1 Answering systems

Natural languages display an array of grammatical strategies to answer polar questions. In this paper we focus on answers consisting of a bare polar particle, such as yes and no in English. Pope (1976) is one of the earliest contemporary discussions of the typology of answering systems.¹ Pope’s categories are very close to the features invoked by Roelofsen & Farkas (2015); our presentation here is influenced by the latter treatment. These authors claim that two binary features must be adopted in the taxonomy of answers.² The first feature, absolute polarity, relates to the polarity of the sentence radical in the long answer. Its values are positive and negative. In (1), one can see short answers and their long counterparts (for the acronyms, see below):

The English particle no in (1a–ii) and (1b–i) is used to convey a negative answer because the corresponding long answer is syntactically marked as negative (it includes the sentential negation -n’t). Analogously, particle yes in (1a–i) and (1b–ii), and particle no in (1b–iii) is used to convey a positive answer because the long answer includes no sentential negative operator.

The second feature we will call relative polarity, and we set its values as agreement and disagreement. Relative polarity encodes the relationship between absolute polarity and the polarity of the question that is being answered. In these terms, (1a–i) (1b–i) are agreeing answers, because their absolute polarity matches the polarity of the interrogative sentences (1a) and (1b) respectively; (1a–ii), (1b–ii) and (1b–iii) are disagreeing answers because they do not match that same polarity (we will return to the optionality between (1b–ii) and (1b–iii) shortly).

Absolute and relative polarity can be regarded as two binary features that combine into four combinations, which we will indicate as Positive Agreement (PA), Negative Disagreement (ND), Negative Agreement (NA) and Positive Disagreement (PD). Pope (1976) and Roelofsen & Farkas (2015) agree that for cognitive reasons, certain combinations are crosslinguistically more marked than others. First, they reason, there seems to be a natural tendency to associate values P and A, and N and D, respectively. As a result, PA and ND are comparatively unmarked moves. Between them, though, ND is the most marked, because disagreement is a marked move with respect to agreement. NA and PD are marked in virtue of their departing from the natural association just mentioned. Of the two, PD is the most marked, because it is a disagreeing answer. The following markedness scale is then derived:

These answer types are expressed differently in different languages. Here, we will only concern ourselves with languages that make extensive use of responding particles (for discussion of languages not relying on responding particles, see Jones 1999, Holmberg 2016 and the references cited therein). The two main types are the Agreement-Disagreement languages (henceforth, A-D) and the Positive-Negative languages (P-N).³

The two patterns differ in the way negative polar questions are answered. English, in (1) above, exemplifies the P-N system. In a P-N language, the answering pattern is sensitive to the polarity of the question: one particle (such as English no) expresses either disagreement with a positive question, as in (1a–ii), or agreement with a negative question, as in (1b–i); vice versa, another particle (such as English yes) expresses either agreement with a positive question, as in (1a–i), or disagreement with a negative question, as in (1b–ii).

P-N languages are often exemplified with English data, even though the consistency of the relevant patterns has only recently been thoroughly investigated. The choice of particle for PD reportedly allows for a degree of optionality: it is often reported for various supposedly P-N languages that as an alternative to the expected yes-particle, the no-particle can also be used in PD answers, as in (1b–iii) above (Kramer & Rawlins 2010; Roelofsen & Farkas 2015). Recent experimental results by Goodhue & Wagner (2017) confirm this optionality.⁴

In A-D languages, one particle is used to express agreement with the propositional content of the question and the other to express disagreement with it, irrespective of the polarity of the question. This pattern is exemplified with Japanese in (3):

Finally, a small subset of P-N languages have three particle systems: besides the usual yes-particle and no-particle, they have a third particle, which is specialized for PD answers:⁵

These three types describe the majority of answering systems with responding particles.

In this paper we will be concerned with one P-N system, that of Italian. We will show that the answering pattern is more complex than (1), and in particular, it is affected by the presence of a narrow focus in the question. We will provide experimental evidence showing that a fronted focus in the question induces a surprising shift to an A-D answering pattern.

The paper is organized as follows. In section 2, our experimental work on Italian is presented in detail: our results reveal that the presence of a fronted focus in polar questions induces a shift in the answering pattern from P-N to A-D. We then turn to the analysis of our results. Recent theoretical approaches to answering particles fall into two broad categories. One line of research assumes that answers consisting in a particle, such as yes or no, actually involve sentential structures affected by ellipsis. In section 3, we propose an analysis of our empirical results in this vein. We argue that in answers to a negative polar question with a narrow focus, syntactic intervention prevents the responding particle from agreeing with the sentence-internal polarity, causing a shift to the A-D pattern. In section 4, we discuss an alternative approach that belongs in the other major group of approaches to answering particles: the one that assumes that answering particles involve forms of propositional anaphora. Farkas & Bruce (2010) and Krifka (2013) belong to this second group.⁶ In order to account for our results, we will rely on Krifka (2013) and argue that focalization affects the relative salience of the propositional discourse referents introduced by the polar question. Section 5 presents the results of a follow-up experiment we carried out to investigate the effect of focalization in situ within the polar question. Section 6 sums up and discusses some theoretical implications and empirical predictions of the two approaches.

2 Nuclear Polar Questions

Having characterized the general answering patterns to polar questions, we now focus on Italian to discuss an interesting deviation from the basic P-N pattern.

An important property of polar questions is the fact that they can host a focal structure involving a narrow focus. This property has been investigated mostly in connection with languages where the focal constituent is displaced to a left-peripheral position and is accompanied by a focus particle, such as Finnish ko (Holmberg 2016) or Russian and Bulgarian li (King 1994; 1995; Dukova-Zheleva 2010). In Italian too, a narrow focus can be fronted in a polar question, as exemplified in (5):

Following the terminology of Cruschina (2012) and Bianchi & Cruschina (2016), we will call this type of question nuclear polar question. Ordinary polar questions, without any visible focus-background partition, we will call total polar questions.

Servidio (2014) observed that negative nuclear polar questions (featuring a narrow focus and sentential negation) elicit an answering pattern that reverses the expected P-N one: the preferred option to express an agreeing answer to a negative nuclear question is sì, which seems to disregard the negative polarity of the question. We therefore decided to experimentally test the answering pattern to nuclear vs. total negative questions.

In section 2.1, we give a survey of the literature on the Italian answering system in general, to serve as background to our research on nuclear questions. In section 2.2, we discuss an experiment that investigate questions with fronted narrow foci; a second experiment dealing with questions with focus in situ is discussed in section 5 below.

2.2 Methods and results

We set up a web-based experiment based on a two-alternative forced choice paradigm hosted by IbexFarm.⁸ The presentation was both audio and visual. The dependent variable was the factor “choice of answer”, with values “sì” and “no”. As independent variables, we had two crossed binary factors (for a total of four conditions). First, “type of questions”: negative total questions vs negative nuclear questions. Second, “state of affairs”: in each experimental set, given a question of the form p?, we tested it both in contexts where p was the case and in contexts where not p was the case (for the presentation of contexts, see below).

We prepared 16 experimental sets of 4 sentences each and divided them in four lists with the Latin Square design, so that each subject saw only one stimulus from each set. The presentation was pseudo-randomized in blocks. As controls, we had sixteen positive polar questions, both total and nuclear, with the same two crossed binary factors (“type of questions” and “state of affairs”). Thus, in the study as a whole, the answering patterns to both positive and negative polar questions have been investigated.

Forty subjects, native speakers of Italian, were administered the test. The trials consisted of a contextual description of a state of affairs that introduced the fragment of a fictional dialogue. After the description of the context, a character asks a polar question. The context and the question were presented in written form and also read aloud by two distinct speakers. The experimental subjects must take the role of interlocutor and answer by choosing either sì or no (bare particles only, no longer answer allowed).

Each trial was preceded by a screen with a written message that informed the participant that next stimulus was charging. After a second, the trial appeared. From the onset of the trial, the text of the contextual description (written in italics) was displayed, as well as the question and the two possible answers (written in blue). After 20 ms from the trial onset, the audio was automatically played back. The audio consisted of a first voice that read the contextual situation aloud, followed by 50 ms of silence, a short beep (40 ms.) and, after 30 ms. of silence, a second voice that read the question. During the audio play back, the text was visible and persisted on the screen after the end of the audio. Participants were allowed to press a button to restart the (entire) audio. In order to express their preference for either sì or no, the participants had to click with the mouse on the text displaying the two alternative answers. The entire experiment (including a short familiarization session of three trials with unrelated material) lasted on average 40 minutes.

One complete experimental set is exemplified below. In square brackets, the values for the two independent factors: nTQ = “negative total question”, nNQ = “negative nuclear question”, p = the speaker must spray the begonias, ¬ stands for logical negation, contexts translated into English:⁹

1. (7)

1. [NTQ, STATE OF AFFAIRS: ¬p]
2. Your garden is infested with parasites. Many different plants are affected. You buy a powerful insecticide. The drug is a liquid that must be carefully sprayed on the affected plants. The seller, though, warns you not to use it on your begonias, because it is very aggressive and might damage the plant. A friend of yours volunteers to spray the insecticide himself, but you forget to tell him about this problem. When he is about to spray the begonias, you stop him brusquely. So he asks you:

1.  
1. a.

1. Non
2. not
1. spruzzo
2. spray-PRS.1SG
1. le
2. the
1. begonie
2. begonias
1. con
2. with
1. l’insetticida?
2. the-insecticide
1. ‘Am I not to spray the begonias with insecticide?’

2. (i)	Yes.
   (ii)	No.

1. (8)

1. [NTQ, STATE OF AFFAIRS: p]
2. Your garden is infested with parasites. Many different plants are affected. You buy a powerful insecticide. The drug is a liquid that must be carefully sprayed on the affected plants. The product is well tolerated by plants, so you can use it also on your beloved begonias. A friend of yours volunteers to spray the insecticide himself. When he is about to spray the begonias, you spot a huge hornet on his shoulder. “Stop!”, you tell him, and you send away the hornet with your glow. He misunderstands the situation and asks you:

1.  
1. a.

1. Non
2. not
1. spruzzo
2. spray-PRS.1SG
1. le
2. the
1. begonie
2. begonias
1. con
2. with
1. l’insetticida?
2. the-insecticide
1. ‘Am I not to spray the begonias with insecticide?’

2. (i)	Yes.
   (ii)	No.

1. (9)

1. [NNQ, STATE OF AFFAIRS: ¬p]
2. Your garden is infested with parasites. Many different plants are affected: among them, a rose bush and a flowerbed with begonias. You buy a powerful insecticide. The drug is a liquid that must be carefully sprayed on the affected plants. The seller, though, warns you not to use it on the begonias, because it is very aggressive and might damage the plant. Your friend volunteers to spray the insecticide himself, but he is unsure if he gets his facts straight. So he asks you:

1.  
1. a.

1. Le
2. the
1. BEGONIE
2. begonias
1. non
2. not
1. spruzzo
2. spray-PRS.1SG
1. con
2. with
1. l’insetticida?
2. the-insecticide
1. ‘(Is it) the BEGONIAS (that) am I not to spray with insecticide?’

2. (i)	Sì.
   (ii)	No.

1. (10)

1. [NNQ, STATE OF AFFAIRS: p]
2. Your garden is infested with parasites. Many different plants are affected: among them, a rose bush and a flowerbed with begonias. You buy a powerful insecticide. The drug is a liquid that must be carefully sprayed on the affected plants. The seller, though, warns you not to use it on the roses, because it is very aggressive and might damage the plant. A friend of yours volunteers to spray the insecticide himself, but he is unsure if he gets his facts straight. So he asks you:

1.  
1. a.

1. Le
2. the
1. BEGONIE
2. begonias
1. non
2. not
1. spruzzo
2. spray-PRS.1SG
1. con
2. with
1. l’insetticida?
2. the-insecticide
1. ‘(Is it) The BEGONIAS (that) am I not to spray with insecticide?’

2. (i)	Sì.
   (ii)	No.

The negative nuclear polar question conditions were designed with a context that introduced salient alternatives to the focal constituent: in the example above, roses and begonias were mentioned. The factor “state of affairs” was manipulated by changing the description accordingly: in one condition the begonias were the ones that were not to be sprayed, in another condition the roses were the ones.

The negative total polar question were all, by design, of the inner negative kind (Ladd 1981). In order to achieve that, the context was enriched to support two different biases in the question (Büring & Gunlogson 2000): a previous epistemic bias that p, and a current evidential bias that ¬p. In the begonias example, in both total question conditions it was suggested that the character asking the question assumes that he must spray the begonias (he has been given the task to spray the whole garden). In addition, it was also made clear that the character had evidence that led him to think that he must not in fact spray the begonias: in one condition, the evidence is genuine; in the other condition, the evidence is the product of a misunderstanding (the other character did not mean to stop him from spraying the begonias).

The results provided a clear confirmation for the hypothesis of an exceptional answering pattern to negative nuclear polar questions. First, let us look at the results for positive polar questions (i.e., the controls), in Figure 1. On the vertical axis is the probability of choosing sì over no. On the horizontal axis, the two values of the factor “state of affairs”. The answer choice for total and nuclear polar questions are drawn in solid red and dotted blue, respectively. We can see that the selection of the particle entirely depends on the state of affairs described in the context: no is used to express disagreement with p (i.e., ¬p) and sì to express agreement. The type of question (nuclear vs. total) does not have any impact on the selection of the particle: the two lines overlap perfectly. Thus, with positive polar questions we observe the expected P-N answering pattern, and the presence of a narrow focus in the question has no impact on the choice of the particle.

Figure 1

First experiment: probability of sì over no in answers to total positive questions and nuclear positive questions with fronted foci.

In answers to negative polar questions, instead, a very different pattern emerges, as shown in Figure 2. In answers to negative total questions, sì is used for PD and no for NA, as expected for a P-N language. On the contrary, in answers to negative nuclear questions, sì is used for NA and no for PD. Thus, the answering pattern to positive and negative nuclear questions corresponds to the A-D pattern exemplified in (3) with Japanese.

Figure 2

First experiment: probability of sì over no in answers to total negative questions and nuclear negative questions with fronted foci.

As summarized in Table 1, the answers to negative polar questions were fitted with a multi-level mixed effects regression with log odds of a sì response as the dependent variable, and “question type” (total vs. nuclear) and “state of affairs” (agreement vs. disagreement) as fixed effects. The model was specified with a deviation coding in which the model’s intercept refers to the grand mean. The most complex random effect structure justified by the data included by-item and by-subject intercepts and by-subject slopes for the effect of “question type”. No main effect of “question type” and “state of affairs” is significant, while their interaction is extremely significant and shows a high coefficient (see Table 1). In other words, the effect of each level of each independent factor strongly depends on the level of the other factor. As shown in Figure 2, the two factors give rise to a perfect cross-over interaction.

Table 1

First experiment: summary of the statistical model.

Formula: answer ~ question.type * state.of.affairs + (question.type | subject) + (1 | item)
AIC	BIC	logLik	deviance	df.resid
636.5	672.6	–310.3	620.5	664
Number of observations = 640; subject = 40; item = 16
Fixed effects:
	Estimate	Std. Error	z–value	Pr(>|z|)
(Intercept)	–0.28487	0.15584	–1.828	0.0676
question.type1	0.04399	0.28378	0.155	0.8768
state.of.affairs1	0.19697	0.25379	0.776	0.4377
question.type1:state.of.affairs1	–6.74981	0.52591	–12.835	<0.001	***

3 An ellipsis approach

Our experimental evidence shows that in Italian, the basic P-N answering pattern shifts to the A-D pattern when the polar question contains a fronted narrow focus. The two patterns are indistinguishable in answers to positive questions (Cf. Figure 1), but they differ sharply in answers to negative questions: in the P-N pattern, the negative particle no is used to confirm the negative proposition expressed by the sentence radical of the question, while in the A-D pattern, the “positive” particle sì is used to confirm it.

In this section, we discuss our results from the perspective of one influential approach to polar particles, which takes them to introduce an elliptical clausal structure (Kramer & Rawlins 2012; Holmberg 2013; 2016). We will first introduce our syntactic assumptions and then develop on the basis of these an account of the answering pattern in nuclear polar questions, according to which the fronted focus yields an intervention effect blocking agreement between the left-peripheral polar particle and the clause-internal polarity of the sentence radical. We will then compare our proposal to previous ellipsis analyses of polar particles.

3.2 Analysis of the data

With this background, we can now propose two realization rules for the Resp layer in Italian:

(18)	a.	[–] ⇒ no
	b.	Elsewhere ⇒ sì

Rule (18a) states that a Resp layer containing exactly one negatively valued feature is spelled out as no. (18b) is an elsewhere rule, stating that in all other cases the Resp head is spelled out as sì. Let us now consider how these rules apply to derive our experimental data, which we summarize in (19) below.

1. (19)

1. 		agreement	disagreement
   i	pTQ (control)	sì	no
   ii	nTQ	no	sì
   iii	pNQ (control)	sì	no
   iv	nNQ	sì	no

Consider first answers to a positive total question (pTQ) like (20):

(20)	[IntP PQ [ Gianni è arrivato]]?

An agreeing answer will have an unvalued REL feature in Resp (indicated by the symbol ∅ in (21)); in addition, the unvalued POL feature does not receive any feature value via Agree, since the internal polarity of the elliptical sentence radical is also unvalued (i.e. positive): as a result, the Resp layer contains two unvalued features (21a). These receive a positive value by default; the elsewhere rule (18b) applies, and Resp is spelled out as sì (21b). From the interpretive viewpoint, the positive Rel feature confirms the non-negative proposition expressed by the sentence radical (21c).

(21)	Agreeing answer to a positive total question
	a.	[RespP {[REL:∅], [POL:∅]} [Gianni è arrivato]]
	b.	{[REL:∅], [POL:∅]} ⇒ {[REL: +], [POL: +]} ⇒ sì
	c.	⟦RespP⟧ = ⟦REL:+⟧ ([λi.ARRIVEi(G)])
		= ([λi.ARRIVEi(G)])

On the other hand, a disagreeing answer will be characterized by a negatively valued REL feature, while the POL feature remains unvalued as above (see (22a)). After the application of the default rule, Resp contains just one negatively valued feature, hence it is spelled out as no, by an application of rule (18a) (see (22b)). At the interpretive level, the [REL:–] feature confirms the proposition contrary to the one expressed by the elliptical sentence radical, as shown in (22c).

(22)	Disagreeing answer to a positive total question
	a.	[RespP {[REL: –], [POL:∅]} [Gianni è arrivato]]
	b.	{[REL:–], [POL:∅]} ⇒ {[REL:–], [POL:+]} ⇒ no
	c.	⟦RespP⟧ = ⟦REL:–⟧ ([λi.ARRIVEi(G)])
		= (by (15b)) (λpst.¬p) ([λi.ARRIVEi(G)])
		= ([λi.¬ARRIVEi(G)])

Let us now consider a negative total question like (23):

(23)	[IntP PQ [ Gianni [NegP non[POL:–] è arrivato]]]?

Here, an agreeing answer will have an unvalued REL feature; on the other hand, the unvalued POL feature in Resp receives the negative value via Agree with the clause-internal polarity of the elliptical sentence radical (24a). As a result, Resp contains just one negatively valued feature, and by (18a) it is spelled out as no (see (24b)). At the interpretive level, the unmarked/positive REL confirms the negative proposition expressed by the sentence radical (see (24c)).

(24)	Agreeing answer to a negative total question
	a.	[RespP {[REL:∅], [POL:–]} [Gianni [NegP non[Pol:–] è arrivato]]]
	b.	{[REL:∅], [POL:–]} ⇒ {[REL:+], [POL:–]} ⇒ no
	c.	⟦RespP⟧ = ⟦REL:+⟧ ([λi.¬ARRIVEi(G)])
		= ([λi.¬ARRIVEi(G)])

The most complex case is a disagreeing answer to a negative total question. Here, REL inherently bears a negative value (expressing disagreement), and the POL feature inherits the negative value of the clause-internal polarity via Agree (25a). As a result, Resp contains two negatively valued features, and by the elsewhere rule (18b) it is spelled out as sì (see (25b)). At the interpretive level, [REL:–] confirms the contrary proposition to the negative one conveyed by the sentence radical, giving rise to a double negation (see (25c)).

(25)	Disagreeing answer to a negative total question
	a.	[RespP {[REL:–], [POL:–]} [Gianni [NegP non[Pol:–] è arrivato]]]
	b.	{[REL:–], [POL:–]} ⇒ sì
	c.	⟦RespP⟧ = ⟦REL:–⟧ ([λi.¬ARRIVEi(G)])
		= (by (15b)) (λpst.¬p)([λi.¬ARRIVEi(G)])
		= ([λi.¬¬ARRIVEi(G)])
		= ([λi.ARRIVEi(G)])15

This accounts for the core positive-negative answering pattern in total questions.

As mentioned in (4) above, certain positive-negative systems like German and French display a specialized particle for PD. This pattern can be easily accommodated by means of an additional rule spelling out the bundle of two negatively valued features, e.g. (26) for German:

(26)	a.	[–], [–] ⇒ doch
	b.	[–] ⇒ nein
	c.	Elsewhere ⇒ ja

Let us now turn to nuclear questions. Recall from (14) above that we have assumed that in answers to a polar question, the elliptical sentence radical contains a Focus layer, by syntactic isomorphism to the preceding question. Our claim is that, since the Focus layer syntactically intervenes between the Resp layer and the clause-internal polarity, it blocks the Agree relation that can provide a negative value to the peripheral POL feature. The effects of the latter are thus neutralized, and we observe a shift to an A-D pattern.

More specifically, the intervention effect follows from featural Relativized Minimality (Starke 2001) as defined in (27):

(27)	Featural Relativized Minimality	(adapted from Rizzi 2010: (24))
	In the following configuration, where X asymmetrically c-commands Z, and Z asymmetrically c-commands Y:
	a local relation cannot connect X and Y if Z intervenes and Z fully matches the specification of X and Y in terms of the relevant features.

In the answer to a nuclear question, the POL probe in Resp corresponds to X, the clause-internal valued POL to Y, and the focused phrase is the intervener Z:

1. (28)

1. 

Importantly, the focused phrase creates an intervention effect, contrary to e.g. the subject noun phrase, because the Focus feature belongs in the same class as the POL feature, namely the class of operator/quantificational features:

(29)	Typology of features                       (adapted from Rizzi 2010: (14))
	a.	Argumental: Person, Number, Gender, Case
	b.	Quantificational: Wh, Foc, Pol,16 Measure, Frequency, …
	c.	Modifier: Evaluative, Evidential, … Manner, Measure, Frequency, …
	d.	Topic

Let us now see how this intervention effect accounts for the observed answering pattern to nuclear questions.¹⁷

As for answers to positive nuclear questions, the intervention of the Focus layer is irrelevant because the clause-internal polarity is unvalued, and there is no feature value to be transmitted via Agree. Hence, the answering pattern is identical to that observed in answers to positive total questions (cf. lines i and iii of (19)). Intervention is instead relevant in answers to negative nuclear questions like (30):

(30)	[IntP PQ [FocP GIANNIF [PolP non[POL: –] è arrivato] ~C]]?

Here the elliptical sentence radical of the answer will contain a [POL: –] feature, by isomorphism to the sentence radical of the question; the negative value could potentially be transmitted to the Resp layer by Agree, but the Agree relation is blocked by the intervening Focus layer (31a). Thus, RespP contains two unvalued features, and by the elsewhere rule (18b) it is spelled out as sì (31b). At the interpretive level, the unmarked REL feature confirms the negative proposition conveyed by the sentence radical (31c).¹⁸

(31)	Agreeing answer to a negative nuclear question
	a.	[RespP {[REL:∅], [POL:∅]} [GIANNIF [NegP non[Pol:–] è arrivato] ~C]]
	b.	{[REL:∅], [POL:∅]} ⇒ {[REL:+], [POL:+]} ⇒ sì
	c.	⟦RespP⟧ = ⟦REL:+⟧ ([λi.¬ARRIVEi(G)])
		= ([λi.¬ARRIVEi(G)])

Conversely, in the case of a reversing/disagreeing answer, REL has a negative value; the unvalued POL cannot establish an Agree relation with the clause internal [POL:–] and remains unvalued (32a). The result is a feature bundle containing just one negative value, which is spelled out as no by rule (18b) (see (32b)). At the interpretive level, the answer confirms the contrary proposition to the negative proposition conveyed by the elliptical sentence radical, and the two negations cancel out (32c).

(32)	Disagreeing answer to a negative nuclear questions
	a.	[RespP {[REL:–], [POL:∅]} [GIANNIF [NegP non[Pol:–] è arrivato] ~C]]
	b.	{[REL:–], [POL:∅]} ⇒ no
	c.	⟦RespP⟧ = ⟦REL:–⟧ ([λi.¬ARRIVEi(G)])
		= (by (15b)) (λpst.¬p)([λi.¬ARRIVEi(G)])
		= ([λi.¬¬ARRIVEi(G)])
		= ([λi.ARRIVEi(G)])

To sum up, the proposed analysis can account not only for the standard P-N answering pattern for total questions, but also for the “exceptional” A-D pattern that is observed in answers to nuclear questions, based on the idea that a narrow focus in the question induces a parallel (albeit unpronounced) focus layer in the elliptical sentence radical of the answer. In addition, the proposed featural characterization of the Resp layer straightforwardly accounts for A-D languages like Japanese, and can easily be extended to account for three particle systems like German or French.

3.3 Comparison with previous approaches

Our proposal was inspired by some previous approaches to polar particles which take them to be the outermost layer of a full-fledged, but phonologically elided, clausal structure. There is, however, one crucial difference. Kramer & Rawlins (2010) and Roelofsen & Farkas (2015), while differing in many respects, agree on the assumption that the elliptical clause of a “short” answer has the same polarity as the corresponding “long answer”, rather than the polarity of the preceding question. This causes a mismatch between the polarity of the question and the polarity of the elliptical clause in reversing answers, as shown in (33) and (34).

(33)	a.	[ Did [TP Ede did steal the cookie]]?
	b.	[ No [NegP he didn’t steal the cookie]]

(34)	a.	[ Didn’t [NegP Ede didn’t steal the cookie]]?
	b.	[ Yes [TP he did steal the cookie]]

Our proposal differs crucially in that the polarity of the elliptical sentence radical is the same as that of the preceding question, for the simple reason that the polar question is the antecedent licensing ellipsis in the answer. We regard this as the null hypothesis for ellipsis licensing. In contrast to this, the above mentioned authors are forced to assume that the sentence radical of the answer, although phonologically null, is not fully parallel to the preceding question on the syntactic and/or semantic level, because of the observed polarity mismatches.

Holmberg (2013; 2016) instead proposes that the elliptical clause is parallel to the sentence radical of the question, but the latter contains a “polarity variable”, with no defined value for the polarity feature. In the answer, the value of the clause-internal polarity variable is determined by the polar particle itself, via Agree:¹⁹

(35)	a. Is he coming?	(Holmberg 2013: 36(19))

(36)

(Holmberg 2013: 37, (20))

We differ from Holmberg in assuming that the sentence radical of a polar question always has an inherently valued polarity, namely, positive in positive questions, negative in negative questions with inner negation (in the sense of Ladd 1981): thus, the Agree relation that we propose in (17) is the reverse of Holmberg’s, and is in line with the conservative view that the (unvalued) probe c-commands the (valued) goal.

As for Holmberg’s insight that polar questions have an “open polarity”, we assume that this is directly introduced by the Polar Question operator merged above the sentence radical, which takes in input the proposition expressed by the latter and returns a polar set, consisting of the proposition itself and its negation (cf. Bianchi, Bocci & Cruschina 2016 and Bianchi & Cruschina 2016).

There is, however, one aspect of our proposal that remains stipulative: the “elsewhere condition” (18b) that yields the non-negative particle sì is stipulated to spell out either the absence of any negative feature or the presence of two negative features in Resp. This is not an entirely natural rule, in that it makes reference to the number of negative values in Resp in a way that seems inherently disjunctive. In this respect, the three-rule system of German in (26), with a specialized particle for doubly negative Resp, seems much more natural. However, it may turn out that on closer inspection even Italian is to be reanalyzed as a three-way system, if we consider Bernini’s (2001: 213) observation that in reversing answers to negative questions, the sì particle typically bears extra stress (cf. (6b)). This point requires further investigation on the prosodic realization of “short” answers.

Taking stock: the analysis proposed exploits the widespread insight that answering particles involve a deleted sentential structure and current assumptions on syntactic locality to account for the particle choice patterns. A functional projection that we label RespP hosts one or two features related to sentence polarity; different bundles of values are realized as different particles, as encoded by the realization rules in (18). In P-N systems one feature in Resp, by hypothesis, is valued via Agree with a polarity projection contained in the elliptical sentence radical. Such operation is blocked by the intervention of the fronted narrow focus in answers to negative nuclear polar questions: the agreeing feature is thus neutralized, leading to an A-D pattern.

This analysis presupposes that the P-N answering pattern for total PQs and the A-D answering pattern for nuclear PQs are absolute, in that the reverse patterns are simply underivable. The experimental results reported in section 2.2 justify this view: in each case, the ratio of preferred over dispreferred option is always approximately nine to one. Things being so, it seems fair to disregard the dispreferred options in our analysis. However, because of the very nature of our experimental methodology, relying on a forced choice task, it cannot in principle be excluded that the dispreferred particle choices might in fact be acceptable (at least to some extent: cf. Bernini 2001 and Andorno & Rosi 2015). Therefore, in the next section we will explore an alternative account which, all other things being equal, is more capable to accommodate a degree of optionality in particle choices.

4 Propositional anaphors

The second candidate account is in the terms of Krifka (2013). The author regards responding particles as propositional anaphors, whose properties are somewhat similar to those of more familiar anaphoric expression (e.g., pronouns). Just like pronouns, responding particles pick up discourse referents (DRs) that must have been previously introduced in the conversation by linguistic or non-linguistic means; however, the discourse referents are of propositional type. Krifka assumes that the utterance of certain portions of the clausal structure in conversation introduces DRs corresponding to their semantic denotations.²⁰ In (37) and (38) are two examples especially relevant to us, i.e., a positive polar question and a negative polar question, respectively:

The introduced DRs are marked in the examples by the subscript ↪. In (37), one DR, labeled d, is introduced by the TP. In (38), remarkably, two DRs are introduced instead: given the negative polar questions in (38), d refers to the proposition p, denoted by TP (that Ede stole the cookie), while d′_N refers to the proposition ¬p (that Ede did not steal the cookie, denoted by NegP).²¹

The postulated semantics for the particles is straightforward: yes picks up a propositional DR and asserts it; no picks up a propositional DR and asserts its negation. Now, since a negative total question introduces two DRs, in principle we expect four possible outcomes:²²

Krifka, working on extant descriptions of English, points out that such full optionality is not in fact observed. To account for that, he formulates two constraints on the combinations of particles and DRs. These constraints are ranked and violable, and interact in an Optimality-Theoretic fashion. The constraints are the following, with (41) dominating (42):²³

The latter will concern us only marginally: in Krifka’s discussion, its role is to account for the fact that disagreeing answers are usually more marked than agreeing answers, and consequently are often expressed by more emphatic means (e.g., a special prosodic contour or a long answer). What is crucial in the account of the exceptional answering pattern is the constraint in (41). The constraint presupposes that a salience ordering exists among DRs, and given two or more DRs in a conversation, reference to the most salient DR must be preferred. In this light, the issue of the criteria of salience must be brought to attention.

As for the salience of DRs, Krifka assumes the following to hold:

… in typical cases in which a negated clause is asserted, the non-negated proposition will already be salient in the context. For example, it is hard to imagine that a sentence like Ede didn’t steal the cookie could be uttered in a context in which the proposition ‘Ede stole the cookie’ is not salient already, e.g. as a possible explanation why the cookie is lacking. (Krifka 2013: §S4.1)

The claim, not further elaborated upon, seems to echo a philosophical and linguistic tradition (Strawson 1952; Givón 1978; Horn 1989) that assumes that a fundamental pragmatic asymmetry exists between positive and negative sentences. The latter, according to this view, can only be used if the proposition corresponding to their positive counterpart has been previously introduced in some capacity. In Givón (1978)’s example: imagine two persons meeting for the first time in a while. All other things being equal, one could answer the other’s question What’s new? with My wife is pregnant, but not with its negative counterpart My wife is not pregnant. For the latter answer to be felicitous, the characters must share a previous knowledge of a possibility, an expectation or the hope for the woman to be pregnant.

To a first approximation, one could extend the same insight to negative total polar questions. Both inner and outer negative polar questions, actually, share an epistemic bias towards p: if a speaker were entirely agnostic as to whether p is the case, she would most likely ask a positive rather than a negative total polar question. This observation supports the view that in contexts where a negative total polar question is asked, the DR corresponding to p is more salient than the DR corresponding to ¬p. If that is the case, the P-N answering pattern is derived, as shown in this tableau:

The candidates listed in (44) are pairings of forms and meanings, i.e., of particles and DRs. Candidate (44d) is rated as the worst because it violates both constraints: it picks up the non-salient negative DR d’_N, and it expresses a disagreeing move. On the other hand, (44c) is the optimal candidate, because it violates neither: it picks up the most salient DR d and asserts its negation, thereby expressing an agreeing answer to the negative polar question. This means that a bare no expresses NA rather than PD. Candidates (44a–b) are suboptimal, because they violate one constraint each; but (44a) is better because it violates a lower ranking constraint: in (44a), the most salient DR d is picked up by the particle but expresses a disagreeing move with respect to the negative question; in (44b), an agreeing answer is expressed by picking up the non-salient DR d’_N. As a result, a bare sì is used for PD rather than NA. Our empirical findings for answers to (inner) negative total questions are in line with Krifka’s predictions.

Now let us turn to negative nuclear polar questions. The introduction of *NONSAL leaves open the possibility than in special cases the optimal choice of particles might be different than what seen in (44), due to a difference in the salience of the available DR. In passing, Krifka (2013) notes that this might be the case of polarity questions containing a focus (Krifka 2013: 14). Why would that be the case? As the reader may recall from section 3.1, Bianchi & Cruschina (2016) have argued that, in the interpretation of nuclear polar questions, a set of focus alternatives of propositional level is involved. The presupposition is introduced that one of the alternatives is true. An example of such an alternative set is shown in (45):

In Krifka’s terms, we can assume that the question in (45) introduces two DRs, corresponding to p = that Gianni did arrive and ¬p = that Gianni did not arrive. Crucially, it is plausible that the DR corresponding to ¬p might be the most salient of the two, because it belongs to the set of alternatives, while its positive counterpart does not. If we can assume as much, the A-D answering pattern is derived, as shown in the following tableau:

The ranking of the constraints is unchanged, but the rating of DRs as far as their salience is concerned is now reversed. (46b) becomes the optimal candidate, because it does not violate any constraint (it picks up the negative DR d’_N, which is now the most salient, and does not involve disagreement). As a result, sì is now now chosen to express NA. The second best candidate is (46d), which again picks up the most salient negative DR d’_N and only violates *DISAGR. No is thus used to express PD. The other two candidates are severely suboptimal, because they violate the higher ranking *NONSAL, in the case of (46c), or both constraints, in the case of (46a). These predictions are the opposite of those in (44), so as a whole an account à la Krifka can derive the crossover effect observed in our experimental results.

5 Narrow focus in situ

In the experiment reported above, nuclear PQs involved a narrowly focused constituent which was displaced to the left periphery of the clause. This displacement has two disambiguating effects. First, focus cannot project (in the sense of Selkirk 1995) beyond the displaced constituent (Bocci 2013). Second, the focus unambiguously takes scope above negation; this, in turn, implies that negation is sentence-internal: it is an “inner negation” in the sense of Ladd (1981).

However, in Italian a narrowly focused constituent is not necessarily displaced to the left periphery, but it can also occur in situ (Bocci 2013 and references cited therein). The question then arises of whether a narrow focus in situ would have the same impact on the answering pattern that we observed in section 2.2 in the case of focus fronting.

In order to tackle this question, we designed a second experiment with the same structure as the one described above: the independent factors were “type of questions” (negative total PQ vs negative nuclear PQ) and “state of affairs” (context supporting the truth of p vs. the truth of ¬p); the dependent factor was the choice of polar particle in the answer (sì vs. no). The stimuli were sixteen experimental sets, each one including the four conditions that arise from crossing of the two independent factors. In each set, the four questions were introduced by an appropriate context, eliciting either a total or a nuclear interpretation for the polar question, and supporting either the proposition expressed by the sentence radical of the question (¬p) or its negation (that is, p). The stimuli were identical to those with the negative nuclear questions, except for the position of the narrowly focused direct object, postverbal in these items, as exemplified in (49)–(50):

41 subjects were administered the test, for a total of 656 observations. The results, plotted in Figure 3, were fitted with a linear mixed logit model. The model included “type of question” and “state of affairs” as fixed factors. The model with most complex random effect structure justified by the data included by-item and by-subject intercepts and by-subject slopes for the effect of “type of question”.

Figure 3

Second experiment: probability of sì over no in answers to total negative questions and nuclear negative questions with Focus in situ.

The statistical results are reported in Table 2. The factor “type of question” does not have a significant main effect on the type of answer. By contrast, there is a highly significant main effect for the factor “state of affairs”. In other words, independently of the type of question (total vs. nuclear), the probability of sì is significantly higher in contexts that suggest that ¬¬p than in contexts that suggest that (¬p). Moreover, the model revealed a significant interaction between the factors “type of question” and “state of affairs”. To better understand the interaction, we fitted two independent models so as to test the effect of “type of question” for each level of the factor “state of affairs”. The results indicate that when the state of affairs suggests that p, the probability to observe an answer sì is significantly lower for nuclear polar questions with focus in situ than for total questions (Estimate 2.291, Std. Error .535, p < .001). Conversely, when “state of affairs” suggests that ¬p, the probability of sì is significantly higher for nuclear questions with focus in situ than for total questions (Estimate –2.96, Std. Error 1.23, p = .016).

As the reader can notice by comparing Figure 2 and Figure 3, the answering pattern to negative nuclear PQs with a focus in situ (dotted blue line in Figure 3) is different from the one observed above with a fronted focus. First, negative agreeing answers (confirming ¬p) are preferably expressed with no, whereas with a fronted focus the particle chosen was virtually always sì. Second, in case of a disagreeing answer confirming p, the choice of particle is at chance level. These results do not mirror the pattern observed with fronted foci, but it is important to stress that they also differ from the consistent P-N pattern that is observed with total questions in this same experiment (solid red line) and in the preceding one. Therefore, we cannot claim that a focus in situ has no effect.

In our view, the different results obtained for nuclear PQs with focus in situ with respect to nuclear PQs with fronted focus might result from two independent sources.

First, we may speculate that the participants in the second experiment, but not in the first one, may have disregarded the focal structure of the nuclear questions and interpreted the questions as total. In the second experiment, where the focus element occurred in situ, the participants could infer the presence of a narrow focus in the questions only from the long descriptive context and the prosody associated with the question. The order of the constituents in the nuclear questions with focus in situ did not contribute in signaling the focal structure. In the first experiment, by contrast, the nuclear questions featured focus fronting and the order of the constituents provided a strong additional clue for the participants to infer the presence of narrow focus in the questions. In fact, the focused constituent in all the nuclear questions was the direct object. In Italian, (non wh-) objects can basically be fronted only when associated with a narrow focus interpretation (when no resumptive clitic occurs, as in our case).

If this reasoning is correct and the participants in the second experiment interpreted in a certain number of trials the nuclear questions with focus in situ as total, we should expect that the results for nuclear questions with focus in situ to be somewhat intermediate between the N–P pattern observed for total questions and the A-D pattern obtained in the first experiment for nuclear questions with focus ex situ. In other words, something similar to what we actually observe in Figure 3.

A second major confounding factor that could affect the second experiment is the interaction between the focus in situ and negation, since, as already noted, in these cases the scope relation is ambiguous. Suppose that the subjects interpreted the intended nuclear PQ by associating the focus with negation, rather than giving the focus wide scope above negation: this yields a question of the form “Is it not XP_Foc that P?” (where P is the non-negated predicate expressed by the rest of the clause), instead of “Is it XP_Foc that not P?”. Suppose, then, that subjects sometimes interpreted the question with Neg taking scope over the focus. Under our first account, an agreeing answer would then have the features [REL:∅] and [POL:–], since focus does not hinder the Agree relation; thus, an agreeing answer would be spelled out as no (cf. (18a) above). On the other hand, a disagreeing answer would have the feature specification [REL:–,POL:–] in Resp, to be spelled out as sì (cf. (18b) above). This would lead to a P-N pattern.

As for the propositional anaphor account, note that if focus is outscoped by negation, the focal alternatives are non-negative, and thus do not raise the salience of the negative DR; the prediction, again, is that the negative nuclear polar question should pattern with the total one. Thus, this interfering factor too may have led to a prevalence of no answers in the agreement (¬p) conditions. On the other hand, the fact that the answers were at chance level in the disagreement (not not p) condition remains an open problem.

In sum, we believe that the impact of these unavoidable confounds make it impossible to test our initial predictions. On the other hand, these results are interesting in that they might partly account for the optionality reported by some authors (Bernini 2001; Roelofsen & Farkas 2015), according to which both particles are equally acceptable in PD answers. We have shown that when the focus structure and the relative scope between focus and negation are crystal clear, as in our first experiment, the answering pattern is quite consistent, although reversed in nuclear vs. total negative polar questions. We suspect that the apparently optional choice of either particle arises in cases where there is a potentially ambiguous scopal interaction between negation and a narrow focus in the PQ.

6 Concluding remarks

In this paper we have discussed an exceptional answering pattern that emerges in Italian in answers to nuclear questions featuring a (fronted) narrow focus. This answering pattern, observed in the previous literature, is supported by our experimental results.

We have discussed two possible approaches to this phenomenon. First, we explored a syntactic account in which the polar particle introduces an elliptical clause. The insight here is that the Focus layer makes the sentence-internal polarity inaccessible to the polar particle (by intervention). Second, a pragmatic account can be based on Krifka’s idea that polar particles are propositional anaphors: the exceptional answering pattern to negative nuclear questions can be derived from the assumption that negative questions introduce two propositional discourse referents, and that narrow focus makes the negative discourse referent more salient than the positive one, since it belongs in the set of alternative propositions evoked by the focus (the opposite is the case in answers to negative total questions).

The pragmatic account is inherently simpler and more elegant, yet we have stressed that it relies crucially on the relative salience of the two discourse referents, which is not easy to assess on the basis of independent evidence. In the end, we believe that the choice between the two approaches will have to be made on a wider empirical basis.

At the cross-linguistic level, the syntactic account makes two predictions. First, as for three particle languages like German or French, given the hypothesis that the “third” particle spells out a bundle with two negative feature values (see (26a)), we predict that it should never appear in answers to nuclear questions: this is because in such answers the Focus layer should block the transmission of one of the two negative feature values to the Resp layer. Second, no exceptional pattern is expected for answers to nuclear questions in agreement-disagreement systems. More generally, it is worth replicating our experiment in other positive-negative languages, to check whether the exceptional answering pattern to nuclear questions has some cross-linguistic stability.

Moreover, it has been noted that other factors besides focus may affect the answering pattern. For instance, Brasoveanu, Farkas & Roelofsen (2013) found that in English, certain quantificational subject in the polar question have an impact on the preferred answer; if their results are replicated and show some cross-linguistic consistency, one could consider how the two approaches explored here could be extended to cover them. These issues remain open for future research.

Abbreviations

M = masculin, NEG = negation, PL = plural, PRS = present, SG = singular.

Competing Interests

The authors have no competing interests to declare.