 2011(Dienes, , 2014. Data and analysis scripts available on the Open Science Framework. 1

Adults data
Prime trials. Adult responses to prime trials were at ceiling for all prime trials (alternative M = 1.00, strong M = 0.96, weak M = 1.00).

Children's data
Prime trials. Children's responses were at ceiling for all prime trials (M's > 97%) except for quantifier strong primes 2 (M = 81%). Consistent with previous literature, children were less likely to select the strong interpretation than adults (t(452) = 5.02, p < .001).
Target trials. As with adults, the rate of implicature responses varied as a function of prime type (Fig. 3, Table 3). There was a main effect of prime (χ 2 = 19.78 p < .001). Participants were more likely to derive an implicature following strong (β = 0.59, SE = 0.172 z = 3.40, p = .002) and alternative (β = 0.76, SE = 0.174, z = 4.35, p < .001) prime trials 1 https://osf.io/7mu8x 2 We note performance on the strong primes is greater than performance on critical trials. This could be due to the visual presence of the alternative making the contrast between some and all more salient and thus the implicature easier to compute. than weak trials. Unlike in adults however, there was no effect of expression (χ 2 = 3.94 p = .268, BF = 0.10). Crucially, there was no evidence of an interaction between expression and prime type (χ 2 = 0.50, p = .780, BF = 0.06) and indeed the Bayes Factor demonstrates that the likelihood of there being no interaction is around 20 times the likelihood that there is. There is thus strong evidence against the prediction that the priming effect on quantifiers should be less than on ad hoc expressions.

Discussion
This study tested children's knowledge of the relation between an implicature trigger and its alternative. We found that children showed good understanding of some and all overall yet were reluctant to derive implicatures on prime trials, consistent with standard findings in the literature (e.g. Noveck, 2001). Conversely, ad hoc implicatures were at ceiling levels of proficiency. More importantly, children exhibited robust priming of scalar implicatures by the alternative, and at a level indistinguishable from those of ad hoc implicatures. Our data show that children have just as much knowledge of the relationship between scalar alternatives and their triggers as between ad hoc alternatives and their triggers, in contrast to the predictions of the lexical alternatives account.

Lexical alternatives account
In the Introduction we discussed results in which pre-exposure of the alternative elevated rates of implicatures. We argued that in order for a lexical alternatives account to explain these findings, it must assume either that children had partial lexical knowledge of the scalemate status of some and all, or, in an extension to the basic account, that children were able to compute scalar implicatures using alternatives retrieved from the context rather than lexically. In turn, these assumptions imply that lexical alternatives must be less accessible than ad hoc alternatives.
Our demonstration that the link between alternatives and triggers was the same for scalars and ad hoc expressions contrasts with this prediction. If there was a stronger link between scalar triggers and alternatives than between ad hoc triggers and alternatives, we should have observed greater priming from the alternative for the ad hoc expressions. This therefore argues against a lexical alternatives account that assumes children have an adult-like understanding of quantifiers but are unable to link the trigger with the alternative.
There may be other, related accounts that are more consistent with

Fig. 2.
Adult's strong responses to target trials. The rate of strong responses to target trials was higher after alternative and strong primes than after weak primes. A. Rees et al. our data, however. Relaxing the constraint that children understand quantifiers fully might explain why children were unable to apply ad hoc reasoning to scalar expressions but were also primed with the alternative in our task. For example, Horowitz et al. (2018) argue that children fail on scalar implicatures because they do not fully understand the class of quantifiers and that this interacts with their ability to retrieve alternatives. It may also be that there are other concepts apart from accessibility that may explain why children did not use ad hoc reasoning when deriving scalar implicatures. For example, Skordos and Papafragou (2016) argue that children have difficulty computing the relevance of the scalar alternatives. However, if children find computation of relevance more difficult for scalar alternatives than for ad hoc alternatives, this effect should also have been present in our priming task: relevance priming should have been less effective for scalar implicatures than for ad hoc implicatures.
In summary, we have tested a prediction of the lexical alternatives account as we interpret it, but we appreciate that there may be other alternatives accounts that make different assumptions and that are more consistent with our findings.

Ad hoc implicatures
Children are reluctant to derive scalar implicatures (e.g., Noveck, 2001) but are more ready to derive ad hoc implicatures (e.g. Foppolo et al., 2021;Horowitz et al., 2018;Stiller et al., 2015;Yoon & Frank, 2019). This effect is seen in our data. Children chose the strong scalar response less frequently than adults on prime and target trials. They also performed at ceiling on ad hoc prime trials. Interestingly however, they chose the ad hoc strong response at over twice the rate of adults in target trials (64% vs 30%). Thus if children are more logical than adults when deriving scalar implicatures, they are more pragmatic than adults when deriving ad hoc implicatures.
This effect has not previously been noted in the literature but our results are not inconsistent with others (e.g. Gotzner et al., 2020;Horowitz et al., 2018;Stiller et al., 2015;Yoon & Frank, 2019). Most authors (e.g., Horowitz et al., 2018;Stiller et al., 2015) obtain ceiling level implicature responses for children and adults. One study that did not have ceiling effects, Gotzner et al. (Experiment 2), also found a greater rate of implicatures among children than adults, although not to the same degree as us. Adults derived conjunctive ad hoc implicatures at a rate of 5% and children at a rate of 14%; and adults derived disjunctive ad hoc implicatures at a rate of 45% and children at a rate of 55% (although the tasks were not identical across age groups).
One interesting explanation for the strong interpretation bias in children is that the strong interpretation is not pragmatic in nature, but instead is part of the semantics of the utterance, as has been proposed for it-clefts (Atlas & Levinson, 1981;Hedberg, 2000). Children might have an initial interpretation that is strong but then learn to apply the weak interpretation as they develop. If this is correct, it has implications for the conclusions of studies that have used ad hoc implicatures as a control condition against which to compare scalar implicatures (e.g., Barner et al., 2011;Horowitz et al., 2018). The idea in these studies is that successful performance on the ad hoc implicatures demonstrates that Fig. 3. Children's strong responses to target trials. The rate of strong responses to target trials was higher after alternative and strong primes than after weak primes. A. Rees et al. children have the general pragmatic and cognitive skills necessary to derive implicatures e.g. combining the negated stronger expression with the basic meaning, and that poor performance on scalar implicatures must therefore be due to their scalar nature i.e. lexical storage of alternatives. However, if the strong interpretation of ad hoc expressions is developmentally prior, and some sort of pragmatic reasoning is required to derive the weak interpretation, then children can be considered pragmatically delayed on both ad hoc and scalar implicatures. General cognitive and pragmatic deficits may therefore play a role in explaining both deficits, thereby obviating the need for scalar specific explanations.

Weak or strong priming?
A potential limitation of our study is that we cannot say whether the strong and alternative prime biased participants away from the weak interpretation, as we have assumed, or whether the weak prime biased participants away from the strong interpretation. In other words, we do not know which interpretation was being primed. For scalars, our assumption was that the weak interpretation was the default and that the strong interpretation was primed. This is consistent with classical accounts of implicatures (Grice, 1989), developmental research concluding that children are biased towards the weak interpretation (e.g. Noveck, 2001), and adult work concluding that adults are faster to respond to weak interpretations (Bott & Noveck, 2004;Huang & Snedeker, 2018; although not always, see e.g., Grodner, Klein, Carbary, & Tanenhaus, 2010). Our assumption may be incorrect however: the weak prime could have been doing the priming.
Recent conference proceedings relate to this question (Marty, Cowan, Romoli, Sudo, & Breheny, 2021;Waldon & Degen, 2020). These studies included a baseline prime trial that was unrelated to subsequent trials. Marty et al. included baseline trials at the start of the task, Waldon and Degen during the task, rotating with other experimental primes. Both studies tested only adults. The results were interesting but somewhat inconclusive with respect to whether participants were primed with the alternative, or with the weak interpretation for scalar triggers. Waldon and Degen's study was not directly concerned with this question but the proceedings appear to conclude that there was no evidence that the all alternative primed strong interpretations for scalar triggers. They nonetheless found that alternatives (both canonical and symmetric) primed responses across expressions generally. Marty et al. found that for participants who had high baseline rates of implicature, i.e. > 50% implicature rate, the weak prime lowered the implicature rate but for those who had low baseline rates, i.e. < 50%, the strong prime/alternative raised them (Paul Marty, personal communication).
More importantly the question of which interpretation is being primed is irrelevant with respect to the lexical alternatives hypothesis. If the strong/alternative prime raised implicature rates, as we assumed throughout, then the alternative must be linked to the scalar trigger just as much as for the ad hoc expressions. If the weak prime suppressed implicature rates, the alternative must have been less accessible, which could also only be explained by assuming children understand the link between some and all. In both cases our data argue against the lexical alternatives account.

Role of the foil card
In Rees and Bott (2018), the alternative prime used a different picture configuration to that used here. In our task, the target card contained a complete set of predicate images, e.g. sharks, and the foil contained a complete set of images corresponding to a different predicate, e.g. monkeys. In Rees & Bott, the target card again contained a complete set of predicate images, e.g. sharks, but the foil contained a partial set of predicate images combined with other images, e.g. sharks and monkeys. The alternative prime cards were therefore identical to the strong prime cards, the difference being that the strong prime sentence referenced the partial set card, sharks and monkeys, and the alternative prime sentence referenced the complete set card, sharks.
The structure of the primes in Rees and Bott (2018) might be said to emphasise the difference between alternative and strong interpretation through comparison between target and foil (all in one card, some-butnot-all in the other). That we obtained a significant priming effect with the current configuration implies that the combination of linguistic expression and target card is sufficient to activate the alternative irrespective of the foil card. Quite possibly, however, the scalar priming effects would have been larger if we had used the configuration used in Rees & Bott. If so, this would have provided an even stronger demonstration of how children understand the relation between some and all.

Conclusion
The primary goal of this study was to investigate whether children's reluctance to derive scalar implicatures was due to a deficit in their knowledge of the relationship between some and all. To this end, we conducted a priming study in which we tested whether children could be primed to derive implicatures by making the alternative more salient. This yielded two major findings. First, children derived ad hoc strong interpretations at twice the rate of adults. While previous studies have consistently found that children derive strong ad hoc interpretations with ease, none have demonstrated that children exceed adults in the rate of strong interpretations. Children therefore have a deficit on ad hoc expressions as well as scalar expressions, albeit in different directions. Second, children displayed significant priming of scalar and ad hoc implicatures, both with the alternative and the strong prime, and at a level indistinguishable from each other. They also displayed poor performance on the scalar implicature primes. This suggests that the root cause of the scalar implicature deficit is not due to the absence of lexical knowledge of the relationship between some and all.

Data availability
Data is available on OSF. Link is included in methods.