Developmental evidence against the theoretical distinction between Horn and pragmatic scales

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Journal of Pragmatics 44 (2012) 1680--1700 www.elsevier.com/locate/pragma

Developmental evidence against the theoretical distinction between Horn and pragmatic scales Anna Verbuk * Department of Linguistics, University of Massachusetts, 226 South College, 150 Hicks Way, Amherst, MA 01003-9274, USA Received 7 October 2011; received in revised form 6 July 2012; accepted 18 July 2012

Abstract A theoretical distinction between Horn and pragmatic scales that are instrumental in generating scalar implicatures (SIs) is widely accepted in neo-Gricean pragmatics; at the same time, this distinction has been questioned in some neo-Gricean and post-Gricean accounts of SIs. In order to explore whether or not this distinction has a reflex on the way in which children acquire SIs, I tested 40 children (4;3-7;7) on computing SIs based on Horn and pragmatic scales. If this distinction is postulated, children are predicted to perform better on computing SIs based on Horn scales. In my experiment, children did significantly better on computing SIs based on pragmatic scales. Moreover, children performed worse on certain Horn scales than on the pragmatic scales, and better on other Horn scales than on the pragmatic scales. I provide theoretical reasons against distinguishing between Horn and pragmatic scales, and propose my own Context-based QUD account of SIs on which children's performance on computing SIs is a function of challenges presented by individual scales. I identify three major linguistic and cognitive acquisitional challenges presented by scales, and how these predict the timeline of SI acquisition. © 2012 Elsevier B.V. All rights reserved. Keywords: Acquisition; Scalar implicature; Horn scale; Pragmatic scale; Question-under-discussion

1. Introduction There has been a great deal of research on the acquisition of a specific subclass of pragmatic meanings -- scalar implicatures (SIs), as in (1), -- but a number of questions remain unanswered. (1)

a. A: Is your coffee hot? b. B: It's warm. c. B's SI: My coffee is not hot. d. The scale the SI is based on:

In previous work on SI acquisition, it was found that children's success on computing SIs varies greatly depending on the experimental methodology that is employed, and that making the SI relevant in a given context, and making the scale salient dramatically increase children's success (e.g., Noveck, 2001; Papafragou and Tantalou, 2004; Barner et al., 2011). From the acquisitional standpoint, in this paper, I will be concerned with exploring linguistic and cognitive prerequisites and challenges relevant to computing SIs. I formalize SI relevance in terms of relevance to a question-under-discussion, and argue that inferring the question-under-discussion and determining that an SI meaning is relevant to it are prerequisites for computing SIs. I experimentally demonstrate that five-year-olds, the youngest children who derive SIs,

* Present address: 74 B Charlesbank Way, Waltham, MA 02453, USA. Tel.: +1 617 901 7916. E-mail addresses: [email protected], [email protected]. 0378-2166/$ -- see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.pragma.2012.07.007

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are already sensitive to considerations of relevance. My experiment shows that arriving at the content of the scale employed in generating an SI is a major acquisitional challenge. I identify general acquisitional challenges associated with scales, such as the degree of contrast between scalemates and the challenge created by context- and speakerdependent scalemates. I also discuss cognitive acquisitional challenges associated with different scales, including those associated with using various kinds of world-knowledge. Based on specific challenges, I predict a time-line of the acquisition of SIs based on different scales, which is supported by my experimental results as well as by results from previous acquisitional studies. From the theoretical standpoint, this paper makes three central contributions. First, I demonstrate that the major neoGricean accounts overgenerate SIs, i.e., predict their occurrence in contexts where these do not arise. Second, I propose my own question-under-discussion based version of a neo-Gricean account that solves this problem. Third, I tested experimentally between predictions of default and context-based accounts of SIs, and found acquisitional evidence in support of context-based but not default accounts. Next, I provide more theoretical background on SIs. SIs are a species of Quantity-based conversational implicatures. The first submaxim of Quantity compels interlocutors to make their contribution as informative as is required for the current purposes of the exchange (Grice, 1989). This submaxim is instrumental in generating SIs. If an interlocutor uses a less informative term when a more informative one is relevant, an SI to the effect that the more informative term does not hold or that the speaker does not know if it holds is often generated (Horn, 1972). The SI in (1c) is based on a scale . By using a weaker scalar item warm, speaker B implicated that the stronger one hot does not hold. Scales employed in generating SIs are typically identified in the literature as belonging to one of two classes: Horn scales and pragmatic scales (e.g., Horn, 1989; Levinson, 2000). Horn scales are usually based on the ordering relation of entailment. The stronger items on the left unilaterally entail all of the items to their right, e.g., in the temperature scale , boiling entails hot and warm, and hot entails warm. Some other examples of Horn scales are , and . Pragmatic scales are defined as being based on an ordering relation other than entailment, such as the level of description, as in scales , part/whole, as in and stages, as in . In (2) is an example of an SI based on a pragmatic scale. (2)

a. A: How much of the apartment has John painted over the weekend? b. B: He has painted a room. c. B's implicature: John did not paint the whole apartment.

To date, a number of experimental studies have been done on the acquisition and adult processing of SIs; researchers have focused almost exclusively on the acquisition and processing of SIs based on Horn scales (e.g., Foppolo et al., submitted for publication; Pouscoulous et al., 2007; Papafragou, 2006; Bott and Noveck, 2004; Breheny et al., 2006) but see Papafragou and Tantalou (2004).1 Next, I briefly summarize some of the seminal studies on SI processing that are relevant to the topic of the current study, and briefly mention some of the previous major experimental findings with respect to children's performance on computing SIs based on different scale classes and individual scales. Previous studies on adult sentence processing focused on exploring the role of context in SI computation by adults, and previous studies on SI acquisition provide some insight with respect to the role of scales in children's success on computing SIs. Building on some of this previous work, the current paper makes a contribution to exploring the role of context and the role of lexical factors in SI acquisition. Breheny et al. (2006) presented experimental evidence based on processing experiments with adults supporting the view that SIs are pragmatic meanings, as predicted by the pragmatic context-based accounts, rather than default inferences that are computed automatically, as predicted by accounts in Levinson (2000) and Chierchia (2004). The default accounts predict that SIs are derived automatically in all contexts, and subsequently cancelled in contexts where they are irrelevant; since deriving and canceling an SI takes longer than just deriving an SI, longer reading times are predicted for contexts where SIs are irrelevant. The pragmatic context-based views predict that SIs are derived by pragmatic reasoning and only in contexts where their content is relevant; irrelevant SIs are not derived. Since deriving an SI takes longer than not deriving it, longer reading times are predicted for contexts where SIs are relevant. Breheny et al. found experimental support for pragmatic accounts of SIs. Bott and Noveck (2004) found similar results; their experiments showed that computing an SI requires additional processing time and results in lower response accuracy compared to processing a scalar item on its semantic meaning, which is predicted on the view of SIs as pragmatic inferences but not on the view of SIs as default inferences.

1 This is in part because SIs based on Horn scales were brought under a spotlight by the theoretical debate between default (e.g., Chierchia, 2004) vs. context-based accounts of how these meanings are computed (e.g., Sauerland, 2004).

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Next, I briefly discuss several studies on the acquisition of SIs that are relevant to the topic of the present paper because they provide evidence regarding the role of scales in children's success on computing SIs. Foppolo et al. (submitted for publication) found significant differences between children's performance on computing SIs based on three Horn scales. In contrast, Papafragou and Tantalou (2004) did not find significant differences in children's performance on SIs based on one Horn scale and two pragmatic scales -- five-year-olds performed equally well on all three; however, while the differences were not statistically significant, there was a sizable difference between the means of correct responses. Pouscoulous et al. (2007) found that the use of two different French words for ‘‘some,’’ quelques vs. certains, did have an effect on children's success on computing SIs. Papafragou (2006) found that children were more successful on computing SIs based on Horn scales relying on Greek equivalents of degree modifiers ‘‘half’’ and ‘‘halfway’’ than on those of aspectual verbs ‘‘start’’ and ‘‘begin.’’ Considered together, previous experimental findings unequivocally suggest that the type of scale and the choice of specific lexical items play a role in children's performance on computing SIs. However, more work needs to be done in order to explore the role of scale classes and lexical challenges in children's performance on computing SIs. The present experiment aims to clarify the issue of whether or not the widely assumed theoretical distinction between Horn vs. pragmatic scales has a reflex on how children acquire SIs based on the two types of scales. I present experimental evidence that weighs in on the theoretical debate between accounts that draw a theoretical distinction between SIs based on Horn scales vs. those based on pragmatic scales (e.g., Horn, 1989; Levinson, 2000) and accounts that do not draw this distinction (e.g., Hirschberg, 1991; Carston, 1998). My experimental findings provide evidence against this theoretical distinction; I found that, contra the prediction of accounts that draw this distinction, children did not do better on computing SIs based on Horn scales. On the contrary, overall, children did significantly better on computing SIs based on pragmatic scales. However, children's performance on individual scales presents a more complex picture. I will argue that the child's performance on computing SIs is not predictable from the class of scale that is employed but rather is a function of major acquisitional challenges associated with certain scales. In this connection, I discuss in detail which of these challenges individual scales are subject to. Prior to discussing my experiment, I will start by providing novel theoretical reasons against drawing the distinction between Horn and pragmatic scales. 2. What contexts are SIs relevant in? 2.1. The neo-Gricean Stance The main reason for postulating a theoretical distinction between Horn and pragmatic scales that was identified in the pragmatic literature is the claim that SIs based on Horn scales are computed unless something in the context of the utterance blocks their computation, while SIs based on pragmatic scales are computed only if they receive special contextual support (Horn, 1989; Levinson, 2000). Next, I will demonstrate that the claim that SIs based on Horn scales are computed unless something in the context blocks their computation is too strong, and introduce my own question-underdiscussion (henceforth, QUD) based account of SIs. Levinson (2000:51--52) remarks that the problem of generalized conversational implicatures (GCIs), SIs being a species thereof, that do not get projected ‘‘. . .may cast some doubt on whether default logics are the right formalism for modeling GCIs, or it might show that they simply need to be bounded by a yet to be described maxim of Relevance’’ (underlined by the author). Levinson notes that, in particular, a typical case where an SI gets canceled is the one where the content of the utterance that gives rise to the implicature is an exhaustive answer to a salient question. (3)

a. A: Does John qualify for the Large-Family benefit? b. B: Sure, he has three children all right. Levinson (2000:88). c. Predicted but evaporated SI: He does not have more than three children. Levinson (2000:50--52) identifies the following classes of contexts where an SI gets canceled. (4)

a. Contexts containing inconsistent background assumptions. b. Contexts where the utterance that may generate an SI has an entailment which is inconsistent with the SI. c. Contexts where an SI is inconsistent with other implicatures that have a higher priority, such as clausal implicatures. d. Contexts where the utterance that generates a potential SI is an exhaustive answer to a salient question.

However, contrary to Levinson's prediction, there are additional contexts where an SI is not generated that cannot be classified as instances of any of the contexts in (4). I provide one such context in (5).

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a. A: I know that John's vacation is coming up. He looks like he really needs some time off. Where is he going on vacation? b. B: Some place where it's warm. c. Horn scale: d. No SI: John is not going some place where it's hot.

According to the account in Horn (1984), SIs based on Horn scales are relevant in neutral and upper-bounded contexts. Horn defines upper-bounded contexts as contexts where the stronger scalar item is relevant. Neutral contexts are defined as the ones where no information about the weaker or the stronger scalar item is provided. However, if one takes a closer look at the neutral contexts, one finds that SIs often do not arise in neutral contexts, as (5) and (6) illustrate. (6)

a. A: I haven’t seen you around in October. b. B: Oh, I was on vacation, and I went to Fresno to visit my relatives. It's warm in Fresno in October. c. Horn scale: d. No SI: it is not hot in Fresno in October.

It goes without saying that I am not the first to point out that SIs are not always computed in neutral contexts. For example, convincing evidence for the non-occurrence of SIs in neutral contexts is presented in Ariel (2004). Ariel (2004) presented her analysis of adult speech corpus data uses of the English most and its Hebrew counterpart, and found that the ‘‘not all’’ SI was generated just in contexts where ‘‘all’’ was contextually expected (Ariel, 2004:670). Since it cannot be argued that SIs reliably arise in neutral contexts, a revision to the account in Horn (1984) is called for. Neither the account in Levinson (2000) nor that in Horn (1984) accurately describes contexts where SIs are relevant and, hence, computed. 2.2. The Relevance-theoretic account To date, the most prominent account that proposed a solution to filtering out non-occurring SI meanings has been the Relevance-theoretic account (e.g., Noveck and Sperber, 2007). I will briefly summarize the Relevance-theoretic account of the SI phenomenon, and then discuss some of the theoretical evidence that contradicts the fundamental assumptions of this account. Noveck and Sperber (2007) claim that only a small fraction of inferences that are analyzed as SIs by the neo-Gricean pragmaticists are implicatures, and that most inferences analyzed as SIs by the neo-Griceans are, in fact, explicatures. It is claimed that explicatures narrow down the denotation of a given scalar term so as to exclude propositions with stronger scalar terms (e.g., some excludes many, most, and all). Crucially, it is also argued that the use of scalar terms generates explicatures that exclude propositions with weaker scalar terms, which have the same theoretical status as explicatures excluding stronger propositions. In Noveck et al.’s own words, ‘‘For instance ‘‘possible’’. . . (‘‘It is possible that Hillary will win’’) is often construed as excluding, on one side, mere metaphysical possibility with very low empirical probability, and, on the other side, certainty and quasi-certainty. . . Since the trimming at the very high probability end is not different from that at the very low probability end, both should be explained in the same way, ruling out the scalar aspect of the ‘scalar implicature’ account.’’ (Noveck and Sperber, 2007:11). On the Relevance-theoretic account, scalar terms are interpreted as generating explicatures of both types when ‘‘. . .the hearer's expectations of relevance in a given context cause the denotation of the scalar term to be narrowed’’ (Pouscoulous and Noveck, 2009:198). In contrast, SI meanings that have the status of implicatures on the Relevancetheoretic account are derived just in contexts where the content of the implicature is relevant to the issue at hand. As Noveck and Sperber (2007) note, ‘‘this occurs when the ‘‘. . .some. . .’’ utterance achieves relevance by answering a tacit or explicit question as to whether all items satisfy the predicate. The fact that it does not answer it positively implicates a negative answer and therefore a narrowed down construal of ‘‘some’’ as excluding all’’ (Noveck and Sperber, 2007:10). In other words, Noveck and Sperber (2007) argue that it is only in contexts where it is relevant for the interlocutors to know whether or not the stronger scalar term holds that the meaning to the effect that the stronger term does not hold has the status of an implicature or pragmatic enrichment. First, how does the Relevance-theoretic account fare on filtering out irrelevant SIs that are problematic for most versions of neo-Gricean accounts? As the reader may verify for herself, the Relevance-theoretic account does not generate non-occurring implicatures in neutral contexts, such as the ones in (5) and (6), while neo-Gricean accounts struggle with filtering out these SIs. On the Relevance-theoretic account, the hearer of (5b) and (6b) would be likely to interpret warm on its narrowed meaning, but would not derive the implicature of ‘‘not hot.’’ Also, on the Relevancetheoretic account, in contexts such as (1), reproduced as (7), the inference from the use of warm to ‘‘not hot’’ has the status of both an implicature intended by a speaker and also the status of an explicature.

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a. A: Is your coffee hot? b. B: It's warm. c. B's implicature: My coffee is not hot.

Horn (2006) presents a number of convincing arguments against the bilateral account of scalar terms endorsed by Relevance Theorists; I will review only some of these arguments here to illustrate that the Relevance Theoretic account of SI meanings cannot be adopted as such. Consider Horn's (2006) arguments against the bilateral account of scalars based on negation data. Horn (2006) points out that a negative answer to a question involving a scalar term has a ‘‘less than’’ meaning, as is predicted by the neo-Gricean but not by the Relevance-theoretic account. (8)

a. A: ‘‘Did many students come to class on Friday?’’ b. B: ‘‘No.’’

The negative answer in (8b) commits the speaker to the proposition that fewer than many students attended the class, e. g., that some did. If many in addition to its lower-bounded meaning of ‘‘at least many’’ generated an explicature ‘‘not all,’’ the negative answer would have given rise to a disjunction: ‘‘either fewer than many students came to class or all of the students came to class.’’ Horn (2006) argues that there is a principled reason why the negation -- the ‘‘no’’ response in contexts such as (8) -- commits the speaker to a proposition that a lower scalar value than the one that was negated holds rather than to the disjunction. The negation in (8) is interpreted as descriptive rather than metalinguistic, hence what is denied is the ‘‘at least’’ semantic meaning of the scalar, i.e., the ‘‘at most many’’ meaning can only be denied through metalinguistic negation. Had scalars given rise to bilateral explicatures, as claimed by the Relevance-theoretic account, the negation in (8) would have been interpreted as giving rise to the disjunction ‘‘either fewer than many students came to class or all of the students came to class.’’ Horn (2006) presents another argument against treating scalars as generating upper-bounding explicatures. (9)

a. A: Did many of the guests leave? b. B: # No, all of them. c. B: Yes, (in fact) all of them. (Horn, 2006:23) Had many generated the explicature of the form ‘‘at most many,’’ the response in (9b), ‘‘no, all of them,’’ would have been natural. Since the meaning ‘‘at most many’’ has the status of a conversational implicature rather than that of an explicature, (9c) is natural because its speaker affirms the semantic lower-bounded meaning of many in (9a) and provides a more informative statement by affirming all. Ariel (2006) argued against Horn's account. I leave the resolution of this issue for future research. The discussion in preceding sections has shown that neo-Gricean accounts overgenerate SIs, and that the Relevance-theoretic account makes wrong predictions with respect to how negation of scalar items is interpreted. Next, I present my own account of SIs, which is neo-Gricean in that it retains the Gricean picture of how conversational implicatures and their SI subclass are derived. At the same time, I termed my account ‘‘context-based’’ because it provides a way of creating fine-grained distinctions between contexts where SIs are and are not generated by way of reinterpreting the Gricean Maxim of Relevance as Relevance to the question-under-discussion (QUD). My account of SIs does not suffer from the deficits of neo-Gricean and Relevance-theoretic accounts that I discussed above. 3. The Context-based QUD account of SIs The Gricean maxim of Relevance, which states, ‘‘be relevant,’’ (Grice, 1989:27) is the least studied and least understood of the maxims. It needs to be further clarified how the maxim of Relevance constrains the projection of implicatures or what it means for an implicature to be relevant or irrelevant in a given context. In order to distinguish between contexts where SIs are and are not relevant, following Roberts (1996), I propose to reinterpret Grice's maxim of Relevance as Relevance to the QUD. Following Stalnaker (1979), Roberts (1996) views discourse as being organized around a series of conversational goals, and considers the attempt to discover the way things are as the primary goal of discourse. The strategy that speakers employ in engaging in the communal inquiry is that of sub-inquires that consist in posing and addressing a series of questions. When discussing a given topic, interlocutors address explicit and implicit questions pertaining to this topic. These questions are structured hierarchically; given a relatively general question, interlocutors address it by answering more specific questions that collectively may provide an answer to the more general

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question. To make this concrete, consider a situation where A, B and C are trying to decide where they will be stationed in an office that they are going to share. In this situation, the general question is as in (10). (10)

Who will sit where?

In order to facilitate addressing this question, the interlocutors may choose to break it up into more specific questions, such as the ones in (11)--(13). (11)

Where will A sit?

(12)

Where will B sit?

(13)

Where will C sit?

The more general question in (10), termed the superquestion, entails the specific questions in (11)--(13), termed the subquestions in Roberts’ framework. The superquestion entails the subquestions in the sense that every proposition that fully answers the superquestion answers each of the subquestions. A proposition that fully answers the superquestion in (10) will provide information concerning where A, B and C will be seated. Roberts (1996) argues that discourse may be conceived of as addressing a series of hierarchically structured questions, which she terms a QUD stack. If a speaker chooses to address a given question in the QUD stack by addressing its subquestion(s), the subquestion(s) is (are) added to the stack. When a question has been answered or has been determined to be unanswerable, this question and the subquestions it entails are removed from the QUD stack. The Gricean principle of Relevance ensures that the question that was added to the stack first will be addressed first; thus the older questions have priority over the more recent questions. Roberts defines the QUD as follows. (14) The question on top of the stack is the (immediate) question under discussion. (Roberts, 1996:11). Consider an illustration of how it is determined what the QUD is at a given point in the conversation. In Roberts’ terminology, ‘‘the last QUD’’ is the same as ‘‘the immediate QUD,’’ which was defined in (14). (15)

Context: A, B and C are discussing what to order in a restaurant so that they can share the food. a. A: So who has ordered what? b. Implicit question: What did B order? c. B: I ordered a chicken parmesan. d. Implicit question: What did C order? e. C: I ordered a pizza with pineapples and olives. f. C to A: And what are you getting? g. A: A Pizza with mushrooms and red peppers.

In (15), the superquestion is, ‘‘So who has ordered what?’’ The interlocutors employ a series of subquestions in order to address this superquestion. A uttered the QUD in (a) explicitly; when (c) was uttered, the QUD had been (b); C uttered the QUD in (f). Note that the superquestion in (a) remains in the QUD stack during the entire exchange in (15). Once (g) has been added to the Common Ground, the superquestion in (a) has been fully answered and thus gets removed from the QUD stack. Roberts proposes to characterize the Gricean notion of Relevance in terms of relevance to the QUD, as in (16). (16)

A move m is Relevant to the question under discussion q, i.e. to last (QUD (m)), iff m either introduces a partial answer to q (m is an assertion) or is part of a strategy to answer q (m is a question). (Roberts, 1996:15).

It needs to be noted that Roberts’ move m may be either explicit or implicit, whereby her definition entails that Relevance governs both what is said and what is implicated. I would like to adopt Roberts’ idea of conceiving of Relevance as relevance to the QUD. In (17), I restate Roberts’ proposal in more traditional neo-Gricean terms and modify it to the effect that it is spelled out how it is relevant to the computation of conversational implicatures.

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The Principle of Relevance: Be relevant to the QUD. Speaker maxim: provide a statement that is relevant to the QUD or the superquestion, bearing the maxim of Quality in mind. Relevance may be achieved either on the level of what is said or on the level of what is implicated. Recipient's corollary: interpret the speaker's statement as relevant to the QUD or the superquestion.

Next, consider how the Principle of Relevance in (17) handles a case where the content of an SI is relevant. (18)

a. A: Do all linguists in your department have grant funding? b. B: Some linguists have grant funding. c. SI: Not all linguists in B's department have grant funding. d. All linguists in B's department have grant funding.

The computation of the SI generated by B's response is provided in (19). (19)

i. ii. iii. iv. v.

vi. vii. viii.

The QUD that A himself posed is, ‘‘Do all linguists in your department have grant funding?’’ B is aware that, given the QUD, it would be relevant to A to know if all linguists B's department have grant funding. In B's response, the quantifier some has the semantics of ‘‘at least some.’’ (18d) entails (18b), whereby the statement in (18d) is stronger than the one in (18b). Given Quantity 1, if speaker B knows that all linguists in B's department have grant funding, it would be misleading for B to tell A that some linguists B's department have grant funding. A assumes that B is obeying the Cooperative Principle and the maxims, including Quantity 1. B is aware of A's assumption and A knows that B is aware of it. Thus, A takes B to be observing Quantity 1 unless B indicates otherwise. Therefore, A infers that the reason why B chose not to express the stronger proposition in (18d) is that he didn’t know for a fact that it was true. A believes that B is in the epistemic position to judge the number of linguists who have grant funding in his (B's) department. A infers that, to the best of B's knowledge, (18d) is false. Trusting B's knowledgeability concerning the number of linguists who have grant funding in his (B's) department, A infers that B knows and is informing A that not all linguists in B's department have grant funding.

Note that in contexts where the content of the SI is relevant, once the hearer figures out that the SI is relevant to the QUD, the SI is computed based on a given scale and the maxim of Quantity is operative in the computation. Considerations of Relevance alone are not sufficient for computing an SI. In contexts where a weaker scalar item is present but a potential SI is not relevant, the hearer determines what the QUD was and how the utterance containing the scalar addresses it. Consider a context where an SI is not relevant, which was previously provided in (6), and is reproduced as (20) below. (20)

a. A: I haven’t seen you around in October. b. B: Oh, I was on vacation, and I went to Fresno to visit my relatives. It's warm in Fresno in October. c. Horn scale: d. No SI: it is not hot in Fresno in October.

B's utterance addresses A's implicit QUD, ‘‘What have you been up to in October?’’ While B's response contains a weaker scalar term warm, no steps are taken toward computing an SI because it is not relevant to the QUD. 3.1. The typology of scales As I have mentioned, one theoretical distinction between Horn and pragmatic scales, which is commonly made in the pragmatic literature, is that, while implicatures based on Horn scales go through unless something in the context prevents this, implicatures based on pragmatic scales go through only if they are supported by the context (e.g., Horn, 1989; Levinson, 2000). As I have shown in the previous section, in order for SIs based on Horn scales to be computed, contextual support is, in fact, needed. On the QUD account of SIs, an SI needs to be relevant to a QUD in order to be computed, and is not computed otherwise.

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An SI based on a pragmatic scale does not arise unless the scale has been made salient in the context (Hirschberg, 1991; Levinson, 2000). Compare (21) and (22) below as an illustration of this point. (21)

a. A: Did John paint the house? b. B: He painted a room. c. Pragmatic scale: d. SI: He did not paint the house.

(22)

a. A: What did John paint? b. B: He painted a room. c. No SI: John did not paint the house.

Within the QUD framework, SIs based on pragmatic scales are supported only in contexts where their content is relevant to a QUD, just as SIs based on Horn scales. While in (21), the content of the SI is relevant to A's QUD, hence the SI is computed, in (22), no SI is computed because no SI is relevant to A's QUD. To summarize, in terms of contexts where SIs are and are not generated, SIs based on both classes of scales are generated iff they are relevant to a QUD. However, while SIs based on pragmatic scales need additional contextual support that comes from the scale having been made salient in the context, SIs based on Horn scales do not need this additional support. Another theoretical distinction between Horn and pragmatic scales that was identified in the literature is the ordering relation that the scale is based on. While Horn scales (in the majority of cases) are defined as being entailment-based,2 pragmatic scales are defined as being based on an ordering relation other than entailment. While most Horn scales are defined as being based on the ordering relation of entailment, entailment is not the only condition on Horn scales. It has been argued at length in the pragmatic literature that entailment is not a sufficient condition on scalehood (Atlas and Levinson, 1981; Gazdar, 1979; Horn, 1989). Some of the additional conditions on Horn scales are as follows. Scalar items need to (23)

(i) (ii) (iii) (iv) (v)

have the same polarity; belong to the same semantic field; be equally lexicalized; be of the same form class; belong to the same register.

Thus the condition in (i) rules out scales such as ; (ii) rules out scales such as ; (iii) rules out scales such as , (iv) rules out scales such as and (v) rules out scales such as . Note that this list may be continued and there is no upper limit on scalehood conditions but, in the interests of space, I will limit myself to the discussion of these major scalehood conditions. In contrast, lexical items on a given pragmatic scale may contrast on some of the dimensions in (23). Thus and are possible pragmatic scales, as is shown below. (24)

a. A: It was dark but John knows that he hit a deer with his car. How does he feel about what he did? b. B: Well, he knows he hit a deer all right. c. Scale: d. SI: John does not regret that he hit a deer.

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a. A: This dance routine was sick. b. B: I think it was just good. c. Scale: d. >> I don’t think it was sick.

Thus one potential theoretical distinction between Horn and pragmatic scales is that there are additional scalehood conditions that apply to Horn but not pragmatic scales. However, I will argue that certain scalehood conditions apply not only to Horn but also to pragmatic scales.

2 One example of Horn scales that are not based on the ordering relation of entailment are scales of the form , which, according to Levinson (2000), are based on the ordering relation of being necessarily referentially dependent. 3 Sick is slang for great.

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Interestingly, the condition of the sameness of semantic field in (23(ii)) applies not only to Horn scales but also to some pragmatic scales. Thus in the case of the part/whole relation based pragmatic scales (e.g., ), the SI typically goes through on the condition that scalar items belong to the same semantic field. Thus the part/whole relation between ‘‘kitchen’’ and ‘‘house’’ may generate SIs because these terms do belong to the same semantic field. In contrast, the part/whole relation between ‘‘cockroach’’ and ‘‘city’’ generally does not generate SIs because these terms belong to different semantic fields. At the same time, certain scalehood conditions on Horn scales are not absolute, such as (23(iii)). The lexicalization constraint is not an absolute rule -- the ‘‘goodness’’ scale is operative in the adult language despite the fact that the stronger item is less lexicalized in the sense of being less commonly used. This evidence related to scalehood conditions is another argument against treating Horn and pragmatic scales as distinct. 3.2. Acquisitional challenges posed by individual scales In view of the discussion of Horn and pragmatic scales in the previous section, no clear acquisitional predictions can be made in terms of the timeline of SI development. In this section, I shift gears and consider factors that make certain scale classes challenging from the acquisitional standpoint. I introduce three major factors that make scales acquisitionally challenging. First, consider a distinction between ‘‘logical’’ and ‘‘world-knowledge-based’’ scales. This distinction is not a theoretical one, but it is important in terms of how the acquisition of SIs based on these classes of scales takes place. In the case of ‘‘logical’’ scales, one typically uses relatively little world knowledge in order to compute an SI. Some examples of ‘‘logical’’ scales are (26)

a. b. c. d. e.

In the case of the ‘‘world-knowledge-based’’ scales, one typically needs to use more world-knowledge in order to compute SIs based on these scales. Some examples of ‘‘world-knowledge-based’’ scales are (27)

a. b. c. d. e.

In order to compute an SI in (28) based on a ‘‘logical’’ scale, one needs to use relatively little world knowledge. (28)

a. A: Are all the cruncks4 here? b. B: Some of them are here. c. B's SI: Not all the cruncks are here. d.

The SI in (28) is computed despite the lack of information about the identity of the cruncks or about any of their attributes. (The SI is relevant to A's QUD because the presence of the entire set of cruncks is being questioned). In contrast, in order to compute an SI relying on a ‘‘world-knowledge-based’’ scale in (29), the child needs to use more world knowledge. (29)

a. A. What size are the cruncks? b. B. They are small. c. B's (possible) SI: The cruncks are not tiny. d.

Note that the SI in (29) will be computed if the information that the cruncks can be tiny is part of the Common Ground. However, if the Common Ground contains only the information that the cruncks can either be small, medium-sized or big,

4

‘‘Crunck’’ is a nonsense word.

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or contains no information about the typical size of the cruncks, then the child will not compute this SI (and nor will an adult). Part/whole relation based scales are another example of ‘‘world-knowledge-based’’ scales because the part/whole relation between the relevant entities needs to be part of the Common Ground and needs to be salient in the child's mind in order for the child to compute the SI. (30)

a. A: Did John clean the house? b. B: He cleaned the kitchen. c. SI: John did not clean the whole house. d.

The contrasts between (28) and (29), and (28) and (30) illustrate the distinction between the ‘‘logical’’ and ‘‘worldknowledge-based’’ scales that I have in mind. In terms of the child's experience, these scales are distinct precisely in terms of the amount of knowledge about the world that she needs to have in order to compute SIs based on the ‘‘logical’’ vs. ‘‘world-knowledge-based’’ scales. In my experiment, I employed two logical Horn scales: the quantifier scale and the connective scale, and eight ‘‘worldknowledge-based’’ scales: two gradable adjective scales and six part/whole relation based scales. Doran et al. (2009) postulate a distinction between scale classes that is somewhat akin to the distinction between ‘‘logical’’ and ‘‘world-knowledge-based’’ scales that I argued for here, though Doran et al.’s distinction is much more specialized. Doran et al. distinguish between domain-independent scales, such as the quantifier scale, and domain restricted scales, such as gradable adjective scales. In domain-independent scales, the relation between scalemates holds irrespectively of what semantic domain it is applied to; in domain restricted scales, stronger scalar values are lexicalized differently in different domains (e.g., sweltering is used to describe atmospheric temperature and sizzling is used to describe food) (Doran et al., 2009:16). The broad distinction between ‘‘logical’’ and ‘‘world-knowledge-based’’ scales that I postulated is not the only one that plays a role in the child's success on computing SIs. Another important distinction is that in terms of the nature of contrast between lexical items. In the case of gradable adjective scales, the contrast between scalemates is highly contextdependent and speaker dependent. For example, the contrast between warm and hot is speaker dependent in that different speakers have different cut-off points when discussing how warm or hot the weather is. Likewise, the temperature of warm soup is different from the warm weather temperature. In the case of the quantifier scale, some lexical items are highly context-dependent and are likely to be speaker dependent. Thus most can refer to different percentages in different contexts -- ‘‘most voters voted for candidate X’’ can be felicitously used a context where 51% (or more) voted for X.’’ In contrast, ‘‘most students hand in their homework on time,’’ can be felicitously used in a context where a significant proportion of students do so rather than just 51%. Another factor that makes it challenging for children to derive SIs based on a given scale is the interference of clausal implicatures. In the case of the logical connective scale, as Geurts (2006) argues, in many contexts, clausal implicatures interfere with the derivation of strong SIs of the form, ‘‘the speaker knows that ‘A and B’ does not hold.’’ When a speaker says ‘‘A or B,’’ the interfering clausal implicatures are of the form, ‘‘the speaker is not sure that A’’ and ‘‘the speaker is not sure that B.’’ Given these clausal implicatures, the speaker cannot be presumed to know whether ‘‘A and B’’ holds, whereby the strong SI cannot be derived. I discuss the issue of SIs based on the connective scale in more detail in section 3.8. Here, suffice it to say that a special challenge related to the interference of clausal implicatures is relevant to the connective scale but not to any of the other scales that I employed in my experiment. To summarize, ‘‘world-knowledge-based’’ scales, scales where scalemates and contrasts between them are highly context-dependent and speaker dependent, and scales where clausal implicatures interfere with strong SI derivation are predicted to pose acquisitional challenges for children. These challenges are summarized in (31). (31)

(i) ‘‘world-knowledge-based’’ scales; (ii) context- and speaker dependent scalemates and contrasts between them; (iii) interfering clausal implicatures.

I predict gradable adjective scales to be highly challenging, since these scales are subject to both (i) and (ii). I also predict the connective scale to be challenging because it is subject to (iii), and predict part/whole relation based pragmatic scales to be challenging because these are subject to (i). The quantifier scale as a whole is challenging because some scalar items on it are subject to (ii). However, in the present experiment, I employed some, which is in a sharper contrast with all than most by virtue of being further from it on the quantifier scale. The acquisitional challenges in (31) have been supported by results from previous experimental work on SIs. For example, Papafragou (2006) found that five-year-olds were significantly less successful on computing SIs based on

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Greek inchoative verbs for ‘‘start’’ and ‘‘begin’’ than for ‘‘half,’’ and argued that this was in part due to the vague nature of inchoative verbs. In terms of the challenges in (31), scales of the form and are subject to the challenge in (ii), while the scale in which ‘‘half’’ is used is not. 3.3. The child's exposure to SIs based on Horn vs. pragmatic scales Finally, one may argue that, while there is no principled theoretical distinction between the two classes of scales in question, there is a major difference between SIs based on Horn and pragmatic scales in terms of the child's experience. Thus one might predict that there will be a difference between the levels of the child's exposure to SIs based on Horn and pragmatic scales, and that this difference might conceivably affect the way in which the child computes SIs based on the two classes of scales. One may argue that SIs based on Horn scales occur frequently in the child's input, while SIs based on pragmatic scales do not. When a child repeatedly computes SIs based on a given Horn scale that are present in her input, eventually, she instantiates this scale in her grammar in some form. Subsequently, when the child is exposed to SIs based on the scale in question, she refers to the pre-existing representation of this scale rather than constructs this scale from scratch based on the current context. However, as I have argued, SIs based on Horn scales are computed only in a limited range of contexts, i.e., in contexts where they are relevant to a QUD, thus they may not be as pervasive as they appear to be. Secondly, in my discussion of the experimental results, I will point out certain additional classes of contexts where potential SIs based on Horn scales do not arise. In view of this, I will speculate that the child's level of exposure to SIs based on different types of Horn scales, such as the quantifier scale, the connective scale and the gradable adjective scales, is likely to vary dramatically. At the same time, it is likely that the child will receive some exposure in her input to SIs based on certain types of pragmatic scales, such as the level of description based ones, e.g., and , and part/whole relation based ones, such as . While the make-up of the part/whole relation based scales that the child is exposed to in her input will vary, once the child has identified the part/whole relation as an ordering relation, this may facilitate inferring other part/whole relation based scales from the context in the future. Needless to say, in order to claim with certainty that children receive more exposure to certain types of scales compared to others, one needs to conduct a large-scale corpus-based analysis of occurrences of SIs based on various scales in child-directed speech. The point that I have made in this section is that, until such a study has been conducted, there are no theoretical reasons to posit a reliable difference between the levels of the child's exposure to SIs based on Horn vs. pragmatic scales, hence no reliable predictions concerning children's performance on computing SIs relying on Horn vs. pragmatic scales can be made based on the exposure factor. 3.4. The experimental predictions My experiment tested between two accounts of scales: the account on which a theoretical distinction between Horn and pragmatic scales is postulated, which will be referred to as the Scale Class based account and the Context-based accounts, which include the QUD account that I developed in the present paper and the Relevance-theoretic account on which this distinction is not made.5 The two accounts make conflicting predictions concerning children's performance on computing SIs based on the two scale classes. The acquisition prediction of the Scale Class based account is that, by and large, in the child's input, instances of SIs based on Horn scales, which are computed in most contexts, will be far more common than those of SIs based on pragmatic scales, which are computed only if some contextual support is present. Thus it is likely that the child would form the relevant Horn scales and be able to compute SIs based on these earlier than she would learn to infer idiosyncratic pragmatic scales from the context and compute SIs based on these. Thus, the Scale Class based account gives rise to H1. (32)

H1: Children do better on computing SIs based on Horn scales than those based on pragmatic scales.

On the Context-based accounts, no theoretical distinction between Horn and pragmatic scales is postulated, hence no difference in children's performance based on these broad classes of scales follows from these accounts. Note also that these accounts do not predict that the child, by and large, will receive more exposure to SIs based on Horn than pragmatic scales. Since, as the QUD-based Context-based account predicts, an SI is computed iff it is relevant to a QUD, it need not be the case that SIs based on Horn scales are overwhelmingly more common in the child's input than those based on

5 It needs to be noted that there are other proposals on which the distinction between Horn and pragmatic scales is not made, Hirschberg (1991) being one example thereof.

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pragmatic scales. Thus children's performance on computing SIs is predicted to be a function of acquisitional challenges that I summarized in (31). No specific prediction concerning children's performance on the broad classes of Horn vs. pragmatic scales is made. Thus Context-based QUD account predicts H2. (33)

H2: Children's performance on computing SIs is a function of challenges presented by individual scales.

The underlying assumption of the QUD account is that SIs are computed iff they are relevant to a QUD. In order to test children's ability to distinguish between contexts where an SI is and is not relevant to a QUD, children were tested on contexts where the SI was relevant to the QUD, and hence was generated, and contexts where a scalar item that may have generated an SI was employed but no SI was relevant to the QUD, hence no SI was generated. On the QUD account, only SIs relevant to the QUD are computed by adults through Gricean reasoning; irrelevant SIs are never computed. Thus, with respect to children's performance on computing SIs, the prediction is that children will not compute irrelevant SIs at any stage because these cannot be generated by Gricean reasoning; the QUD account predicts H3 below. (34)

H3: Children do not go through the stage of computing irrelevant SIs.

The Relevance-theoretic account, being a Context-based account, makes predictions that are identical to those of the Context-based QUD account. Different versions of the Scale Class Based account (e.g., Horn, 1989; Levinson, 2000; Chierchia, 2004, among others) would make different predictions concerning children's performance on contexts where the implicature does not get projected, but I will not discuss each of these here in detail in the interests of space. However, the default varieties of these accounts in Levinson (2000) and Chierchia (2004) predict the opposite of H3. On these accounts, the presence of a weaker scalar item is what triggers the computation of an SI, and irrelevant SIs are first computed and then subsequently canceled. On these accounts, it is plausible that children go through a stage of computing both relevant and irrelevant SIs prior to having learned to cancel SIs by pragmatic reasoning. Hence, the accounts in Levinson (2000) and Chierchia (2004) predict H4: (35)

H4: Children go through a stage of computing irrelevant SIs.

3.5. Method Three independent variables were employed: (i) the type of scale (Horn/pragmatic); (ii) relevance of implicature to the QUD (relevant/not relevant); and (iii) the child's age (younger vs. older group). The dependent variable was the number of the child's SI computation responses. Three conditions were employed: (i) an SI based on a Horn scale is relevant to the QUD; (ii) a potential SI based on a Horn scale is not relevant to the QUD; (iii) an SI based on a part/whole relation based pragmatic scale is relevant to the QUD. The child's performance was measured in terms of the number of SI computing responses. In the relevant SI conditions (i) and (iii), the target response was computing the SI; in the irrelevant SI condition (ii), the target response was not computing the SI. A mixed design was employed. A total of four Horn scales were used: , , and . Six scenarios on the basis of the four scales were used, the total being 24 scenarios. In 12 of the 24 scenarios, the content of the implicature was relevant to the QUD and in 12 it was not; the two sets of scenarios were minimal pairs. Crucially, the test sentence that did or did not generate the SI was identical in each of the minimal pairs. Every child received 12 scenarios based on Horn scales in 6 of which the implicature was relevant and in 6 of which it was not. (Every child was given only one member of every minimal pair). In group one, children received 3 scenarios where the scale was employed and the SI was relevant; 3 scenarios where the scale was employed and the SI was relevant; 3 scenarios where the scale was employed and the SI was not relevant; 3 scenarios where the scale was employed and the SI was not relevant; and 6 scenarios where part/whole relation based pragmatic scales were employed. In group two, children received 3 scenarios where the scale was employed and the SI was not relevant; 3 scenarios where the scale was employed and the SI was not relevant; 3 scenarios where the scale was employed and the SI was relevant; 3 scenarios where the scale was employed and the SI was relevant; and 6 scenarios where pragmatic scales were employed. The minimum number of SI computing responses in the relevant SI based on Horn scales condition was 0; the maximum number of SI computing responses in this condition was 6. The minimum number of SI computing responses in the relevant SI based on pragmatic scales was 0; the maximum number of SI computing responses in this condition was 6. The minimum number of SI computing responses in the irrelevant SI condition was 0; the maximum number of SI computing responses in this condition was 6.

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3.6. Participants and the procedure A total of 40 children aged 4;3-7;7 who were native speakers of English were tested. All of the children attended child care centers and elementary schools in Amherst and Northampton, Massachusetts. For the purposes of analyzing the data, children aged 4;3-5;11 (M=5;03) will be referred to as the younger group; there were 20 children of this age range. Children aged 6;1-7;7 (M=6;10) will be referred to as the older group, and there were also 20 children of this age range. I chose to divide children into these particular age groups because in previous research on the acquisition of SIs it was shown that four- and five-year-olds are the youngest children who begin to demonstrate mastery of SIs based on some scales, namely the quantifier scale and ad hoc scales (Foppolo et al., submitted for publication; Papafragou and Tantalou, 2004). However, it has also been shown that four- and five-year-olds experience difficulties with computing SIs based on other types of scales, e.g., in Foppolo et al.’s experiment and in Papafragou (2006). Thus four- and five-year-olds are an age group that has the mastery of pragmatic reasoning instrumental in computing SIs but they are able to compute only SIs based on a few types of scales. I treated six- and seven-year-olds as a distinct age group because I expected these children to exhibit mastery of more scales. I am interested in tracing the time-line of children's mastery of different scale classes through examining results of these two age groups. The experimental technique that I used was loosely based on the experiment in Papafragou and Tantalou (2004). The storyline was as follows. Tiger gave different animals a series of tasks. If an animal had performed a task successfully, Tiger rewarded it with a jewel; if not, Tiger gave it a card as a consolation prize. The child's task was to answer the question, ‘‘What will Tiger give animal X?’’ and to justify her answer. In the condition where the content of the potential implicature was not relevant to the QUD, an animal successfully performed Tiger's task. The target answer was, ‘‘Tiger will give animal X a jewel.’’ In the condition where the content of the implicature was relevant to the QUD and the SI arose, an animal failed to complete its task. The target answer was, ‘‘Tiger will give animal X a card.’’ In (36) below, an example of a story where an SI based on the Horn scale is relevant to the QUD is provided. (36)

a. Tiger said, ‘‘I feel like drawing a picture but I can’t find my crayons. I need all of my crayons because I want to draw a rainbow. Monkey, I want you to find all of my crayons for me.’’ Monkey found some of the crayons. b. Q: What will Tiger give Monkey? Why? c. Target answer: a card. d. QUD: Did Monkey find all of the crayons for Tiger?

(37) is an example of a story where a potential SI is not relevant to the QUD, hence does not arise. (37)

a. Tiger said, ‘‘I feel like drawing but I can’t find any of my drawing stuff. I want to draw a car. Monkey, I want you to help me find something to draw with.’’ Monkey found some of the crayons. b. Q: What will Tiger give Monkey? Why? c. Target answer: a jewel. d. QUD: Did Monkey find something to draw with for Tiger?

The reader may object to the irrelevant SI condition by arguing that if the child answers that a character should get a jewel, this may be because the character fulfilled the task he was requested to perform, and not because the child did not compute an irrelevant SI.6 However, if a child were to compute an SI, the SI meaning would be highly salient in her mind as a meaning that was intentionally communicated by the speaker. In (37) above, the salient SI meaning would be, ‘‘Monkey did not find all of the crayons.’’ Once the child had derived this irrelevant SI, she would be asked by the experimenter, ‘‘What will Tiger give Monkey?’’ Having derived the SI to the effect that Monkey failed to find all of the crayons, the child would respond that Tiger won’t reward Monkey with a jewel, and, instead, give him a card. Note that if a child computed the irrelevant SI, she did not compute the QUD in (37d); computing this QUD would have prevented her from deriving the SI. Therefore, in answering the experimenter's question, ‘‘What will Tiger give Monkey?’’ the child would base her answer just on the content of the SI, ‘‘Monkey did not find all of the crayons.’’ That is, the child would not view Monkey's performance against the background of the QUD in (37d) in answering the experimenter's question. Instead, the child would view Monkey's performance as defined by the SI, ‘‘Monkey did not find all of the crayons,’’ in answering the experimenter's question. Hence, the child who computes SIs in the irrelevant SI condition would provide non-target responses in this condition, i.e., would refuse to reward the character.

6 One of the anonymous reviewers pointed out that even if the child computes an irrelevant SI in a story such as (37), she may still reward the character with a jewel based on the fact that the character who was working on a given task fulfilled this task.

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If the child does not derive SIs in the irrelevant SI condition, she will respond to the experimenter's question that the character should be rewarded with a jewel, i.e., she will provide target responses. In the irrelevant SI condition scenarios, a character is asked to do a chore and successfully carries it out, so the child is expected to reward the character for doing so. Note that both children who are as yet unable to derive any SIs and children who are able to derive SIs are predicted to respond in this fashion. On the default varieties of the Scale Class based account, in the irrelevant SI condition, young children will be predicted to compute SIs by default without taking their relevance into account. Once the child has computed the SI, the SI meaning would be highly salient in her mind. Having derived the SI, the child would provide a non-target response. The default account also predicts that if the child is able to filter out irrelevant SIs, she will cancel the SI in the irrelevant condition, and then provide the target response. Next, I will briefly introduce my experimental items in which the connective scale was used. Above, I cited Geurts’ (2006) observation that in many contexts clausal implicatures generated by the use of the or prevent interlocutors from deriving the SI generated by the use of the or. Thus the clausal implicature to the effect that the speaker does not know if disjunct A holds and the clausal implicature to the effect that the speaker does not know if disjunct B holds prevent the SI to the effect that the speaker knows that A and B does not hold from being generated. In my experimental scenarios, I used the or in contexts where these clausal implicatures were not generated, thus nothing interfered with the derivation of the SI, as one of my or scenarios in (38) illustrates. (38)

a. Tiger said, ‘‘Monkey, I’d like to borrow your motorcycle and your car. I want to drive them both to see which is faster. Can you lend me your motorcycle and your car?’’ Monkey said, ‘‘I can lend you my motorcycle or my car.’’ b. Q: What will Tiger give Monkey? Why? c. Target answer: a card. d. QUD: Will Monkey lend Tiger both his motorcycle and his car?

All of my relevant or SI scenarios were permission contexts where clausal implicatures were not generated because the speaker of the or sentence did not implicate her lack of knowledge about either of the disjuncts. Finally, consider an example of an experimental item where an SI is based on a pragmatic part/whole relation based scale. (39)

a. Tiger said, ‘‘I didn’t have time to clean the house lately. I haven’t swept the floor in a while, and there is dust everywhere. Monkey, I want you to clean my house for me. Monkey cleaned the kitchen. b. Q: What will Tiger give Monkey? Why? c. Target answer: a card. d. QUD: Did Monkey clean Tiger's house?

The SI in (39) is based on a scale . The target answer is ‘‘a card’’ because the SI, ‘‘Monkey did not clean Tiger's house,’’ is relevant to the QUD, hence is computed. Since pragmatic scales become operative only in contexts where an SI is relevant to a QUD, I did not have a condition where an SI based on a pragmatic scale is not relevant. 3.7. Results First, I discuss children's performance on computing SIs based on Horn vs. pragmatic scales. To remind the reader, the Scale Class based account gives rise to H1. (40)

H1: Children do better on computing SIs based on Horn scales than those based on pragmatic scales.

This hypothesis was not supported by the results of any age group or the overall results. Children's numbers of SI computation responses were subjected to a three-way analysis of variance (ANOVA). As I previously mentioned, I employed three independent variables: children's age (the younger group and the older group), the type of scale (Horn and pragmatic scales) and relevance of an SI to a QUD (relevant and irrelevant SIs). The dependent variable was the number of children's responses indicating that they computed an SI. I compared children's performance on computing relevant SIs based on Horn scales vs. those based on pragmatic scales. The ANOVA analysis indicated that the difference between the older children's group's performance on the two types of scales was not significant. Out of the total of six test items where an SI based on a Horn scale was relevant, children provided M=3.60, SD=2.39 of target SI computation responses; out of the total of six test items where an SI based on a pragmatic scale was relevant, children provided M=4.30, SD=2.17 of target SI computation responses;

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F(1,18) = 2.92, p<.10. Percentagewise, older children computed 59% of SIs based on Horn scales and 70.8% of relevant SIs based on pragmatic scales. The younger children were more successful on computing the relevant SIs based on pragmatic scales than those based on Horn scales. The ANOVA analysis indicated that the difference between the younger children's group's performance on the two types of scales was significant. Out of the total of six test items where an SI based on a Horn scale was relevant, children provided M=2.35, SD=2.23 of target SI computation responses; out of the total of six test items where an SI based on a pragmatic scale was relevant, children provided M=3.40, SD=2.37 of target SI computation responses; F(1,18) = 8.18, p=.01. Percentagewise, younger children computed 39% of SIs based on Horn scales and 57% of relevant SIs based on pragmatic scales. Fig. A.1 shows younger and older children's performance on computing SIs based on Horn vs. pragmatic scales. Overall, 40 children of the younger and older groups did better on pragmatic scales than on Horn scales. The ANOVA analysis indicated that the difference between 40 children's performance on the two types of scales was significant. Out of the total of six test items where an SI based on a Horn scale was relevant, children provided M=2.95, SD=2.21 of target responses; out of the total of six test items where an SI based on a pragmatic scale was relevant, children provided M=3.87, SD=2.31 of target responses; F(1,36) = 25.834, p<.001. Percentagewise, the younger and the older groups combined provided 49% of target responses in the relevant Horn scale condition and 65.4% of target responses in the relevant pragmatic scale condition. The Context-based QUD account did not make a specific prediction concerning children's performance on the broad classes of Horn vs. pragmatic scales but predicted H2 on which children's performance on computing SIs based on different scales is a function of acquisitional challenges in (31). The experimental results provide evidence in favor of this hypothesis. Children's performance on computing relevant SIs is summarized in Table 1. Gradable adjective Horn scales pose a particular challenge for younger and older children. The Horn scale poses a challenge for the younger children, but the older children begin to show mastery of this scale. In terms of computing SIs relying on the part/whole relation based pragmatic scales, younger children are at chance and older children begin to show mastery of SIs based on pragmatic scales. In contrast, both younger and older children show mastery of the quantifier Horn scale. I will discuss in section 3.8.1 in detail how children's performance on each of the scales reflects the challenges (or lack thereof) associated with the given scale. Next, I will present the results related to children's ability to determine if a potential SI is relevant to a QUD in the given context. Children's numbers of SI computation responses were subjected to a three-way analysis of variance (ANOVA). To remind the reader, the three independent variables are children's age (the younger group and the older group), the type of scale (Horn and pragmatic scales) and relevance of an SI to a QUD (relevant and irrelevant SIs). The dependent variable is the number of children's responses indicating that they computed an SI. I compared children's performance on the relevant SIs based on Horn scales condition and the condition where a potential SI based on a Horn scale was not relevant. The null hypothesis is that children's performance on the two conditions is the same. The ANOVA analysis indicated that the difference between the older children's group's performance on the relevant vs. irrelevant conditions was significant on all four Horn scales. In (41), means of SI computation responses out of a total of 3 test items are provided; the minimum number of SI computation responses is 0 and the maximum number is 3. To remind the reader, in the relevant SI condition, the target response is computing an SI, whereas in the irrelevant SI condition, the target response is not computing an SI. (41)

Older children (6;1-7;7-year-olds). M=6;10. N=20. some: relevant: M=2.40, SD=1.26; irrelevant: M=0, SD=0. F(1,19) = 36, p=.001 warm: relevant: M=1.50, SD=1.17; irrelevant: M=0, SD=0. F(1,19) = 16.2, p=.001 or: relevant: M=2.10, SD=1.44; irrelevant: M=.50, SD=.70. F(1,19) = 9.85, p=.006 good: relevant: M=1.20, SD=1.54; irrelevant: M=0, SD=0. F(1,19) = 6.0, p=.025

The ANOVA analysis indicated that the difference between the younger children's group's performance on the relevant vs. irrelevant conditions was significant on the and scales, and not significant on the Table 1 Younger and older children's target SI computing responses in relevant SI conditions where Horn and pragmatic scales were used. Type of scale

Horn

Pragmatic

Age group

some

or

warm

good

Part/whole scales

Younger Older

83% 80%

23% 70%

37% 46.6%

13% 40%

57% 70.8%

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and scales. In (42), means of SI computation responses out of a total of 3 test items are provided; the minimum number of SI computation responses is 0 and the maximum number is 3. (42)

Younger children (4;3-5;11-year-olds). (M=5;03). N=20. some: relevant: M=2.50, SD=.97; irrelevant: M=.20, SD=.42 F(1,19)=47.13, p<0.000 warm: relevant: M=1.10, SD=1.10; irrelevant: M=.10, SD=.31. F(1,19)=7.62, p<.013 or: relevant: M=.70, SD=1.25; irrelevant: M=.30, SD=.67. F(1,19)=.79, p<.385 good: relevant: M=.40, SD=.96; irrelevant: M=0, SD=0. F(1,19)=1.71, p<.207

While the younger children performed poorly on computing relevant SIs based on the and scales, they did not compute irrelevant SIs based on these scales. Thus H3 predicted by the QUD account was supported. Children do not go through a stage of computing irrelevant SIs. H4 predicted by two varieties of the Scale Class based account of SIs was not supported, as children did not go through a stage of computing irrelevant SIs. 3.8. Discussion 3.8.1. Acquisition challenges posed by individual scales On the Scale Class based account, a theoretical distinction is made between Horn and pragmatic scales, and this distinction is predicted to have a reflex on the child's performance on computing SIs based on the two classes of scales. Horn scales are predicted to be less challenging than pragmatic scales. On the Context-based QUD account, the child's performance on computing SIs is predicted to be a function of challenges in (31), and no theoretical distinction is made between Horn and pragmatic scales that would have a predictable reflex on the scale acquisition timeline. The experimental results conform to the prediction made by the Context-based QUD account rather than to that made by the Scale Class based account. When children's performance on individual scales is considered, it becomes obvious that the experimental results do not support a broad theoretical distinction between Horn and pragmatic scales. While the quantifier scale is the only scale that the younger and older children have mastery of, the younger children perform around chance on pragmatic scales and worse than at chance on other types of Horn scales, and the older children show some mastery of pragmatic scales and the Horn connective scale but still do poorly on the gradable adjective scales. These results clearly suggest that what predetermines the timeline of the child's mastery of individual scales are specific challenges associated with individual scales. I identified the major acquisitional challenges associated with scales in (31), which is reproduced below. (43)

(i) ‘‘world-knowledge-based’’ scales; (ii) context- and speaker dependent scalemates and contrasts between them; (iii) interfering clausal implicatures.

As I mentioned above, the connective scale was predicted to be challenging because of interfering clausal implicatures. As my experimental results have shown, the younger five- and six-year-old children had no mastery of the connective scale. This result is not surprising in the light of Grice's original conception of the implicature associated with the or and work on the or by Geurts (2006). Grice's (1989) original argument was that or is used in contexts where one wishes to posit a non-truth-functional reason for accepting P v Q. (44)

a. The prize is either in the garden or in the attic. b. Ignorance implicature: The speaker doesn’t know for a fact that the prize is in the garden. Grice (1989:44).

The context in (44) is an instance where affirming disjunct ‘‘P’’ is more informative than affirming a disjunction ‘‘P or Q.’’ In contrast, the use of the or generates an SI in contexts where affirming a conjunction ‘‘P and Q’’ is more informative than affirming a disjunction ‘‘P or Q’’. The ignorance implicature in (44b) is not derived by making use of the scale and, hence, is not an SI. In Geurts (2006), it is demonstrated that, contra the widely accepted view, the SI associated with the or arises only in a very limited range of contexts. In a vast majority of cases, the SI is not derived and either an ignorance implicature is derived, as in (44), or a disjunctive reading of the sentence is computed but not via an SI. According to Geurts (2006:2), in order for a stronger SI of the form ‘speaker knows that not P’ to be derived, the competence assumption, ‘‘the speaker is knowledgeable about the alethic status of the stronger statement,’’ needs to be fulfilled. Geurts demonstrates that, while in the case of the some, the competence assumption is easily derivable, in the case of the or, the competence assumption can be derived only in a very limited range of contexts, (45) being one example thereof.

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a. A to B: You may have an apple or a pear. b. Stronger statement: You may have an apple and a pear.

In (45), the competence assumption is that A knows whether or not he will allow B to have an apple and a pear, whereby the use of the or may give rise to an SI. (46) below is a case where an SI cannot be generated. (46)

a. A: John had an apple or a pear. b. Stronger statement: John had an apple and a pear.

According to Geurts (2006:3), in (46), since speaker A does not know that disjunct P holds and does not know that disjunct Q holds, he cannot be assumed to know if the stronger statement ‘‘P and Q’’ holds, hence the competence assumption cannot be derived and an SI cannot be computed. Thus clausal implicatures of the form ‘‘speaker A does not know that disjunct P holds’’ and ‘‘speaker A does not know that disjunct Q holds’’ prevent the hearer from deriving the SI. All of my relevant SI scenarios based on the scale were contexts where the competence assumption was satisfied, i.e., they were precisely the instances where the use of the or generated an SI. However, in view of the above theoretical discussion and the challenge in (31(iii)), children's poor performance on the connective scale is only to be expected. In the majority of uses of the or that the child is exposed to, either an ignorance implicature is generated or a disjunctive reading of the sentence is generated but not via an SI. It is for this reason that the scale takes a relatively long time to get lexicalized. Next, I will discuss children's performance on gradable adjective scales, which are subject to challenges in (31(i)) and (31(ii)). The following factors prevent the child from constructing gradable adjective scales early on. Interlocutors’ use of gradable adjectives is highly context-dependent. A speaker may use the adjective warm to describe a +75F8 weather in May and a +40F8 weather in December in Massachusetts. In describing the May weather, the speaker may be referring to his own standards of warmth, while in describing the December weather, the speaker may be referring to the December standards of warmth. Moreover, different speakers may refer to a +80F8 weather in July as either warm or hot, depending on their personal perceptions. Being exposed to this kind of contradictory input, the child will experience difficulties in constructing gradable adjective scales. An additional challenge that the gradable adjective scales pose for the child is the fact that the child may be unsure if the adjectives are lexicalized to the same degree. One of the conditions on Horn scales is that lexical items that constitute a Horn scale have to be equally lexicalized. However, some scales violate this condition. In my experiment, I employed the scale, which violates the condition in question. It is likely that the term wonderful is much less frequent in the child's input than the term good. Thus the child may wonder if wonderful is as lexicalized as good. Because the child may (justly) classify the stronger items on the ‘‘goodness’’ scale as less lexicalized than the weaker ones, this may prevent her from constructing this scale early on. Another stumbling block that children are likely to run into in constructing gradable adjective scales is their perception of the degree of contrast between adjacent scalar items. The knowledge concerning the degrees of contrast between specific scalar items is language-specific information that is acquired from the input. Suppose that for English-speaking adults, fantastic is stronger than great on the relevant ‘‘goodness’’ scale. However, the two items are close, if not adjacent, on the ‘‘goodness’’ scale, and great is fairly high on the scale. Thus it is likely that an adult would compute an SI from the speaker's use of great to ‘‘not fantastic / marvelous / fabulous etc.’’ only in contexts where it has been made explicit that a greater degree of goodness than that designated by great is relevant to the QUD. That is, if a QUD is of the form, ‘‘Isn’t x fantastic / marvelous / fabulous?’’ the SI ‘‘not fantastic’’ from the use of great may be computed; however, if the QUD is, ‘‘How did you like x?’’ this SI will not be computed from the use of great. As a result, it is likely that the use of great would generate an SI only in contexts where a QUD contains a stronger scalar item. It is easy to imagine that, given her limited experience with language use, the child is likely to be unsure about the degree of contrast between the given adjacent scalar items. There may be a stage where the child has constructed the ‘‘goodness’’ and ‘‘temperature’’ scales but perceives the contrasts between good vs. wonderful and warm vs. hot as being as subtle as the contrast between great and fantastic is for adults. Thus some children may experience difficulty in computing SIs based on gradable adjective scales not because they have not constructed the scales but because they are yet to infer the degree of contrast between the specific scalar items that exists in the adult language. Moreover, speaker variation plays a role here as well. There are speakers who commonly use terms such as great, fantastic and fabulous, and there are those who never use these terms but prefer to express the highest praise through using litotes such as ‘‘not bad.’’ A speaker who eschews the terms that are ranked high on the ‘‘goodness’’ scale may never intend an SI by using the term good because, in her I-language, good may be ranked as strongest. Such I-language uses related specifically to gradable adjective scales are likely to be part of the child's input. This type of input may delay the child's construction of the relevant scale because the child is exposed to uses of gradable adjectives that are not the

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strongest on the relevant Horn scales in contexts where the stronger scalar item is relevant. In sum, contextual factors, the issue of lexicalization, the degree of contrast between the given adjectives and I-language uses of gradable adjectives are the factors that make constructing gradable adjective scales challenging. Note that none of the complications posed by the connective scale and gradable adjective scales are relevant to the quantifier scale, which was reflected in children's performance on the four Horn scales employed in the experiment. 3.8.2. Children's mastery of relevance I tested children's ability to arrive at the QUD and distinguish between contexts where an SI is relevant to the QUD, and hence is computed, and ones where no SI is relevant to the QUD. I found that children do not go through a stage where they compute SIs across the board. While some younger children did not compute any relevant SIs, they did not compute any irrelevant SIs either. While children's performance on computing SIs based on different scales varied, children computed only a negligible number of irrelevant SIs based on Horn scales. The group of the younger children computed irrelevant SIs in 4 instances out of 120, and the older children did so in 5 instances out of 120. According to the Context-based QUD account, children are not predicted to compute irrelevant SIs because these cannot be arrived at by Gricean reasoning. Only the relevant SIs can be computed by Gricean reasoning. Consider S. P.’s (4;6) responses to the stories where SIs based on the scale are relevant. (47)

S. P. (4;6): A card. Experimenter: Why? S. P.: He didn’t find all of them. [them=crayons]. S. P. (4;6): A card. Experimenter: Why? S. P.: He didn’t give him all of them. [them=ribbons].

Next, consider D. A.’s (6;5) responses to the stories where SIs based on the scale are not relevant.

(48)

D. A. (6;5): A jewel. Experimenter: Why? D. A.: Tiger asked him to find some drawing stuff. [=crayons]. D. A. (6;5): A jewel. Experimenter: Why? D. A.: Because Monkey gave him ribbons when he wanted some.

One may raise the following objection to the claim that the presence vs. absence of a QUD that a potential SI is relevant to predetermines whether or not the SI is computed. One may argue that in the stories in condition one where an SI based on a Horn scale is relevant to the QUD, one cannot tell if the SI arises as a result of the presence of an (implicit) QUD or simply as a result of a stronger scalar item having been made salient, which, in turn, makes the pertinent Horn scale salient. I would like to argue that if the child were unable to compute the QUD that made the content of the SI relevant, he would not have been able to compute the SI by Gricean reasoning. The content of the Horn scale (e.g., the quantifier scale in (36)) on its own does not tell the child that the content of the SI is relevant in the given context. Moreover, if a child is at a stage where she has constructed the quantifier scale, the presence of a weaker scalar item such as some in (37) that is part of this scale, in principle, could have been construed as a signal that the quantifier scale is relevant. The data have shown this not to be the case. At the same time, in natural discourse, it need not be the case that whenever an SI is relevant to a QUD, the pertinent Horn scale has been made salient in the given context, as (49) illustrates. (49)

a. A's QUD: How many students came to John's class on Friday? b. B: Some of them came to class. c. Scale: d. SI: Not all students came to John's class on Friday.

4. Concluding remarks In the present paper, I have provided experimental and theoretical evidence for the Context-based QUD account of SIs and evidence against the Scale Class based account of SIs. Firstly, I have argued that the generalization that SIs based on Horn scales are computed unless something in the context of the utterance prevents their computation is too strong. I demonstrated that, in fact, both SIs based on Horn and pragmatic scales are generated iff they are relevant to a QUD. Secondly, I have provided evidence against the generalization that additional conditions on scalehood constrain the make-up of Horn but not pragmatic scales. I have shown that (i) some conditions on scalehood apply to both Horn and pragmatic scales and (ii) that some Horn scales violate certain conditions on scalehood. Experimentally, I showed that the child's success on computing SIs is not predictable from the ordering relation that the scale is based on (entailment-based Horn scales vs. non-entailment-based pragmatic scales). Children's timeline of the mastery of scales provides evidence against the theoretical distinction between Horn and pragmatic scales. In this paper, I have discussed the following prerequisites that the child needs to master in order to compute SIs:

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(i) going through the steps of Gricean reasoning that are required for computing Quantity-based implicatures; (ii) picking up on or inferring from the context the QUD that the SI is relevant to; (iii) inferring the content of the scale employed in generating a given SI.

As far as prerequisite (i), I found that 83% of the younger children (M=5;03) were able to compute SIs based on the quantifier scale, which is evidence that children of this age are able to employ Gricean reasoning. This result is consistent with findings of other researchers working on the acquisition of SIs (Papafragou and Tantalou, 2004 and Foppolo et al., submitted for publication). Concerning prerequisite (ii), I argued that my results have shown that the youngest children tested had mastery of it because they computed the relevant but not the irrelevant SIs. As far as prerequisite (iii) is concerned, inferring the content of scales that give rise to SIs presents a special challenge. Specific challenges posed by the individual scales are a major difficulty the child faces in mastering SIs. I identified the following acquisitional challenges associated with scales: (51)

(i) ‘‘world-knowledge-based’’ scales; (ii) context- and speaker dependent scalemates and contrasts between them; (iii) interfering clausal implicatures.

One of the central experimental findings that I discussed here was that children start out by computing SIs by Gricean reasoning just in contexts where these meanings are relevant. This result supports context-based accounts of SIs (e.g., the QUD-based account developed in this paper and the Relevance-theoretic account) and provides evidence against default accounts of SIs (e.g., Levinson, 2000; Chierchia, 2004). On context-based accounts, the child is predicted to take considerations of Relevance into account prior to computing the SI. On default accounts, the presence of a weaker scalar item automatically triggers the computation of an SI and considerations of relevance come into play only once the SI has been computed, whereby canceling the SI requires additional pragmatic reasoning. Lastly, I discussed the influence of the presence of SIs in the child's input on her success in computing SIs based on a given scale. While at first blush it seems that children must be exposed to more instances of SIs based on Horn scales in their input, which, in turn, might enable the child to acquire these meanings earlier, I pointed out that in reality this may not be the case. Firstly, I pointed out that SIs based on Horn scales arise in a limited range of contexts, namely, just the ones where the content of the SI is relevant to the QUD. Secondly, SIs based on some classes of pragmatic scales, such as scales based on the level of description, e.g., or stages are likely to be frequent in the child's input. To date, most of the acquisitional experiments on SIs focused on Horn scales because these scales are accorded a special status. In future studies on the acquisition of SIs, SIs based on pragmatic scales ought to be devoted as much attention as those based on Horn scales in view of the experimental evidence against the distinction between the two scale classes that I presented in this paper. Acknowledgements I am grateful to the teachers, children and parents of child care centers and schools in Amherst, MA and Northampton, MA where I ran the experiment. I am also grateful to Tom Roeper, Jill de Villiers, Christopher Potts and Laurence Horn for their feedback. I would also like to thank the anonymous reviewers. Appendix A Test sentences: : (1-3); : (4-6); : (7-9); : (10-12); pragmatic: (13-18). (1) Monkey gave Tiger some of the ribbons. (2) Deer found some of the knives. (3) Monkey found some of the crayons. (4) Monkey said, ‘‘I can teach you how to peel bananas or how to whistle.’’ (5) Deer said, ‘‘I can bring you some blueberries or strawberries from the forest.’’ (6) Monkey said, ‘‘I can lend you my motorcycle or my car.’’ (7) Deer made Tiger a good boat. (8) Deer made a good wardrobe for Tiger. (9) Monkey gave Tiger a good backrub. (10) The soup was warm. (11) Deer made warm apple cider for Tiger.

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(12) (13) (14) (15) (16) (17) (18)

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Monkey started a fire and it got warm in the house. Deer cleaned the left corner of the kitchen table. Deer cut the nails on Tiger's pinky fingers. Monkey cleaned the kitchen. Deer scratched Tiger's left paw. Deer cleaned the right corner of the window. Monkey washed Tiger's right paw with a sponge.

See Fig. A.1.

[(Fig._A1)TD$IG] Relevant Implicatures Based on Horn and Pragmatic Scales

Mean Correct

5 4.5 4 3.5 3

YOUNG OLD

2.5 2 1.5 1 0.5 0 HORN

PRAG

Fig. A.1. Younger and older children's target SI computing responses on the relevant Horn and pragmatic scale conditions.

References Ariel, Mira, 2004. Most. Language 80 (4), 658--706. Ariel, Mira, 2006. A ‘just that’ lexical meaning for most. In: von Heusinger, K., Turner, K. (Eds.), Where Semantics Meets Pragmatics (Current Research in the Semantics/Pragmatics Interface). Elsevier, London, pp. 49--91. Atlas, Jay D., Levinson, Stephen, 1981. It-clefts informativity and Logical Form. In: Cole, P. (Ed.), Radical Pragmatics. Academic Press, Inc., New York, pp. 1--61. Barner, David, Brooks, Neon, Bale, Alan, 2011. Accessing the unsaid: the role of scalar alternatives in children's pragmatic inference. Cognition 118, 87--96. Bott, Lewis, Noveck, Ira A., 2004. Some utterances are underinformative: the onset and time course of scalar inferences. Journal of Memory and Language 51 (3), 437--457. Breheny, Richard, Katsos, Napoleon, Williams, John, 2006. Are generalised scalar implicatures generated by default? An on-line investigation into the role of context in generating pragmatic inferences. Cognition 100, 434--463. Carston, Robyn, 1998. Informativeness, relevance and scalar implicature. In: Carston, R., Uchida, S. (Eds.), Relevance Theory: Applications and Implications. John Benjamins, Amsterdam, pp. 179--236. Chierchia, Gennaro, 2004. Scalar implicatures, polarity phenomena and the syntax / pragmatics interface. In: Belletti, A. (Ed.), Structures and Beyond. Oxford University Press, Oxford, pp. 39--103. Doran, Ryan., Baker, Rachel E., McNabb, Yaron, Larson, Meredith, Ward, Gregory, 2009. On the nonunified nature of scalar implicature: an empirical investigation. International Review of Pragmatics 1, 211--248. Foppolo, Francesca, Guasti, Maria Teresa, Chierchia, Gennaro, submitted for publication. Scalar implicatures in child language: failure, strategies and lexical factors. Gazdar, Gerald, 1979. Pragmatics: Implicature, Presupposition and Logical Form. Academic Press, New York. Geurts, Bart, 2006. Exclusive disjunction without implicature. Semantics Archive, retrieved June 20, 2008, from http://semanticsarchive.net/ Archive/TBjM2Y2Y/. Grice, Paul, 1989. Studies in the Way of Words. Harvard University Press, Cambridge, MA. Hirschberg, Julia, 1991. A Theory of Scalar Implicature. Garland, New York. Horn, Laurence, 1972. On the Semantic Properties of the Logical Operators in English. Indiana University Linguistics Club, Bloomington, IN. Horn, Laurence, 1984. Toward a new taxonomy for pragmatic inference: Q-based and R-based implicature. In: Schiffrin, D. (Ed.), Meaning, Form and Use in Context: Linguistic Applications (GURT '84). Georgetown University Press, Washington, DC, pp. 11--42. Horn, Laurence, 1989. A Natural History of Negation. University of Chicago Press, Chicago. Horn, Laurence, 2006. The border wars: a neo-Gricean perspective. In: Turner, K., von Heusinger, K. (Eds.), Where Semantics Meets Pragmatics. Elsevier, Oxford, pp. 21--48. Levinson, Stephen, 2000. Presumptive Meanings: The Theory of Generalized Conversational Implicature. MIT Press, Cambridge, MA. Noveck, Ira, 2001. When children are more logical than adults: experimental investigation of scalar implicatures. Cognition 78, 165--188.

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Noveck, Ira, Sperber, Dan, 2007. The why and how of experimental pragmatics: the case of scalar inferences. In: Burton-Roberts, N. (Ed.), Advances in Pragmatics. Palgrave, Basingstroke, pp. 184--212. Papafragou, Anna, 2006. From scalar semantics to implicature: children's interpretation of aspectuals. Journal of Child Language 33 (4), 721--757. Papafragou, Anna, Tantalou, Niki, 2004. Children's computation of implicatures. Language Acquisition 12 (1), 71--82. Pouscoulous, Nausicaa, Noveck, Ira, 2009. Going beyond semantics: the development of pragmatic enrichment. In: Foster-Cohen, S. (Ed.), Language Acquisition. Palgrave Macmillan, London, pp. 196--215. Pouscoulous, Nausicaa, Noveck, Ira A., Politzer, Guy, Bastide, Anne, 2007. A developmental investigation of processing costs in implicature production. Language Acquisition 14 (4), 347--375. Roberts, Craige, 1996. Information structure: towards an integrated theory of formal pragmatics. OSU Working Papers in Linguistics 49, Papers in Semantics, pp. 91--136. Sauerland, Uli, 2004. Scalar implicatures in complex sentences. Linguistics and Philosophy 27 (3), 367--391. Stalnaker, Robert, 1979. Assertion. In: Cole, P. (Ed.), Syntax and Semantics 9. Academic Press, New York, pp. 315--332. Anna Verbuk specializes in first language acquisition of semantics and pragmatics. She received a Ph.D. in Linguistics from UMass, Amherst in 2007. Her dissertation was on the acquisition of scalar implicatures. Her experimental work often bears on resolving theoretical disputes concerning the division of labor between semantics and pragmatics. The acquisitional goal of her work is constructing the time-line of the child's pragmatic development. She published articles in Language Acquisition and Journal of Pragmatics, and has presented her work at a number of conferences. She held postdoctoral appointments at McGill University and the University of Illinois at Urbana-Champaign.