Responding to alternative and polar questions

Marıa BiezmaCarleton University

maria biezmagarrido@carleton.ca

Kyle RawlinsJohns Hopkins Universityrawlins@cogsci.jhu.edu

1 INTRODUCTION

This paper gives an account of the differences between polar and alternative questions, as well as an ac-count of the division of labor between compositional semantics and pragmatics in interpreting these typesof questions. The main proposal for alternative questions (ALTQs) is that they involve a strong exhaustivitypresupposition for the mentioned alternatives (following Karttunen and Peters 1976; Bartels 1999; Rawlins2008a; Biezma 2009; Aloni et al. to appear). We derive this compositionally from the meaning of the finalfalling tone (after Bartels 1999; Zimmermann 2000) and its interaction with the pragmatics. ALTQs areexhaustive in two ways: they exhaust the space of epistemic possibilities, as well as the space of discoursepossibilities. In contrast, we propose that polar questions are the opposite: they present just one alternativethat is necessarily non-exhaustive. Our account covers a large range of empirical data, focusing on answersand responses to alternative questions. We develop the compositional part of the proposal using a Ham-blin semantics for questions (Hamblin 1973; Kratzer and Shimoyama 2002), suggesting that the pragmaticproperties of these two question types follow directly from their compositional structure.

In what follows we offer a more detailed overview of the proposal, §1.1 and an outline of the paper,§1.2.

1.1 The proposal in more detail

Alternative questions (ALTQs)1 are non-wh questions standardly characterized by interrogative morpho-syntax, the presence of disjunction, and a characteristic intonation. Some stereotypical examples are in (1).(In (1) small caps mark pitch accents on the disjuncts; we will provide a more detailed description of theintonation in alternative questions below.)

(1) a. Did ALFONSO or JOANNA give you a ride?

b. Do you want COFFEE or TEA?

c. Are you STAYING or LEAVING?

1See Karttunen 1977a; Bolinger 1978; Karttunen and Peters 1976; Groenendijk and Stokhof 1984; Larson 1985; Higginbotham1991; von Stechow 1991; Bartels 1999; Gawron 2001; Han and Romero 2002; van Rooy and Safarova 2003; Han and Romero2004b; Beck and Kim 2006; Rawlins 2008a,b; Biezma 2009; Groenendijk and Roelofsen 2009; Roelofsen and van Gool 2009;Aloni et al. to appear; Pruitt and Roelofsen 2010, 2011; Rawlins to appear; Roelofsen 2012, a.o. Unfortunately, in this paper wewill not be able to address in detail the most recent work that has appeared while this paper is under review, most notably Pruitt andRoelofsen 2011.

1

The main function of an ALTQ is to offer an unbiased choice between the alternatives offered by thedisjunction. When responding to an alternative question, the most natural thing to do is to pick one of theoffered alternatives; for e.g. (1a) one might simply respond, “Joanna did.” By “unbiased” we mean that byusing an ALTQ the speaker signals that they do not consider one of the answers to be more or less likely(van Rooy and Safarova 2003). This stands in contrast to possible answers to most other types of questions,including polar questions (Bolinger 1978; Buring and Gunlogson 2000). Some stereotypical examples ofpolar questions are in (2).

(2) a. Did anyone give you a ride?

b. Do you want coffee?

c. Are you staying?

The questions in (2) explicitly spell out only one alternative; we return in detail to their alternativestructure in §3.2, there arguing that they function to highlight a particular alternative from some contextuallysalient set. We will label polar questions spelling out only one alternative, like in (2), as POLQs. However,we can also have polar questions in which disjunction is used to invoke more than one alternative. At firstsight disjunctive polar questions look similar to the the ALTQs in (1). However, the two kinds of questionsdiffer in intonation (Bartels 1999).

(3) a. Do you want coffeeL∗H−or teaL∗H−H%? [Polar Question]

b. Do you want coffeeL∗H−or teaH∗L−L%? [Alternative Question]

Two descriptive differences emerge: ALTQs have a pitch accent on non-final disjuncts that is lackingin disjunctive POLQs, and ALTQs have a final falling contour instead of the final rise seen in POLQs ingeneral. However, as Pruitt (2008b,c) shows, the key difference between pairs like (3a) and (3b) is in thefinal intonation – experimentally, this is the cue that parsers use when deciding which kind of question theyare hearing. The non-final pitch accents are neither necessary nor sufficient.2 The alternative reading comesabout when the final intonation is falling, whereas the polar reading comes about when there is final risingintonation. The alternative reading, the reading for (3b), is which of these two things do you want: you wantcoffee or you want tea?, whereas the reading for (3a), the yes/no reading, corresponds with the paraphraseis it the case that you want either coffee or tea? Given Pruitt’s result, we will focus on the interpretation ofthe final falling tone in ALTQs, and set aside the internal pitch accents.

We take this difference in the final intonation between POLQs and ALTQs to be visible at LF in theform of a “closure” operator, leading to different semantics and pragmatics for the two kinds of questions.This can be seen in the different kind of answers and responses to POLQs and ALTQs. Possible answers topolar questions are typically marked with yes and no, where yes signals an answer matching the alternativepresented in the content of the polar question. The alternative raised in a polar question influences thealternatives that may be available to a speaker, but does not sharply constrain them. For example, the

2We follow Pruitt (2008b) most directly in our assumptions about the intonation of alternative and polar questions. Accordingto Pruitt, “a canonical alternative question contains (i) a pitch accent on the first disjunct; (ii) a H phrasal/boundary tone at the endof the first disjunct; (iii) a H pitch accent on the final disjunct; and (iv) L phrasal and boundary tones (L-L%) on the final disjunct.Features (i) and (ii) create the impression of a rise at the end of the first disjunct, while (iii) and (iv) cause the perception of afinal fall. Features (i) and (ii) are often accompanied by a pause before or, but this does not appear to be required. Some havealso noted that there is variation in the identity of the pitch accents in an Alt question (whether H or L), and perhaps in the phrasaltone of the non-final disjunct (again, whether H or L).” With respect to polar questions Pruitt (2008b) indicates that “the notablefeatures of a yes/no question, when defined in parallel to an alternative question are: (i) no pitch accent on the first disjunct; (ii)no phrasal/boundary tone on the first disjunct; (iii) a L pitch accent on the final disjunct; and (iv) H phrasal and boundary tones(H-H%) on the final disjunct. The combination of features (iii) and (iv) in yes/no questions creates the percept of a final rise,while a lack of a significant pitch movement is characteristic of the first disjunct.” According to Bartels 1999, there is also greaterinter/intra-speaker variability in polar questions than alternative questions.

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addressee of the question in (2b) may answer no, and yet indicate that they prefer some tea instead. Whereashad wanting tea been the alternative spelled out in the question, the answer (in this scenario) would havebeen yes. This is somewhat different from what we observe in alternative questions. After an alternativequestion has been asked, the answers involve choosing from the alternatives spelled out. This difference inthe exhaustivity of alternatives between POLQs and ALTQs is illustrated in (4). (In examples we will use #to indicate any kind of infelicity / inappropriateness in context.)

(4) Scenario: You are in charge of coordinating the cooks for the colloquium dinner. John is one of thecooks. The menu is pasta, fish and stew.a. (Scenario variant: You have already assigned the task of making the stew to someone else.)

You: Are you making pastaL∗H−or fishH∗L−L%? (ALTQ)John: # (No,) I am making the stew.John′: Wait, I was planning on making the stew, can’t I do that?

b. (Scenario variant: No one has been assigned any of the tasks.)You: Are you making pastaL∗H−or fishL∗H−H%? (disjunctive POLQ)

John: X (No,) I am making the stew.

Data of this kind indicates that the utterance of the question in (4a) signals that the only possibilitiesfor John are either making pasta or making fish. By uttering this question, the speaker limits the possibleanswers to those alternatives specifically expressed in the question. To invoke a different alternative is notappropriate in this discourse. The speaker presupposition is signaled by the final falling intonation, and itneeds to be accommodated by the addressee. This is illustrated by John’s alternative response (perfectlyfine), in which he wonders why the questioner is assuming that stew is not an option anymore.

Things are different in the case of (4b). The question in (4b) has only a polar reading (notice the finalrise): is it the case that you are making pasta or fish? John’s response in this case is not odd, since thequestioner is not limiting the available possibilities to just making pasta or making fish. The questioner mayhave guessed that pasta or fish are amongst John’s favorite dishes and so decided to spell only them out, butthey are not excluding them altogether.

We propose that the difference in the consideration of possible alternatives has to do with exhaustivityand the lack of it, connecting it directly with the issue of what is or isn’t an answer to an alternative question.In §3.1 we link exhaustivity in alternative questions to the intonational contour observed by Zimmermann(2000) in the context of conjunctions of various types.3 Zimmermann proposes that a final falling intonationon a conjunction structure indicates the presence of an exhaustivity operator at LF, signalling that the listexhausts the range of possibilities.

In this paper, we address both the meaning of POLQs and ALTQs, and the differences between themboth in the semantics and in the pragmatics. While we will give a compositional account of the intonationalmeaning involved in ALTQs, we will not give an explicit account of the effect of final rising intonation onPOLQs (this is a substantial problem, going well beyond just plain polar questions; see Gunlogson 2001,2008 a.o. on this matter). In a similar vein, while we do include the full range of alternative questions inthe scope of this paper, in order to keep our investigation manageable, we limit ourselves to “plain” polarquestions, and exclude various more complicated types (e.g. negative polar questions, tag questions, etc.;see Ladd 1981; Buring and Gunlogson 2000; van Rooy and Safarova 2003; Romero and Han 2004; Han andRomero 2004a; Reese 2007, a.o.).4 There are a wide range of open questions concerning the relationship of

3This idea builds on Biezma 2009. Pruitt (2008b) also (independently of Biezma 2009) suggests associating Zimmermann’swork with exhaustivity in questions: “it is promising to note that the same notion of closure is put to work in the semantics of[ALTQs] here and in the cases discussed by Zimmermann (2000)” (Pruitt 2008b, pg. 23).

4See e.g. Han and Romero 2004b among many others on negative questions such as (i) and (ii). We leave for future researchthe interaction of such questions with disjunction.

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these question-types with ALTQs that we will not explore here, for example, the relationship of the notionof “bias” in ALTQs to negative polar questions (Buring and Gunlogson 2000; van Rooy and Safarova 2003).

When investigating the semantics of POLQs and ALTQs the contrast between POLQs and alternativequestions formed by two opposite alternatives (ALTQVNs) is quite important:

(5) a. i. Do you want coffee? [POLQ]ii. Do you want coffee or not? [ALTQVN]

b. i. Are you coming? [POLQ]ii. Are you coming or not? [ALTQVN]

The alternatives in (5a-ii) are you want coffee and you do not want coffee, and the alternatives in (5b-ii) areyou are coming and you are not coming. On the one hand, asking such questions has a very similar effectto asking the corresponding (plain) polar questions, e.g. “Do you want coffee?”; in both cases the answerinvolves saying yes or no to the proposition you want coffee. However, despite the apparent similarities,Bolinger (1978) points out that the two kinds of questions are by no means interchangeable. He offers arange of different scenarios in which POLQs are fine, whereas the use of an ALTQVN is not. The exampleabove refers to the contrast in context in which and invitation is made. Another of of Bolinger’s contexts,this time referring to conversation starters, where only a POLQ is appropriate, is illustrated below:

(6) Conversation Starters: Trying to start a casual conversationa. Do you like to play golf ? [POLQ]b. Do you like to play golf or not? [ALTQVN]

ALTQVNs are crucial to our goals for the paper: any analysis of alternative vs. polar questions needsto explain both differences and similarities between POLQs and the special case of ALTQVNs. However,the differences between these kinds of questions have often been set aside. Indeed, the traditional semanticsgiven to POLQs and ALTQVNs does not predict any interpretive differences between the two (e.g. Hamblin1973; Karttunen 1977a; Groenendijk and Stokhof 1984). We propose an analysis on which the differencebetween POLQs and ALTQVNs follows from a crucial linguistic difference in their respective structures:the presence/lack of an exhaustivity operator at LF indicated by final falling intonation. This idea leadsadditionally to a new account of the semantics of polar questions, involving a simpler alternative structureand composition than is typically assumed – they denote just a singleton Hamblin alternative. Thus wepropose that the semantics of POLQs and ALTQVNs is not as similar as might be expected, and consequentlydifferences in their pragmatics are expected.

One influential proposal that attempts to explain the POLQ/ALTQVN contrast appears in van Rooy andSafarova (2003). Van Rooy and Safarova (2003) propose that many of Bolinger’s observations should beaccounted for in a decision-theoretic framework. According to their account, the ‘utility value’ for all theanswers5 to ALTQs is equal (no answer is preferred over the others), whereas for a POLQ the utility valuefor the answer corresponding to the content proposition is higher than its negation (i.e. a positive answerto a positive POLQ is preferred to a negative answer).6 Since ALTQVNs are alternative questions, vanRooy and Safarova’s (2003) explanation for the differences between POLQs and ALTQVNs is that whena POLQ is uttered, a positive answer is preferred whereas the utterance of an ALTQVN does not signal a

(i) Aren’t you coming? (Outer negative POLQ) (ii) Are you not coming? (Inner negative POLQ)

5A possible answer has a greater utility value than another if the answer is more in line with the questioner’s goals (e.g. involvesmore overlap with the possible worlds corresponding to those goals).

6In van Rooy and Safarova’s notation, for a positive polar question ‘?q’: UV(q) > UV(¬q), and for an alternative question‘?(p∨q)’, UV(p)≈ UV(q).

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preference for any answer.7 This paper does not give an account of how this difference in utility valuesmight be derived, if it is to be derived at all. We suggest that the semantic/pragmatic differences we proposefor POLQs and ALTQVNs can lead to the derivation of the right relationship between utility values, thusallowing a connection between the alternative structure of the question types and van Rooy and Safarova’s2003 proposal.

In sum, we propose and provide empirical support for a semantics of POLQs that differs from the se-mantics of ALTQs in the presence/lack of an exhaustivity operator at LF, and in the alternative structure ofthe two types. When the exhaustivity operator is present, a question presents an exhaustive list of alterna-tives, but when it is not, the question presents a non-exhaustive list (or singleton). One advantage of theanalysis proposed here is that the question operator is the same in both types of questions. This uniformity,we suggest is an improvement on more standard Hamblin-style accounts, which traditionally stipulate aspecialized POLQ operator as a solution to technical issues, without empirical support. With respect to thesemantics of ALTQs, this paper offers extensive empirical arguments that the possible answers to ALTQsconsist only of the propositions provided by the disjuncts, i.e. are exhaustive. Versions of this idea havebeen assumed in several prior works on questions (Belnap and Steel 1976; Karttunen and Peters 1976; Hig-ginbotham 1991; Bartels 1999), but arguments for or against the idea have been underdeveloped. Arguingfor this answering space becomes important now since there are recent analysis of ALTQs that assume thatnot only the disjunct propositions are the possible answers (see Groenendijk and Roelofsen 2009 a.o.).

In developing a semantics for non-wh-questions, we propose a particular bridge between the semanticsand pragmatics of such questions. Namely, these question provide information about what alternatives aresalient relative to an existing Question Under Discussion (QUD; Ginzburg 1994; Roberts 1996 a.o.). In theQUD framework (Roberts 1996; Ginzburg 1996; Buring 2003; Beaver and Clark 2008; Farkas and Bruce2010; Ginzburg to appear), discourse is understood as a communal inquiry into the resolution of the currentsalient question,8 We hope that this proposal can set the stage for explaining a wide range of discoursephenomena about the interaction of such questions and their responses, though in the present paper we willleave many such phenomena untouched. The overarching research agenda for the semantics and pragmaticsof questions in which this paper is embedded is illustrated in (7).

(7)

Compositional semantics:

Interface:

Discourse model:

Construct alternatives(Hamblin)

Align semantic alternativesand discourse alternatives

(Update discourse alternatives)

Track structured flowof discourse alternatives

(Discourse model)

Module Function of module

From the picture in (7), the present paper offers a proposal for the two first steps concerning non-wh-questions: a proposal that differentiates them semantically, and hence, a proposal that differentiates in how

7van Rooy and Safarova (2003) extend their proposal to (outer) negation polar questions, which we do not discuss in this paper.8This approach follows much work on the philosophy literature (see Grice (1975); Stalnaker (1974); Lewis (1979)). hence

responding to questions involves choosing between the contextually salient alternatives that can be the answers. On this respect,ALTQs enumerate all the possible alternatives amongst which the addressee has to choose, whereas POLQs indicate one amongstothers.

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they shape the discourse alternatives. We will leave a full exploration of the interaction of this proposal witha formalized model of discourse for the future.

1.2 Outline

In this section we have reviewed the main ideas in our proposal for the semantics and pragmatics of al-ternative questions, and the relationship between polar and alternative questions. The rest of the paper isorganized as follows: in §2 we consider a range of empirical properties of alternative/polar questions andtheir responses that an analysis should account for; much of this section involves exploring the role of ex-haustivity and mutual exclusivity, as well as some facts about the “bias” of the types of questions, and thenature of question-question sequences. We then build our proposal compositionally. In §3 we lay out ourassumptions about the syntax of alternative and polar questions and propose our semantic account of thedifferences between polar and alternative questions.

2 ON THE ALTERNATIVE STRUCTURE OF ALTERNATIVE QUESTIONS

In the next several sections, we investigate some of the core data that must shape an analysis of alternativequestions. In §2.1 and §2.2, we explore a range of data leading to the conclusion that alternative questionsare exhaustive. There are two focuses: in root contexts, we explore complicated differences between typesof responses, leading to the conclusion that not all responses to ALTQs are answers. In embedded contexts,we arrive at a similar conclusion, that not all logical/doxastically accessible possibilities play a role inthe alternative structure of an ALTQ, corresponding to the responses that are not answers. The followingsections set the stage for the semantics and pragmatics of ALTQs and POLQs that will be developed in theremainder of the paper.

2.1 Two views on the nature of alternative questions

If the meaning of a question corresponds to its possible answers, in order to understand alternative questionswe must investigate the spectrum of their answers. For any ALTQ, there are certain answers that will alwaysbe possible, corresponding to the disjuncts that make up the utterence.

(8) A: Would you like soup or salad H∗L−L%?

B: (I’ll have) soup.

B′: Salad.

We term responses corresponding to the disjuncts in alternative questions, as in (8), “most compliant”responses. It is clear that, no matter the analysis, the mentioned alternatives must play a role in the alternativestructure of an alternative question – if anything is an answer to an alternative question, the most compliantresponses are. We take this to be uncontroversial. But do answers of this type exhaust the possible responsesto ALTQs? The answer is no, and this is where complications emerge.

Logically, someone might want neither soup nor salad. Or they might want both. The “neither” caseincludes scenarios where B wants nothing, or they want something else instead of the mentioned alternatives(for some ALTQs, one of these maybe be unlikely or impossible). The B and B′ answers above don’t dealwith these two cases, and we must say something about what role, if any, the cases play in the semantics ofALTQs. We also must say what role they play in the pragmatics, as relevant responses are certainly licensedfor at least this particular ALTQ:

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(8) B′′: (I’ll have) neither.

B′′′: (I’ll have) both.

We term these responses “less compliant” responses. (For this particular question, the “both” responseis somewhat marked or inappropriate; we will return to this issue later.) Are B′′ and B′′′ answers to thequestion?9 If they are not answers, of course one must also say what they are, and why they are licensed.It is on this point that researchers have diverged. Our proposal, following Belnap and Steel 1976 (see their§1.32, 2.32, as well as Karttunen and Peters 1976; Higginbotham 1991; Bartels 1999), is that such responsesare not answers to an immediately preceding ALTQ, but rather deny the presuppositions of the question.10

Their licensing can be reduced to the licensing of presupposition denials/rejections in general (see Maierand van der Sandt 2003; von Fintel 2004; Spenader and Maier 2009 a.o.). In order to motivate this proposal,though, we will first spell out the competing analysis, and then go through a range of empirical evidence.

On the one hand, Karttunen (1977a); Groenendijk and Stokhof (1984), and more recently, Groenendijkand Roelofsen (2009) include the “both” and “neither” cases in the alternative structure of ALTQs, and con-sequently predict that such responses are true answers in some sense (though Groenendijk and Roelofsen2009 have an explanation for their markedness). The alternative structure on this type of analysis is repre-sented pictorially in (9). (Note that this is a general schema of this kind of analysis, and Groenendijk andRoelofsen’s treatment of the “both” alternative is slightly different; see below.)

(9)

(only) soup (only) salad

soup+salad

no soup or salad

A key difference among the accounts that work like this is what they do with the additional alterna-tives. Groenendijk and Roelofsen 2009 provide the most complete treatment of this kind; acknowledgethe markedness of “neither”/“both” answers, but deal with them in the pragmatics, rather than the alterna-tive structure. In particular, they give a system for deriving conversational implicatures against these twopossibilities. The proposal is interesting and so we will sketch how it works; see Groenendijk and Roelofsen(2009) for the full logical details, which we will not do justice to here. (In that paper, see fig. 9 on p. 27 fora summary of their proposed alternative structure of alternative and polar questions.)

The cases of “neither” and “both” work somewhat differently; we will discuss “neither” first. What iscommon to both cases is that an ALTQ is in competition with a disjunctive polar question, and the hearerreasons about why the ALTQ might be chosen. G&R define a formal notion of homogeneity: updates are(roughly) more homogeneous if they are more informative and/or less inquisitive. (The slogan is “Say more,ask less!”) This notion gives rise to general Gricean Quantity-like scales that rank different related types

9Note that while “neither” and “both” are convenient tools for abbreviating these kinds of responses, the issue is not specific tothese two items, and isn’t really about the meaning of “neither” or “both”, except insofar as one would like a theory that explainswhy they are so convenient for two-alternative ALTQs. Note, for instance, that 3-alternative ALTQs don’t license these items. Whatwe assume is basically a standard Barwise and Cooper (1981)-style treatment; “neither” and “both” require a plural antecedent ofexactly size 2, and are compatible with split antecedents introduced by disjuncts. “Neither” (if defined) is a negative quantifier overthe atoms of the antecedent group, and “both” is a definite operator over the antecedent.

10Belnap and Steel 1976 term these responses as ‘corrective answers’ – answers in the sense that by denying a presupposition,they eliminate every possible alternative. We also assume that denying the presupposition of a question does this, but do not takethis consequence to be indicative of answerhood.

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of moves. On their logic for alternative and polar questions, it follows that alternative questions (?(p∨q))are always less homogeneous than corresponding polar questions with disjunction (?!(p∨ q); the ! forcesclassical disjunction in this formula). These are distinguished primarily with intonation in English:

(10) G&R homogeneity scale: ?!(p∨q) (disjunctive POLQ)� ?(p∨q) (ALTQ)

(11) a. Do you want coffee or tea L∗H−H%?b. � Do you want coffee or tea H∗L−L%?

Asking an ALTQ therefore triggers neo-Gricean reasoning about why the questioner didn’t ask the corre-sponding, more homogeneous, disjunctive POLQ. The key is that this POLQ on their system would allowanswers that address the “neither” option (e.g., responding “no” to (11a)). Since the disjunctive polar al-ternative would directly ask about the “neither” case, the prediction is that asking an alternative questionimplicates that the questioner is excluding the “neither” alternative, because if they were interested in thatpossibility, they would have asked the disjunctive polar version.

The markedness of “both” also follows from pragmatic reasoning on this proposal, but the mechanismabove won’t derive it, so they propose a different account of the “not both” inference. Groenendijk andRoelofsen (2009) provide a general notion of compliance for responses; we will not expand this in detailhere, but the basic notion corresponds to more traditional notions of partial answerhood: a response is“an optimally compliant response just in case it picks out exactly one of the alternatives proposed by [thequestion].” A response that uses a sub-issue of the question is also compliant, just less compliant. In anALTQ, it turns out that, given these definitions, the answers corresponding to the individual disjuncts arecompliant, but the “both” response is not compliant, despite being more homogeneous. The alternativequestion jointly with the two possible answers leads a hearer to conclude that the speaker purposefullyexcluded the non-compliant response, and therefore the question implicates the “both” proposition to befalse. (See Groenendijk and Roelofsen 2009 §6.2, last paragraph.)

These two proposals are certainly an elegant account of the logical facts – the necessary reasoningfollows from very general principles of the logical system developed in their paper. But is it the rightanalysis (or more generally, right kind of analysis) of the natural language data? We will argue that it is not;with the right data it is possible to differentiate this proposal from competing analyses. (Of particular interestto the derivation of exhaustivity is the data from alternative unconditionals, where exhaustivity effects stillarise but polar interrogative clauses are disallowed; see §2.2.2.3.) It is worth noting that for the case ofmutual exclusivity, our approach while different in the details is closer to the proposal in Groenendijk andRoelofsen 2009 than for exhaustivity. That is, their proposal involves effectively, exclusifying the disjuncts,and our analysis will do something similar at a more semantic level.

On the other hand, Belnap and Steel (1976), Karttunen and Peters (1976), Bartels (1999), Rawlins(2008a), and Biezma (2009) exclude the “neither”/“both” cases from the denotation of ALTQs altogether,and consequently predict that such responses are not in fact real answers of any kind. The basic idea isthat the question presupposes that neither the “both” alternative nor the “neither” alternative are possible.The 4-alternative-type analyses struggled from the problem of explaining why “neither”/“both” are markedresponses; this second type of analysis has the reverse problem. They must say something about why suchresponses are licensed at all, and what their status is. The proposal beginning in Belnap and Steel 1976 isthat responses of this type address the presuppositions of the question. Therefore, their licensing should bedetermined by the general licensing conditions of presupposition denials of all sorts.11

The alternative structure involved in this type of analysis is shown in (12), where the grayed area repre-sents logically possible cases that are presupposed away.

11We will not develop an account of presupposition denials here, but it is clear that this project transcends question-answerdialogues; see Maier and van der Sandt (2003); von Fintel (2004); van Leusen (2004); Spenader and Maier (2009) a.o. See alsoIsaacs and Rawlins’s (2008) analysis of responses that deny the antecedent of a conditional question; they similarly propose thatsuch responses are not answers but presupposition denials.

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(12)

(only) soup (only) salad

soup+salad

no soup or salad

There are also several possible combinations of the pieces of these two analyses. We might allowthe “neither” alternative to appear in the denotation, but not the “both” alternative (a more semantic formof what Groenendijk and Roelofsen 2009 do via Compliance; this has been proposed in Higginbotham1991), and vice versa. Consequently, there are four conceivable analyses for alternative questions withtwo disjuncts. And of course the situation becomes more complicated with more than two disjuncts. Thepresuppositional account, like the implicature account, predicts that such responses should not have the samestatus as full answers, but the two differ in their precise predictions about the nature of such responses. (Animportant point here is that we believe the presuppositional analysis could be straightforwardly implementedin Groenendijk and Roelofsen’s (2009) overall Inquisitive Semantics system; our criticisms of Groenendijkand Roelofsen (2009) are about the particular analysis of alternative questions, not the larger frameworkproposed there.)

The choice of whether alternative questions are exhaustive/mutually exclusive makes many predic-tions not just about assertive/informative responses – questions can be followed by other questions, andthese complex discourses involve interaction of the questions. While we will not address the full range ofquestion-question sequences in this paper, it is helpful to consider at least a simple case that initially moti-vates the exhaustivity claim. When a constituent question is followed by an alternative question, the impactof the ALTQ intuitively can have a ‘retroactive’ effect on the alternatives raised by the constituent question.

(13) What do you want to drink? Would you like coffee or tea H∗L−L%?

In isolation, the constituent question would leave the options potentially quite open, i.e. in principle therecould be many possible contextually salient answers to the constituent question, the assumed QUD at thetime. But the ALTQ continuation further specifies the questioner’s assumptions about what drinks the hearercan choose, namely the ones mentioned in the disjuncts, making clear what are the only possible answersto the QUD. This effect is quite surprising on an analysis where the disjuncts in an ALTQ do not exhaustthe possibilities. ALTQs in this kind of sequence seem to serve the function of making the alternatives froma prior constituent question explicit. With this initial motivation for an exhaustivity account, we move to adetailed investigation of the response system for ALTQs.

Two main questions emerge from this section. First, of the above possibilities, what is the correctanalysis for alternative questions? Second, how should the correct alternative structure be derived compo-sitionally? We must also address questions such as what the correct analysis is of “neither”/“both”-typeresponses, and why they are sometimes, but not always, appropriate. The following sections explore thestatus of different responses to alternative questions, and the implications for their pragmatics.

2.2 Answers and responses to alternative questions

In this section we explore a range of empirical differences between core answers and less compliant re-sponses to alternative questions, as well as corresponding differences that show up with alternative questionsin non-root positions. One main conclusion is that less compliant responses don’t pattern like answers. A

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second main conclusion is that including the neither/both possibilities in the alternative structure of alterna-tive questions consistently makes wrong predictions for the semantics of embedded and adjoined alternativeinterrogatives.

Much of this data points to alternative questions having a fairly strong exhaustivity presupposition –that the alternatives introduced by the disjuncts exhaust the possibility space that the question is askedover. It also points to a mutual exclusivity presupposition – that the disjunct-introduced alternatives do notoverlap at all. Consequently we arrive at, for alternative questions at least, a strong version of “Hamblin’spicture” (Hamblin 1958; Groenendijk and Stokhof 1997). That is, the alternatives introduced by ALTQsmust exhaust the space of possibilities, and must be mutually exclusive; not just that, but this space onlyincludes the alternatives corresponding to disjuncts. We will in fact conclude that the exhaustivity effect isstrong in consequence of the “list closure” intonation appearing on alternative questions, converging withZimmermann’s (2000) analysis of this intonation on a range of coordinate structures in English. Whilewe will not take a strong stand on Hamblin’s picture in general (see e.g. recent controversy in Velissaratou2000; Isaacs and Rawlins 2008; Groenendijk 2009; Groenendijk and Roelofsen 2009 on whether conditionalquestions obey Hamblin’s picture or not), it seems clear that the constraints it implies are necessary for theproper analysis of alternative questions, in order to account for the data in the present section. (We willsuggest that the semantics of polar questions do not obey it, though their pragmatics do.)

2.2.1 The peculiarity of “neither”/“both” responses It is clear that understanding the status of “neither”-and “both”-type responses is crucial to understanding alternative questions. Such responses are peculiar ormarked in a range of ways. Our “less compliant” label is intended to capture this intuition – in general theyseem less compliant with the questioner’s goals. But to support this we need more empirical diagnostics.

A first observation is that less compliant responses are not always appropriate or felicitous. This standsin contrast to the more compliant responses, which are licensed in any discourse situation.

2.2.1.1 Variable felicity

A scenario in which both respose types are licensed is the prototypical example sentence for alternativequestions:

(14) Scenario: A is a waiter, B a restaurant customer.A: Would you like coffee or teaH∗L−L%?B: Neither, thanks.B′: Both, please.

What seems to be important to this scenario is that the questioner is probably aiming at fulfilling the hearer’sdesires (i.e. the power dynamic is biased towards the hearer), and there is no particular complication tothe questioner in satisfying both possibilities – the restaurant can charge for both. Even here, the “both”response is, if not inappropriate, somewhat unexpected. The “neither” response seems fairly natural.

However, even changing the example slightly can lead to the “both” answer seeming less appropriate:

(15) Scenario: A is an airplane steward, B a passenger.A: Would you like chicken or fishH∗L−L%?B: Neither.B′: # Both.

Here, the “neither” response still seems acceptable, but it is much stranger for the airplane passenger torequest both meals. Crucially, in this scenario it is more of a burden on the questioner to try to fulfill bothpossibilities, and the power dynamic is less biased in the sense that A isn’t necessarily aiming at fulfilling

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B’s every whim. We can invert this example with a scenario where the passenger accidentally has beengiven the two meal pouches and is asked whether (s)he will give the chicken or the fish back to the steward;now the “neither” response becomes odder.12 The licensing of these responses are heavily dependent on thecontext, and how easy the power dynamic makes it to reject certain possible assumptions(/presuppositions)on the part of the speaker about the context.

Finally, let us move to a scenario where neither of the extra responses is felicitous.

(16) Scenario: A is a professor, B a student in A’s class.A: Are you going to take the final exam or write a term paperH∗L−L%?B: # Neither.B′: # Both.

Here the student clearly has to choose one of the mentioned alternatives. The power dynamic (and assump-tions about how classes work) prevents them from going outside these two options. It is possible to modifythe scenario to make the B response felicitous – to do this, we have to have it actually challenge one of A’sassumptions.13

(17) Scenario: A is a professor and thinks B is taking her class for a grade, but B is not.A: Are you going to take the final exam or write a term paperH∗L−L%?B: Neither – I’m only auditing.

It is clear that the context can be manipulated to block the less compliant answers. What about the morecompliant responses, corresponding to the mentioned alternatives? Attempts at biasing the question or thecontexts so as to block one of these alternatives do not work (putatively leaving one disjunctive alternativeplus a less-compliant alternative available, on other accounts), rendering the question itself infelicitous. Forexample:

(18) A: # You will fail if you don’t take the exam, but are you going to take the final exam or write aterm paperH∗L−L%?

To the extent this question is acceptable, it permits either answer (a scenario where the teacher is willingto let the student make the bad choice). This difference in status between the less/more compliant responsesneeds explanation.

2.2.1.2 Variable presence

Many alternative questions do not involve the possibility of “both”/“neither” responses. The way to excludethese in the question itself is with an “or not” ALTQ (what we will be referring to elsewhere in the paper asan ALTQVN):

(19) Are you going to the party or notH∗L−L%?

The two alternatives are already non-overlapping, and cover all the possibilities, just by themselves. Sincethe two alternatives in the question in (19) are opposite alternatives, i.e. you go to the party and you donot go to the party, there is no room for any extra responses. It is also possible to ask such questions incontexts which explicitly exclude the “neither” or the “both” possibilities. In fact, the professorial exampleabove can be seen as this kind of example, but perhaps more interestingly, it is possible to do it with an overtutterance.

12Thanks to Ana Arregui (p.c.) for suggesting this scenario.13The original exam scenario in (16) was suggested by Chris Brumwell (p.c.), and this variant was suggested by Michael Wagner

(p.c.).

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(20) Are you going to take the final exam or write a term paperH∗L−L%? You can only choose one. / Youhave to do one.

On the other hand, an alternative question can be forced to allow “neither”/“both”-type responses byexplicitly mentioning them in a disjunct. This overrides the variable felicity effects described in the previoussection – as with any mentioned alternative, the corresponding response becomes “more compliant” as longas the question itself is felicitous.

(21) Are you going to take the final exam, write a term paper, or neitherH∗L−L%?

(22) Are you going to take the final exam, write a term paper, or bothH∗L−L%?

(21) very clearly suggests that there is some valid path to completing the class where the student doesn’t doeither of these typically required pieces of work – perhaps they have enough extra credit to pass even withoutdoing one of the final options. Similarly, (22) suggests that they may do both, perhaps for extra credit.Again, the conclusion is that the mentioned alternatives have a different status than the “neither”/“both”-type alternatives, even when the content of the disjunct corresponds to what would otherwise be a lesscompliant answer.

2.2.1.3 Hedging particles and speaker uncertainty

There is a certain class of particles/adverbs that mark a lack of coherence in the discourse structure (Schiffrin1988). A common reason for lack of coherence is speaker uncertainty. The particles include “well”(Schiffrin’s focus), “actually”, and so on. This class of item is commonly licensed on “neither”/“both”responses to ALTQs, but not on the core responses.14

(23) A: Would you like fish or chickenH∗L−L%?B: Well/actually, do you have a vegetarian optionL∗H−H%?B′: Well/actually, could I have both? (I need some extra for my infant son here.)B: # Well/actually, fish.

On a similar note, the “neither”/“both” possibilities can be addressed by backing off to a very weakmodal question without such hedging particles. This is not so with the core responses.

(24) A: Would you like fish or chickenH∗L−L%?B: Is there any chance I could have something vegetarianL∗H−H%?B′: Is there any chance I could have bothL∗H−H%? (I’m really hungry.)B: # Is there any chance I could have fishL∗H−H%?

In an absolute sense this kind of data is less informative than might be hoped. The distribution of “ac-tually”/“well” is quite complicated, and the particles have many licensing contexts – they might be licensedunder either the presuppositional account or the implicature account. (Since both denying a presuppositionand an implicature may result in lowered discourse coherence.) As responses go, it is actually more unusualthat core answers to alternative questions do not generally license the particles, than that the less-compliantresponses do. (In comparison, standard complete answers to constituent questions license the particles givenappropriate context.)

14Note that “actually” is also licensed, even on a more compliant answer, if it marks a sort of speaker-internal lack of coherence:suppose a passenger is really spaced out while reading a book (the book is very interesting) and then the steward comes alone andsays “Do you want coffee or tea?”. At that point the passenger realizes that he is indeed thirsty and says, “Actually, a coffee wouldbe great!” In this case the speaker is effectively responding to their own internal dialogue, marking that they suddenly realized thata coffee would be good.

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The main point to draw from this section is that core responses and less-compliant responses to alter-native questions differ; less-compliant responses are more susceptible to hedging and marking of speakeruncertainty. We might explain this by supposing that less compliant answers are presupposition denials (infact, “well” etc. appear naturally on presupposition denials), but this might also be explained if the parti-cles mark denials of an implicature. The distinction between more and less compliant responses is quitesurprising, though, on a classical four-alternative account.

2.2.1.4 Interaction with partial answerhood

If “neither”/“both”-type responses are answers, then responses that rule out one or both of those possibilities,but leave other alternatives open, should be partial answers. For example, a partial answer to a constituentquestion can rule out just one possibility among many:

(25) A: Who is bringing the saladL∗H−H%?

B: Not Jim.

Partial answers are licensed by ALTQs; this can be seen from 3 (or more)-alternative ALTQs.

(26) A: Does Alfonso want coffee, tea, or waterH∗L−L%?

B: He doesn’t want water.

However, partial answers of the kind predicted by taking “neither”/“both” responses to be answers arenot licensed.15 One example of this type would involve restating the alternatives; we might also explicitlyexclude the two non-core possibilities.16

(27) A: Does Alfonso want coffee or teaH∗L−L%?

B: # He wants one of the two.

B′: # He doesn’t want both.

B′′: # He doesn’t want neither.

15The account argued for in this paper proposes that ALTQs present all the alternatives available in the context of utterance:ALTQs presuppose that the alternatives presented in the disjuncts exhaust all possibilities. An anonymous reviewer points out thatin such an account, the response He doesn’t want fish to the ALTQ Does Alfonso want fish or chicken? should be considered acomplete answer: even if the speaker uses a negative statement, they identify only one alternative by eliminating the only otherpossibility. However, as this reviewer points out, He doesn’t want fish does not seem to have the same status as He wants chicken.We agree with the reviewer that the intuitive status of these two responses is not the same: He wants chicken is always going tobe an answer to the alternative question, whereas he doesn’t want fish can simply express a lack of complete knowledge aboutAlfonso’s desires, only becoming a real answer under very specific discourse conditions. Let us first consider the case in which thequestion is a formulaic version of Is he going to have chicken of fish? In this case, the negative response could be taken as indicatingan answer if the speaker has some epistemic authority regarding what the third person is going to have (imagine the speaker is themother of the toddler named Alfonso), or if the negative response is about the speaker himself: I won’t have fish. But, stating thenegative of one alternative does not commit the speaker to knowledge of the other alternative. Even though the two propositionspick out the same set of possible worlds in this context, the speaker has a choice, and by choosing the negative version of the claim,the speaker indicates that they are not willing to be a Source (in the sense of Gunlogson 2008) for the positive version of the claim.Therefore, in order to account for the reviewer’s intuition we must assume that a response can be treated as a complete answer (inthe relevant sense) only if it does commit the speaker to being a Source for a complete resolution of the issue, on top of semanticrequirements for complete answerhood. We will leave further exploration of this assumption for the future. In this case, strongassumptions would be required for a third party to be a Source for claims about someone’s desires.

16There is a certain class of responses that essentially agrees with the exclusion of other options; for example, “Well, I knowAlfonso wants one of the two..., but I do not know which.” These are licensed only if their effect is to protest complete ignorance asto the answer – i.e. they have the distribution of “I don’t know”-type responses in general. They also require the degree of hedgingmarked by “well”.

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This effect is stable across contexts and types of ALTQs. It is unexpected on an account where the “nei-ther”/“both” possibilities play any role in the question meaning – we would expect such responses to befelicitous. Even if the question conversationally implicates that the “neither” option is excluded, we wouldstill expect e.g. (27B) to be licensed with the function of affirming this implicature, something generallypossible.

2.2.1.5 Summary

Less compliant responses to alternative questions (e.g. the “neither”/“both”-types) do not pattern with themore compliant responses, and therefore they must have a different status than regular answers. Giventhat we are uncontroversially assuming the more compliant responses to be answers, this suggests that theless-compliant responses aren’t. They are not always licensed, their licensing status is highly dependent oninferential factors, and when explicitly put into the alternative structure of a question, they gain a differentstatus (patterning with more compliant responses). Some, but not most data in this section is compatiblewith an account where these responses are answers but that the question conversationally implicates thatthey aren’t the true answers (as in Groenendijk and Roelofsen 2009). All of the data is compatible with anaccount where less compliant responses are not answers at all, but presupposition denials.

In summary, the analysis of alternative questions, in order to be fully compatible with the response dataexplored in this section, must include a presupposition that rules out alternatives not introduced by disjunctsin an alternative question. We now turn to the alternative structure necessary for accounting for embeddedalternative questions.

2.2.2 Non-root alternative questions One of the major insights underlying the modern understandingof question meaning is that the semantics of embedded questions is not fundamentally different than that ofroot questions (Karttunen 1977a; Groenendijk and Stokhof 1984). The way this semantics integrates intothe larger linguistic context is of course quite different between the two cases, but this is through no fault ofthe interrogative clause itself. Therefore, it is worth examining the behavior of ALTQs in non-root contexts,with the aim of cataloging the status of the “neither” and “both”-type alternatives. We examine here threecases. The first, and most standard non-root case, is that of alternative questions selected for by attitudeverbs; we will consider both extensional and intensional attitude verbs. The second is alternative questionsin subject position, focusing on “depends on” and related verbs. The third is adjunct alternative questions,sometimes called ‘unconditionals’.

The data to be presented below shows that we see mutual exclusivity effects in embedded contexts.Before proceeding to the details, let us mention that it is not clear how the notion of Compliance fromGroenendijk and Roelofsen (2009) is intended to be used for the case of embedded questions, since it isreally about sequences of moves (e.g. answers to root questions). Given that we do see mutual exclusivityeffects in embedded contexts, if the pragmatic account is to go through, it will need to be extended to thosecontexts. This is perhaps an unfair criticism since Groenendijk and Roelofsen (2009) were focusing onquestions in discourse, and may be able to extend the logical system to force a mutual exclusivity inferencein these cases as well, but currently we do not see how to do it. (The situation is analogous to implicature“freezing” effects (Chierchia 2006), and this might be one strategy to save the implicature account.)

2.2.2.1 Complements of attitude verbs

Suppose Henry knows that the plan was originally for either Alfonso or Joanna to make a salad (they weresupposed to decide between them which one would do it). Henry learns that both of them are having carproblems and might not be able to make it to the grocery store, and so maybe neither of them will actuallybe able to bring it. Henry’s pondering of this scenario cannot be described with an embedded alternative

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question with only two disjuncts, though if the new possibility is mentioned, an embedded alternative ques-tion becomes good. (As with root alternative questions, it is crucial to control for intonation; without thefinal fall, this sentence can get a polar reading, which is compatible with this scenario.)

(28) # Henry wondered whether Alfonso or Joanna would bring the salad. H∗L−L%

(29) Henry wondered whether Alfonso, Joanna, or no one would bring the salad. H∗L−L%

This judgment is unexpected under an account where the “neither”-alternative plays a role in the alter-native structure; Henry’s wondering in (28) should include the possibility of neither bringing a salad even ifthat alternative is not explicitly mentioned.17 What we find is that the possibility of neither of them bring-ing the salad has to be explicitly mentioned in this scenario, i.e. it has to be turned into a more-compliantalternative.

Similarly, if Henry instead learns that they were also considering collaborating on the salad, (28) is nota correct description of his pondering. We must again introduce the “both” alternative explicitly to describethe scenario:

(30) Henry wondered whether Alfonso, Joanna, or both Alfonso and Joanna would bring the salad.

Likewise, an account that makes the “both”-alternative part of the question meaning would lead us to expectfelicity of (28) in the modified scenario, but what we find is that explicit mention of this alternative isnecessary.

2.2.2.2 Subject position ALTQs

Similar effects can be seen with subjects of verbs like “depend on”. The following sentence is simply notcompatible with Joanna being in a really bad mood and bringing nothing, or being in a really great moodand bringing both an entree and a bottle of wine.

(31) Whether Joanna brings an entree or a bottle of wine H∗L−L%will depend on her mood.

We would expect compatibility with these possibilities being selected by some value of her mood, unlessthey aren’t in the alternative structure of the subject question at all.

2.2.2.3 Alternative unconditionals

Similar evidence can be derived from unconditionals. First we show that unconditionals involve an adjoinedalternative interrogative clause (which has sometimes been in doubt). Given this, anything we learn abouthow an ALTQ works in adjoined position bears on the properties of alternative questions in general.18

Alternative interrogative clauses can be adjoined, as well as selected for, leading to structures sometimescalled ‘unconditionals’ (Zaefferer 1991; Gawron 2001; Rawlins 2008a). Such structures have all the surface

17Note also that negation doesn’t change the judgment. Suppose Henry should have been pondering the scenario but didn’t:

(i) # Henry failed to wonder whether Alfonso or Joanna would bring the salad.

18A reviewer points out that the evidence in this section is not cross-linguistically general. This is true (see Haspelmath andKonig 1998), as many languages use a different type of adjunct for alternative unconditionals, but does not mitigate the impact ofthe argument. This paper in general is focused primarily on English alternative and polar questions, and while we expect that muchof what we are describing is cross-linguistically applicable, this is an open question. Given that alternative unconditionals involvean adjoined ALTQ, by examining their properties we certainly learn about English ALTQs in general. That other languages donot license the adjunction of alternative interrogatives is a puzzle about unconditionals and clausal adjunction in general, not aboutALTQs (or any other clause type that is used in a particular language as an unconditional adjunct). See Rawlins 2008a ch. 4 formore discussion of the licensing problem for clausal adjuncts.

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properties of an alternative interrogative: they have interrogative morphology (“whether”), they have anecessary disjunction, and they obligatorily carry the intonational pattern of an alternative interrogative:

(32) Whether Alfonso or Joanna is bringing the salad, it will have feta cheese on it.

(33) Henry asked whether Alfonso or Joanna is bringing the salad.

See Rawlins 2008a for further arguments; the case that they are the same kind of clause is quite clear.Given this, alternative unconditionals provide further insight into the nature of alternative questions, and

in particular, strong evidence against the presence of the less-compliant responses in the alternative structure.Assume the pre-theoretical idea that unconditionals involve quantification over the alternatives given by theinterrogative that is adjoined (one way or another, this underlies every account of the construction; seeZaefferer (1990); Izvorski (2000a,b); Gawron (2001); Rawlins (2008a)). If the denotation of an alternativequestion involved either the set of worlds where both alternatives were true, or the set of worlds whereneither alternative was true, we would predict quantification over these possibilities. We do not find this,and assuming that these worlds participate in the question meaning would make incorrect predictions aboutthe felicity conditions and truth-conditions of unconditionals.

Suppose that we are planning a potluck, and we (mutually) know that either Alfonso or Joanna mightbring a salad, but that maybe no one will, and this has just been under discussion. In this scenario, it is oddfor one of us to utter (34):

(34) # Whether Alfonso or Joanna brings a salad, we will have enough food.

However, if the worlds where neither brought a salad were in the running for quantification (i.e. on a 4-alternative account), we would expect felicity. Now consider a case where, last I had heard, maybe neitherof them will bring a salad. However, if no one brings one, we won’t have enough food. We are talkingabout the planning of the potluck, and you utter (34). The prediction of an extra-partition account is that itshould simply be false – there is a case under consideration where we don’t have enough food. The actualinterpretation is quite different, however. What happens is that the hearer will accommodate the assumptionthat one of them will bring a salad, and consequently the sentence is true in this scenario.

Similar scenarios can help to understand the role of mutual exclusivity. Suppose that one more saladwouldn’t be enough food, but two would. We know that either Alfonso or Joanna might bring a salad, andthat possibly both will, and this has just been under discussion. In this scenario, it is odd for one of us toutter (35).

(35) # Whether Alfonso or Joanna brings a salad, we will not have enough food.

The prediction is similar to the one above – this should be felicitous and false. However, it is odd. If thescenario is adjusted so that the hearer is more open to accommodating that only one of them will bring it(e.g. we haven’t just been discussing that, you have talked to them both recently, and I haven’t), then thesentence is felicitous and true. The quantification over salad-bringing possibilities simply cannot involvethe case where both bring a salad.

The evidence from unconditionals is clear – the only alternatives that play a role in the denotation of analternative interrogative are ones where exactly one of the disjuncts is true. In fact, we take this evidenceto be among the strongest (for English ALTQs at least), since the effect is so clearly truth-conditional.19 In

19It is also extremely hard to explain under an analysis where ALTQs are in pragmatic competition with POLQs, as in Groe-nendijk and Roelofsen 2009. This is because English in general disallows the adjunction of polar “whether”-clauses (Gawron 2001;Rawlins 2008a), so there is no competitor structure for the unconditional case.

(i) * Whether Alfonso brings the salad, we will not have enough food.(ii) * Whether Alfonso or Joanna brings the salad, we will not have enough food. [note: without ALTQ intonation on adjunct]

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cases where such an assumption (that there are no other possibilities, and no overlap between possibilities)was not previously explicit, we are typically able to accommodate them without difficulty. An account thatincludes “neither”/“both”-type alternatives in the question meaning can’t be reconciled with this data.

2.2.3 Interim conclusions, and presuppositions Two immediate conclusions can be drawn from thedata in this section. Alternatives corresponding to the disjuncts have a different status from those corre-sponding to cases where none or more than one of the disjuncts is true (“neither”/“both” cases, for 2-disjunctquestions). Furthermore, our arguments lead to the conclusion that this second class of possibilities be en-tirely absent from the alternative structure of ALTQs.

The conclusion we arrive at, then, is that alternative questions presuppose exhaustiveness and mutualexclusivity, and the presupposition is present in root and non-root environments.20

What then is the status of responses that address these excluded possibilities? The natural answer (Bel-nap and Steel 1976) is that they are presupposition denials, used to address some assumptions that thespeaker is making, rather than answer the immediate question at hand. Treating such responses as presup-position denials at once explains why they are marked and variably present, and why the correspondingalternatives seem to play no role whatsoever in the semantics of embedded alternative questions. The impli-cature account can explain some but not all of the first part of the data, but none the embedding facts.

There are two arguments we will briefly discuss that what is being denied is a presupposition. First, theinferences (especially in contexts where they are strongly present, such as the exam or final paper example(16)) are intuitively backgrounded. Second, and more conclusively, exhaustivity / mutual exclusivity projectlike standard presuppositions and in particular are subject to “filtering”, i.e. cancellation of the presupposi-tion in certain structures (Karttunen 1973). The crucial filtering structure is the consequent of a conditional.The standard filtering example in (36) eliminates the existence presupposition triggered by the possessive asan inference from the whole sentence. We can similarly eliminate the exhaustivity inference from an ALTQin a parallel fashion, illustrated in (37).

(36) If Alfonso has a sister, his sister will want to come to his wedding.

(37) If I only have water and tea, and you are having something, are you having water or teaH∗L−L%?

(37) involves filtering in the sense that the content of the “if”-clause is a paraphrase of what the presup-position we are proposing would do. This example does not presuppose (or entail at all) that there are onlywater and tea as options – this is exactly the behavior we’d expect if the inference is a presupposition. And

20Roelofsen and van Gool (2009) suggest that “disjunctive interrogatives with closure intonation generally do not exhibit anyexhaustivity effects.” At first glance, this seems to be entirely the opposite of our conclusion. But the point they are making issomewhat different, and they mean something else by ‘exhaustivity’. They say, in fn. 6, that “ It should perhaps be emphasizedthat closure is not interpreted here as signaling exhaustivity (as in Zimmermann 2000). That is, [(i), R&vG’s 35a] does not implythat ‘nobody else plays the piano’ or something of that kind.”

(i) Does Ann or Bill play the piano? H∗L−L%

We agree that this would be an undesireable inference to predict from an alternative question, and it is potentially predicted byapplication of Zimmermann’s closure operator (or an “only”-style operator applied to the individual disjuncts). But this is not whatwe mean by exhaustivity, and this is not what has been proposed in the ALTQ literature (Belnap and Steel 1976; Karttunen andPeters 1976). When developing our semantics, we give a closure operator inspired by Zimmermann, but it is not Zimmermann’sexact operator and does not predict R&vG’s undesirable inference. The disjuncts exhaust the possibilities in two ways: first, thereis no salient possibility (world) in which neither of them plays the piano. Second, in answering the question (as opposed to denyingpresuppositions), a hearer must choose one of those alternatives rather than picking another.

We do expect that some kind of exclusivity algorithm should be applied to the disjuncts (see fn. 25), and it would need to beone that also avoids the undesirable inference. The mutual exclusivity presupposition we use here avoids it, as would innocentexclusion or some similar procedure.

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a “neither” response is completely out as a response to (37), exactly the predicted behavior if exhaustivityis a presupposition.

3 THE SEMANTICS OF ALTERNATIVE AND POLAR QUESTIONS

This section presents an account of the compositional semantics of alternative and polar questions, in theframework of compositional Hamblin semantics (Hamblin 1973; Kratzer and Shimoyama 2002). (The anal-yses are directly translatable to other frameworks, such as Inquisitive Semantics; Groenendijk and Roelofsen2009.) We will first discuss alternative questions, building on the data in the previous section, and then turnto polar questions. This analysis is based on three key desiderata explored in the previous segment of the pa-per: (i) alternative questions appear to present a complete (/exhaustive) list of alternatives for the answerer tochoose from, (ii) responses that go outside of this alternative set pattern with presupposition denials, ratherthan answers per se, and (iii) alternative questions and polar questions have different uses in discourse; inparticular, polar questions are more ‘open’ and do not express this kind of exhaustivity.

3.1 Alternative questions

The compositional analysis of alternative questions we develop here is based on the one hand on the focussemantics analysis of ALTQs in von Stechow (1991); Beck and Kim (2006), and the Hamblin analysis ofdisjunction developed in Alonso-Ovalle (2005, 2006); Simons (2005) (which builds off of Rooth and Partee1982; Partee and Rooth 1983). The basic idea is that the function of an ALTQ is to present alternativesthat the answerer should choose between; the Hamblin analysis of disjunction allows the alternative set tofollow compositionally from the internal structure of the question in a way that is uniform with other casesof disjunction.

The Hamblin analysis of disjunction is given in (38). A version of this definition is first seen in vonStechow (1991), aimed at alternative questions (his ex. 48), and more recently proposed by Alonso-Ovalle(2005); Simons (2005) as a rule for disjunction in general.

(38) J[X or Y]K =def

JXK∪ JYK

If X and Y denote singleton sets (the normal case), their disjunction will denote an alternative set with twoalternatives. In a Hamblin account, what happens to these alternatives depends on what operator the alter-native set later composes with. To derive a classical meaning for disjunction, the set could be existentiallyclosed over, using an operator such as the standard one in (39). (This is effectively the analysis of disjunc-tion in Rooth and Partee 1982, implemented with a different scope mechanism.) In a Hamblin semanticsalternative sets compose in a “pointwise” fashion: for function application, each member of the functionalternative composes with each member of the argument set. (Of course, if both are singleton, this behaveslike standard Fregean FA.)

(39) Hamblin existential operator (Kratzer and Shimoyama 2002)J∃ αK= {λw .∃p ∈ JαK : p(w) = 1}

(40) (Hamblin) Pointwise Function Application (FA) (Kratzer and Shimoyama 2002)If α is a branching node with daughters β and γ , and Jβ Kg,c ⊆ Dσ and JγKg,c ⊆ D〈στ〉, thenJαKg,c =

def{a ∈ Dτ | ∃b∃c(b ∈ Jβ Kg,c∧ c ∈ JγKg,c∧a = c(b))}

In (41) is an example existential derivation that results in truth-conditions matching classical disjunction,using these definitions.

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(41) Alfonso danced or sang.J∃ [Alfonso danced or sang]K =

{λw′ .∃p ∈ {λw .a danced in w,λw .a sang in w} : p(w′) = 1}

∃ JAlfonso danced or sangK ={λw .a danced in w,λw .a sang in w}

JAlfonsoK ={a}

Jdanced or sangK ={λx .λw . x danced in w,λx .λw . x sang in w}

JsangK ={λx .λw . x danced in w} Or′

orJsangK =

{λx .λw . x sang in w}

Pointwise Function Application (PFA) is illustrated by the step combining the subject with the disjoinedVP; the subject is a singleton set and distributes over the alternatives provided by the disjuncts.

An important part of Kratzer & Shimoyama’s Hamblin semantics, and work building on it, is the disas-sociation between Hamblin operators, which manipulate alternatives but do not introduce them, and certainlexical items that introduce Hamblin alternatives in the first place. This is of course motivated by what hasbeen argued to be overt decomposition in languages such as Japanese. In languages where there is no overtdecomposition, the implication is that there must be a covert operator. As Kratzer 2005 says (p. b26–27c),with regard to indefinites in German: “Since irgendein indefinites have no quantificational force of theirown, but are lexically specified as existentials, they need to agree with a matching [∃] operator. Followingthe spirit of Heim (1982), we might assume that [∃] is introduced together with modal and certain otheroperators as a result of what she refers to as ‘existential closure of nuclear scopes’.” Disjunction has a ‘clas-sical’ meaning without modals (and behaves differently in modal contexts; see Alonso-Ovalle 2006 a.o. fordiscussion in the context of a Hamblin semantics), so this existential feature on this account must be presentwithout a modal, i.e. present (freely inserted) in the nuclear scope of a clause. (This, we take it, is also in thespirit of Heim (1982)). To summarize, the disjunction can carry an existential feature, which some higheroperator must agree with, leading to what Kratzer describes as ‘existential concord’.

A key component of the Hamblin analysis of disjunction in particular is also the disassociation of theoperator (in the above example, ‘∃’, providing existential force) and the alternative-introducing functionof disjunction (captured by the entry for ‘or’). The reason this disassociation is important for disjunctionis that disjunction does not just associate with existential force, but rather can be compatible with a rangeof operators in various contexts. Introduction of alternatives is the unifying character of all instances ofdisjunction, but differences between different cases of disjunction (and non-classical inference patternsin natural language) can be explained by interaction with different operators (Alonso-Ovalle 2004, 2005;Rawlins 2008a).

In particular, the Hamblin account of disjunction in ALTQs involves alternatives being collected by,instead of an existential operator, the question operator. Most Hamblin operators collect alternatives andproduce a singleton set (i.e. they create the equivalent of a regular proposition in this system), but the func-tion of a question operator is in fact to leave alternatives intact – producing a question meaning. In the caseof root questions, the resulting alternative set is used pragmatically to raise an issue (the exact mechanismwill depend on the theory; on our proposal, this happens by updating the question under discussion). Inthe case of embedded questions, the alternative set will be used by the verb that selects for the question.Disjunction is therefore featurally underspecified, and its featural content can be ‘checked’ by at least exis-

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tential force and question operators. (See Alonso-Ovalle 2006 for a thorough exploration of the idea in thecontext of modal operators in a K&S semantics; building on Aloni 2003; Simons 2005. In certain cases, itseems that disjunction is compatible with universal force as well; we will not discuss these here.)

The result is a very simple denotation for the question operator:

(42) Question operator (v.1, preliminary) (from Kratzer and Shimoyama, §3)q[[Q]α]

y=def

JαK

We will assume that this plugs into the syntax in a very straightforward way. In particular, we followmost recently Beck and Kim (2006); Rawlins (2008a) in assuming that “whether” is a complementizercarrying the [Q] operator, corresponding to a null C[Q] in root clauses (Baker 1968, 1970; Bresnan 1972;Stockwell et al. 1973).21

(43) Syntax of an alternative interrogativeCP

C′

C

whether[Q]

TP

... or ...

On the analysis schematized in (43), the primary relationship between “whether” and disjunction is a se-mantic one, mediated by Hamblin PFA. This analysis contrasts with the analysis of Larson (1985); Hanand Romero (2004b) where there is operator movement from the left edge of disjunction to Spec,CP. Wewill not try to decide between the two analyses (see Beck and Kim 2006; Rawlins 2008a) and simply notethat in principle, a Hamblin semantics could be applied to the operator-movement syntax as well, though itis a more natural fit with the no-movement account. Most of the empirical issues that decide between thetwo proposals (e.g. nature of locality effects in ALTQs, and whether they are island effects or interventioneffects) are orthogonal to the problems we discuss here.

A full derivation of a question given the no-movement assumption, parallel to (41), is shown in (44).Because disjunction can agree with the [Q] operator, no existential operator is necessary.22

(44) whether[Q] Alfonso danced or sangJQ [Alfonso danced or sang]K ={λw .a danced in w,λw .a sang in w}

whether[Q]JAlfonso danced or sangK =

{λw .a danced in w,λw .a sang in w}

(identical to subtree in (41))

The upshot is that on a compositional Hamblin semantics, the compositional treatment of alternativequestions follows elegantly from an independently motivated treatment of disjunction, with the standardmechanisms for manipulating alternative sets in that framework.

For “or not” alternative questions we will adopt the same set of assumptions. When “or not” appearssentence finally, we assume that there is an elided TP licensed by a feature in a high Σ, as in Merchant (2003,2006); Kramer and Rawlins (2009). This is the same kind of ellipsis seen in e.g. “if not”, “maybe not”,

21Note that throughout this paper, when discussing question operators, we mean the type that indicates ‘force’ or some suchconcept, not the type that appears on interrogative pronouns (Aoun and Li 2003); see Cable 2007 for discussion of the distinction.

22Is one possible? In some cases, yes – this can lead to a polar question reading.

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“I believe not”, etc. (see (45)). The structure of examples like (46), where the “or not” appears adjacent to“whether”, is much less clear, and we won’t take a strong stand here (we aren’t aware of any satisfactoryaccount). One possibility is that “whether or not” has grammaticalized as a single special embedded questionoperator. We will be abstracting away from this and treating the two types of “or not” questions the same,as we aren’t aware of any semantic or pragmatic difference.

(45) a. whether John is coming to the party or notb. whether John is coming to the party or [ΣP not [TP John is coming to the party]]

(46) Alfonso asked whether or not John is coming to the party.

For “or not” questions, assuming ellipsis allows us to analyze alternative questions with “or not” like anyother alternative question. With this background out of the way we return to the treatment of the questionoperator – is the analysis in (42) adequate as it stands?

There is a missing piece to this simple picture, and this is the source of the exhaustivity and mutualexclusivity effects demonstrated in §2. The alternatives that the analysis so far derives may overlap, and/orboth be false. Two options immediately present themselves. First of all, these effects could follow fromthe properties of the question operator (or the nature of questions themselves). This idea has been pursuedin Karttunen and Peters (1976) and Rawlins (2008a), and is quite natural given “Hamblin’s picture” – theidea that questions in general are associated with these properties (Hamblin 1958; Groenendijk and Stokhof1984, 1997). The other approach, following most directly Biezma (2009), is to take these effects to followfrom a closure operator spelled out with the intonational contour seen on alternative questions (see alsoBartels 1999; Pruitt 2008a; Rawlins 2008a). The main support for this approach is that the same contour isgeneral to English list constructions of all types (Zimmermann 2000), and we can therefore gain a unifiedunderstanding of the meaning of this contour across different conjunction structures.

Here we take a combined approach. We argue that exhaustivity is semantically encoded by means ofa closure operator, signalled by the final falling intonation, and treat this operator as directly linked to thepragmatics of questions. This way we establish a bridge between semantics and discourse.

Following Zimmermann 2000 §2.3, we take it that closure intonation generally applies to a list, andindicates that “nothing but the list items has the property in question”. We propose that the “property inquestion” for alternative questions is being one of the salient alternatives in the context of utterance, oneof the possible answers to the QUD.23 That is, unlike other types of questions, alternative questions do notask a ‘new’ question (they don’t establish a new QUD that participants agree on solving) but rather areparasitic on the propositional alternatives that are already salient (they constrain the possible answers tothe already established QUD). That is, alternative questions provide a list of alternatives currently in theQUD, and presuppose that no other alternatives are salient. We assume that such alternatives must exhaustthe epistemic possibilities and not overlap, following Hamblin. Thus, alternative questions ask a questioninvolving the complete set of propositional alternatives in the current QUD in a context.

We do not intend to give a complete analysis of the pitch contour appearing on alternative questions here.(As a reminder, by this contour we mean the final falling tone, and the possibly-option pitch acccents onnon-final disjuncts; Bartels 1999; Pruitt 2008a.) Rather, we will give an account that works for alternativequestions, and suggest some open issues. First, it is clear from Zimmermann (2000) that the same pitchcontour appears on the full range of conjunction structures involving “and” and “or”. Should these casesreceive a unified analysis with alternative questions? Our proposal could in principle be generalized toat least other disjunctions, but we will not attempt to explore the full ramifications here. Rather, we willsimply stipulate a definition that works for phrases that carry a [Q] feature and contain a disjunction. In

23As discussed above, the set of salient alternatives in a context corresponds to the notion of Question Under Discussion inthat context; Roberts 1996; Ginzburg 1996; Buring 2003; Beaver and Clark 2008; Farkas and Bruce 2010; Ginzburg to appear a.o.,though we will not formalize this idea here.

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other words, we take the final fall in alternative questions to be specific to this kind of clause type, and leavegeneralization for the future. Second, we will not attempt to derive as such the constraint that (in English)this contour occurs only with conjunction structures and in no other case. Third, following Bartels 1999;Pruitt 2008a we take the primary semantic impact of this contour to be an operator scoping over an entireinterrogative clause. However, it is an open question whether the non-final components of this contour (i.e.the pitch accents on non-final disjuncts) also have some interpretive consequences; see Bartels 1999 ch. 4for some discussion. We will not attempt to resolve this issue here.

Here is our proposal for the closure operator, based on Zimmermann (2000) and Biezma (2009):24

(47) Closure operatorq[ [[Q] α]H∗L−L%]

yc =

def

q[[Q] α]

yc defined only if SalientAlts(c) =

q[[Q] α]

yc

Constraint: α must contain a disjunction.

(48) Definition: SalientAlts(c) is the set of propositional alternatives that are salient in the context ofinterpretation c. (The possible answers to the QUD).

The claim here is that an exhaustive list produces a set of alternatives that are co-extensive with the full setof salient alternatives in a given context. No alternatives are left out of the list, and no extra alternativesare included. Accommodating this presupposition amounts to inferring what the questioner is assuming thecomplete set is. Crucially, we assume that alternatives can be salient without explicit mention, for examplefollowing a constituent question. In this kind of context there will of course typically be uncertainty as towhat the alternatives actually are, and this is why an alternative question is useful.

We further assume that the set of salient alternatives exhausts the epistemic possibilities, and is mutuallyexclusive, both of these in the Hamblin-picture sense. This is formalized in (49) by reference to the contextset of a given context (csc), which represents mutual public commitments (Stalnaker 1978). (The particulardetails here are directly based on Rawlins 2008a, who follows Karttunen and Peters 1976.)

(49) Constraint on salient propositional alternative sets in a context c(i) ∀w ∈ csc : ∃p ∈ SalientAlts(c) : p(w) = 1 (Exhaustivity)

(ii) ∀w ∈ csc : ∀p,q ∈ SalientAlts(c) :(

p = q∨¬(p(w)∧q(w))

)(Mutual exclusivity)

These constrainst are a straightforward implementation of a domain-restricted “Hamblin’s picture”, wherethe domain is the context set, following most directly Groenendijk 1999. Constraint (i) ensures that everyviable (i.e. present in csc) world corresponds to at least one alternative, and constraint (ii) that every viableworld corresponds to at most one alternative.25 In combination with the closure operator, an asker of an

24While this operator in the text is left specific to [Q], and hence can be construed as a specialized operator for alternativequestions, it is easily generalized to all propositional lists. We will leave for future work the empirical consequences. Zimmer-mann’s discussion focuses on cases where the lists are not of propositions, and we do not consider these here. A reviewer raisesthe question of whether it is fair to claim, as we have in the text, that there is a shared [Q] operator across all question types, if thisclosure operator is specific to alternative questions. We believe the answer is yes: we have still identified a common core acrossdifferent question types.

25 As pointed out to us by both an anonymous reviewer, and Floris Roelofsen (p.c.), the formulation of the exclusivity con-straint in (49-ii), though relatively standard in the question literature, runs into well-established problems related the combinationof non-overlapping constraints for disjunction, with “or both” disjunctions (Stalnaker 1975 fn. 14, Simons 2005 fn. 44). In gen-eral, though non-overlap constraints (also, “genuineness”, “alternativeness” constraints) have proven desirable in many disjunctiveproblems, they tend to predict, as the standard Hamblin mutual exclusivity constraint does, that alternatives cannot be subsets ofother alternatives. This is exactly what an “A or B or both” disjunction involves. The problem of “or both” ALTQs seems to be aspecial case of the general problem, which we will leave for later research. (E.g. “Would you like coffee, whiskey, or both?”) Weare aware of three solutions in the literature. First, Stalnaker’s alternativeness constraint (“a disjunctive statement is appropriatelymade only in a context which allows either disjunct to be true without the other”), he suggests (fn. 14) may admit exceptions aslong as the exceptions (i) are obviously exceptions, and (ii) are not pointless (have a salient explanation for the violation of the

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alternative question requires of the input context that it make salient all and only the mentioned alternatives,and that it ensure they have no overlap or gaps relative to what is publicly assumed to be possible.

For example, take the ALTQ in (44). This question presupposes that the context make salient just twoalternatives, one where Alfonso danced, and one where he sang, and it (intuitively) raises an issue thatwould be resolved by choosing between these alternatives. The constraints in (49) amount to the questionerpresupposing that there be no worlds in the context set at which he neither danced nor sang, and no worldsat which he both danced and sang. The motivation is the exhaustivity/exclusivity data in (2), where weshowed that alternative questions in fact do exhaust the epistemic possibilities, and responses that challengethis (e.g. suggest that he neither danced nor sang) have the status of presupposition denials. To explicatethis, however, we must connect up the notion of “salient alternatives” with the act of questioning in a slightlymore precise fashion.

The idea is that alternative questions are a kind of hybrid between exhaustive lists and questions, andtheir list-like nature (following Zimmermann) forces a match between the alternatives provided by the listand the set of salient alternatives (/the QUD). Consequently, the listed-alternatives must also obey the con-straint in (49), leading to epistemic exhaustivity/exclusivity effects. At the same time, alternative questionsstill raise an issue, and so can be used to make precise what exactly a prior issue consists of.

Two questions therefore arise for every question type: (i) how the salient alternatives (the ‘input QUD’ indynamic terms) in a given context constrain when instances of that question type can be used in that context,and (ii) how use of that question type affects the set of salient alternatives in the resulting context (the ‘outputQUD’). Traditional analyses of questions have focused only on (ii), but our proposal for alternative questionssuggests that answering (i) may be key as well. We will not give a full answer to (i) or (ii) for constituentquestions, but we will give a proposal for answering both for polar questions. Like ALTQs, we suggest thatpolar questions must align with the set of salient alternatives in a context, but not exhaustively.

Before proceeding to polar questions, we briefly sketch in somewhat more detail how the response datafollows from the semantics and exhaustivity constraints developed here. We will consider the example in(50).

(50) A: Is Alfonso or Joanna bringing the salad H∗L−L%?

Compositionally, the question is built as follows. The disjunction consists of two referring expressions,each denoting a singleton set of type e: {a} and { j}. The denotation of the disjoined phrase therefore is theset {a, j}, their union. This composes pointwise with the property denoted by “be bringing the salad”, givinga two-alternative set containing propositions: {λw . a is bringing the salad in w,λw . j is bringing the saladin w}. The question operator (in the preliminary version) leaves this set unchanged, handing it off to the

constraint). This explanation relies on the fundamentally pragmatic (in fact, pseudo-Gricean) nature of Stalnaker’s formulation.Second, Simons 2005 (fn. 44) suggests that an exhaustifying operator (e.g. “only”) be applied to each disjunct recursively, whichwould lead automatically to mutual exclusivity of alternatives. A similar proposal has been made in recent work on “Hurford’sconstraint” (see e.g. Chierchia et al. 2009, 2011). Third, in an extensive discussion of the “or both” problem, Alonso-Ovalle2006 proposes (§3.8) that a Fox 2006-style “innocent exclusion” algorithm applied to disjunction solves the problem, generatingexclusive alternatives only when possible. (This solution was also suggested to us by Floris Roelofsen, p.c.) We favor this lattersolution, or some variant of it, given its general motivation in the recent literature on free choice. (See also Menendez-Benito’s 2006Obligatory Exclusification Hypothesis, which resembles our proposed constraint in its generality of application – she proposes thatpropositional alternatives are always exclusified, and adopting one of the semantic solutions to the “or both” problem would leadus to this hypothesis as well.) It is worth noting, however, that innocent exclusion does not generate non-overlapping alternativeswhen one disjunct is “or both”, in contrast to Simons’ proposal, though in other relevant cases it will ensure non-overlap. It isunclear as of yet whether a strong or weak exclusification procedure is empirically correct, and in most cases, the two proposalsgenerate the same results. As long as some exclusification algorithm is applied to disjunction in a normal alternative question, theexhaustivity presupposition in (i) alone will derive that there are no worlds in the context set on which alternatives overlap.

We take it as an open question what the correct treatment of exclusification is when “or both” is present, across the full range oftypes of disjunction, and therefore in this paper we will not develop a more sophisticated treatment than what is seen in constraint(49-ii) in the body.

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closure operator. The closure operator introduces the presupposition that exactly these two alternativesare the salient alternatives in the context, i.e. in informal terms, the QUD. As such, they must obey theexhaustivity constraint in (49). This constraint tells us that there can be no worlds that cross-cut the twoalternatives, where both of them bring a salad. It also tells us that there can be no alternatives outside the twoalternatives, where they both bring something else (or nothing). A “neither” response, therefore, denies thepresupposition introduced by the closure operator, introducing the claim that there must have been anotheralternative that should have been included in the list as well.

This account, with an appropriately developed notion of questioning, handles for the full range of datain 2.2, making many desirable predictions.

In §2.2.1 we discussed the variable felicity of “neither” and “both”. Obviously, propositions corre-sponding to e.g. “Neither / someone else is bringing the salad” are not compatible with the kinds of contextsthat (50) presupposes, and therefore in general have the status of presupposition denials. Their licensingis consequently distinct from the licensing of true answers. With an appropriate theory of presuppositiondenial, the variable felicity follows: for example, it is easier to deny a presupposition when in a position ofauthority, and harder when not. As with all presupposition denials, the tendency towards extra marking isalso expected.

It moreover predicts that a variant like (51) will behave differently, as discussed in §2.2.1.2.

(51) A: Is Alfonso, Joanna, or neither bringing the salad H∗L−L%?

This question does presuppose that the context is compatible with neither of the two bringing a salad, andso therefore responses corresponding to this alternative can be answers following (51).

The account can also straightforwardly make the right predictions for embedded cases, as long as asuitable notion of “salient alternatives in a context” is extended to attitude reports – the context will typicallyneed to be ‘internal’ to the report, as in e.g. Heim 1992; Aloni and van Rooy 2002; Isaacs and Rawlins 2008.In the case of alternative unconditionals, again the prediction is exactly what is needed – the alternative setprovided compositionally is empirically what is shown to be quantified over in §2.2.2.3. (See Rawlins2008b,a for an analysis.)

With these predictions, we now turn to polar questions.

3.2 Polar questions

The account of polar questions we develop here is, at first glance, somewhat further from the standardapproach than our account of alternative questions. In it we attempt to reconcile the established standardapproach with a number of lurking problems in the linguistic data on polar questions (and related types).The theory presented in this section sets the stage for a pragmatic-semantics interface account of askingpolar questions aimed to interact with a theory of discourse that make predictions regarding phenomenainvolving question-question and question-answer sequences. As a baseline, in our discussion we will uni-formly assume a syntax where a polar question has a [Q] operator of some type in the usual position (C),and nothing else special.26 The challenge then is to identify the content of this operator.

The idea of the standard approach is that polar questions denote a size-two set of alternative propositionsthat is in fact identical to that of an ALTQVN. One alternative corresponds to the content proposition (theproposition that would be formed by looking at the sentence without its force operator), and the other to thenegation of the content proposition. On a compositional Hamblin account there is no alternative introducing

26The major competing hypothesis (see Larson 1985; Han and Romero 2004b a.o.) would be to take polar questions to be “ornot” questions with a silent “or not”. This of course leads to problems explaining all the ways we have noted that ALTQVNs behavedifferently from POLQs. Given the range of data we have discussed, we take this approach to be a non-starter, at least for English.

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element (e.g. no disjunction, no “wh”-item), and so it is necessary to have a specialized polar questionoperator that introduces these alternatives.27

(52) Standard account of polar questions (to be argued against)Where JαK = {A} (undefined if not a singleton set28):JQ[POL] αK= {λw .A(w),λw .¬A(w)} (Hamblin 1973 p. 50)

The object A here is what we have been calling the content proposition. It is clear that this alternative struc-ture is, at least for some cases, the meaning necessary for embedded polar questions. That is, wonderingwhether it is raining involves wondering which of the two alternatives, the content proposition or its nega-tion, is the right one. Knowing whether it is raining involves being able to correctly identify which of thecontent proposition and its negation corresponds to the facts of the evaluation world.

But for reasons that will shortly become clear, we do not take this to be the basic meaning of a polarquestion. Rather, we take the semantics of a polar question to in fact be the singleton set. In the case of rootquestions, the idea of the account is that polar questions serve to present an alternative, and an answererchooses between that alternative and other salient alternatives. We show that this approach is foreshadowedby a number of empirical puzzles, and will allow us pragmatic differences between alternative and polarquestions.

One way to view this approach is that we are taking seriously the point that, alone of all question types,polar questions compositionally lack any alternative-introducing item. That is, they alone do not showthe dissasociation that the Hamblin account leads us to expect. Though we will not dwell on embeddedquestions, we suggest that when necessary, a pragmatic mechanism is available to coerce a singleton setinto the above 2-alternative denotation, in order to resolve a constraint against singleton sets imposed onnon-root polar questions.

There are two other proposals of this type that we are aware of. The earliest is Roberts (1996), whichinvolves a singleton-set semantics but a substantially different pragmatics. Pruitt and Roelofsen (2010) also(independently) give a recent account where polar questions are multi-dimensional, with the behavior onedimension resembling our account – the ordinary dimension is the standard size 2 alternative set, and thereis an additional ‘highlighting’ dimension that involves a singleton containing the content proposition. Ontheir semantics, this second dimension typically plays the role that our single dimension does, and so thetwo proposals converge on a similar idea. (See fn. 38 for more details.)

A side-effect of the single-alternative analysis is that, unlike many Hamblin approaches to questions, wedo not take the difference between an assertion and a question to be the difference between singleton andnon-singleton alternative sets. But in fact this move is well-supported empirically (see §3.2.1 below), and itis well known that the ‘force’ of an utterance is underdetermined by its semantics.

What this suggests is that there is a single question operator across question types that collects alter-natives, rather than multiple operators for polar vs. other question types (as a more standard compositionalHamblin approach requires). We further propose that the question operator presupposes that the set of alter-natives involved in the question must be among the set of salient alternatives in a context, or (informally) theQuestion Under Discussion, and that the resulting QUD (modeled here as the union of the existing proposi-tions and the content of the question) be non-trivial. This last constraint is due to Beck and Kim 2006 andis a convenient way of encoding the fact that questions raise issues.

(53) Question operator (v.2, final version)q[[Q]α]

yc=JαKc

27A Groenendijk and Stokhof (1984)-style approach leads to a more elegant unified account of polar and constituent questions,where a polar question amounts to the 0-place special case of a variable-binding question operator. There the challenge is to unifyalternative questions with the other two types, in the context of a larger theory of disjunction. See Gawron (2001) for one attempt.

28This will force a polar question with a disjunction to have a covert ∃ operator.

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defined only if(i) JαKc ⊆ SalientAlts(c) or if SalientAlts(c) = /0, and(ii) |JαKc∪SalientAlts(c)|> 1.

In the case of a polar question, the alternative set handed to the question operator is singleton, and theonly requirement is that it is one of the alternatives salient in the context. (The case where there are nosalient alternatives corresponds to a discourse-initial question.) An alternative question imposes a strongerrequirement, because of the closure operator – the alternatives provided by disjunction are not just amongthe salient alternatives, but are the only salient alternatives.

We take it that typical cases of embedded questions (though not all; see §3.2.2 below) impose theconstraint in (54). This is another, stronger, version of Beck and Kim’s 2006 constraint, which could beunified with the above question operator – as we do not intend to tackle embedded questions in detail here,we will treat (54) rather as a proof of concept. To resolve the mismatch inherent in our semantics for polarquestions, we will assume the coercion operation in (55).29

(54) Anti-singleton constraint schema For any Q-embeddeding verb V:(ii) J[V [[Q] α]]K is defined only if |J[[Q] α]K|> 1

(55) Anti-singleton coercionIf |JαK| = 1, where α is of type 〈st〉 and denotes {A}, then α can be coerced (as a last resort) intothe denotation {λw .A(w),λw .¬A(w)}

This coercion operation performs exactly the same function as the Hamblin polar Q-operator sketched abovein (52), but we have moved the function into the domain of repairing a type-mismatch (or more generally,composition failure due to presupposition failure). This is arguably not any more stipulative than the se-manticized account, and we will suggest that it has a range of benefits.

What is involved in asking a root polar question on this account? An answerer must choose between thementioned alternative (the content proposition), and some salient alternatives that they must infer from thecontext and are members of the set of salient alternatives (SalientAlts(c)).There are a number of proposalsabout polar questions that share the same basic idea, that “answering” them really involves accepting or notaccepting the mentioned alternative: for Gunlogson (2001) polar questions create an imbalance in the publiccommitments (the speaker makes a claim that they are explicitly not committed to) that must be resolved.For Farkas and Bruce (2010), a polar question involves putting the content proposition on the “table”,and responding to that proposition in some way. The idea also resembles the notion of ‘highlighting’ inRoelofsen and van Gool (2009) and Pruitt and Roelofsen (2010). Here we take it that a polar questionobligatorily raises an issue in discourse, as with other questions (because of the non-singleton constraint),but the only direct evidence it provides about the content of that issue is given by the content proposition.Hence, answers to a polar question fundamentally address that content proposition in some way.

The primary benefit of this account is the explanation it provides of the differing behaviors of alternativeand polar questions and the consequent differences in the pragmatics. We will turn to such cases shortly.However, there are other, more general reasons to adopt such an account, which we review in the nextseveral sections.

3.2.1 Polar questions without question marking In detaching the function of questioning from thesemantics (and in fact, the presence of a Q operator) of a polar question, we are in fact re-iterating an old,if not often examined, point. It has been well known for some time that there are various ways of asking apolar-ish question without using a polar interrogative; we focus on cases recently discussed in Gunlogson

29Another case where this coercion operation might apply is discourse-initial POLQs where no salient alternatives can be found.As long as salient alternatives can be found, it will not apply.

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(2001, 2008). Gunlogson discusses both the case of rising declaratives that act polar-like in some ways, andregular declaratives30 that act like polar questions in the right context.

(56) Context: you are sitting in a windowless conference room, and your colleague comes in drippingwet and wearing a jacket. The weather report this morning said it would be sunny all day. You say:a. [Is it raining?]L∗H−H%

b. [It’s raining?]L∗H−H%

c. [It’s raining.]H∗L−L%

While there are important differences in the pragmatics of each of these cases, a common underlying threadis that the goal of each utterance is not to convey information. Rather, it is to raise an issue that the hearercan then address. In each case, the speaker is not in a position to verify, except indirectly, if it is in factraining, and the hearer is; the hearer can respond with “yes” or “no”.

To handle cases like these, Gunlogson also adopts analyses where questioning is not about partitioningthe context, and on her account none of the questions above denotes an alternative set. Rather, all ofthe relevant denotations are propositional (as in our proposal), and a (propositional) utterance acts as apolar question if it signals an imbalance between a questioner and an addressee’s information state. UnderGunlogson’s account, roughly, an utterance is a question in a particular context if it does not add anyinformation to the addressee’s ground, and implies that the addressee may actually be an authority withrespect to the proposition, not the speaker.31 Our account does not work precisely the same way, but theintuition is based on Gunlogson’s – a polar question involves presenting a single alternative when the publiccontext does not decide between that alternative and some unstated other possibilities, but the addresseeis in a position to decide for or against this alternative. Answering a polar question is about affirming ordenying the content proposition, and the identification of a propositional utterance as a polar question liesin the pragmatics.

A related expectation emerges from the point that there is no alternative-introducing item in polar ques-tions, in contrast to all other types. If there were a type of polar-like question where a Hamblin alternative-introducing operator were demonstrably present, we predict that question type would have a different se-mantics and consequently a different pragmatics than what we are proposing for English POLQs.

3.2.2 Doubt-type verbs We mentioned above that not all verbs do have an anti-singleton presupposi-tion. The paradigm case is dubitatives in many languages (Karttunen 1977b; Huddleston 1994), includ-ing English. The English facts are that “doubt” allows as complements “that”-clauses, polar interrogativeclauses, but not alternative or constituent interrogatives:32

(57) a. Alfonso doubts that it is raining.b. Alfonso doubts whether it is raining.

(58) a. * Alfonso doubts whether it is raining or not.

30While we annotate the example below with a final fall, this is not nearly so obligatory as in an alternative question. See Bartels(1999) for an in depth discussion of the possible intonational marking of declaratives.

31To be more specific, Gunlogson (2001) (ex. 136) proposes the following definition:

(i) An utterance of L with descriptive content p is a polar question in C iff (a) and (b) hold:a. L is uninformative with respect to csAddr(C).

b. If csSpkr(C + L) ⊆ p, the Speaker’s commitment to p is mutually understood as contingent upon the Addressee’scommitment to p.

See Gunlogson (2001, 2008) for further details.32There is no distinction between “if” and “whether” clauses here, the split is entirely along alternative vs. polar lines.

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b. * Alfonso doubts whether or not it is raining.

c. * Alfonso doubts whether it is raining or snowing.

d. * Alfonso doubts what the weather is.

Moreover, both the “that” and the “whether” case appear to mean the same thing; we are not aware of anytruth-conditional differences.

The present account of polar questions allows for an elegant account of both the selectional facts and themeaning of the grammatical examples: “doubt” has a single entry that selectionally does not differentiateamong types of (finite) CPs, but S-selects for singleton alternative sets. This is predicted to be possibleon the present account of polar questions, since without coercion, the semantics of a “that” and a polar“whether” clause are identical – a singleton set containing the content proposition.3334 35

3.2.3 Disjoined polar questions A puzzling fact that has been seldom discussed in previous literature(but see Belnap and Steel 1976 p. 91, Rawlins 2008a exx. 156–158, and Pruitt and Roelofsen 2010) isthat alternative interrogatives (complete with closure intonation) can be formed out of polar-interrogativeclauses in both root and embedded positions. Note that closure intonation is obligatory in all of the followingexamples – complex polar interrogatives cannot be formed by this strategy.36 (Example (59) is from Belnapand Steel 1976 p. 91.)

(59) [Is it a bird or is it a plane?]H∗L−L%

(60) Alfonso knows [whether it is a bird or whether it is a plane.]H∗L−L%

On the one hand, this is not exactly the most common way of asking an alternative question (smaller dis-juncts are less marked), and so might be considered an empirical footnote. On the other hand, trying toaccount for this data wreaks havoc on all standard analyses of polar questions we are aware of. Supposethe above standard account of the semantics of each “whether”-clause were combined with the standardHamblin disjunction mechanism – this generates a size-four alternative set that is completely different fromwhat we want: {

λw . it is a bird in w, λw . it is not a bird in w,λw . it is plane in w, λw . it is not a plane in w

}Each alternative is orthogonal (overlapping) with two of the others (assuming the possibility of bird-planes),and the alternative set doesn’t match at all the intuitive meaning of the questions. (Belnap and Steel: “[it]is just a way of asking...whether it is a bird on the one hand or a plane on the other. That is, the resultantquestion has just two answers, “bird” and “plane”. We take “neither” as a correction.”) In fact the meaningin both root and embedded contexts is no different than if the disjunction were scoped lower. An analogousproblem arises on Groenendijk and Stokhof 1984-derived accounts as well. (See also Pruitt and Roelofsen(2010) for a discussion of the shortcomings of this alternative structure.) Given that this alternative structure

33What we do not explain is why it should be dubitatives that have this selectional property, cross-linguistically.34A related case that we will not discuss in detail is embedded “if”-polar questions (Adger and Quer 2001; Eckardt 2006).

Here, independently of the selecting verb, polar questions (but only the “if”-type) often act intuitively to check the alternativecorresponding to the content of the “if”-clause, rather than supply a straightforward two-alternative issue to the selecting verb. Thisbehavior is somewhat unexpected on the standard account, and in our system one way of thinking about this is that the coercionoperator above is not applying normally, but much more work would need to be done to explain the full range of data of this typediscussed in the literature.

35See Pruitt and Roelofsen 2011 for a discussion of this data that appeared while this paper was under review.36It is possible in embedded cases to have disjoined polar clauses, but no complex question is formed. This reading can be

enforced by introducing “either” following the verb; see Rawlins (2008a, ex. 158) for discussion.

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seems to make entirely the wrong predictions, we will set it aside – the standard account of polar questionsneeds some modification to handle this data.

The present analysis of polar questions handles this data in exactly the right way. Since each polarinterrogative clause denotes a singleton set, Hamblin disjunction will combine these singleton sets togetherto form a two-alternative set of exactly the same type as if disjunction had scoped lower. Clauses structuredlike this are guaranteed to be at least size two, and so will never be subject to the coercion operation – theywill never act in the “standard” polar way in embedded clauses. The closure operator can then apply nor-mally to this alternative set. (We do assume that the [Q] feature must percolate up in conjunction structures,licensing closure on the larger disjunctive phrase; a more general account of the closure intonation wouldalso solve the licensing issue here. The closure intonation cannot scope on the individual “whether”-clauses,as they do not contain a disjunction.37

Our account consequently predicts disjunction to be possible in this position, with the same meaning asan ordinary ALTQ.38

3.2.4 Answer particles The final argument supporting the account of polar questions adopted in thispaper comes from the literature on answer particles. In this literature the privileged status of the of thespelled-out alternative in polar questions has proven to be crucial for understanding the behavior of answerparticles. This status is unexpected if, as in the standard account of polar questions, the semantics of polarinterrogatives treated equally the spelled-out alternative and its negation.

Traditionally, answer particles such as English “yes”/“no” seem to be some of the best intuitive evidencefor the standard approach to polar questions. If “yes” and “no” are answers, It is quite natural, for positivepolar questions, to identify one alternative as the “yes” alternative, and the other, the “no” alternative.

37A reviewer raises the question of why closure intonation is apparently required when two polar interrogative clauses aredisjoined. That is, a disjunctive polar question cannot be formed from this structure.

(i) # Is that a bird or is it a plane? (intonation: single final rise)(ii) Is that a bird or a plane? (intonation: single final rise)

While our account predicts the correct interpretation when the closure operator is present, it does not predict this acceptabilitycontrast, as disjunction could associate directly with [Q] without an existential or closure operator. We will leave this data pointfor future exploration, and are not aware of any account that does make this prediction. One possibility is that it is in fact theclosure operator, not Q itself, that licenses disjunction. A second possibility is that this structure is good, but (for reasons yet to bedetermined) the intonation pattern required for (i) is blocked for phonological reasons. There is a different intonation pattern thathas been claimed to have a similar meaning: a different reviewer raises the question of how we would handle what Roelofsen andvan Gool (2009) term an open question (their notation):

(iii) Is that a bird↑ or is it a plane↑.

Unfortunately our investigation of this data suggests that it is not general to the dialects of English we have access to. Ourinformants do accept a varient of this construction where the two questions are separate sentences (cued by a pause), and the “or”is a prefaced/particle or (see Schiffrin 1988 ch. 6 a.o. for more on the particle use of conjunctions). It is perhaps unsurprising that(iii) should have to be structured into separate utterances, given Krifka’s 2001 constraint against disjunction of speech acts. (AnALTQ of this type, on our analysis, does not involve the disjunction of speech acts.) Hence, we will not provide an analysis of thisdata here.

38 See Pruitt and Roelofsen 2010 for an independently developed account of this data that works along similar (but multi-dimensional) lines: they have an ordinary alternative meaning for polar questions as well as a ‘highlighting’ dimension (note thatthey do not frame the approach as a multi-dimensional one per se). The ordinary meaning is the standard alternative structure. Theirproposal is that polar questions highlight just the content alternative, and so their meaning in the highlighting dimension is the sameas our ordinary meaning for a POLQ. For the present set of data, they apply disjunction to the highlighted alternatives, as we doin the ordinary meaning, generating the same result. Alternative questions highlight all disjuncts, so the highlighted alternatives ofdisjoined POLQs converge with ALTQs on their proposal, though the ordinary meaning does not. In our proposal, there is only theordinary dimension, and it is the ordinary alternative structures of the two types that converge in this special case.

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However, a range of recent work on answer particles has shown that this alignment of the alternativestructure with the answer particles is deeply problematic, both in English, and cross-linguistically (Pope1972; Laka 1990; Holmberg 2001; Farkas 2007, 2009; Farkas and Bruce 2010; Holmberg 2007; Kramerand Rawlins 2009, 2010). Answers to positive questions cross-linguistically pattern, more or less, likeEnglish (except of course for well-known cases where a language doesn’t have answer particles at all; seeMcCloskey (1991)).

We will not go into the relevant data in detail here for space reasons, but a common in nearly all the workon answer particles cited above is that the behavior of answer particles is determined solely by the contentproposition of a polar question (or its syntactic structure), not the traditional two-alternative semantics for apolar question. (See especially Farkas and Bruce 2010 for development of this point.) Thus this traditionalidentification of “yes” and “no” with positive and negative Hamblin alternatives has not survived detailedexploration in the literature.

3.3 Polar vs. alternative questions

We have proposed an account of POLQs and ALTQs in which they have different semantics, and conse-quently this account makes predictions about their pragmatic behavior. POLQs present one of many alter-natives under consideration in discourse, whereas ALTQs present all of the alternatives to be considered indiscourse. In this final section we spell out several predictions made by this proposal. The larger projectof understanding both question-answer and question-question sequences remains open, and we will leave afull, formalized account of the pragmatics for future work.

The core distinction is that alternative questions present an exhaustive list of the alternatives in SalientAlts(c),but polar questions only spell out one of the alternatives in such set. Suppose that the questioner is askingthe hearer what they are bringing to a pot-luck, and that as far as the hearer knows, there are a wide range ofoptions for what the could bring. In this kind of context, the choice between asking a POLQ and an ALTQcan serve to indicate how the questioner’s assumptions might align with this. A POLQ simply indicatesthat the hearer thinks that the content proposition is an alternative, but an ALTQ indicates much strongerassumptions about what the range of options is.

(61) a. Are you making pasta?

SalientAlts(c)you are making pasta

you are making stew (implicit)you are making fish (implicit)

...

b. Are you making pasta, stew or fish?

SalientAlts(c)you are making pastayou are making stewyou are making fish

3.3.1 Question-question sequences In the present account, both POLQs and ALTQs raise issues thatare aligned with the set of salient alternatives in the context. The key difference is in what assumptionsthey introduce about this set. A polar question, on our account, identifies one alternative that is salient andis silent about the others, but an alternative question must exhaustively list the alternatives in the context.By choosing to spell out, using a polar question, some particular alternative amongst others, the speakerdemonstrates a ‘bias’ towards such alternatives and their corresponding answers, though much work remainsin spelling out the consequences. By choosing to list all of the alternatives (in the face of the possibilityof uttering a polar question), a speaker instead chooses a sort of neutrality. Hence, a particular POLQ andALTQ may allow for the the same answer, but what is learnt in the the process is quite different.

For example, considering the following question-question sequences. The key intuition is that a POLQor an ALTQ following a constituent question does not ask an independent question, but is rather a continu-ation of the prior question in some way.

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(62) a. A: What are you cooking for tomorrow’s party? Are you cooking pasta?B: I’m making risotto, I think.

b. A: What are you cooking for tomorrow’s party? Are you cooking pasta or stew? H∗L−L%

B: I’m making stew, I think.B: #I’m making risotto, I think.

The key difference is that in (62a), the questioner leaves open the full range of dishes B could be cooking,and hence a perfectly fine answer ignores the mentioned alternative. The polar question simply indicates thatthey take the mentioned alternative to be one of the possible alternatives. In contrast, the alternative questionfollowing a constituent question ‘closes off’ the alternatives, by presupposing that the list is complete,and hence a response that goes outside the list is infelicitous (without further marking such as “well”, aspredicted, see discussion in 2.2).

In summary, the account makes two desireable predictions: (i) in discourse, both POLQs and ALTQs canbe ‘continuations’ of a prior line of questioning, and (ii) the two involve different presuppositions about whatthe line of questioning involves. Polar questions leave open what the rest of the salient alternatives mightbe, whereas ALTQs provide a means of making explicit exactly what the questioner takes these alternativesto be.

3.3.2 Questioning in discourse As seen at the beginning of the behavior, polar questions and “or not”alternative questions can behave differently in the same discourse context (Bolinger 1978). The presentaccount predicts such differences in behavior. While we will not fully explore this prediction in this paper,as it is quite a substantial topic, first we explain the prediction and briefly show why it is desireable. Thedistinction follows from the fact that “or not” ALTQs presuppose exactly two salient alternative propositions,which semantically exhaust the space of possibilities. For the following examples, imagine that it has beenestablished that there are three epistemically possible meals that the addressee may cook: pasta, stew andfish. Against this background, we predict that a POLQ is compatible with a different alternative structure inthe discourse context than the “or not” question, which would necessarily ‘bundle’ together the non-pastaalternatives:

(63) a. Are you making pasta?

SalientAlts(c)you are making pasta

you are making stew (implicit)you are making fish (implicit)

b. Are you making pasta or not?

SalientAlts(c)you are making pasta

you are not making pasta

Why would this prediction be desireable? Bolinger (1978) discussed a range of empirical distinctionsbetween polar questions, and “or not” alternative questions. We will not attempt to cover the full rangeof the Bolinger data here (see Biezma 2009 for further discussion), but illustrate how our account adds tocoverage of this data with two examples. As we saw in §1.1, Bolinger noted that in discourses involvinginvitations/offers, and conversation starters, among other cases, “or not” alternative questions, ALTQVNs,and POLQs are not equivalent. In each case the “or not” question is not appropriate.

(64) Conversation Starters: Trying to start a casual conversationa. Do you like to play golf?b. # Do you like to play golf or not?H∗L−L% [ALTQVN]

(65) Invitations/offers: Your friends just arrived at your housea. Do you want some water?

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b. # Do you want some water or not?H∗L−L% [ALTQVN]

Both cases receive essentially the same treatment on our account. In each case, the question is roughlydiscourse-initial under a specific social situation. Because of this, the set of salient alternatives in each kindof situation is highly underspecified, and the social context is one where it is expected to be open. Theprediction of our analysis in general is that an ALTQVN will presuppose much more substantial constraintson the set of salient alternatives than a POLQ; a POLQ will serve to draw attention to one alternative out ofpotentially many, and an ALTQVN will signal that the questioner believes that those are the only two salientalternatives. The latter is not compatible with such contexts, because it forces the ‘bundling’ of potentiallymany epistemically available alternatives into a single one, corresponding to the negative disjunct, in thesescenarios without any reason to do so.

In the conversation starter example, the POLQ naturally leaves open the possibility that the hearer hasgreat freedom of response. That is, the questioner signals that they think the ‘golf’-alternative is a possibility,but leaves open what other alternatives might be salient. A natural response might involve other preferredsports, or even other hobbies depending on the precise details of the context. The ALTQVN in contrastrequires that the immediate context make exactly two alternatives salient: the answerer likes to play golf,or the answerer doesn’t like to play golf. While there may be many contexts in which this presuppositionwould make sense, it is not appropriate as a conversation starter, because of the constraints imposed on thehearer. This distinction is exactly what our account of POLQs and ALTQs predicts.

Our account makes a similar prediction about the offer example. An offer made with a polar ques-tion leaves open what other alternatives there might be, allowing the answerer a wide range of freedom inresponding. An “or not” alternative question, in contrast, presupposes that the immediate context makessalient only two alternative propositions, in this case one where the hearer wants water, and one where theydon’t. The discourse is placed into what Biezma 2009 describes as a ‘conversational cul-de-sac’, and in thissocial situation, this kind of move is inappropriate.

Many issues remain to be explored in understanding polar vs. “or not” alternative questions. We leave afuller exploration of these issues to the future.

3.3.3 On choosing what to spell out On the account developed in this paper, polar and alternativequestions both serve a similar ‘function’: to make explicit some alternatives that are salient in a context.They differ in what they presuppose about those alternatives: whether they exhaust the context, or not. Theprediction, then, is that when a speaker wants to make some alternatives explicit (as opposed to, e.g., askinga constituent question), they have a choice between at least a polar and an alternative question. (There are,of course, other ways to list salient alternatives.) This immediately raises the question of how a questionermakes that choice, and what a hearer will infer from that choice. In this respect our analysis builds on vanRooy and Safarova (2003), which proposes that the two question types differ in what they imply about theutility values of propositions in the content of the question, and speakers/hearers reason about the choice ofquestion type based on these utility values. van Rooy and Safarova propose that alternative questions implythat the utility value of the alternatives is equal, and a polar question implies that the utility value of thecontent proposition is higher than its negation. Our analysis has not directly implemented the idea of utilityvalues. However, we will briefly sketch some expectations about why a particular choice might or might notbe made on the part of a questioner.

Consider the running example, where a questioner knows that they can offer coffee, tea, or water, andthe hearer is not certain what the questioner can offer. This epistemic assymetry will guide the choice inan offer context straightforwardly. The alternative question listing all three alternatives exhaustively is theneutral choice – it makes no assumptions about what the hearer knows, or desires. A polar question, on theother hand, would be appropriate if the questioner thinks that one drink is a more likely choice (perhapsthe hearer is known to prefer coffee). Thus, in a sense, the ‘utility’ of each alternative follows from simple

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conversational reasoning about the hearer’s knowledge state, preferences, etc. In a factual context, similarreasoning can be invoked. Suppose the questioner is at a potluck, and knows that the salad may have beenbrought by one of two people: John or Mary. If they ask the exhaustive alternative question of someone,they take for granted this assumption but no others. A polar question, on the other hand, does not encode thisassumption but rather focuses on one particular alternative, perhaps because they think it the most likely. Apolar question would also be appropriate if the questioner knows that John might have brought the salad,but not who else. We leave a full exploration of this kind of conversational reasoning, and its connection toutility values in the sense of van Rooy and Safarova (2003), for future work.

4 CONCLUSION

In this paper we have given an articulated compositional semantics and for both polar and alternative ques-tions that bridges with the pragmatics and hence makes predictions of the behaviour of these questions indiscourse.The proposal explains a range of new and old differences and similarities between the two kindsof questions: (i) the different types of responses one can give to polar and alternative questions, and (ii) arange of contexts where the two types have a different felicity, including both Bolinger’s examples.

We have argued for a very simple compositional semantics for polar and alternative questions, makinguse of the Hamblin semantics framework. The differences between the two types of questions begin in thesemantics. For alternative questions, the alternative structure of the question is provided by the interaction ofdisjunction with a question operator. The only true complete answers to an alternative question are answerscorresponding to exactly one of the disjuncts that the question spells out. Other felicitous (but marked)responses try to go outside these alternatives are not direct answers at all to the alternative question. Rather,they are pragmatically licensed: they deny the presuppositions of the ALTQ.

In polar questions, we have proposed that there is no compositional introduction of alternatives, and theonly alternative-related operator in the structure is the question operator itself. We have further proposedthat the question operator is the same in POLQs as in ALTQs, a substantial but necessary departure from theclassical Hamblin treatment of questions. The consequence is that polar questions denote a single alterna-tive, an idea that we have argued converges with a range of recent work on polar questions. Furthermore,this idea leads to the desirable prediction of a number of pragmatic differences.

A major difference beyond the lack of the obligatory alternative disjunction is the lack of a closureoperator in a polar question. We have proposed that final falling intonation indicates the presence of aZimmermann-style closure operator at LF signaling that the alternatives spelled out are the only alternativesavailable in the context. Polar and alternative questions differ on the presence/absence of a closure opera-tor, and so polar questions introduce a non-exhaustive list (typically size 1) of alternatives, and alternativequestions introduce an exhaustive list.

The semantic difference between polar and alternative questions is key in explaining the difference intheir pragmatics. Because they are non-exhaustive, polar questions leave open the possibility that some othercontextually available alternative, besides the one presented by the POLQ, is available, whereas alternativequestions present all the alternatives that there are (and presuppose this). Crucially, when uttering a polarquestion, the speaker chooses one alternative amongst the set of contextually available alternatives and, bydoing so, the speaker favors the spelled-out alternative over the others. However, in alternative questions,by spelling all the alternatives that there are, no bias towards any of them is indicated. Not only that, abias is potentially indicated, against choosing any particular one of the salient alternatives to mention).Under the current account, many aspects of the concept of bias in (positive) polar and alternative questionsfollow from the system, and can be explained pragmatically by appealing to the discourse structure. Inparticular, we have argued that the function of polar and alternative questions respectively is to identify

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either a non-exhaustive set of alternatives (again, typically just one) or an exhaustive set of alternatives withthe immediately salient Question Under Discussion in the discourse context. We have shown that this leadsto a range of correct predictions about the contexts that the two types of questions can appear in.

Further work will be needed to spell out all the consequences of our proposal. In particular, there isa wide range of data that we have not yet dealt with. We have been concerned with polar and alternativequestions, but have not discussed polar questions involving negation, nor have we talked about other inter-esting alternative questions such as English are you coming or what? The investigation of these other typesof questions both in English and cross-linguistically will provide more insights regarding refinements to thesystem proposed here, and shed light on further investigations on discourse models.

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