The emergence of scalar meanings

This paper analyzes the emergence of scalar additive meanings. We show that in Basque the same particle ere can obtain both the “simple additive” reading (akin to English too) and the “scalar additive” reading (akin to English even) but we argue that we do not have to distinguish two types of ere. We provide evidence, by means of a production and a perception experiment, that the reading is disambiguated by means of prosody (the placement of nuclear stress), which is a correlate of focus. We argue that the scalarity effect is generated by the combination of two presuppositions (a focus-induced one and a lexical one) and the assertion of the sentence.


INTRODUCTION
Languages vary in the way they generate different additive readings. There are languages with particular lexical particles to express simple additive and scalar additive readings (cf. English too vs. even) but in Basque, the same particle, ere, is used to express simple additive as well as scalar additive values. Thus, in this language, a string like (1) with the same lexical items and word order can obtain either a simple additive reading and a scalar additive reading. In this paper we provide experimental evidence that the simple additive and the scalar additive interpretations are distinguished by means of prosody, which is a main correlate of informationstructure. We report two (production and perception) experiments showing that prosody (in particular, association to nuclear stress and post-focal pitch compression) is what creates the scalar additive interpretation of the additive particle. Besides, in order to account for how the scalar interpretation arises, we propose that the scalar interpretation of the particle ere is derived by combining the two presuppositions created by the sentence containing ere, i.e., the lexical-semantic contribution of ere and the focal presupposition, and the assertion of the sentence.
The paper is organized as follows: in Section 1.1 we briefly overview the semantic contribution of focus-sensitive operators like even in English. Section 1.2 presents the properties of the Basque particle ere, which can create both a simple additive and a scalar additive interpretation. In Section 2, we present the production and the perception experiments that we ran.
In Section 3 we provide a novel analysis of the derivation of scalar interpretations from constructions with a lexically unambiguous simple additive particle, and finally, Section 4 concludes the paper.

THE ASSOCIATION WITH FOCUS OF EVEN
Before we move on to see the properties of the Basque particle ere in Section 1.2, we will first concentrate on the English focus-sensitive operator even, on its semantic properties and on its contribution to the sentence it appears in. The semantics of even has been of great interest for linguists for some years now (cf. Jackendoff, 1972;Karttunen and Peters, 1979;Rooth, 1985Rooth, , 1992von Stechow, 1991;Wilkinson, 1996;Guerzoni, 2002;Giannakidou, 2007, a.o.). The literature agrees in treating it as a focus-sensitive operator. Take, e.g., the example in (2), where "Bill" is the associated element of the particle even and bears the focus feature (represented by the subscript F here and throughout): (2) John invited even [Bill] F .
In a sentence like (2), it is generally assumed that the focus-sensitive operator even is truth-conditionally vacuous (cf. Karttunen and Peters, 1979) and that the sentence has two main contributions: on the one hand it asserts "that John invited Bill" and on the other it provides two presuppositions: (i) the existential presupposition that "there are other x-s besides Bill such that John invited those other x-s," cf. (3-a) 1 ; and (ii) the 1 We abstract from the discussion of whether the existential presupposition is needed in order to account for even's semantic contribution or not (cf. Horn, 1972;Krifka, 1991;von Stechow, 1991). In fact, considering that we will be arguing in this paper that the primary meaning of the Basque particle ere is that of a "simple additive," cf. Section 3, it is out of question whether this particle contributes the existential presupposition; it definitely does. scalar presupposition that "for all x-s under consideration besides Bill, the likelihood of John inviting those x-s is bigger than the likelihood of John inviting Bill," cf. (3-b) 2 .
(3) a. Existential presupposition: Therefore, the contribution of the focus-sensitive particle even is to relate the asserted proposition to a set of alternative propositions (à la Rooth, 1985Rooth, , 1992 which are obtained by substituting the element that bears the focus feature by its contextually relevant alternatives. These alternatives are ranked in a "likelihood" scale which gets its value by means of the context, e.g., scale of difficulty, scale of animosity, scale of friendship, etc. So, basically, the particle even contributes to the sentence by creating a scale of likelihood (e.g., scale of friendship) and by locating the asserted proposition, "that John invited Bill" in the case at hand, at the bottom of this scale.

> > John invited Peter > John invited Bill
Interestingly, when even occurs in a negative context such as the one in (5) the scalar presupposition that we described in (3-b) is reversed, as shown in (5-b) (cf. Karttunen and Peters, 1979;Rooth, 1985Rooth, , 1992Wilkinson, 1996).
John did not invite even [Bill] F . a. Existential presupposition: Thus, in this case, the existential presupposition says that "there are other x-s besides Bill such that John didn't invite those other x-s" and the scalar presupposition says that "for all x-s under consideration besides Bill, the likelihood of John inviting Bill is bigger than the likelihood of John inviting those other x-s." In other words, whereas in (2) Bill was the least likely person to be invited by John, in (5) the presuppositions are reversed and Bill is considered to be the most likely person to be invited by John.
In the next section, we will concentrate on the Basque particle ere and see what its properties and behavior are.

THE BASQUE PARTICLE ERE
Now, let us turn our attention to the Basque additive particle ere. This particle is virtually unstudied [see some descriptions in Euskaltzaindia (1994), Hualde and Ortiz de Urbina (2003), and Ondarra (2007)].
From a syntactic point of view, ere can appear almost freely in any position of the clause, which, in neutral statements has the order S-IO-DO-V (6): following the subject (7), the indirect object (8), or the direct object (9) However, it should be noted that ere cannot appear inside DPs (11), nor in sentence-initial position -given that it is an enclitic particle [cf. (12)]-, and that, in general, speakers also find it quite marked in sentence-final position (13): Next, we will analyze the semantic contribution of ere.

SEMANTIC CONTRIBUTION OF ERE
Regarding its semantic nature, ere's core semantic contribution is that of a simple additive. Thus, a simple statement like (14-a) could coherently be followed by something like (14-b):  erosi. buy Jon too is the one that bought cider.
However, the particle ere can also be employed to convey scalar additive values. Thus, a sentence with the same lexical items and word order of (14-b) can also have a scalar meaning, as represented in (19). "For all x-s under consideration besides Aitor, the likelihood that Jon invited those x-s is greater than the likelihood that Jon invited Aitor." In other words, it can also have the very same semantic import as English even (cf. Section 1.1) associating to the element preceding it. Likewise, under this reading the particle displays a similar behavior to that of even and, for instance, the scalar presuppositions brought up by ere are reversed under negation. Example (21) shows an instance of this reversal, whose corresponding presuppositions are presented in (22-a): "For all x-s under consideration besides Aitor, the likelihood that Jon invited Aitor is greater than the likelihood that Jon invited those x-s" Hence, it would seem that phrases containing ere are completely ambiguous regarding the simple or scalar additive interpretations and that the listener would have to resort to discourse pragmatics in order to infer the correct interpretation of the sentence. What is more, it should be noted that ere is the only particle available in Basque to produce either simple additives or scalar additives [as opposed to other languages that have different items in the lexicon for different readings (cf. the references in Section 1.1)]. Notwithstanding, in this paper we will argue that this is not the case for Basque, i.e., that even if strings like (1) can correspond to the two readings, this is so just because out of any context written strings like (1) do not provide a representation of the intonation of the clause, and the information structure of the sentence is underspecified in the text. In fact, in Section 2 we will report the results of two experiments showing that prosody (nuclear stress placement) is a key factor in disambiguation 4 . From this observation, in Section 3 we will provide an analysis of the syntaxsemantics-phonology interface proposing that the scalar additive reading derives directly from the simple additive reading and the information-packaging of the sentence.

AN EXPERIMENTAL ANALYSIS OF THE DISAMBIGUATION OF SIMPLE AND SCALAR ADDITIVITY
So far, we have argued that the particle ere can generate both simple additive and scalar additive interpretations, as shown in the examples in (23) and (24), whose only change is the interpretation of ere: However, we will show that this potential ambiguity is just an illusion, and that prosody plays an important role in teasing apart the two readings. Thus, in order to test the variability in the interpretations of constructions with ere we designed two experiments. Experiment 1 is a production experiment designed to test the prosodic patterns associated to different readings (cf. Section 2.1.1) and Experiment 2 is a sentence-comprehension task where subjects had to judge the potential interpretations of utterances with ere with varying prosodic patterns (cf. Section 2.2). Then in Section 2.3 we briefly wrap up the main conclusions deriving from the two experiments; briefly, that different prosodic patterns (in particular, differences in the prosodic representation of information packaging) are associated to the different interpretations of the additive particle.

THE PRODUCTION EXPERIMENT
Experiment 1 was designed to assess the prosodic differences between sentences uttered with the simple reading in mind and sentences uttered with the scalar reading in mind.

Experimental setting and participants
Experiment 1 is a laboratory phonology production experiment where 9 female participants (age M = 37.7, SD = 3.4), all native speakers of Central Basque (variety of Ordizia) were asked to utter, in as a natural way as possible, pairs of identical strings corresponding to simple additive and scalar additive interpretations 5,6 . In order to elicit the data, a presentation was shown in a laptop screen containing texts (written in the local dialect) that clearly favored one of the interpretations. There were three different strings, and two conditions per string which we term "Simple" and "Scalar", all of them containing the same syllable in the accented positions in the element preceding the particle ere (/ru/) and the verb following it (/di/). All participants read the same set of sentences. Below we show the three strings (between brackets "<>") and the six scenarios we employed to elicit them (here syllables /ru/, /re/, and /di/ are highlighted in boldface, but there was no such highlighting in the questionnaire presented to participants). Items ( Askotan pasatzen da klaseko danok azterketetan nota ona ateatzea eta beak suspenditzea. Halare, lehengon jarri ziguten azterketa hain erraza izan zan, <Irunek ere gaindittu dola>. English translation: Irune is, by far, the weakest in our class. Often times, we all get good grades and she gets an F. However, the exam that we got the other day was such an easy one that <Irune ere (=even) passed the exam>.
(26) a. Hegazkinaren istripuaren hotsa Hondarribian eta Lezon aditu da, eta <Irunen ere aditu da.> 5 We recorded 10 speakers in total, but the recordings of one of them had to be rejected before analysis given that she continuously stopped when reading. 6 Our home institution does not require approval by any ethical committee for this sort of studies. This applies both to Experiment 1 and Experiment 2.
English translation: The sound of the plane-crash was heard in Hondarribia and Lezo, and < it was heard in Irun ere (=too) >. b. AHTren obratarako Ezkion egiten ari diren leherketak normalean Ordizian, Tolosan eta asko jota Andoainen aditzen dira, baina lehengoan egin zuten leherketa hain handia izan zen <Irunen ere aditu zela.> English translation: The sounds of the explosions for the works of the high-speed train in Ezkio are normally heard in Ordizia, Tolosa and, at most, in Andoian. However, the other day they made such a big explosion that <it was heard in Irun ere (=even)>.
Participants were asked to provide three repetitions of each string and condition so we got a total of 162 utterances (3 strings × 2 conditions × 3 repetitions × 9 speakers). In each of these utterances we took measurements in three syllables (/ru/, /re/, and /di/), so we analyzed 486 syllables in total (in a range of dimensions, as we explain below).

Data and measurements
We measured syllable duration (in ms.), F0 mean and maxima (in Hertz), and intensity mean and maxima (in dB.) in the three syllables, as well as the F0 declination between F0 maxima in syllables /ru/ and /di/, which amounts to 5 measurements per syllable, and 16 measurements per utterance, to a total of 7776 measurements.

Results 7
We found significant differences between the two experimental conditions in both duration and F0 measurements 8 . Syllable /ru/ showed the same average duration in both conditions (M = 0.11, SD = 0.02), however, there were significant differences in the duration of syllable /re/ between the utterances on the Simple condition (M = 0.13, SD = 0.03) and those on the Scalar condition (M = 0.11, SD = 0.03), t (80) = 5.24, p < 0.001, r = 0.51). Syllable /di/, like syllable /ru/ showed no significant duration difference.
In general, F0 values showed greater effects of the experimental manipulation. Observe, for instance, Figure 1, displaying F0 means in the three syllables that we measured.
As can be seen in the plot in Figure 1, on average, syllable /ru/ was pronounced with significantly higher Regarding intensity, both conditions were also distinguished (and note that this contrasts with previous studies on Central Basque intonation, which observed no correlation between nuclear stress and intensity values (cf. Irurtzun, 2013)). Observe as an illustration the plot in Figure 2, displaying intensity means in the three syllables.

Summary
The acoustic measurements discussed above show a clear difference between strings uttered in the Simple condition and strings uttered in the Scalar condition. And this is a remarkable fact, for the contexts of the utterance were unambiguous enough so that speakers would not convey any differences in their prosodic marking (that is, the exact interpretation of ere (simple vs. scalar) could be inferred from the context alone, but our observation is that even in this situation the tunes are different). In general, we saw that the stress associated to the element preceding the particle ere in the Scalar condition is stronger (in F0 and intensity) than in the Simple condition which, we would like to argue, is a signature of their focal nature (as narrow focus is associated to nuclear stress in Basque). Also, in the Scalar condition the region following this element displays reduced F0 values in comparison to the Simple condition, which would be linked to the well attested effect of post-focal pitch compression (cf. Elordieta, 1997Elordieta, , 2003Elordieta and Irurtzun, 2009;Irurtzun, 2013;Hualde and Elordieta, 2014). The conclusion of Experiment 1 is that speakers associate different prosodic patterns to different interpretations of the same string. In particular, strings associated to a scalar additive interpretation are characterized by having nuclear stress assigned to the element associated with ere (the element preceding it). Now the question that emerges is whether this intonational pattern is enough in and of itself to convey the intended meaning. That is, whether native speakers can identify the intended interpretation of each utterance. This is the goal of Experiment 2.

THE PERCEPTION EXPERIMENT
Experiment 2 was designed to assess the interpretations associated to strings uttered with different prosodic patterns.

Experimental setting and participants
We designed a magnitude-estimation task with the help of a Visual Analog Scale (VAS) with unambiguous interpretations at both ends (see Figure 3). For the VAS, we took advantage of the fact that all Central Basque speakers are bilingual speakers of Spanish and Basque, and thus we designed a judgment task with unambiguous Spanish sentences at both ends (with también "also" and incluso "even"), as shown in Figure 3 9 .
Thirty two Southern Basque speakers 10 (21 female, age M = 31.6, SD = 8.9) were asked to listen to three strings which were uttered with two different interpretations in mind. Stimulus utterances were taken from the natural productions of a participant in Experiment 1. There were 3 test sentences in two conditions each (Simple and Scalar):  Figures 4-9 show the pitch tracks corresponding to these stimuli (F0 in red over the spectrogram, waveform in blue).
Besides, for item (28), sentence "Irunek ere gainditu du" [(Even) Irune (too) passed the exam], we created an additional pair of test items: Condition Synth1, a manipulation of the item for "Scalar" by stylizing F0, raising the peak of the pitch accent in the subject by 25 Hz, and flattening the post-accentual region (Figure 10), and Condition Synth2, a manipulation of the item 9 The experiment was conducted with the LingMarket website that we designed for data-gathering (URL: https://isqi.iker.univ-pau.fr/). 10 All participants were L1 Basque speakers, or 2L1 Basque and Spanish speakers. All were fully competent in both languages. Also, they had to fill a short questionnaire before the experiment in order to assess that their linguistic capacities in Basque reached the European Framework C1 level. for "Scalar" by stylizing F0, raising the peak of the the pitch accent in the subject by 50 Hz and flattening the post-accentual region (Figure 11)  Irunek ere gainditu du

FIGURE 5 | Pitch track corresponding to test item (28), Condition: Scalar.
11 These test items were generated with Praat (Boersma and Weenink, 2014). Subjects listened to experimental items in isolation (i.e., with no context at all) and were instructed to judge the range of possible interpretations of each utterance in the VAS by cutting the judgment line in two: if they thought that the utterance was completely ambiguous and it could equally represent the two readings, subjects were instructed to place the delimiter in the middle of the line (as in Figure 12).
If they thought that it represented more the reading to the left, but still leaving some plausibility to the reading to the right they should place the delimiter on whichever place they felt on the left (see, for example Figure 13).
Alternatively, if they judged that the utterance was unambiguous in the other direction, they should place the delimiter more to the right. Subjects were explicitly instructed that they could place the delimiter at any point in the line. Besides the validity of the technique was controlled with completely unambiguous fillers that could only have one of the interpretations and hence should be placed at the extreme left or right boundary of the line. As we said, there were 8 test utterances in a questionnaire comprising a total of 40 utterances (the rest were fillers). Items were presented in a pseudo-randomized order, and in order to avoid any effect of a spatial-numerical association of response codes (cf. i.a. Dehaene et al., 1993) simple additive and scalar additive interpretations were presented both to the right and to the left of the VAS line in a random fashion (counterbalanced). Participants were instructed that they could listen to test items as many times as they wanted, but they could do just one mouse-click to cut the line, according to the interpretation they gave to the utterance they listened (the system was designed not to allow rethoughts or corrections). That is, once an utterance was evaluated, participants could not reevaluate it again.

Data and measurements
We measured participants' judgments on the VAS scale from 0 to 100 points (0, the value on the leftmost edge, 100 the value on the rightmost edge). Overall, judgments show a clearly skewed distribution. Figure 14  As Figure 14 shows, responses to different conditions show a different behavior, with clearly skewed distributions, significantly so in the cases of conditions Simple, Synth1 and Synth2. In order to assess the robustness of the differences between conditions we departed from the classical null hypothesis significance testing (NHST) and performed a Bayesian estimation of differences between group means. In fact, many works have emphasized the limits of NHST methods like t-tests and their weakness vis à vis outlier data-points, which can affect greatly the analysis of the results of a sentence comprehension task like the one we designed (cf. i.a. Wagenmakers, 2007;Kruschke, 2011Kruschke, , 2013Wetzels et al., 2011). In particular, we performed a pairwise comparison of the pooled judgments of Simple (M = 19.08, SD = 25.33) and Scalar (M = 50.78, SD = 35.70) items following Kruschke, 2013's BEST Markov chain Monte Carlo (MCMC) sampling method. Figure 15 provides an overview of the outcome of the Bayesian estimation of difference between groups for a MCMC sample of 100,000 parameter values. As can be observed in the upper left panel, the mean of credible values for the mean of group 1 (i.e., the Simple condition) is 13.8, with the 95% highest density interval (HDI) ranging from 8.78 to 19.6, whereas the mean of credible values for Group 2 (the Scalar condition) is 51.7 with the 95% HDI between 43.8 and 59.9 (these are values of the MCMC posteriors). The difference between μ 1 and μ 2 is 37.8 on average, with 100% of the credible values well above zero. Thus, we can confidently conclude that the groups' means are indeed different (for comparison, the result of a paired t-test on these data is also clear: t (95) = −6.59, p < 0.001, r = 0.56). Also, a credible difference is observed in the standard deviations of the two conditions (Simple Mo = 16.6 vs. Scalar Mo = 33.9), whereby the 100% of credible differences are greater than zero. Thus, not only is the mean of the Simple condition credibly smaller than the mean of the Scalar condition, but the standard deviation of the Simple condition is also credibly smaller than that of the Scalar condition, which means that, on average, items in the Simple condition are interpreted as simple additives and as less ambiguous than items in the Scalar condition, and that judgments for the Simple condition are more stable than those for the Scalar condition. The posterior also indicates that the effect size is large, since the histogram of the 100,000 credible effect sizes has a mode of −1.38 and a 95% HDI that excludes zero. As expected, analogous comparisons of the data for the other conditions in Figure 14 also showed sharp credible differences between the Simple condition and the rest (means in Figure 14 with dashed lines), since the judgments given by the participants shifts toward an unambiguously scalar interpretation with conditions with more marked accents (Simple < Scalar < Synth1 < Synth2).

SUMMARY FROM THE EXPERIMENTAL RESULTS
In sum, our experiments show that constructions with ere can vary in their interpretations between the simple and the scalar additivity readings. However, this should not be interpreted as genuine ambiguity. In fact, Experiment 1 showed that the tunes associated to expressions with ere in contexts describing simple addition and scalar addition tend to differ; on average, the elements preceding ere in the scalar condition are associated with a focus intonation whereas in the simple condition they are not. This correlates with a clear shift in the interpretation of the sentence since, as Experiment 2 shows, stimuli extracted from the simple addition environments are clearly interpreted as simple additives, but items extracted from scalar addition environments shift their interpretation toward the scalar value, and the interpretation gets more scalar with stronger accents. Thus, we can conclude that there is a correspondence between the nonfocal or focal nature of the element preceding the additive particle ere and the interpretation of the sentence as simple addition or scalar addition. The question is why? This is the issue that we tackle in the next section.

PROPOSAL: THE EMERGENCE OF SCALAR MEANINGS
In this section, we provide a novel analysis of how scalar interpretations of the Basque particle ere arise. In a nutshell, the analysis that we want to put forward has the following two ingredients: (i) the scalar value of ere is derived from the simple additive value of ere; in other words, we will only have a single lexical entry, i.e., the simple additive ere; (ii) the "least likelihood" reading or the "scalarity" derives directly from the combination of the two presuppositions of the sentence containing ere and the assertion of the sentence.
In order to account for the derivation of the scalar interpretation, i.e., the even reading, we will make use of the semantics of focus. Roughly, a main contribution of focus is the introduction of a presupposition to the effect that the property denoted by the sentence containing a focal element holds of some individual (cf. i.a. Geurts and van der Sandt, 2004), besides, focalization is generally taken to evoke "focus alternatives." For instance, Rooth argues that a sentence which contains a focalized element has two denotations: (i) the "Ordinary Semantic Value" ([[ ]] O ) which is just the proposition denoted by the sentence, and (ii) the "Focus Semantic Value" ([[ ]] F ) that is a set of propositions obtained by the substitution of the focal phrase by "alternatives" that match it in syntactic and semantic types (cf. Rooth, 1985Rooth, , 1992. So, for instance, the focused sentence in (31), which presupposes "that someone loves Paula," would have the meaning represented in (32)  Actually, we employ Rooth's formulation but any semantic theory of focus that assumes focal presuppositions will equally work for our proposal.

Etxeberria and Irurtzun
The emergence of scalar meanings That is, sentence (31) could be uttered in a situation where it is assumed that someone loves Paula, and we identify who that someone is by uttering (31), akin to saying that "it's Mary that loves Paula." Now, with these ingredients in mind, how do we get the scalarity (least likelihood) reading for a sentence like (33) with the Basque particle ere?
[Jon] F ere etorri da. Jon ere come AUX Even Jon came.
Our proposal is that the scalar interpretation of sentences like (33) derives directly from the combination of two types of Frontiers in Psychology | Language Sciences February 2015 | Volume 6 | Article 141 | 10 presuppositions: on the one hand, we have the focal presupposition which forces us to reconstruct a context that presupposes "that someone came" (cf. Geurts and van der Sandt, 2004), and on the other hand, we also have the lexical-semantic contribution of ere, which when asserted generates the simple additive interpretation (34). The combination of these two presuppositions, one contextual (the focal one) and one lexical (the asserted simple additive), is what creates the complex presupposition "that someone came and (s)he is not Jon" (35). So this is a situation where we expect anyone but Jon to come. However, the expression of a sentence like (33) asserts "that Jon came," clashing with our expectations (someone came and (s)he is not Jon), which is what brings about the counter-expectation reading that "Jon is the least expected/likely person to come," i.e., the scalar meaning. It is the joint computation of the assertion and the presuppositions that generates this meaning. In a nutshell, in these constructions an interpretation emerges where we expected anyone but Jon to come, and assert that Jon came, and this clash is what creates the counter-expectation reading (i.e., the scalar meaning).

CONCLUSIONS
In this paper, we have seen that in Basque the same particle ere can generate the "simple additive" reading as well as the "scalar additive" reading. In order to assess the potential ambiguity of constructions with ere we ran a production and a perception experiments and we concluded that prosody (in particular, nuclear stress and post-focal pitch compression) affects the interpretation of the additive particle. When the element preceding ere bears nuclear stress (i.e., when it is focal) the sentence gets a scalar interpretation.
Observing these facts, we have argued that the scalar value of constructions with ere is derived from the simple additive value of this particle, i.e., the simple additive value is the basic lexical meaning of this particle. The scalarity effect is generated by the combination of two presuppositions of the sentence containing ere [a lexical one (the lexical additive value of ere), and a focal one (the focal presupposition)] with the assertion of the sentence.