2.1 Krifka (2013)

Krifka (2013) explains interchangeability by arguing that negative sentences introduce multiple antecedents for yes and no to pick up. Consider the likely interpretation of the propositional anaphor that in the following two examples:

That can either take the proposition that B won the jackpot or its negation as its antecedent, and which interpretation is more likely depends on the plausibility of the different readings given our world knowledge (winning a jackpot is unlikely and therefore should be unexpected). In Krifka’s analysis, yes and no are propositional anaphora which, just like that or so, require linguistic antecedents. Polar particles are different from regular propositional anaphora, however, in that they do not just refer to a proposition, they also either assert it (in the case of yes) or assert its negation (in the case of no). Krifka therefore treats yes and no as standing in semantically for entire speech acts, and assumes that they have a corresponding syntactic phrasal category which Krifka calls ActP. This analysis aims to explain their syntactic distribution. For example, it can account for why it is not possible to say Yes surprised me.

The antecedents for polar particles are contextually salient linguistic expressions that denote propositions, which Krifka (2013) calls propositional discourse referents. A positive PQ as in (4) makes available a discourse referent d anchored to the TP, which denotes the proposition Jane is coming:

The particle yes can pick up this discourse referent d as in (4a) and assert Jane is coming. It cannot assert ¬d as there is no antecedent denoting that proposition. Similarly, no can only negate d producing ¬d as in (4b) because d is the only antecedent available. To produce d, no would need to be able to negate an antecedent that is equivalent to ¬d, but there is no such antecedent available in the context in (4). Krifka’s account hence correctly predicts the non-interchangeability of yes and no in the context of a positive polar question (1).

The key idea accounting for interchangeability in negative contexts in Krifka’s analysis is that these structures make two antecedents available, similar to (3). The first antecedent is the embedded antecedent d anchored to the TP, which denotes the positive proposition Jane is coming. The second antecedent is d′ anchored to the NegP, which denotes the negated proposition Jane is not coming:

In (5a), yes asserts d, and no asserts its negation. In (5b), yes asserts d′ (which is equivalent to ¬d), and no asserts its negation.

Under this analysis, bare polar particles are in principle expected to show the same interchangeability in negative contexts, since they should also be able to pick up one of the two antecedents. However, Krifka makes additional assumptions about pragmatic factors which affect which uses of polar particles in general and bare particles in particular should be more or less preferable given a certain discourse. We will return to these finer grained claims when discussing the experimental results.

2.2 Kramer and Rawlins (2009)

Under Krifka’s analysis, yes and no are syntactically not related to the sentences that follow them. They form separate speech acts, and the relation to a following sentence would be guided by the same principles that guide sequences of speech acts in discourse more generally. Prior analyses have often assumed a much more direct syntactic relation between the particle and the following sentence, however, in which yes and no are part of the structure of the following sentence. For example, Kramer & Rawlins (2009; referred to as K&R), building on Laka (1990), propose that yes and no are adverbs in the specifier of the functional polarity head in the left periphery.⁸ According to K&R’s account, the use of no is constrained in that it can only occur if the following, optionally elided, sentence contains negation. This is achieved formally by assuming that no has an uninterpretable negative feature (uNEG) that must enter into a negative concord chain with an interpretable negative feature (iNEG). Yes does not contribute any features, and thus is not constrained by the polarity of the following sentence. This explains why both are compatible with negative responses to negative questions.

While for Krifka the use of polar particles without a following sentence is unexceptional, under this analysis such cases are analyzed as fragment answers, where the TP-complement of the polar projection has been elided. As in all fragment answers, ellipsis requires an appropriate antecedent. K&R assume with Merchant (2001) that elided structure and the antecedent have to mutually entail each other. In the context of a negative question, the antecedent for ellipsis is simply the TP of the question:

Yes and no are both predicted to be acceptable in (6) and (7). No is in a negative concord relationship with iNEG in the elided constituent. Yes, on the other hand, does not place any syntactic requirements on the follow-up sentence, and hence is also acceptable here. The source of the interchangeability of yes and no in negative answers to negative questions is therefore that both particles are compatible with cooccurring with a clause that contains negation.

One issue with this account is that it only deals with one half of the interchangeability phenomenon, negative answers. As K&R note themselves, it is not obvious under their analysis why no can appear with a positive clause in response to a negative PQ, e.g. No, she IS coming. Since no contains a uNEG feature, it must enter into a negative concord chain with an iNEG feature, but there is none present in such a response. To explain this use of no, K&R claim that there is a second lexical entry for no that encodes, in combination with an obligatory intonational peak on the auxiliary, a reverse feature uREV, similar to reverse particles such as French si and German doch. Ellipsis is argued to be impossible in reversing no responses due to the obligatory intonational peak on the auxiliary. While K&R do not discuss positive yes responses to negative questions, for example Yes, she IS, we believe that their account predicts that ellipsis should be impossible, since there is no appropriate antecedent.

What about polar particles in response to a positive question? The analysis of the use of yes in positive responses is straightforward. The elided structure is simply identical to the antecedent Jane is coming provided by the question, see (8a). The reason no cannot be used in a positive response is also clear: There is no syntactic negative feature that it could enter into a concord chain with, and no is therefore not licensed, see (8b).

But how do no responses convey negative answers to positive questions? It would seem that the positive question cannot provide the required antecedent for the elided negative sentence in (8c). K&R argue that in such cases, an iNEG feature appears in the polarity head, higher up in the structure than the ellipsis site, see (8c).

This account of the use of no works technically, but it seems a bit ad hoc in that it runs counter to the idea that ellipsis is licensed by mutual entailment. Both Krifka (2013) and Roelofsen & Farkas (2015) note an additional problem: Since yes does not impose any syntactic requirement on the structure it occurs in, there is actually nothing in this account to stop yes from appearing in negative responses to positive PQs. Thus contrary to fact, the response in (9) is predicted to be entirely acceptable.

We turn now to an account in the same vein as Kramer & Rawlins (2009) that addresses some of these issues.

2.3 Holmberg (2013; 2016)

Holmberg (2013; 2016), like Kramer & Rawlins, treats yes and no as specifiers of a functional projection, and analyzes bare particles as fragment answers in which everything but the polar particle remains unpronounced.

For Holmberg, yes and no are operators that assign positive and negative values respectively to the polarity head of their complement. The polarity head contains a polarity variable that can have one of three values: Positive [+], negative [–], and open [±]. Positive polar questions have open polarity, according to this analysis. Consider (10), where the PolPs in the answers are elided.

The polarity variables of the answers in these cases are different from that of the question, an apparent problem since the identity condition on ellipsis seems to be violated. Holmberg argues, however, that elided pronoun variables can have different interpretations than their antecedents, and he suggests that polarity variables behave in the same way. For example, Jane took her car, and Amanda did, too has an interpretation where Amanda took her own car. The idea then is that yes and no bind an elided polarity variable and assign it [+] or [–] respectively. The feature value [–] would be spelled out as not if the following sentence were not elided.

While Krifka finds the source of interchangeability in the possibility of either picking up the entire proposition in the context or just the one embedded under negation, Holmberg finds its source in a structural ambiguity in the negated context sentence. According to his analysis, negation in English attaches at two different heights. High negation attaches between TP and vP, and low negation is adjoined to vP/VP. When A asks the question “Is Jane not coming?”, B is free to interpret the question as having high or low negation. If it is low as in (11a), then the polarity head is open and yes and no are both free to bind it. Yes will produce a negative response (11a-i), while no produces a double negative, which reduces to a positive response (11a-ii). If negation is high, as in (11b), then the polarity head is negative and yes requires an unelided clause to change it to positive (11b-i), while no forms a negative concord chain with it (11b-ii).⁹

The structural ambiguity of the two attachment heights of negation in the polar question is what makes yes and no interchangeable in negative contexts in this account. The two polar questions (11a) and (11b) are string identical and interpretively indistinguishable.¹⁰ Similar to the analysis in K&R, a bare yes cannot convey a positive answer, but must be followed by an overt clause as in (11b-i). Holmberg (2013) notes that in some contexts, bare yes seems to be able to convey a positive response to a negative question. He suggests that intonation may play a crucial role in making such responses felicitous though he does not discuss what the intonation may be or how it interacts with his account to make the response felicitous.

2.4 Roelofsen and Farkas (2015)

Unlike Krifka (2013), Roelofsen & Farkas (2015; referred to as R&F) do not find the source of interchangeability in the presence of two potential antecedents, nor do they find it in a structural ambiguity in the context as Holmberg (2016) does. Rather, building on Farkas & Bruce (2010), which was in turn inspired by Pope (1972), R&F attribute the interchangeability of yes and no to their ability to encode two different types of features. On this view, polarity particles in English do “double duty”: They can either signal the polarity of the answer being given or they can signal whether the present response agrees or disagrees with a prior utterance. According to R&F, absolute polarity features are responsible for the former function, while relative polarity features perform the latter.

Roelofsen & Farkas (2015) assume a polarity projection in the left periphery whose head takes a clausal argument, which is elided in the case of bare particle utterances, similar to Kramer & Rawlins (2009) and Holmberg (2016). There are two types of features that are realized on the polarity head. The absolute features [+] and [–] presuppose that the complement of the polarity head has positive or negative polarity respectively.¹¹ The relative features [AGREE] and [REVERSE] each introduce presuppositions relative to a unique most salient antecedent in the discourse: [AGREE] presupposes that the complement has the same polarity and identical propositional content to the antecedent, while [REVERSE] presupposes that the complement has opposite polarity and complementary propositional content to the antecedent. Yes is capable of realizing [+] or [AGREE], while no is capable of realizing [–] or [REVERSE]. Only one of the features it realizes needs to be present to license the polar particle.

This system is demonstrated in (12) and (13). Since positive responses to positive sentences only meet the presuppositions of the [+] and [AGREE] features, and only yes can realize those features, only yes is acceptable in (12a). Mutatis mutandis, only no is acceptable in (12b). Responses with the features [AGREE, –] or [REVERSE, +] would be infelicitous since in each case one of the features would trigger a presupposition failure.

In response to negative sentences, the situation is different. The two valid responses in (13a) and (13b) contain features that can be realized by either yes or no. Thus either particle can be used in either response. This is how R&F explain interchangeability.

In (13a), yes is licensed by the presence of [AGREE], and no is licensed because [–] is present. Likewise, in (13b) yes is licensed because of the presence of [+] and no is licensed because of the presence of [REVERSE]. Responses with the feature combinations [AGREE, +] and [REVERSE, –] are not felicitous, since one of their presuppositions would not be fulfilled.

Similar to Krifka’s analysis, R&F’s account is in principle compatible with bare particles conveying either response, but just like Krifka, they make additional assumptions that predict bare particle interpretations to be more constrained, and we return to these when we discuss the experimental results.

2.5 Summary and synthesis

Now that we have reviewed several theories of polar particles, let’s recap how they differ: First, they differ in the structural analysis of polar particles themselves. Some treat them as separate speech acts, syntactically unrelated to the following clause (Krifka 2013: the pure sentential anaphor view), others treat them as part of the syntactic structure of the following clause, which may possibly be elided (Kramer & Rawlins 2009; Holmberg 2013; 2016; Roelofsen & Farkas 2015: the single structure view). Second, they differ in their accounts of interchangeability. They attribute interchangeability to the presence of multiple potential antecedents (Krifka 2013), to a structural ambiguity in the context sentence (Holmberg 2016), or to the ability of yes and no to realize absolute or relative polarity features (Roelofsen & Farkas 2015, building on Farkas & Bruce (2010) and Pope (1972)).

Are there any arguments that can distinguish between these accounts on these two points? In the following we will make several novel observations that bear on these issues. But before discussing these observations, we note that the various accounts we discussed also differ in other ways. First, they make more fine grained claims about the possible readings of bare particles, and about which of the four possible combinations of polar particles and responses in the interchangeability paradigm in (2) are more or less felicitous. As mentioned before, we postpone discussion of these more fine-grained issues until section 4, in which we discuss results from our production experiments that bear on these predictions. Second, these accounts differ in their crosslinguistic empirical reach. The proponents of each of these accounts discuss ways that they can be extended to explain the behavior of polarity particles crosslinguistically. However, Roelofsen & Farkas (2015) and Holmberg (2016) are more ambitious than Krifka (2013) in this regard in that they each make proposals for how their accounts might make universal predictions for polar particle responses. Krifka’s account would need to be extended in nontrivial ways in order to make such universal predictions. Given space limitations and the fact that our experiments below focus only on English, we will not engage in an in depth discussion of these issues.

3.1 The form of the contradiction contour

The example in (21) exhibits a common use of the CC.¹⁸ The image in Figure 1 is a pitch track of a particpant’s performance of B’s utterance made using Praat (Boersma & Weenink 2017).

Figure 1

A visual representation of B’s utterance in (21).

According to Ladd (1980: 150), the CC begins with a rise-fall, followed by a low-rise pitch accent on the nuclear or main stress of the sentence. The initial high-fall is likely to be preceded by a rise if the utterance involves multiple syllables preceding the syllable carrying the final accent, such as in our example (21). On a monosyllable like no, the tune starts high and falls to the low pitch accent before the final rise.¹⁹

Pierrehumbert & Hirschberg (1990) transcribe the nuclear tune of the CC in ToBI as L* L-H%, while Constant (2012) transcribes it as L*(+H) L-H%. These transcriptions do not capture the fact that the CC necessarily has an initial rise or at least starts high before reaching the final low pitch accent. This pre-nuclear part of the CC is reflected in Ladd’s (1996) transcription L*+H L* L-H% and Bartels’s (1999) H+!H* L* L-H%. Hedberg et al. (2013) conduct a corpus study that lends support to Ladd’s and Bartels’s transcriptions, and they further observe that the CC may have one or more L* pitch accents before reaching the obligatory final L*L-H% nuclear tune (Hedberg et al. 2003: 2).²⁰

A problem we see with these transcriptions is that it is not clear that the initial rise or high tone is a pitch accent, that is, it does not need to align with a stressed syllable. For instance, in the monosyllabic no in (21), the tune reliably starts high despite that there can only be one pitch accent, and it is a low one. Moreover, in longer utterances, the initial rise-fall (or high-fall) does not necessarily align with a stressed syllable, contrary to what we would expect if it were the result of a pitch accent (cf. Ladd 1980: 150). Thus, we believe a more accurate transcription might be %H L* L-H%, with the possibility of iterated L* pitch accents after the initial %H in cases where multiple words are accented.

3.2 Keeping the contradiction contour separate from the phonetically similar rise-fall-rise contour

Pope (1972: 139–147) observes the use of a rising-falling-rising intonation in responses contradicting a previous statement, which she characterizes as a “B-accent”, drawing on Jackendoff (1972) who discusses B-accents in the context of contrastive topics. Utterances with a final B-accent were later analyzed as involving the so-called rise-fall-rise contour (RFR, Ward & Hirschberg 1985), which is usually transcribed as L*+H L-H%.

We believe that the tune Pope observes is not the RFR/B-accent, but the CC. Arguably, the two contours have often been confounded. In fact, Liberman & Sag (1974) analyze certain examples that are now widely agreed to exhibit the RFR as involving the CC. In response to Liberman & Sag, Ladd (1980: 148–152) gives compelling arguments for distinguishing the two, but identifies a particular set of circumstances in which they are practically indistinguishable, thus providing an explanation for the common confusion. We illustrate Ladd’s insights with the following examples:²¹

The example in (22a) has the CC with the nuclear stress falling on the object. (22b) has the RFR with subject focus, hence the nuclear accent falls on the subject. Ladd’s insight is that these two types of utterances sound very similar to each other, despite the difference in tune and prominence location. Varying the choice of tune and prominence such that we have CC + broad focus and RFR + subject focus produces two intuitively indistinguishable contours.

Ladd (1980) also helps us convince ourselves that, despite appearances, the intonational tunes in (22) are really different. If we replace the subject Jane with a polysyllabic name with stress at least three syllables in, like Alvarado, then the phonetic form of the two contours are clearly distinct:²²

Whereas the contour in (23a) rises and falls utterance initially, in (23b) the contour does not start rising until the third syllable ra. This is because RFR locates its initial rise on the stressed syllable of the focussed constituent, whereas the CC’s rise fall always occurs utterance initially.

When we try to use these two utterances in a context that motivates the use of the RFR but not the CC, we can see that they are also clearly semantically distinct:

The meaning of the CC as described by Liberman & Sag (1974) requires some element of contradiction, which is not motivated in the context in (24), hence (24a) is infelicitous, whereas the requirement is clearly met in (23), so (23a) is felicitous. The RFR, on the other hand, signals that the utterance is incomplete or that some further implication is intended.²³ This contribution is compatible with the contexts in both (23) and (24), but has a very different effect on meaning from the CC: When the CC is used in (23a), B simply conveys that she disagrees with A’s statement; when the RFR is used in (23b), B conveys that while Alvarado does like movies, there is someone else who does not (or at least remains noncommittal about others). There is no such implication in (23a). This incomplete/implication meaning of RFR is also compatible with (24), where it implies that there may be others who like movies as well, and B isn’t sure whether she has completely answered A’s question.

Thus it is clear that the CC and the RFR are distinct contours with distinct semantic contributions. While the RFR necessarily involves some sort of implication about focus alternatives, the CC necessarily involves a sense of contradiction. Ladd teaches us that when we are in doubt about which contour is in question, we should try to construct the example so that the first stress does not appear until at least three syllables in.

We turn now to the task of producing a more precise characterization of the sense in which the contradiction contour contradicts.

3.3 The meaning of the contradiction contour

About the meaning of the contradiction contour, Liberman & Sag (1974: 421) write, “This contour is appropriate (although of course optional) just when the speaker is using the utterance that bears it to contradict—he may contradict what has just been said by another, he may contradict some assumption or implication of what has been said or done by another, or he may contradict himself” [boldface ours, replaces underlining in the original text]. Defining the notion of “contradict” in this quote is not trivial, as is anticipated by the authors, who allow for contradictions of implications of both verbal and non-verbal actions. If we were to define a contradiction as two contradictory sentences in the logical sense, then we would not predict the use of the contradiction contour in responses to PQs, as in for example (25).²⁴

The apparent antecedent of the CC is not a prior assertion, but the information provided by the context and the question, which at best imply evidence in favor of the negative response (for discussions of the notion evidence in negative questions, an issue we will take up below, see Büring & Gunlogson 2000; Trinh 2014; Roelofsen & Farkas 2015; Krifka 2017). Clearly, a weaker notion of contradiction is needed.

One possible analysis is that an utterance of p(CC) requires a propositional discourse referent anchored to ¬p, and thus involves a propositional anaphor similar to polar particles under Krifka’s (2013) or Roelofsen & Farkas’s (2015) analyses. But such an analysis would miss an important difference between polar particles and the CC. Consider (26), in which A asks a positive PQ.

The judgments in (26b) through (26e) are exactly as expected given existing theories of polar particles: Since A asks a positive PQ, yes and no can only be used as in (26b) and (26c). (26d) and (26e) are unavailable. Note however, that using the CC on a positive response as in (26a) is perfectly acceptable here. An analysis that treats the CC as similar to polar particles creates the following puzzle: Why is the CC licensed on a positive response here when interchangeability is not licensed?

To explain how the CC is licensed, we will adapt ideas about contextual evidence introduced by Büring & Gunlogson (2000) for constraints on polar questions. We propose that the CC requires contextually salient evidence against the asserted proposition. We define evidence as follows:

As Büring & Gunlogson note, contextual evidence needs to be publicly available. We further note that contextual evidence can come from any kind of perceptual experience or from interlocutors’ actions, including speech acts. Moreover, contextual evidence does not necessarily affect the speaker’s commitments or expectations about p (Büring & Gunlogson 2000: 8). For example, the contextual evidence for p in (28) and (29) does not seem to affect B’s commitment to ¬p:

Using p as a label for the proposition that there are mountain lions around here, we take (28) and (29) to both be contexts in which there is contextual evidence for p by our definition in (27). In (28) evidence for p is in the form of B’s perception of scat (combined with B’s expertise), and in (29) the evidence for p is in the form of A’s assertion of p. In both cases B asserts ¬p despite the evidence for p. This presumably means that B’s commitments or expectations have not been altered with respect to p by the new evidence. So, while evidence for p is some publicly available feature of the context that would ordinarily increase the likelihood that p is true, it needn’t necessarily cause B to change her own beliefs about p.

Before demonstrating the role that this notion of evidence plays in the meaning of the CC, we note that it is independently needed for other linguistic phenomena. For example, it can be motivated based on broad principles of question answering. Consider Roberts’s (1996/2012: 21) formulation of Gricean relevance (Grice 1989):

Suppose that questions denote sets of alternative propositions (Hamblin 1973). For Roberts, a partial answer is a proposition the contextually entails that one of the Hamblin alternatives is true or false. There may be reason to recast relevance in terms of our notion of contextual evidence in (27) by adjusting (30) with the italicized part in (31).

(31), but not (30), is broad enough to be compatible even with very indirect responses to questions, such as in (32):

B’s response does not contextually entail that Jane is not coming, thus it does not provide a partial answer to the QUD according to (30). It is nevertheless an intuitively valid response. When combined with world knowledge about visiting mothers, it provides evidence for the proposition that Jane will not come to the meeting by our definition of evidence in (27), that is it increases the likelihood that the proposition is true. Since this proposition is the negation of a partial answer to A’s question, B’s response counts as providing evidence against an answer, and (31) is met.

The need for a notion of contextual evidence such as (27) is further motivated by its use in Büring & Gunlogson (2000); Sudo (2013); Trinh (2014), among others, to state generalizations about the felicity of negative questions:

Furthermore, the notion of evidence is arguably crucial in characterizing the licensing condition on rising declaratives (see Gunlogson 2001; Nilsenovà 2006; Trinh 2014; Goodhue & Wagner 2015; Farkas & Roelofsen 2017: for recent analyses of rising declaratives along these lines):

For example, in (28) in which B sees mountain lion scat, B could use There are mountain lions around here? to convey her incredulousness. In fact, a question rise on a declarative is by far the contour speakers prefer to use to convey incredulity in North American English (Goodhue et al. 2016). This suggests that an analysis of rising declaratives in terms of speaker bias in favor of the proposition would be too strong (though see Westera 2017 for a defense of a speaker bias analysis). Rather, rising declaratives seem to require contextual evidence for p, and are compatible with speaker bias in either direction.

With the notion of contextual evidence in (27) in place, we return to the task of characterizing the meaning of the contradiction contour. Following Truckenbrodt (2012), we assume intonational contours compose with proposition denoting constituents and act as partial identity functions, placing felicity requirements on the utterance.

The resulting assertion will have the same propositional content as p. It is the tension between presupposing contextual evidence for ¬p and being true iff p is true that creates the signal of disagreement that the CC is known for.²⁶²⁷

Returning to our comparison between the CC and polar particles, we can see that they are similar in that they are both dependent on previous context, but they differ in that polar particles require a discourse referent denoting a certain proposition, while the CC merely requires contextual evidence for a certain proposition. This explains the asymmetry in (26).

Our analysis of the CC is similar to that of Liberman & Sag’s (1974) in that we tie its meaning to the notion of contradiction, but it is more precise and is therefore able to address an objection that Pierrehumbert & Hirschberg (1990: 293) raise via the following example:

In (36), B is in some sense trying to contradict A’s claim that the election is not over, thus Pierrehumbert & Hirschberg note that Liberman & Sag’s analysis incorrectly predicts B’s utterance to be felicitous. Under our analysis, the infelicity is expected, since what A asserts does not present evidence against the truth of the proposition B asserts (that CBS made an announcement). Similarly, in (37) it is odd to use the CC, but if the order of the two statements is reversed as in (38), using the CC in the response is possible:

A’s claim in (37) that there are mountain lions does not provide evidence against B’s claim that Alvarado made a claim about the lack of mountain lions. However, B’s claim in (38) that Alvarado made a claim about there being no mountain lions does provide evidence against A’s claim that there are. A more vague description of the CC’s meaning as in Liberman & Sag (1974) does not predict this contrast. But our analysis of the CC in (35) combined with our characterization of contextual evidence in (27) has more empirical bite. The CC only looks for contextual evidence against the matrix proposition it combines with. It cannot see more deeply embedded propositions.²⁸ Thus in (37), it combines with p, the proposition that Alvarado said ¬q, and there is no evidence against p in the context, so the CC utterance is infelicitous. But in (38), the CC combines with q, that there are mountain lions around here, and B’s utterance provides evidence against q since B asserts p, which embeds ¬q under the verb said (see Simons 2007 for an argument that utterances of the form X said p introduce evidence for p). So while the CC cannot see embedded propositions in its complement, utterances in the preceding discourse can provide contextual evidence for propositions embedded within them, at least in some cases.²⁹

There are other observations in the prior literature that pose a challenge to our analysis, however. Pierrehumbert & Hirschberg (1990) argue that the contour we describe can also be used in completely non-contradictory speech acts such as in greetings (e.g. Good morning (CC)!). We also note here the similarity of the contour we analyze as the CC and O’Connor & Arnold’s (1973) “low bounce” intonation, which they demonstrate can be used to ask a question, among other things. If what we call the contradiction contour can really also be used in these different types of speech acts, then our characterization of its meaning may not be general enough to cover all its uses. We leave it to future work to determine if these other cases are indeed instances of the contradiction contour, or whether they may be another distinct contour.

4.2 Naturalness results

Figure 2 displays a plot for the naturalness ratings of responses to positive PQs in experiment 1.

Figure 2

Naturalness ratings of responses to positive polar questions in experiment 1.

As expected, when indicating a positive response to a positive PQ, yes is rated as highly natural and no is rated as unnatural, and vice-versa in negative responses. Yes and no are therefore indeed not interchangeable in response to positive PQs.³⁵

Figure 3 displays plots for experiments 1, 2 and 3: The experiment 1 plot (left) shows how participants rated responses to negative PQs, while the experiment 2 plot (middle) and the experiment 3 plot (right) show ratings for full sentence responses and bare particle responses respectively to negative rising declaratives.

Figure 3

Naturalness ratings of responses in three experiments. Experiment 1 (left), responses to negative polar questions. Experiment 2 (middle), responses to negative rising declaratives. Experiment 3 (right), bare particle responses to negative rising declaratives.

We observe that yes/yeah and no are overall acceptable in both positive and negative responses. Experiment 3 exhibits certain nuances to be discussed shortly, but nevertheless has a qualitative pattern that is distinct from responses to positive PQs in Figure 2. Taken together, the results indicate a high degree of interchangeability of English polar particles when used in response to negative questions or rising declaratives.

We fitted cumulative link mixed model regressions for each experiment (Christensen 2010), with random intercepts and slopes for participant and item (see Table 1). We also ran a cumulative link mixed model regression with random intercepts and slopes for participant and item on all of the data combined, so that we could check for statistically significant differences between the different experiments.³⁶

First we consider the models for experiments 1 and 2. The interaction between PARTICLE and ANSWER, which is the largest effect, is due to the fact that in positive answers, both yes/yeah and no are equally acceptable, while in negative answers, yes/yeah is rated as significantly less natural than no. Moreover, PARTICLE had an overall effect in that no responses are rated more natural than yes/yeah responses, and ANSWER had an overall effect in that positive responses are rated more natural than negative responses. These effects are driven by the fact that no is more acceptable than yes/yeah when the answer polarity is negative. No is not more acceptable than yes/yeah in general. Likewise, positive responses are not more acceptable than negative responses in general.

The pattern of the naturalness ratings for experiment 3 are somewhat different from those for experiments 1 and 2. Yeah-am not responses are still rated as significantly less natural than no-am not responses, however there is a clear main effect of ANSWER in that positive responses are significantly less natural than negative responses in general.

Considering now the model for all of the data, we note significant differences between the data from experiment 1 and 2, and between experiment 1 and 3: Overall, the polar particle responses are rated slightly less natural in response to polar questions than in response to rising declaratives. We had no expectations about this, and do not expect there to be a theoretical motive behind it.

As one would expect from Figure 3, there is a large effect of ANSWER polarity on the difference between experiments 1 and 3. Positive (am) responses were significantly less natural in experiment 3 than in experiment 1. There are no other significant differences between experiment 1 and the other two experiments.

4.3 Intonation results

The recorded responses in experiments 1, 2 and 3 were annotated for intonational contour by an RA and the first author. We annotated contours on polar particles and their following sentences separately. After listening to a subset of the data, we determined the vast majority of productions fell into one of three intonational categories: Declarative fall, contradiction contour (CC), and rise fall. Intonations were marked “unclear/other” if it did not fit any of these categories, and “problematic” in case of disfluencies, recording errors, etc. Polar particles were marked as “none” when the participant produced a single contour over the whole utterance.

The form and meaning of contradiction contours were discussed in section 3. Declarative falls have a high final pitch accent followed by a fall, H* L-L%. Rise fall intonation is an upstepped high pitch accent that can appear on either the particle or the following sentence.

Counts and percentages of intonations used in response to PQs and rising declaratives in experiments 1, 2 and 3 are summarized in Table 3.³⁸

Considering Table 3, we can see that declarative falling intonation is by far the most frequent contour observed, followed by CC, and then rise fall. There were relatively few contours that fell into the other/unclear category, suggesting that the annotation scheme was well suited to the data.

Cooper & Ginzburg (2011) claim that when no is used to convey a positive response to a negative PQ, it will bear a distinct rise fall tune. We think that our rise fall category corresponds to what they have in mind, however it does not have the restricted distribution they have suggested. While it does appear more frequently in positive responses to negative sentences, it is well represented in negative responses as well, as demonstrated in Table 4. Moreover, it was produced relatively infrequently (see percentages). Thus it does not seem likely that the rise fall is the special intonation hypothesized by theorists to be reserved only for positive responses to negative sentences.

Before moving on, we note that we believe that the production of rise fall in our data set was correlated with verum focus prominence shifts, that is prominence shifts to the auxiliary, for example Yes, I AM coming. Roelofsen & Farkas (2015) argue that verum focus is obligatory in positive disagreeing responses, but we note that, like rise fall, it appeared in both positive and negative responses in our data. We believe this makes intuitive sense: Verum focus can emphasize the truth of an assertion regardless of whether it has the same or opposite polarity of the preceding sentence. E.g. when responding to the negative PQ Are you not coming to the presentation?, both verum focus and rise fall intonation can appear on either a positive response (No, I AM coming), or a negative response (No, I’m NOT coming).

The tune with the most interesting distribution in our results was the contradiction contour (CC): It was produced almost exclusively in positive responses to negative sentences. Figure 4 shows the proportion of CC that participants produced in response to various antecedents: Positive polar questions (left), negative polar questions (second from left), negative rising declaratives (second from right), and in bare particle responses to negative rising declaratives (right). The top panels show the proportion of CC produced by participants on the particles themselves, while the bottom panels show the proportion of CC on the following sentences. Positive sentence answers are in blue, negative in purple. For instance, the Exp1-PosPQs column (leftmost) shows that the CC was produced on the sentence in 36% of trials in which positive sentences followed the particle no, but only in 2% of trials in which negative sentences followed the particle no.

Figure 4

Proportion of CC produced on particles and on sentences in response to three different kinds of sentences. (From left to right) responses to positive polar questions, responses to negative polar questions, responses to negative rising declaratives, and bare particle responses to negative rising declaratives.

Descriptively, the CC appears quite frequently in positive responses (blue), but hardly ever in negative responses (purple), suggesting an effect of ANSWER polarity. In each case, the rate of CC is greater on following sentences than on the particles themselves. Rates of CC are greatest in response to rising declaratives (experiments 2 and 3), followed by responses to negative polar questions (experiment 1-Negative), and with the least amount produced in response to positive polar questions (experiment 1-Positive).

Furthermore, in responses to PQs only, the CC appears more frequently on no than yes, suggesting an effect of PARTICLE choice.

We fitted a mixed effects logistic regression for the combined data with random intercepts and slopes for participant and item (for discussion on the advantages of mixed effects regressions, see Baayen 2008; Jaeger 2008; Barr et al. 2013). The dependent variable was whether or not the CC was produced. The model tested whether it matters that the response was positive or negative (ANSWER), and that yes or no was used (PARTICLE). It also tested whether it matters that the context sentence was positive or negative (CONTEXTPOS.VS.NEG., the difference between the positive half of the experiment 1 and the rest of the data), whether the context consisted of a polar question or a rising declarative (CONTEXTPQ.VS.RISEDEC, the difference between the negative half of experiment 1 and experiments 2 and 3), and whether the particle was bare or not (CONTEXTFULL.VS.BARE, the difference between experiment 2 and experiment 3), as well as interactions between PARTICLE and these latter predictors (see Table 5).

The effects of ANSWER and POLARITY just mentioned are borne out by the model. We also found several other effects: More CC is produced in response to negative PQs and rising declaratives than in response to positive PQs (CONTEXTPOS.VS.NEG). More CC is produced in full sentence responses to rising declaratives than bare particle responses (CONTEXTFULL.VS.BARE). Finally, as one might expect from plot 4, whether yes or no was used had a fairly large effect on the difference in CC production between responses to positive and negative sentences (PARTICLEY.VS.N.:CONTEXTPOS.VS.NEG) and on the difference between PQs and rising declaratives (PARTICLEY.VS.N.:CONTEXTPQ.VS.RISEDEC).

5.2 Results

The results showing the percentage of positive interpretations chosen are visualized in Figure 5. Results for yes are in blue, no in purple. Particles that were originally followed by a positive sentence are in the left panel, those originally followed by a negative sentence are in the right panel. Within each panel, particles bearing declarative falling intonation are on the left, particles bearing the CC are on the right.

Figure 5

Percent positive I am interpretations of bare particle responses by PARTICLE (yes vs. no, INTONATION (CC vs. Dec), and ORIGIN (whether the particle was originally part of a positive or negative response in the production study that it was culled from).

The CC made participants more likely to interpret the particle as conveying a positive answer. There were also more positive interpretations if the particle yes was used. For the particle yes, it didn’t seem to matter whether it originated from a positive or negative response—the rate of interpreting it positively was roughly the same. However, for the particle no, it mattered whether it was originally followed by a positive or a negative sentence, with the latter making negative interpretations more likely. So besides obvious main effects of PARTICLE and INTONATION, it looks like there may be an interaction between PARTICLE and ORIGIN.

We fitted a logistic mixed effects regression, which included PARTICLE, INTONATION, ORIGIN, and all interactions, with random effects and slopes for participant and item (see Table 6).

The largest significant effect was for INTONATION. Particles bearing the CC were significantly more likely to be interpreted as a positive sentence, e.g. I am coming to the presentation (26% positive interpretation with Dec, 65% with CC). There was also an effect of the choice of PARTICLE. Yes responses were significantly more likely to be interpreted as conveying a positive sentence response, e.g. I’m coming to the presentation (30% for no, 53% for yes).

Whether an utterance was originally uttered in a negative agreeing response or a positive disagreeing response (our factor ORIGIN) did not significantly affect interpretation (p > 0.32), nor was there an interaction between ORIGIN and INTONATION (p > 0.39). This gives our intonational annotation some validation—there could have been some crucial prosodic cues revealing the intent of the speaker that is not captured by annotating whether they used the CC or not, or maybe what we annotated as CC could have been quite different depending on which type of utterance it occurred in. But there is no evidence for either of these conceivable problems with the way we annotated the data.

On the other hand, participants were more likely to interpret no responses as agreements with the negative question when the no sound file came from a negative agreement response in experiment 1 than when it came from a positive disagreement response (the interaction between ORIGIN and PARTICLE in Table 6). We make two observations about this effect: First, because there were relatively few CCs produced in confirming responses in the production experiments, the perception experiment could not be completely balanced. That is, there were only three noes followed by negative sentences that were produced with the CC in experiment 1, and only two yeses. To have had a completely balanced design, we would have needed eight of each. Therefore, the data for this experiment includes relatively few observations in which polar particles that were originally followed by a negative sentence bore the CC (the rightmost dots in figure 5—this is likely why the error bars are larger here than elsewhere in the plot). Since there are fewer negative-origin CCs, we might expect any effect of ORIGIN to be attributable to INTONATION. That is, fewer CCs result in more negative interpretations, given the strong effect that the CC has on interpretation.

The second observation is that despite this lack of balance leading to possible interference by INTONATION, it must be noted that even the negative-origin no responses bearing Dec intonation were interpreted as a negative response more frequently than the positive-origin no responses with Dec intonation. Thus, it seems likely that this interaction effect between PARTICLE and ORIGIN is at least in part genuine: Negative-origin noes must sound more negative to our participants than their positive-origin counterparts. This means that there is likely an effect of prosody on these no responses not captured by the intonation annotation. We note that this effect is smaller than the main effects of INTONATION and PARTICLE.

5.3 Discussion

The questions we set out to answer were: How are bare polar particle responses to negative sentences interpreted? Does the contradiction contour (CC) affect the interpretation of bare particles? We found that in response to negative PQs, bare yes is interpreted as a positive response at about chance level (53% of trials), while bare no is interpreted as positive in 30% of trials. However, intonation has a big effect on bare particle interpretation, both in the case of yes and no. Particles bearing the CC are interpreted as positive in 65% of trials, while particles bearing a declarative contour are interpreted as positive in only 26% of trials.

None of the theories discussed above explicitly considers predictions for the interpretations of bare polar particles that have different intonations. The theory of Krifka (2013) predicts that in order to convey a positive response to negative PQs, no must be followed by an overt sentence. Holmberg (2016) makes the same prediction for yes. Roelofsen & Farkas (2015) predict negative interpretations of bare particles to be preferred, other things being equal. One might read this as meaning that a systematic manipulation of intonation could alter the expected interpretation. On the other hand, R&F claim that positive interpretations of polar particles will require an overt following clause with verum focus. Thus, our results are not directly anticipated in the previous literature. However theorists have suggested that intonation could have some effect, and that positive responses to negative questions in particular would bear a special intonation, even if that intonation is predicted to appear on a following clause. Our results lend empirical support to this intuition, but expand on it by identifying for the first time that this unique intonation is the CC, that it can appear on bare particles themselves, and that it has a large effect on the interpretation of bare particles.

Given our proposed meaning for the CC, we could ask why positive interpretations are not at 100% when the CC is present. After all, in order for the CC to be licensed on a bare particle in response to a negative PQ, the intended response must be positive, right? Actually, not quite. Note that using the CC on a negative response to a negative question is possible in principle, if there is also positive contextual evidence (in addition to the negative evidence necessary to license the negative question). The contexts in our perception experiment may have been open enough to leave some room for listeners to posit that there may have been such evidence. Sometimes, even asking a negative PQ can suggest that the speaker considers there to be some evidence for p (in addition to evidence for not p). For example, the following question (adapted from examples by Trinh 2014) both suggests contextual evidence that B is not left-handed (antecedent for CC in (44a)), and given the lower odds of being left-handed the formulation of the question suggests a prior belief of A that B is left-handed, which B can take as positive evidence (antecedent for CC in (44b)):

The fact that negative PQs can license CC in both responses might explain why not all CC-bearing particles were interpreted as positive.

The main effect of PARTICLE is that yes responses were significantly more likely than no responses to be interpreted as conveying a positive sentence response. Viewed through the lens of Krifka’s theory, this is expected since a pragmatic constraint is in effect, *NONSAL: Being anaphoric to a less salient discourse referent is dispreferred. Since the negative discourse referent is typically less salient, both yes and no prefer picking up the inner, positive discourse referent, which results in a positive response interpretation for yes and a negative interpretation for no. R&F also predict no to be more frequently interpreted as a negative response, since it realizes the [–] feature of the [AGREE, –] response. However, they predict positive responses to the be the most marked, thereby requiring an overt following clause, so they predict that bare particles will more likely be interpreted as negative responses in general. This latter prediction does not fit with the effect we found here. Holmberg predicts bare yes should only be interpreted negatively, which is exactly the opposite of the main effect of PARTICLE in our experiment.

Suppose Krifka’s theory is right, participants are driven by *NONSAL to interpret polar particles as picking up the inner antecedent. But now we have a question: If the positive antecedent is preferred, why is yes with declarative intonation only interpreted as positive in under 50% of observations? It should be interpreted positively much more of the time. This can be explained if there is a preference to use the CC whenever possible. Failing to use the CC in a context where there is negative evidence (such as in response to negative PQs) then licenses the inference that the speaker must agree with the negative evidence. The absence of the CC is a cue in favor of the outer, negative antecedent.⁴⁰

There is an aspect of Kramer & Rawlins’s (2012) results that diverge from ours. They found that when trying to convey a positive response (I am), bare yes is mostly judged false, while no is judged more ambivalently. In our experiment, yes was more likely than no to be interpreted as conveying a positive response. The discrepancy might be due to the fact that Kramer & Rawlins did not control for intonation. Our participants were more likely to produce the CC on no than on yes (production experiment 1), and bare particles carrying the CC are more likely to be interpreted as positive (perception experiment). It is plausible then that Kramer & Rawlin’s participants imagined more no responses with the CC when silently reading the dialogues, leading to more positive interpretations, while yes was imagined with more Dec intonation. This would lead to more negative interpretations of yes than no, and therefore more judgments of falsity when the particle was meant to convey a positive response in K&R’s experiment. We note that the possibility of such issues is a good argument in favor of controlling for intonation when asking participants for judgments about bare particle responses.

Before moving on, we would like to note that the interpretation patterns found here differ in a substantive way from the naturalness ratings found in the production experiments. The latter were best predicted by the theory of Roelofsen & Farkas (2015), especially the fact that yes and no were rated equally natural when conveying a positive response. On the other hand, as just argued above, Krifka’s (2013) theory best predicts the preference to interpret yes as a positive response more frequently than no in the perception experiment. This difference in results will be discussed in detail in section 7.

6.2 Results and discussion

From Figure 6, it looks like there is an interaction between PARTICLE and ANSWER with yes being rated as less natural than no when giving a negative response, as we saw in the production experiments in section 4. The polarity of the CONTEXT preceding the antecedent appears to be unlikely to have any effect, except perhaps on yes, I’m not responses, which appear to be rated slightly more natural in negative contexts (median 5 in negative contexts to median 4 in positive contexts). If this three-way interaction is significant, it would lend support to Krifka’s hypothesis that preceding context polarity modulates naturalness ratings. The null hypothesis is that the preceding context has no effect.

Figure 6

Naturalness ratings by three factors: PARTICLE (yes vs. no), ANSWER (I am vs. I am not), and CONTEXT (whether the sentence preceding the sentence that yes and no respond to was positive or negative).

We fitted a cumulative link mixed model regression with all three factors and all possible interactions, with random intercepts and slopes for participant and item (see Table 7). We found a significant main effect of PARTICLE, as well as a significant interaction between PARTICLE and ANSWER, as expected and like in the other production experiments. We did not find a significant three way interaction (p > 0.67), nor were any other factors significant. A likelihood ratio test revealed no difference between this model and one with only PARTICLE, ANSWER and their interaction (p > 0.46).

Therefore, we fail to reject the null hypothesis. No, I’m not responses are rated more natural than their yes counterparts regardless of context, which is predicted by Roelofsen & Farkas’s (2015) and Holmberg’s (2016) accounts. However, we note that, according to Meijer et al.’s (2015) results, context polarity had no effect on naturalness in German either, yet the result did not clearly fit with R&F’s predictions. Therefore, when taking our results together with Meijer et al.’s, the results of both experiments demonstrate that controlling for the polarity of a preceding context sentence has no effect on preference patterns in either English or German, at least not in this experimental paradigm.

Thus, it seems that the answer to question iii, “If the negative sentence that the polar particle responds to is itself responding to a negative sentence, are preference patterns affected, and in particular is yes now more acceptably interpreted as a negative response?” is no. Naturalness ratings of particle responses appear to be insensitive to systematic manipulation of the polarity of context sentences.

Nevertheless, we think there is some merit to the intuition that in a context like (45), yes more naturally indicates a negative, agreeing response, whether as a bare particle or with a following overt sentence. We point out that we only fail to reject the null hypothesis here, and that it is possible that the experiment is underpowered. In future work, we would like to see other experimental designs used to test whether context can affect preference patterns. If, after further testing, yes-negative responses remain dispreferred regardless of context, then it seems likely that a context-insensitive theory is on the right track.