On a concessive reading of the rise-fall-rise contour: contextual and semantic factors

. This paper presents three auditory rating experiments on the rise-fall-rise contour (RFR). Experiment 1 provides experimental evidence that the RFR makes dis-agreeing with a prior statement more natural than neutral intonation would. Additionally, the data show that the RFR exhibits a valence asymmetry, noted by G¨obel (2019): the amelioration of a disagreement is greater when the RFR is used in a positive reply to a negative statement than in a negative reply to a positive statement. Experiments 2 and 3 investigate factors contributing to this asymmetry, showing that it disappears in replies to questions and is weakened when the reply contains an additive particle. Based on these results, we argue that the RFR has a scalar meaning, following G¨obel (2019), with the relevant scale being contextually determined and resulting in an ambiguity resembling the Focus-particle at least .

1. Introduction.This paper addresses the question how intonation affects and conveys linguistic meaning through the lens of intonational contours, or "tunes", specifically, with a case-study on the so-called rise-fall-rise contour (RFR).The RFR has been characterized as conveying a sense of uncertainty or incompleteness on the speaker's part (Ward & Hirschberg 1985). 1 In apparent opposition to this characterization, the RFR can also be used more antagonistically, as in the naturally occuring example in (1).Here, Dewey's reply seems to challenge Hal's prior statement, but without straightforwardly contradicting it.
(1) Hal: I mean, you can't just break into a zoo, role a couple of elevens and suddenly become ... the dean of a university.Dewey: I did...
(Malcolm in the Middle: S7, E20; AUDIO) The goal of this paper is to substantiate the tension between uses of the RFR as in (1) and its prior characterization empirically and explore relevant factors by presenting three auditory rating studies.We argue that there are in fact distinct uses of the RFR that resemble an ambiguity of the English Focus-particle at least, and support the proposal by Göbel (2019) that the RFR indicates the presence of a higher alternative on a variable scale.The structure of the paper is as follows.Section 2 discusses details of prior accounts of the RFR and introduces the idea of a parallel between the RFR and at least.Section 3 presents the three experiments and Section 4 provides discussion of the results.

Background.
2.1.PRIOR ACCOUNTS.The seminal account by Ward & Hirschberg (1985) is primarily concerned with cases as in (2) where the RFR intuitively is used as a hedge that avoids a more definitive answer to the question while still intending to be relevant.Ward & Hirschberg's proposal centers the use of the RFR around speaker uncertainty in relation to a scale and its scalar values, either regarding the appropriateness of evoking such a scale, the particular choice of scale, or the choice of a newly added value on a given scale.Applied to (2), we could then say that there is uncertainty about "the relative positions of Missouri and the Mississippi on a geographical scale ordered from east to west" (W&H: 767).
(2) A: Have you ever been West of the Mississippi?B: I've been to Missouri... (WARD & HIRSCHBERG 1985, (62)) In more recent work, the intuition that the RFR conveys uncertainty has been implemented in terms of incompleteness by Constant (2012) and Wagner (2012).For Constant, the RFR resembles Focus-particles like only in that it quantifies over alternatives and conveys that all assertable alternatives (= those alternatives whose truth-value is not yet known) cannot be safely claimed, formalized as in (3) as a conventional implicature. 2Wagner proposes a similar analysis, with the difference that (i) relevant alternatives are speech acts rather than propositions and (ii) that there is an alternative speech act that could have been made, rather than focusing on what alternatives are not claimable, see (4). 33) RFR ϕ ci = ∀p ∈ ϕ f s.t.p is assertable in C: the speaker cannot safely claim p.
(4) RFR = λS.∃S' in S g a , S ↛ S' and performing S' might be justified: S These two accounts capture the distribution of the RFR in quantifier scales as in ( 5), where the RFR is felicitous with the middle value some but infelicitous with the extreme values none or all.None is odd because it rules out all higher alternatives such that the RFR applies vacuously since there are no alternatives left to be quantified over (Constant) or there is no alternative speech act to be made (Wagner), and all is odd for similar reasons since another alternative such as some is already entailed by it.In contrast, some leaves alternatives open that can then be marked as not being claimable or as the alternative speech act that was not made, hence the characterization of the RFR as conveying incompleteness (see also Goodhue et al. 2016 for experimental evidence).
(5) A: Did you feed the cats?B: I fed { #none / some / #all } of them... (with RFR) A different approach comes from Westera (2019) (see also Westera 2017), who focuses on the role of the RFR in the discourse structure, specifically the Question Under Discussion (QUD, Roberts 2012).According to Westera, the RFR indicates that a conversational maxim in relation to the main QUD has been suspended and instead a secondary QUD is being addressed.A potential benefit of this view is that it may allow including cases of contrastive topic, that share a similar prosodic profile, into a unified theory.However, to what extent such a unification is warranted is an open question.

G ÖBEL (2019).
The main approach that this paper builds upon comes from Göbel (2019).
The central data point provided there is the observation that the RFR shows an asymmetry in replies to statements that contrast in the valence attributed to what is being discussed: while the RFR is natural as a response to A's negative characterization of Dexter in (6a) when descriptively opposing the previous statement with a positive characterization, the reverse -a negative reply to a positive statement -is markedly odd.We will dub this contrast in acceptability the "valence asymmetry".Notably, this data point is unexpected on the accounts discussed in the previous subsection.To evaluate Ward & Hirschberg (1985), let's assume that the scale under consideration is a "goodness" scale, and what the replies convey is uncertainty about where to locate Dexter in virtue of his actions.It is unclear why (6a) would be more appropriate in this case than (8b) given that knowing someone gives to charity is compatible with being uncertain whether they are a horrible person, and knowing that someone murders people is compatible with being uncertain whether they are a great person. 4For Constant (2012) and Wagner (2012), it is equally unclear why (6a) should leave alternatives open but not (6b), and for Westera (2019) there is no obvious difference in terms of the secondary QUDs (6a) and (6b) give rise to either.The solution Göbel (2019) proposes is that the RFR indicates that there is an alternative that ranks higher on a given scale, essentially borrowing from ideas present in prior accounts.Let's again imagine a goodness scale that goes from pure evil on one end to pure virtue on the other, illustrated in Figure 1.In (6a), A's statement places Dexter toward the bottom of the scale.B's reply then suggests that Dexter is located higher.In contrast, in (6b) B's statement starts Dexter off toward the top and A's reply adds a negative counterpoint.As a consequence, the carrier utterance of the RFR does not contribute a higher alternative but a lower one and results in oddness. 5The account additionally predicts the contrast in (5): both none and all fail to leave higher alternatives open, while some leaves all.6 2.3.PARALLEL TO AT LEAST.Interestingly, the valence asymmetry in ( 6) is not unique to the RFR, but can also be observed with concessive (or evaluative) at least (Nakanishi & Rullmann 2009).The characteristic feature of concessive at least is that alternatives are ranked according to desirability, for instance in (7) conveying that feeding some of the cats is still better than feeding none of them.
(7) At least Cameron fed SOME of the cats (... it could've been less).
When using concessive at least in the same dialogues as ( 6) but with a falling contour, we see the same -intuitively even clearer -pattern: at least is felicitous with a positive reply (8a), while it is infelicitous with a negative reply (8b) (8) a. A: Dexter is such a horrible person.
B: At least he gives to charity.b.B: Dexter is such a great person.
A: # At least he murders people.
The parallel of the RFR with at least crucially does not end there.In addition to the concessive interpretation, at least also has an epistemic interpretation that has been tied to uncertainty (Geurts & Nouwen 2007).Taking (9) as illustration, the speaker only commits to Cameron having fed no less than some of the cats while leaving open the possibility that she fed all of them.( 9) Cameron fed at least SOME of the cats (... maybe even all of them).
This meaning of epistemic at least resembles prior accounts of the RFR that focus on its uncertainty or incompleteness component. 7The resemblance goes as far as epistemic at least showing the same acceptability pattern with quantifiers as we saw in (5), namely being incompatible with extreme ends of a scale: (10) A: Did Cameron feed the cats?B: She fed at least { #none / some / #all } of them.
Based on this parallelism of the RFR with distinct interpretations of at least, we propose that the RFR is prone to a similar type of ambiguity.This view would allow us to reconcile theoretical accounts that emphasize the uncertainty and incompleteness component of the RFR with the valence asymmetry.Moreover, it would allow us to make sense of cases like (11), where the RFR is felicitous despite the truth of the higher alternative ten being known, showing that uncertainty or incompleteness are relevant but not sufficient.On the ambiguity view of the RFR, (11) would simply be a case of a concessive usage.
(11) A: Did you feed all ten cats?B: I didn't feed all ten, but I fed NINE of them... (with RFR) (AUDIO) However, an initial obstacle to this approach is the question what factors contribute to the ambiguity and determine the respective interpretation.We will explore this question in Experiments 2 and 3. Beforehand, Experiment 1 will be dedicated to substantiating the valence asymmetry empirically.
3.1.1.MATERIALS & DESIGN.The main goal of this experiment was to provide quantitative data on the valence asymmetry.To do so, we used short dialogues modeled after (6) that varied the "valence" of each utterance, shown in ( 12).
auditorily presented with a dialogue and had to provide a naturalness rating on a scale from 1 (completely unnatural) to 6 (completely natural) based on how they thought the response sounded given the context.There were three practice trials after receiving instructions, followed by 48 stimuli.
The experiment concluded with a chance to provide feedback.A test version of the experiment can be accessed at https://prosodylab.org/ ˜agobel/conepi/conaddRatingBare/ ?SESSION_ID=test&mode=experiment.
3.1.3.PARTICIPANTS.29 participants were recruited from Prolific.acand paid $2.20 each.Five participants were excluded due to failing the headphone check, leaving 24 for data analysis.3.1.5.DISCUSSION.The experiment revealed several notable findings.First, participants strongly preferred dialogues where context utterance and target utterance had the same valence over dialogues that featured some opposition.While this was the numerically largest effect, it is also of least interest to this investigation such that we will put it aside.Second, the RFR ameliorated this mismatch penalty.Albeit novel, this finding is in line with prior accounts of the RFR insofar as expressing uncertainty or incompleteness may be viewed as more polite in an otherwise confrontational dialogue and hence improve ratings.Finally and most crucially, the extent to which the RFR ameliorated the penalty was larger in dialogues where the context utterance was negative and the carrier utterance of the RFR contributed a positive counterpoint compared to dialogues with a positive starting statement and a negative counterpoint.This last pattern is evidence for the valence asymmetry observed in Göbel (2019) and the argument made in this paper, namely that there is a concessive reading of the RFR alike to at least.
A follow-up question to this argument, mentioned in Section 2. 3, is what makes this reading of the RFR available.A relevant hint in this regard comes from the fact that the prior literature has mostly focused on uses of the RFR in replies to questions or out of context, whereas Göbel (2019) and Experiment 1 investigated replies to (value) statements.A possible contrast between questions and statements is furthermore in line with intuitions and may thus be expected to contribute to the choice between an "epistemic" and a "concessive" reading of the RFR.The next experiment examines this connection.

MATERIALS & DESIGN.
The goal of this experiment was to test whether replies to questions exhibit the same valence asymmetry we observed for replies to statements in Experiment 1.All design aspects of this experiment were identical to Experiment 1, with the sole exception that context utterances were changed from statements to questions, as in ( 13): 3.2.4.RESULTS.Coding & Data Analysis were the same as Experiment 1 (see Section 3.1.4).
The average ratings by condition are shown in Figure 3.The first thing to note is that we again observe a mismatch penalty, with higher ratings for match than for mismatch, reflected in a significant RESPONSE MATCH effect (z = -8.89,p < .001***).Additionally, ratings for positive contexts are lower than negative contexts in match cases, reflected in a significant effect of CONTEXT-VALENCE (z = 4.81, p < .001***),but higher in mismatch cases, which shows up as a significant interaction of CONTEXT-VALENCE and RESPONSE MATCH (z = -5.47,p < .001***).The second notable pattern is that there is little to no difference between neutral intonation and rfr across the board, with the exception of the match conditions in positive contexts, resulting in a marginal effect of INTONATION   3.2.5.DISCUSSION.As in Experiment 1, participants considered dialogues that matched in valence more natural than those that mismatched.Moreover, this mismatch penalty was larger when the context question was negative than when it was positive.However, since this effect was largely independent of intonation, we will put it aside here.
More crucially, using questions -instead of statements as in Experiment 1 -seemed to render the difference between neutral intonation and the RFR almost non-existent.The only exception were higher ratings for the RFR in the match condition in positive contexts.Most importantly, there was no evidence for a valence asymmetry like we observed in Experiment 1.While the relevant three-way interaction was marginally significant, it went in the opposite direction to what we would have expected, namely with the RFR increasing the mismatch penalty in positive contexts rather than decreasing it less.The results thus provide support for the idea that using the RFR to reply to a question or to a statement affects what reading it receives.
Following Göbel (2019), we assume that the two readings can be modeled in terms of different scales that are determined pragmatically, for instance mediated by a QUD (e.g.Beaver & Clark 2008).For statements as in Experiment 1, the scale is evaluative, as discussed in sec 2.2.For questions as in this experiment, the relevant notion is truth, which can be modeled in terms of a scale of informativity.What is at stake in the question whether the bike ride was terrible or great then is to what extent the reply a definitive answer.Crucially, both positive and negative replies leave open "stronger", more definitive answers, such that the RFR is equally acceptable independently of valence, in contrast to what we saw in Experiment 1.
The following experiment explores a potential semantic factor for the interpretation of the RFR, namely the role of additive particles, based on the intuition that adding such a particle to the RFR utterance weakens the valence asymmetry.3.3.EXPERIMENT 3.

MATERIALS & DESIGN.
The goal of this experiment was to test whether an additive particle like also would neutralize or at least weaken the valence asymmetry observed in Experiment 1. Design and materials were identical to Experiment 1, except that the target utterances now contained also, as in ( 14): amelioration of the RFR is greater in negative contexts than positive ones is less clear here, and in fact not supported by a significant three-way interaction (z = 0.63, p = .53).3.3.5.DISCUSSION.The results provided some support for the intuition that an additive particle weakens the valence asymmetry of the RFR: even though both the mismatch penalty and the amelioration of it by the RFR were comparable to Experiment 1 where also was absent, there was no statistical evidence that the amelioration differed between the two contexts.However, the numerical trend was still in line with a valence asymmetry.Moreover, the relevant comparison here is between the presence of an effect in Experiment 1 and the absence of the same effect in this experiment, rather than based on an effect within the same experiment, and should thus be taken as tentative evidence only.A proper confirmation that additive particles weaken the valence asymmetry will therefore be left for future research.
We may nonetheless wonder why additive particles would have such an effect.The potential explanation we want to put forward here is that the way the reading of the RFR gets determined interacts with the meaning of also.Additive particles are commonly analyzed as presupposing the truth of an alternative proposition (e.g.Heim 1992).In doing so, the interpretation of the RFR may become biased toward an "epistemic" reading that is concerned with informativity where valence is irrelevant and hence the valence asymmetry gets weakened.This approach would point toward an interesting issue of compositionality between two types of meanings -Focus-particles and intonational contours -that have been treated -including here -as making similar contributions based on relations to alternatives.How to spell out this connection in detail, however, goes beyond the scope of this paper and will be left for future work.
4. General Discussion.This paper presented data from three auditory rating experiments on the RFR.Experiment 1 substantiated a contrast between the acceptability of the RFR in positive replies to negative statements and negative replies to positive statements, as argued by Göbel (2019), which we dubbed the valence asymmetry.We interpreted this finding as evidence for a "concessive" reading of the RFR, resembling concessive at least.Experiment 2 investigated replies to questions rather than statements and showed that the valence asymmetry disappears in this case.We took this change to point toward questions inducing a distinct, "epistemic" reading, again borrowing from a parallel with at least.On this view, the two readings can be unified by assuming that the RFR indicates the presence of a higher alternative but on different scales that are pragmatically determined.Finally, Experiment 3 explored the intuition that the inclusion of an additive particle like also weakens the valence asymmetry, for which we found tentative evidence.If confirmed, this finding raises interesting questions about how the meaning of intonational contours interacts compositionally with different parts of its carrier utterance.
Apart from this issue, there are two others we want to briefly discuss here.The first concerns the role of alternatives in the advocated theory.As mentioned earlier, the two readings are not taken to only differ in the type of scale involved but also in how they generate alternatives.For the "concessive" reading from Experiment 1, the relevant higher alternative is contributed by the host utterance of the RFR, with a prior statement being the proposition that the alternative is higher than.For the "epistemic" reading from Experiment 2, the higher alternative is an alternative to the host utterance itself, similar to how the assumed alternative to some in the quantifier cases (5) from Section 2.1 is all.A prediction of this view then is that the RFR should in principle be compatible with extreme scale values as long as it contributes an alternative that is higher than some previously mentioned one and receives a concessive reading. 9Future research will have to show whether this prediction is borne out.
The second issue is about the meaning of intonation at large.Here, we took the RFR to contribute its meaning holistically rather than attempting to attribute associate smaller meaning components with the individuals parts of the contour, but we can ask what such a decompositional account may look like.The RFR is prosodically analyzed as, using ToBI annotation, consisting of an L*+H pitch accent, a L-phrasal accent, and a H% boundary tone.We will put the phrasal accent aside here and focus on the pitch accent and the boundary tone.According to Pierrehumbert & Hirschberg (1990), the L*+H accent evokes a scalar meaning, which is consistent with the view of the RFR adopted here.Regarding the high boundary tone, there are a number of recent accounts of rising declaratives to draw from.Rudin (2022) proposes that the characteristic feature of rising intonation is that they lack speaker commitment, which seems incompatible with the valence asymmetry given that for both types of replies the speaker is intuitively committed to the truth of the proposition.Jeong (2018) argues that rising intonation opens a meta-linguistic issue, which again seems to lack a clear path for explaining the valence asymmetry per se, but may capture the intuitive sense of indirectness and the resulting politeness effect.We aim to address the question about the contribution of the final rise in future work.
3.1.4.RESULTS.Coding & Data Analysis.CONTEXT-VALENCE was sum coded given there was no basis for choosing one over the other as a baseline.INTONATION and RESPONSE MATCH, on the other hand, were dummy coded, with match and neutral as reference levels.Data were modeled with ordinal mixed effects with the maximal structure allowing convergence.Results and analysis files with more details on the full models of this and the following experiments, as well as experimental files and stimuli, can be found at the associated OSF repository: https: //osf.io/t36qkTheaverage ratings by condition are shown in Figure2.The most notable -although less interesting -pattern concerns higher ratings for match than mismatch conditions, reflected in a significant effect of RESPONSE MATCH (z = 17.19, p < .001***).Looking at only match conditions next, we see higher ratings for neutral intonation compared to the rfr, reflected in a significant effect of INTONATION (z = -7.20,p < .001***).However, when comparing the INTONATION difference for match with mismatch, the penalty for the rfr decreases, reflected in a significant interaction between INTONATION and RESPONSE MATCH (z = 5.30, p < .001***).Moreover, this amelioration of the penalty is greater with negative context sentences -and hence positive target sentences -than with positive context sentences, evidenced by a three-way interaction of INTONATION, RESPONSE MATCH, and CONTEXT-VALENCE (z = 2.25, p < .05*).