Responding to alternative and polar questions∗

Marıa BiezmaUniversity of Massachusetts Amherst

maria@linguist.umass.edu

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 explicitaccount of the division of labor between compositional semantics and pragmatics in interpreting these typesof questions in discourse. The main proposal for alternative questions (ALTQs) is that they involve a strongexhaustivity presupposition for the mentioned alternatives (following Karttunen and Peters 1976; Rawlins2008; Biezma 2009; Aloni et al. to appear). We derive this compositionally from the meaning of the finalfalling tone (after Zimmermann 2000) and its interaction with the pragmatics. ALTQs are exhaustive in twoways: they exhaust the space of epistemic possibilities, as well as the space of discourse possibilities. Incontrast, we propose that polar questions are the opposite: they present just one alternative that is necessarilynon-exhaustive (this follows from the pragmatics of questioning). Our account covers a large range of em-pirical data (sketched in the remainder of this introduction): answers and responses to alternative questions,embedded polar and alternative questions, and most importantly, question-question sequences in discourse.

In this paper we argue in favor of an account of polar and alternative questions that relies on very sim-ple syntax and semantics. We make use of semantic elements independently argued for in the literature andintegrate questions within a larger semantic and pragmatic picture; the pragmatic properties of questions fol-low directly from their compositional semantics. We develop the proposal in a framework that combines acompositional Hamblin semantics for questions (Hamblin 1973; Kratzer and Shimoyama 2002) with a struc-tured discourse representation of questions that are under discussion (Roberts 1996; Buring 2003; Beaverand Clark 2008; Ginzburg to appear).

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) are non-wh questions standardly characterized by interrogative morpho-syntax, the presence of disjunction, and a characteristic intonation. Some stereotypical examples are in (1).

∗This paper is a draft submitted for publication. We would like to thank Luis Alonso-Ovalle, Pete Alrenga, Scott AnderBois,Jan Anderssen, Ana Arregui, Chris Barker, Rajesh Bhatt, Daniel Buring, Greg Carlson, Sandy Chung, Cleo Condoravdi, DonkaFarkas, Annahita Farudi, Lyn Frazier, Hans-Martin Gartner, Christine Gunlogson, James Isaacs, Ruth Kramer, Angelika Kratzer,Bill Ladusaw, Jim McCloskey, Paula Menendez-Benito, Chris Potts, Kathryn Pruitt, Geoff Pullum, Floris Roelofsen, Rich Thoma-son, Michael Wagner, and Gigi Ying; as well as audiences at Ohio State University, SALT XIX, UCSC, SALT XX, JHU, Michigan,MIT (von Fintel/Iatridou seminar in 2009), and University of Rochester for comments at different stages of this work. We alsobenefitted from discussion in Floris Roelofsen’s spring 2010 semantics seminar taught at UMass Amherst. Of course, remainingerrors are our own.

1

(In (1) small caps mark pitch accents on the disjuncts; we will discuss a more detailed descriptions 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?

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 great 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.1 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.

1We 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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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 for the two kinds of questions. This can be seenin the different kind of answers and responses to POLQs and ALTQs. Possible answers to polar questionsare typically marked with yes and no, where yes signals an answer matching the alternative presented in thecontent of the polar question. The alternative raised in a polar question influences the alternatives that maybe available to a speaker, but does not sharply constrain them. For example, the addressee of the question in(2b) may answer no, and yet indicate that they prefer some tea instead. Whereas had wanting tea been thealternative spelled out in the question, the answer (in this scenario) would have been yes. This is somewhatdifferent from what we observe in alternative questions. After an alternative question has been asked, theanswers involve choosing from the alternatives spelled out. This difference in the exhaustivity of alternativesbetween 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.2 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,

2This 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).

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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.).3 There are a wide range of open questions concerning the relationship ofthese 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).

One particular focus of the present paper is alternative questions formed by opposite alternatives (ALTQVNs).

(5) a. Do you want coffee or not?b. Are you coming or not?

The alternatives in (5a) are you want coffee and you do not want coffee, and the alternatives in (5) are you arecoming and you are not coming. On the one hand, asking such questions has a very similar effect to askingthe corresponding (plain) polar questions, e.g. “Do you want coffee?”; in both cases the answer involvessaying 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 a range ofdifferent scenarios in which POLQs are fine, whereas the use of an ALTQVN is not. Two of Bolinger’scontexts, where only a POLQ is appropriate, are illustrated below: requests (6) and inference drawing (7).

(6) Requests: Marriage proposala. Will you marry me?b. # Will you marry me or not? [ALTQVN]

(7) Drawing inferences: (Scenario: A conversation talking about David.)a. A: I just saw David.

B: Is David back from Toronto?b. B′: # Is David back from Toronto or not? [ALTQVN]

In addition to the differences noted by Bolinger (1978), we discuss new data illustrating the differencesbetween the two types of questions regarding the options made available to the addressee. We term this thecornering effect (Biezma 2009):4

(8) Scenario: You are in charge of coordinating the cooks for the colloquium dinner. John is one of thecooks. You talked to John yesterday and he said he would make stew but did not confirm whetherhe would also make pasta. Dinner is soon and you need to know what is happening with the pasta.a. You: Are you making pasta?

John: (Silence and dubitative faces)

3See 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.

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

4The cornering effect was first described and accounted for in Biezma (2009). The proposal made in this paper keeps thecore of the proposal for the final explanation of the cornering effect in Biezma (2009). However, this paper further developsa detailed compositional semantic analysis for polar and alternative questions different from the default semantics of questionsadopted in Biezma (2009), that we argue actually explains the cornering effect. That is, the semantic analysis provided here allowus to formally flesh out the bridge between the semantics and the pragmatics, and derive the pragmatic behavior. Additionally, thecornering effect is just one case among the range pragmatic phenomena that the independently motivated system provided in thepresent paper can explain.

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You: Are you making pasta or not?b. You: Are you making pasta?

John: (Silence and dubitative faces)You: (C’mon) Are you making pasta?

Intuitively, when an ALTQVN is used as in (8a), there is a reduction in the set of responses availableto the addressee. As (8a) illustrates, the questioner uses an ALTQVN to try to ‘force’ an answer from theaddressee. The use of a question asking about logically opposite alternatives, you make pasta, p, and youdon’t make pasta, ¬p, results in the cornering of the addressee. This effect is not observed if the POLQ isinstead uttered again. As (8b) illustrates, the effect of a POLQ here, if any, is that of plain insistence. Thegeneralization is that ALTQVNs are the preferred question type for seeking information when the addresseeappears to be withholding it and the speaker wishes to close the issue.

The discussion above makes it clear that understanding ALTQVNs is crucial to our goals for the paper:any analysis of alternative vs. polar questions needs to explain both differences and similarities betweenPOLQs and the special case of ALTQVNs. However, the differences between these kinds of questions haveoften been set aside. Indeed, the traditional semantics given to POLQs and ALTQVNs does not predict anyinterpretive differences between the two (e.g. Hamblin 1973; Karttunen 1977a; Groenendijk and Stokhof1984). We propose an analysis on which the difference between POLQs and ALTQVNs follows from acrucial linguistic difference in their respective structures: the presence/lack of an exhaustivity operator atLF indicated by final falling intonation. This idea leads additionally to a new account of the semantics ofpolar questions, involving a simpler alternative structure and composition than is typically assumed – theydenote just a singleton Hamblin alternative. Thus we propose that the semantics of POLQs and ALTQVNsis not as similar as might be expected. We argue that the difference in the semantics further shapes theirbehavior in discourse, leading to the account of cornering and the pragmatic effects discussed by Bolinger.

In sum, we propose and provide empirical support for a semantics of POLQs that differs from thesemantics of ALTQs in the presence/lack of an exhaustivity operator at LF. When the exhaustivity operatoris present, a question presents an exhaustive list of alternatives, but when it is not, the question presentsa non-exhaustive list. One advantage of the analysis proposed here is that the question operator is thesame in both types of questions. This uniformity is an advantage, since traditionally the justification forhaving two different operators (on a Hamblin account) is given as a solution to technical issues, withoutempirical support. With respect to the semantics of ALTQs, this paper offers extensive empirical argumentsthat the possible answers to ALTQs consist only of the propositions provided by the disjuncts, i.e. areexhaustive. Versions of this idea have been assumed in several prior works on questions (Belnap and Steel1976; Karttunen and Peters 1976; Higginbotham 1991), but arguments for or against the idea have beenunderdeveloped. Arguing for this answering space becomes important now since there are recent analysisof ALTQs that assume that not only the disjunct propositions are the possible answers (see Groenendijk andRoelofsen 2009 a.o.).

With a semantics for POLQs and ALTQs in place, we propose a natural way of connecting the semanticswith the pragmatics of questions aided by a discourse model based on structured Questions Under Discus-sion (Roberts 1996; Buring 2003; Beaver and Clark 2008; Ginzburg to appear). This kind of model tracksdifferent questions that discourse participants may be addressing in a hierarchical way, with more specificand salient QUDs being lower in the structure. Basically, the alternatives provided by the compositionalsemantics of a question must either update or be aligned with the most salient QUD. Different type of ques-tions may impose further constraints on this alignment, and in particular, we propose that ALTQs requirethe most salient QUD to align with only the mentioned alternatives. POLQs in contrast provide an alterna-tive that must be present in the most salient QUD, but leave open the issue of what other alternatives arepresent in the discourse. Asking a question of course also can result in a change in the QUD structure, or arefinement of precisely what the structure is of the salient questions under discussion. Asking an alternative

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question following a constituent question may significantly change the assumptions about what alterna-tives were present in discourse. Asking a polar question will ensure simply that the content alternative ispresent. We suggest that the cornering effect, and in general many differences between POLQs and ALTQsfollows from this pragmatics. The pragmatics itself follows directly from the semantics we propose (andindependently motivate) for polar and alternative questions. The general architecture for questions and thesemantics/pragmatics interface that we develop in this paper is summarized in (9).

(9)

Compositional semantics:

Interface:

Discourse model:

Construct alternatives(Hamblin)

Align alternatives and QUDUpdate QUD

Track structured QUDs(Roberts/Buring)

Module Function of module

1.2 Outline

In this section we have reviewed the main ideas in our proposal for the semantics and pragmatics of alter-native questions and their pragmatic differences. The rest of the paper is organized as follows: in §2 weconsider a range of empirical properties of alternative/polar questions and their responses that an analysisshould account for; much of this section involves exploring the role of exhaustivity and mutual exclusiv-ity, as well as some facts about the “bias” of the types of questions, and the nature of question-questionsequences. We then build our proposal compositionally. In §3 we lay out our assumptions about the syntaxof alternative and polar questions and propose our semantic account of the differences between polar andalternative questions, and in §4 we explore the pragmatics derived from such semantics. In this section wemainly focus on question-question sequences, which have been largely unexplored in the literature.

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 answers to them. For any ALTQ, there are certain answers that will

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always be possible, corresponding to the disjuncts that make up the utterence.

(10) 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 (10), “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:

(10) 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?5 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), is that such responses are not answers to an immediately preceding ALTQ, but rather deny thepresuppositions of the question.6 We will further suggest that when they are licensed, it is because they doaddress some higher, possibly implicit and coerced, QUD.7 In offer-type ALTQs, it is typically quite easyto find such a QUD, e.g. “what would you like to eat?” In order to motivate this proposal, though, we willfirst 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, andconsequently predict that such responses are true answers (though Groenendijk and Roelofsen 2009 have anexplanation for their markedness). The alternative structure on this type of analysis is represented pictoriallyin (11). (Note that this is a general schema of this kind of analysis, and Groenendijk and Roelofsen’streatment of the “both” alternative is slightly different; see below.)

5Note 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.

6Belnap 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.

7We will return to QUDs later in §4. For now, let’s assume that the QUD in a certain discourse is the (implicit) question thatthe participants are committed to answer.

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(11)

(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 alternatives.Groenendijk and Roelofsen 2009 acknowledge the markedness of “neither”/“both” answers, but deal withthem in the pragmatics, rather than the alternative structure. In particular, they give a system for derivingconversational implicatures against these two possibilities. The proposal is interesting and so we will sketchhow it works; see Groenendijk and Roelofsen (2009) for the full logical details, which we will not do justiceto here. (In that paper, see fig. 9 on p. 27 for a summary of their proposed alternative structure of alternativeand 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 typesof 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:

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

(13) 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 (13a)). 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 (that we will not expand); the ex-haustified answers (e.g. “only salad” etc.) are compliant responses to ALTQs but the conjunctive (“both”)answer is not. (Note that we will be using the term “compliant” below in a completely different way.)A “both” response would, however, be more homogeneous(/informative). A “both” response would alsobe a compliant response to a disjunctive POLQ. Therefore, the questioner (in choosing as the form of thequestion an ALTQ) must have had some reason for picking a question that excludes this more informativeresponse from being a compliant response, i.e. they must have already excluded the possibility from theirprivate information state. Therefore, the hearer can conclude that the “both” alternative would be false.

These two proposals are certainly an elegant account of the facts – the necessary reasoning follows fromvery general principles of the logical system developed in their paper. But is it the right analysis (or moregenerally, right kind of analysis) of the natural language data? We will argue that it is not; with the right data

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it is possible to differentiate this proposal from competing analyses. (Of particular interest to the derivationof exhaustivity is the data from alternative unconditionals, where exhaustivity effects still arise but polarinterrogative clauses are disallowed; see §2.2.2.3.) It is worth noting that for the case of mutual exclusivity,our approach while different in the details is closer to the proposal in Groenendijk and Roelofsen 2009 thanfor exhaustivity. That is, their proposal involves effectively, exclusifying the disjuncts, and our analysis willdo something similar at a more semantic level.

On the other hand, Belnap and Steel (1976), Karttunen and Peters (1976), Rawlins (2008), and Biezma(2009) exclude the “neither”/“both” cases from the denotation of ALTQs altogether, and consequently pre-dict that such responses are not in fact real answers of any kind. The basic idea is that the question pre-supposes that neither the “both” alternative nor the “neither” alternative are possible. The 4-alternative-typeanalyses struggled from the problem of explaining why “neither”/“both” are marked responses; this secondtype of analysis has the reverse problem. They must say something about why such responses are licensedat all, and what their status is. The proposal beginning in Belnap and Steel 1976 is that responses of thistype address the presuppositions of the question.8 We will be adopting and expanding this idea – suchresponses deny the presuppositions of a question, but are licensed in cases where they do address somerelated or super-ordinate Question Under Discussion that is salient in the discourse (in the case of the alter-native question do you want coffee or tea?, this superordinate question would likely be what do you want todrink?).

The alternative structure involved in this type of analysis is shown in (14), where the grayed area repre-sents logically possible cases that are presupposed away.

(14)

(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 predictionsnot just about assertive/informative responses – questions can be followed by other questions, and thesecomplex discourses involve interaction of the questions. We will focus on this data in §4, but at present itis helpful to briefly present a simple case that initially motivates the exhaustivity claim. When a constituent

8See also Isaacs and Rawlins’s (2008) analysis of responses that deny the antecedent of a conditional question; they alsopropose that such responses are not answers but presupposition denials.

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question is followed by an alternative question, the impact of the ALTQ intuitively can have a retroactiveeffect on the alternatives raised by the constituent question.

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

In isolation, the constituent question leaves the options potentially quite open. But the ALTQ continuationfurther specifies the questioner’s assumptions about what drinks the hearer can choose. This effect is quitesurprising on an analysis where the disjuncts in an ALTQ do not exhaust the possibilities. ALTQs seem to insome cases serve the function of making the alternatives from a prior constituent question explicit. With thisinitial motivation for an exhaustivity account, we move to a detailed investigation of the response systemfor 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. Asecond 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 – thatthe alternatives introduced by the disjuncts exhaust the possibility space that the question is asked over. Italso points to a mutual exclusivity presupposition – that the disjunct-introduced alternatives do not overlapat all. Consequently we arrive at, for alternative questions at least, a strong version of “Hamblin’s picture”(Hamblin 1958; Groenendijk and Stokhof 1997). That is, the alternatives introduced by ALTQs must ex-haust the space of possibilities, and must be mutually exclusive; not just that, but they only include thealternatives corresponding to disjuncts. We will in fact conclude that the exhaustivity effect is strong in con-sequence of the “list closure” intonation appearing on alternative questions, converging with Zimmermann’s(2000) analysis of this intonation on a range of coordinate structures in English. While we will not take astrong stand on Hamblin’s picture in general (see e.g. recent controversy in Velissaratou 2000; Isaacs andRawlins 2008; Groenendijk 2009; Groenendijk and Roelofsen 2009 on whether conditional questions obeyHamblin’s picture or not), it seems clear that the constraints it implies are necessary for the proper analysisof alternative questions, in order to account for the data in the present section. (We will suggest that thesemantics 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.

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2.2.1.1 Variable felicity

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

(16) Scenario: A is a waiter, B a restaurant customer.A: Would you like coffee or tea?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.

Even changing the example slightly can lead to the “both” answer seeming less appropriate:

(17) Scenario: A is an airplane steward, B a passenger.A: Would you like chicken or fish?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 fulfillingB’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.9

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

(18) 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 paper?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.10

(19) 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 paper?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:

9Thanks to Ana Arregui (p.c.) for suggesting this scenario.10The original exam scenario in (18) was suggested by Chris Brumwell (p.c.), and this variant was suggested by Michael Wagner

(p.c.).

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(20) A: # You will fail if you don’t take the exam, but are you going to take the final exam or write aterm paper?

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):

(21) Are you going to the party or not?

The two alternatives are already non-overlapping, and cover all the possibilities, just by themselves. Sincethe two alternatives in the question in (21) 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.

(22) Are you going to take the final exam or write a term paper? You can only choose one. / You haveto 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.

(23) Are you going to take the final exam, write a term paper, or neither?

(24) Are you going to take the final exam, write a term paper, or both?

(23) 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, (24) 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.11

11Note 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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(25) A: Would you like fish or chicken?B: Well/actually, do you have a vegetarian option?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.

(26) A: Would you like fish or chicken?B: Is there any chance I could have something vegetarian?B′: Is there any chance I could have both? (I’m really hungry.)B: # Is there any chance I could have fish?

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.)

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:

(27) A: Who is bringing the salad?B: Not Jim.

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

(28) A: Does Alfonso want coffee, tea, or water?B: He doesn’t want water.

However, partial answers of the kind predicted by taking “neither”/“both” responses to be answers arenot licensed. One example of this type would involve restating the alternatives; we might also explicitlyexclude the two non-core possibilities.12

(29) A: Does Alfonso want coffee or tea?

12There 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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B: # He wants one of the two.

B′: # He doesn’t want both.

B′′: # He doesn’t want neither.

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. (29B) 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.

Of course this is only part of the picture – less compliant responses are still licensed, and therefore avalid kind of response; we return to their licensing later. The proposal will be that, when licensed, theyanswer some salient but possibly covert “super-question” to the overt question (e.g. “what do you want todrink”). In cases where the context rules out the necessary super-question, these responses are not licensed.

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 inference

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in 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 alternativequestion 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.)

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

(31) 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 (30) should include the possibility of neither bringing a salad even ifthat alternative is not explicitly mentioned.13 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, (30) is nota correct description of his pondering. We must again introduce the “both” alternative explicitly to describethe scenario:

(32) 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 (30) 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.

(33) 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.14

13Note 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.

14A 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 of

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Alternative interrogative clauses can be adjoined, as well as selected for, leading to structures sometimescalled ‘unconditionals’ (Zaefferer 1991; Gawron 2001; Rawlins 2008). Such structures have all the surfaceproperties of an alternative interrogative: they have interrogative morphology (“whether”), they have anecessary disjunction, and they obligatorily carry the intonational pattern of an alternative interrogative:

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

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

See Rawlins 2008 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 (2008)). 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 (36):

(36) # 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 (36). 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 (37).

(37) # 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 evidence

the 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 2008 ch. 4 formore discussion of the licensing problem for clausal adjuncts.

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to be among the strongest (for English ALTQs at least), since the effect is so clearly truth-conditional.15 Incases 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.16

What then is the status of responses that address these excluded possibilities? The natural answer(Belnap and Steel 1976) is that they are presupposition denials, used to address some assumptions thatthe speaker is making, rather than answer the immediate question at hand. In fact, in later sections we willexplore the idea that such responses are licensed just in case they felicitously address some larger question inthe discourse. Treating such responses as presupposition denials at once explains why they are marked andvariably present, and why the corresponding alternatives seem to play no role whatsoever in the semanticsof embedded alternative questions. The implicature account can explain some but not all of the first part ofthe 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(18)) 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 (38) eliminates the existence presupposition triggered by the possessive as

15It 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 2008), 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]

16Roelofsen 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. 19), 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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an inference from the whole sentence. We can similarly eliminate the exhaustivity inference from an ALTQin a parallel fashion, illustrated in (39).

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

(39) If I only have water and tea, and you want something, do you want water or tea H∗L−L%?

(39) does not presuppose (or entail at all) that there are only the two mentioned options, exactly thebehavior we’d expect if the inference is a presupposition. And a “neither” response is completely out as aresponse to (39), exactly the predicted behavior if exhaustivity is a presupposition.

In the following section, we turn to the compositional semantics of the two types of questions, and thenin §4, build on the semantics to explain the interactions of polar and alternative questions with the discoursestructures they appear in.

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.) Since the semantics of questions is inextricably tied with their pragmatics, some details of the se-mantics/pragmatics interaction will be deferred until §4. We will first discuss alternative questions, buildingon the data in the previous section, and then turn to polar questions.

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

(40) 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. (This is effectively the analysis of disjunction in Rooth and Partee 1982, implemented with adifferent scope mechanism.) In a Hamblin semantics alternative sets compose in a “pointwise” fashion: forfunction application, each member of the function alternative composes with each member of the argumentset. (Of course, if both are singleton, this behaves like standard Fregean FA.)

(41) (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))}

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In (42) is an example existential derivation that results in truth-conditions matching classical disjunction.

(42) 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.

A key component of the Hamblin analysis of disjunction is the disassociation of the operator (in thiscase providing quantificational force) and the alternative-introducing function of disjunction. Introductionof alternatives is the unifying character of all instances of disjunction, but differences between differentcases of disjunction can be explained by interaction with different operators (Alonso-Ovalle 2004, 2005;Rawlins 2008)

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). In thecase of embedded questions, the alternative set will be used by the verb that selects for the question. Theresult is a very simple denotation for the question operator:

(43) 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 fol-low most recently Beck and Kim (2006); Rawlins (2008) 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).17

(44) Syntax of an alternative interrogative

17Note 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.

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CP

C′

C

whether[Q]

TP

... or ...

On the analysis schematized in (44), 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 2008) 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 (42), is shown in (45).

(45) 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 (42))

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”,“I believe not”, etc. (see (46)). The structure of examples like (47), 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; see AnderBois (2009) for what is clearly a single question operator that performs a similar functionin Yukatek Maya. We will be abstracting away from this and treating the two types of “or not” questions thesame, as we aren’t aware of any semantic or pragmatic difference.

(46) 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]]

(47) 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 (43) adequate as it stands?

There is a missing piece to this picture, and this is the source of the exhaustivity and mutual exclusivityeffects demonstrated in §2. The alternatives that the analysis so far derives may overlap, and/or both be false.Two options immediately present themselves. First of all, these effects could follow from the properties ofthe question operator (or the nature of questions themselves). This idea has been pursued in Karttunen and

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Peters (1976) and Rawlins (2008), and is quite natural given “Hamblin’s picture” – the idea that questionsin general are associated with these properties (Hamblin 1958; Groenendijk and Stokhof 1984, 1997). Theother approach, following most directly Biezma (2009), is to take these effects to follow from a closureoperator spelled out with the intonational contour seen on alternative questions (see also Bartels 1999; Pruitt2008a; Rawlins 2008). The main support for this approach is that the same contour is general to English listconstructions of all types (Zimmermann 2000), and we can therefore gain a unified account of the meaningof this contour across different conjunction structures.

Here we take a combined approach. We argue that exhaustivity is semantically encoded by means ofa closure operator and further argue that this operator is directly linked to the pragmatics of questions.This way we establish the right bridge between semantics and discourse. First, propositional alternativesin question meanings must exhaust the possibilities and not overlap. Second, alternatives in the scope of aclosure operator must exhaust the complete set of salient alternatives in the context of utterance; the fullimpact of this will not be completely developed until the semantics developed in this section is integratedwith the pragmatics of questioning. (We will equate the set of salient alternatives with the Question UnderDiscussion in the sense of Roberts 1996.)

Here is the closure operator, based on Zimmermann (2000) and Biezma (2009):18

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

yc =

def

q[[Q] α]

yc defined only if SalientAlts(c) =

q[[Q] α]

yc

Left intuitive for the moment is the notion of salient alternatives in a given context (we will return to itbelow). The claim here is that an exhaustive list produces a set of alternatives that are co-extensive withthe full set of salient alternatives in a given context. No alternatives are left out of the list, and no extraalternatives are included. Accommodating this presupposition amounts to inferring what your interlocutoris assuming the complete set is.

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 2008.)

(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.19 In combination with the closure operator, an asker of an

18See also discussion in Pruitt 2008bThis is easily applied to all propositional lists; Zimmermann focuses on cases where thelists are not of propositions, and we do not consider these here.

19 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 as

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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 (45). 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 that wouldbe resolved by choosing between these alternatives. The constraints in (49) require that there be no worldsin the context set at which he neither danced nor sang, and no worlds at which he both danced and sang. Themotivation is the exhaustivity/exclusivity data in (2), where we showed that alternative questions in fact doexhaust the epistemic possibilities, and responses that challenge this (e.g. suggest that he neither danced norsang) have the status of presupposition denials. To explicate this, however, we must connect up the notionof “salient alternatives” with the act of questioning.

The connection for alternative questions is straightforward (see (48) above) – they are a kind of hybridbetween exhaustive lists and questions, and their list-like nature (following Zimmermann) forces a matchbetween the alternatives provided by the list and the set of salient alternatives. Consequently, the listed-alternatives must also obey the constraint in (49), leading to epistemic exhaustivity/exclusivity effects.

For other types of questions, there are two parts to this issue: how the salient alternatives in a givencontext constrain questioning in that context, and how questioning affects the set of salient alternatives inthe output context.20 Hamblin’s picture, as it is usually understood, is a special case of a conceivable answerto the second question, where questioning for all question types always fully determines the set of salientalternatives in the output context, which then obey the constraint in (49). What we will eventually proposehas two parts: (i) non-list questions do not always constrain the input set of salient alternatives, but are moretypically constrained by them, and (ii) polar questions are different from alternative questions in that theyonly contribute to determining one among potentially many salient alternatives. (That is, polar questions donot obey Hamblin’s picture, though the contexts they lead to do.)

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”, giving

long as the exceptions (i) are obviously exceptions, and (ii) are not pointless (have a salient explanation for the violation of theconstraint). 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.

20For alternative questions, the answer is the same: the input context matches the listed alternatives (this notion of course needsmuch more precision), and the output context also has the listed alternatives as the salient ones.

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a two-alternative set containing propositions: {λw . a is bringing the salad in w,λw . j is bringing the saladin w}. The question operator (currently) leaves this set unchanged, handing it off to the closure operator.The closure operator introduces the presupposition that exactly these two alternatives are the salient alter-natives in the context (what this means is as yet unformalized). As such, they must obey the exhaustivityconstraint in (49). This constraint tells us that there can be no worlds that cross-cut the two alternatives,where both of them bring a salad. It also tells us that there can be no alternatives outside the two alternatives,where they both bring something else (or nothing). A “neither” response, therefore, denies the presupposi-tion introduced by the closure operator, introducing the claim that there must have been another alternativethat should have been included in the list as well. This account, with an appropriately developed notion ofquestioning, accounts for the full range of data in 2.2, making many desirable predictions. For instance, itcorrectly predicts that if the “neither” alternative is included in the list, the status of corresponding responseswill change. It predicts that these extra responses will be typically hedged or unavailable, depending on thecontext. It also makes the right predictions for embedded cases, as long as a suitable notion of “salientalternatives in a context” is extended to attitude reports (the context will typically need to be ‘internal’ tothe report, as in e.g. Heim 1992; Aloni and van Rooy 2002; Isaacs and Rawlins 2008).

With this example, 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). Thetheory presented in this section is intended to set the stage for the pragmatics-semantics interface accountof asking polar questions developed in the following section. As a baseline, in our discussion we willuniformly assume a syntax where a polar question has a [Q] operator of some type in the usual position (C),and nothing else special.21 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 introducingelement (e.g. no disjunction, no “wh”-item), and so it is necessary to have a specialized polar questionoperator that introduces these alternatives.22

(51) Standard account of polar questions (to be argued against)Where JαK = {A} (undefined if not a singleton set23):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, wondering

21The major competing hypothesis (see Larson 1985; Han and Romero 2004b a.o.) would be to take polar questions to be“or not” questions with a silent “or not”. This of course leads to problems explaining all the ways we have noted that ALTQVNsbehave differently from POLQs. Given the range of data we have discussed, we take this approach to be a non-starter. It shouldbe noted that this is likely to be an English-specific conclusion. AnderBois 2009 discusses in depth an apparently polar questionconstruction in Yukatek Maya that behaves semantically and pragmatically like the English “or not” question, and the languagedoes not obviously have other polar constructions.

22A Groenendijk and Stokhof (1984)-style approach leads to a more elegent 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.

23This will force a polar question with a disjunction to have a covert ∃ operator.

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whether 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 (in the following sections) to resolve tensions in majorpragmatic differences between alternative and polar questions. One way to view this approach is that weare taking seriously the point that, alone of all question types, polar questions compositionally lack anyalternative-introducing item. Though we will not dwell on embedded questions, we suggest that when nec-essary, a pragmatic mechanism is available to coerce a singleton set into the above 2-alternative denotation,in order to resolve a constraint against singleton sets imposed on non-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 behaviorone dimension resembling our account – one dimension is the classical alternative set, and one dimensioninvolves a singleton containing the content proposition. On their semantics, this second dimension typicallyplays the role that our single dimension does, and so the two proposals converge on a similar idea. (See fn.31 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 means then, 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 (again, postponingthe discussion of precisely what determines this set until §4, though for now it can be thought of as a QUD).

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

yc=JαKc

defined only if JαKc ⊆ SalientAlts(c), or if SalientAlts(c) = /0.

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 (53). This constraint is due to Beck and Kim 2006; there they treat it as part of the questionoperator, but suggest that it might follow from the properties of embedded questions and the pragmaticsof root questions. (Below we will adopt a similar constraint in the pragmatics, as well.) To resolve themismatch inherent in our semantics for polar questions, we will assume the coercion operation in (54).24

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

24Another 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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(54) 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 (51), 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 betweenthe mentioned alternative (the content proposition), and some salient alternatives that they must infer fromthe context (more on this later). There are a number of proposals about polar questions that share the samebasic idea, that “answering” them really involves accepting or not accepting the mentioned alternative: forGunlogson (2001) polar questions create an imbalance in the public commitments (the speaker makes aclaim that they are explicitly not committed to) that must be resolved. For Farkas and Bruce (2010), apolar question involves putting the content proposition on the “table”, and responding to that propositionin some way. The idea also resembles the notion of ‘highlighting’ in Roelofsen and van Gool (2009) andPruitt and Roelofsen (2010). Here we take it that a polar question obligatorily raises an issue in discourse,as with other questions (the non-singleton constraint applies to it, as well), but the only direct evidenceit provides about the content of that issue is given by the content proposition. Hence, answers to a polarquestion fundamentally address that content proposition in some way. We make this notion more precise inthe section on polar and alternative questions in discourse, §4.

The primary benefit of this account, in the context of the present paper, is the explanation it providesof the differing behaviors of alternative and polar questions in discourse. Before proceeding to an in-depthdiscussion of the pragmatics, we first briefly review a range of other reasons to adopt an interface accountof polar-questioning.

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(2001, 2008). Gunlogson discusses both the case of rising declaratives that act polar-like in some ways, andregular declaratives25 that act like polar questions in the right context.

(55) 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 a

25While 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.

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polar 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.26 Our account does not work precisely the same way, but the intuitionis based on Gunlogson’s – a polar question involves presenting a single alternative when the public contextdoes not decide between that alternative and some unstated other possibilities, but the addressee is in aposition to decide for or against this alternative. Answering a polar question is about affirming or denyingthe content proposition, and the identification of a propositional utterance as a polar question lies in thepragmatics.

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. This isexactly what AnderBois (2009) argues for “polar” questions in Yucatec Maya: there, the item that appearsto be specifically a polar question operator is morphologically related to disjunction and indefinites. Ander-Bois shows that on a range of diagnostics (including the Bolinger data) what are apparently polar questionpattern with English ALTQVN questions. On our account, this item would act to introduce alternatives,unlike the Q operator in English polar questions.

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:27

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

(57) a. * Alfonso doubts whether it is raining or not.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.2829

26To 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.27There is no distinction between “if” and “whether” clauses here, the split is entirely along alternative vs. polar lines.28What we do not explain is why it should be dubitatives that have this selectional property, cross-linguistically.29A 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 alternative

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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 2008 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.30 (Example (58) is from Belnapand Steel 1976 p. 91.)

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

(59) 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 in general), and so might be considered an empirical footnote. On the other hand,trying to account for this data wreaks havoc on all standard analyses of polar questions we are aware of.Suppose the above standard account of the semantics of each “whether”-clause were combined with thestandard Hamblin disjunction mechanism – this generates a size-four alternative set that is completely dif-ferent from what 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 structureseems 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 –they will never act in the “standard” polar way in embedded clauses. The closure operator can then applynormally to this alternative set. Our account consequently predicts disjunction to be possible in this position,with the same meaning.31

corresponding 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.

30It is possible in embedded cases to have disjoined polar clauses, but no complex question is formed. This reading can beenforced by introducing “either” following the verb; see Rawlins (2008, ex. 158) for discussion.

31 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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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.

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; Kramer and Rawlins 2009,2010). Answers to positive questions cross-linguistically pattern, more or less, like English (except of coursefor well-known cases where a language doesn’t have answer particles at all; see McCloskey (1991)). But fornegative polar questions, all bets are off. A basic observation is that perhaps the most likely expectation onthe standard account, that “yes” and “no” simply reverse function, is uncommon in the languages that havebeen studied (though this is not a particularly representative sample). When discussing negative questionshere we have in mind “inner” negative questions, e.g. “Did Alfonso not go to the party?” Outer negativequestions present additional challenges.

Three patterns are more common. One is exemplified by (most dialects of) English (Kramer and Rawlins2009) and in it, the negative and positive particles simply neutralize in the context of a negative question,both corresponding to the negative alternative (the content proposition). A closely related pattern simplydisallows positive responses to negative questions, licensing only the correspondent of “no”. Finally, manylanguages have particles that “reverse” the polarity of a negative question (e.g. German “doch”, French“si”), but can’t be used with a positive question; these languages typically also disallow the positive answerparticle following a negative question (Farkas 2007, 2009; Farkas and Bruce 2010). What is to be made ofall this? If we are to take the distribution of answer particles as direct evidence for the alternative structureof polar questions (as in the intuitive argument for the standard approach), and not ignore the full range offacts, the story is clearly going to be very complicated, and different from any approach previously proposed(including the one we are advocating here). Not only that, a strict correspondence between alternatives inquestion meanings and answer particles is doomed by the fact that many answer particles can be used torespond to a range of speech-act types, not just questions (Farkas and Bruce 2010).

However, if we don’t try to hold to this strict correspondence, there is a common thread in nearly allthe work on answer particles cited above that is quite informative in the present context. (See especiallyFarkas and Bruce 2010, the most worked-out account to date.) In all accounts, it is the form and/or meaningof only the alternative determined by the polar interrogative itself, that serves to license and determine themeaning of an answer particle. That is, it does not seem to be a binary alternative structure that matters forunderstanding polairty particles, but the nature of the singleton alternative determined by the content of thePOLQ. A subsidiary point, also present on all the cited accounts, is that although answers(/responses) topolar questions can be marked with answer particles, the particle is not the answer itself (this is especiallyclear on ellipsis accounts; see Laka 1990; Holmberg 2001; Kramer and Rawlins 2009). This is exactly thekind of account of answer particles predicted by the present account of polar questions, where the questionpresents only one alternative corresponding to the content proposition, and not at all by the standard one.

Having laid out these supporting arguments, we now turn to the main issue at hand: the analysis of polarand alternative questions in discourse, and the semantics/pragmatics interface for such questions.

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4 DISCOURSE

In this section we propose an account of the discourse properties of alternative and polar questions. The pro-posal is that the behavior of these questions in discourse follows from independently motivated principlesof discourse in combination with the compositional semantics, and in particular the alternative structure andpresuppositions, developed in §3. Because polar questions involve one alternative semantically, an answerermust choose between that alternative and some salient, unstated alternatives.32 Reasoning about these al-ternatives follows straightforwardly from Immediate Question Under Discussion (IQUD)-based theories ofdiscourse (Roberts 1996; Buring 2003; Beaver and Clark 2008; Ginzburg to appear) – the salient alternativesreferred to in the previous section are in fact alternatives present in some IQUD.

An alternative question presents an exhaustive, rather than open, set of alternatives, and this exhaustivityforces the discourse structure licensing an alternative question to be quite different. In particular, it requiresthe local IQUD to contain only the listed alternatives; cornering effects follow because asking an ALTQVNfollowing a POLQ sharply constrains the alternatives (besides the content proposition) that might otherwisehave been inferred in the case of a polar question.

On our account, neither polar nor alternative questions function primarily to introduce a new QUD.Rather, each in a different way serves to draw attention to alternatives that are present in some possiblyimplicit but salient QUD.

We will first present some basic background about the particular theory of discourse we assume, and thenturn to question-answer sequences. Next, we show how the system handles question-question sequences,what we take to be a crucial (but underexamined) empirical domain for understanding questioning. Finally,in §4.4 we will discuss an alternative approach to the distribution of POLQs, ALTQs and ALTQVNs, inparticular van Rooy and Safarova’s (2003) proposal, and how it relates to ours.

4.1 The basics

One main goal of this section is to give an account of the (in)felicity of sequences of utterances involvingmultiple speakers. Consequently we need to make some assumptions about the nature of the larger structureof discourse. There are many theories of the structure of discourse (see e.g. Polanyi 1988; Asher 1993; vanKuppevelt 1995, 1996; Roberts 1996; Ginzburg 1996; Gunlogson 2001; Asher and Lascarides 2003; Buring2003; Gunlogson 2008; Farkas and Bruce 2010; Ginzburg forthcoming). Our goal here is not to argue forany particular theory of discourse, but in interests of concreteness we must pick one. We make use ofBuring’s (2003) model; it is particularly useful for understanding the nature of question-answer discourses.Buring’s D-Trees will prove very useful when explaining sequences of questions and their possible response,as well as sequences of questions. However, we believe that what is said about questions and responses inthis paper could be implemented in any other sufficiently elaborated theory of discourse, as long as somenotion corresponding to Roberts’ (Immediate) Question Under Discussion ((I)QUD), and some analogue of

32This notion resembles, to some extent, AnderBois’s (2010) notion of fine-grained alternatives (sub-alternatives to an alter-native picked out semantically by a question) – i.e. these are like sub-alternatives of the traditional negative alternative (that ouraccount lacks). However, the details of AnderBois’ account are different – fine-grained alternatives are present in the main alter-native corresponding to the polar question’s polarity, rather than opposing it. Both alternatives in an ALTQVN have fine-grainedalternatives. This is effectively the opposite of our proposal, and we cannot currently see how to reconcile the intuition behindfine-grained alternatives with the empirical motivations for the current proposal. A full comparison will have to wait for a later day.It is worth noting that AnderBois’ aim is in large part to handle high negative polar questions, a data point that we are purposelyexcluding.

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Kuppevelt’s hierarchical tree-based discourse structures, are present.Buring (2003), building on Roberts’s (1996), proposes a hierarchical discourse model with the assump-

tion that discourse is driven and is structured by (possibly implicit) questions. (See also Beaver and Clark(2008); Ginzburg (to appear) for recent defenses of this kind of theory.) A speaker’s utterance either at-tempts to resolve some question under discussion, or posits a question that could be answered by discourseparticipants. This corresponds to a view in which the purpose of discourse is a communal inquiry (followingmuch work in philosophy of language, see especially Grice 1975; Stalnaker 1978; Lewis 1979). The goal ofcooperative participants in a given discourse is to answer the (accepted, current) IQUD. (Beaver and Clark2008 refer to this as the Current Question). In order to achieve this goal, the participants in a discoursedevelop different strategies. These strategies correspond to the different subquestions that will lead to thefinal answer to the main question –what Roberts (1996) terms the Big Question.

Buring (2003) makes use of a theoretical device in which the discourse is represented in a D(iscourse)-tree, (60).

(60) Discourse

Question

subq

answer

subq

answer

subq

subsubq

answer

subsubq

answer

subq

answer

Question

answer

(Buring 2003, ex.(6))

The Big Question corresponds to the top most question in a d-tree. Every node in the d-tree represents a(possibly implicit) discourse move; following Buring we take the representation of a move to be a syntacticstructure (though this is not crucial here). D-trees encode a total order of moves (though some may beimplicit), determined by a depth-first traversal of the tree. At any point in a discourse, there will be aquestion that is the most recent one (the IQUD/Current Question), and answers to that question are attachedas daughters.

D-trees amount to a generative theory of discourse structure. Given this, a Question-Answer pair iswell-formed iff there is a well-formed d-tree which contains it, (61a). The system also predicts that aQuestion1-Question2 sequence is well-formed if there can be a d-tree in which Q1 immediately dominatesQ2, (61b). We will not recapitulate the full details of Buring’s 2003 system (in particular, see the appendixto that paper), focusing instead on what we modify.

(61) a. Q

A

b. Q1

Q2 (Buring 2003, ex (7))

Buring sketches two conditions that characterize the set of well-formed d-trees: informativity, (62a),and relevance, (62b, Buring’s ex. 8):

(62) a. Informativity: Don’t say known things, don’t ask for known things!b. Relevance: Stick to a question until it is sufficiently resolved!

As Buring points out, (assertive) informativity can be checked against the participants’ common ground/ context set (Stalnaker 1978). The informativity of a question in a context can be defined in a similar

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way; given an appropriate definition of a complete answer, a question will be uninformative in a context ifthe common ground entails a complete answer to that question (see e.g. Groenendijk 1999). With respectto relevance, Buring assumes that “A is an answer to Q if A shifts the probabilistic weights among thepropositions denoted by Q.” Given some notion of answerhood, Buring’s first attempt to define relevance isin (63) (Buring 2003, ex. (9)).

(63) Relevancea. An assertion A is relevant in a d-tree DT iff A is an answer to the Q(uestion) U(nder) D(discussion)

for A in DT.33

b. A question Q is relevant in a d-tree DT iff at least one answer to Q is an answer to the QUD forQ in DT.

These constraints, as they stand in Buring (2003), set out a theory of discourse for purposes of under-standing contrastive topic and related phenomena. However, they will be of good service to us in whatfollows. In the next section we will see how a hierarchical discourse model like the one presented in thissection, in combination with the semantics of POLQs and ALTQVNs, can account for the pragmatic effectswe have observed.

4.2 Sequences of questions and responses

To connect up the appearance of questions in the discourse structure with their compositional semantics, wepropose the following constraint (where IQUD(M) in Buring’s system is the immediate QUD for a move Min a d-tree):

(64) For any move M, the context of interpretation cM for M includes an element called SalientAlts(cM).SalientAlts(cM) = IQUD(M).

That is, the contextual parameter appearing in the semantics of POLQs/ALTQs refers to the QUD forthe move. This immediately predicts an interaction between both POLQs and ALTQs, and the d-trees theyappear in. The alternative presented by a POLQ will have to be one of many alternatives present in the QUDfor the move. An ALTQ in contrast will have to list all the alternatives in the QUD for the move. In a typicalcase the QUD will be provided by an explicit or implicit constituent question that did not fully define theexact alternatives involved. Let’s see an example. The corresponding d-trees for the discourses in (65) arein (66) (we will discuss them later in more detail):

(65) a. A: What are you cooking for tomorrow’sparty? Are you cooking pasta?

B: I’m making pasta, I think.

b. A: What are you cooking for tomorrow’sparty? Are you cooking pasta or stew?

B: I’m making pasta, I think.

(66) a. What are you cooking for tomorrow’s party?

Are you cooking pasta?

I’m making pasta

(Are you cooking stew?)

b. What are you cooking for tomorrow’s party?

Are you cooking pasta or stew?

I’m making pasta

The IQUD of the assertion “I’m making pasta” is an explicit question asked by the other participantin the discourse. This (questioning) discourse move is made by uttering a semantic question (either aa POLQ or an ALTQ) asked in order to find an answer to the Big Question “what are you cooking for

33For any move M, the QUD for that move is the move M′ immediately dominating it. (Buring 2003, pg 7)

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tomorrow’s party?” For the questioning move of asking either a POLQ or an ALTQ to be felicitous, thealternatives in the semantic object, SalientAlts(cM), need to correspond with the alternatives in the discourse(the constraint in (64)). POLQs present one of many alternatives in SalientAlts(cM), whereas ALTQs presentall the alternatives in SalientAlts(cM)

To make this precise, we need to state exactly what the IQUD is at any point in the discourse. We turnto this issue now.

Buring, focusing mainly on QUDs that arise from explicit or implicit constituent questions, takes theIQUD to be the set of alternatives provided by the semantics of an immediately dominating question. Wewill adopt this principle for constituent questions (rule (ii) below). However, a core part of our proposal isthat both polar and alternative questions serve a different function: to provide more information about anexisting IQUD. As such, they don’t serve to change the QUD, at least as their primary function. These rules,as well as one for the discourse-initial state, are given in (67).

(67) Where M is a move:(i) IQUD(M) = IQUD(M′) (if there is an immediately dominating move M′ that is not a constituentquestion)(ii) IQUD(M) = JM′KcM′ (if M′ is a constituent question)34

(iii) IQUD(M) = /0 (if there is no immediately dominating move)

(68) Constraint on discourse: If M is a move immediately dominated by some node, then |IQUD(M)| ≥ 2.(see Beck and Kim 2006 and ex. 53 earlier.)

In our examples in (66), the IQUD of the assertion move is the immediately dominating POLQ or ALTQ.The IQUD for these is, in turn, the constituent question first asked. The alternatives presented either in thePOLQ or in the ALTQ have to be amongst the alternatives in their IQUD, the constituent question. Theconstraint in (68) establishes that there has to be always more than one alternative (see discussion in §3.2).35

Given the connecting principle in (64), it is useful to repeat the definitions from the semantics section,substituting in explicit reference to the immediate QUD:

(69) Question operator (IQUD version)q[[Q]α]

ycM=JαKcM defined only if JαKcM ⊆ IQUD(M), or if IQUD(M) = /0.

(70) Closure operator (IQUD version)q[ [[Q] α]H∗L−L%]

ycM=

q[[Q] α]

ycM defined only if IQUD(M) =

q[[Q] α]

ycM

Our proposal now takes its complete form. The effect of the closure operator signaled by the final fall on anALTQ is to presuppose that the alternatives contained in the question exhaustively describe the immediatequestion under discussion. A polar question (involving only the presupposition from (69)) identifies one al-ternative in the IQUD, leaving open what the others might be. Polar and alternative questions are guaranteedto be Relevant in d-trees that they are capable of appearing in (i.e. that satisfies the presuppositions), andso can provide a different sort of strategy for adressing a Big Question: helping an interlocutor by makingexplicit some or all of the alternatives that are available to them.36

Do polar and alternative questions ever change the QUD? We will see one particular case below wherewe propose that they do, locally adjusting the granularity of the question to ‘bundle’ together alternatives

34We would prefer not to stipulate this, but currently it is not clear how to technically accomplish this.35One issue this system leaves open is whether disjunctive polar questions cannot, may, or must involve a Hamblin ∃ operator or

not, i.e. whether disjunction in these questions can interact directly with the question operator. The classical view is that it cannot(this is enforced by the version of the Hamblin POLQ operator presented earlier in (51)), but Pruitt and Roelofsen (2010) propose(in different technical terms) that it can. The issue should ideally be settled empirically.

36Notice also that the rules as set up block discourse initial polar and alternative questions, the prediction being that one mustinfer some implicit QUD in order to license them. We take this to be, basically, a correct prediction. In certain cases, for polarquestions one might also use the coercion operation in (54) to satisfy this constraint, following Beck and Kim.

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into a larger one. In d-tree terms, this will result in a local limitation on what sisters are possible. First,though, we will deal with more basic cases involving just questions and answers.

4.2.1 Question-answer sequences: two types of strategies Let us start by examining a discourse struc-ture beginning with a POLQ, in (71).

(71) A: Do you want coffeeL∗H−H%?B: Yes, thank you.B′: No, thank you, I would prefer tea.

A possible d-tree corresponding to the dialogue in (71) looks like (72). (From now on, we will usesuperindexes to signal the actual utterances and their respective order. Questions without superindexes areassumed to be implicit but not uttered. This is simply a matter of notation, as the same information couldbe reconstructed from the d-tree along with Buring’s EXPLICIT function.)

(72) (WHAT do you want to drink?)

1Do you want coffee?

2Yes, thank you / 2′No, thank you, I would prefer tea

(Do you want tea?) (Do you want a soda?)

A possible (perhaps the only) interpretation of the overt discourse in (71) is that the Big Question concernswhat the addressee wants to drink. In order to find out the answer for the QUD, the questioner adopts theovert strategy37 of asking whether the addressee wants coffee via the POLQ “do you want coffee?”. Thepolar question ensures that, of the alternatives resulting from the “what” IQUD, one of them is a coffee-alternative. It does not place further constraint on the alternatives (though we assume that there must beothers, constrained by world knowledge). One way of looking at this is that POLQs do not have final risingintonation, and thus there is no closure operator – the list of alternatives (in this case, a list of size one) isnot exhaustified. A consequence is that there are non-overt but epistemically available alternatives, perhapscorresponding to the possibility that the addressee wants tea, or that the addressee wants a soda. Sincesuch alternatives haven’t been overtly mentioned, they must be inferred depending on the context. Onceinferred, the addressee of the question may respond by requesting one of those alternatives, as in (71). B’answers no to the possibility of wanting coffee. On this view, English “yes” and “no” involve addressingonly the content alternative of a preceding polar question (or declarative), following Farkas and Bruce 2010;Kramer and Rawlins 2009. A “yes” response fully resolves the IQUD, but a “no” response leaves otheralternatives open (and thus often appears with a continuation). This view of polar questions predicts thatit will always be felicitous to choose one of the other available alternatives, e.g. in the case of an offer, torequest something other than the mentioned alternative. As with other non-overt components of a d-tree, theprecise nature of the non-mentioned alternatives that are present when a polar question is asked are highlyvariable.

A word needs to be said regarding why the speaker might decide to spell out one particular alternative(i.e. the possibility that the addressee wants coffee, in the above example) instead of other alternativesalso epistemically available from their perspective. For example, suppose that the epistemically availablealternatives, from the questioner’s perspective, are that the addressee wants coffee, tea or a soda. In therunning example, the speaker decides to spell out just the alternative in which the addressee wants coffee.

37We follow Roberts (1996) when defining strategies of inquiries as “sequences of set-up moves, or questions, designed to (atleast partially) satisfy the aims of the game, while obeying the game’s constraints. Given that the main goal is to answer the BigQuestion, a reasonable strategy will involve a plan to do this by developing sub-goals which are easier to achieve and are logicallyrelated to each other in such a way as to facilitate achieving the main goal.” (Roberts 1996, pg. 4–5)

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Why would they do so? There are many possibilities, in fact, and we take it that a hearer will reason aboutthem. One is that they would make this choice because they think coffee is the most likely or relevantalternative for some, highly context-specific, reason. For example, imagine that the questioner wants toplease the addressee, and knows that the addressee is a diabetic. Though they know they have some (sugary)soda that they could offer, it is very unlikely that this is the most useful alternative to acquaint the addresseewith. Between the other two alternatives they might try to decide which one is the most likely one, i.e. theone the addressee may prefer or is most likely to choose. Another possibility compatible with the accountis that the questioner might simply choose at random if it isn’t very important.

The basic idea surrounding this reasoning is inspired by van Rooy and Safarova (2003): a speaker willchoose the alternative to structure a polar question around based on reasoning about what alternative (ifany) would be most useful for some purposes, and a hearer will reason about this also. The questioner(and possibly the hearer) reasoning about the utility value in terms of beliefs or desires, in van Rooy andSafarova’s (2003) sense,38 is a special case (see §4.4 below). Our approach is more general (we will returnto a detailed comparison with van Rooy and Safarova’s account below), and makes somewhat differentpredictions by not tying reasoning about the choice of alternative directly to the semantics. For instance,it predicts that a polar question can be appropriate when the (information-seeking) questioner thinks thatthe probabilities of the answers are equally likely, though it isn’t the most typical use.39 Of course if thealternatives aren’t equally likely (for some reason), all other things being equal, a polar question introducingthe likely alternatives will be the preferred question type. (In this respect we concur with van Rooy andSafarova 2003.) In short, many contextual factors affect the choice of alternatives to spell out; when thespeaker wants to please the addressee, these include the speaker’s knowledge of the addressee’s interests,wishes, capabilities. (If the goal is not to please the addressee, alternatives would be chosen following othercriteria).

To summarize so far, we have proposed that the primary function of a POLQ is to ask a question in-volving at least the alternative provided by the content of the question. This much is standard, but we havefurther claimed that a polar question involves potentially many implicit alternatives; these correspond todifferent strategies the questioner could have chosen in order to address the Big Question. An answer to apolar question, when marked with “yes”, corresponds to the mentioned alternative from the question. Ananswer marked with “no” rejects the mentioned alternative in some way, and consequently must involve oneof the implicit alternatives.

A POLQ (in contrast to an ALTQ, discussed shortly) does not presuppose that the addressee has tochoose only amongst the spelled out alternatives from the question (since there is of course only one) andconsequently the addressee has room to choose amongst one of the other epistemically available alternatives

38van Rooy and Safarova (2003) propose that we choose what alternative to spell out regarding its utility (an an alternative canhave more utility if it is more informative or it agrees more with the questioner’s goal). See §4.4 for more details.

39Notice that this kind of reasoning is not specific to questions. We can find the same phenomenon in every occasion in whichthe speaker has to choose between alternatives and between ways of identifying sets of alternatives. Imagine that John is visitingNew York and is having a beer at the counter in a bar. It so happens that the person next to him, Tim, is the curator of the MOMA.They start talking and John asks him what are the most interesting things to see in the MOMA, and Tim answers as in (i).

(i) Well, you can visit Monet’s paintings and Richard Serra’s sculptures.

Tim chooses to recommend Serra’s sculptures and Monet’s paintings considering that those are the most popular items in themuseum and the average tourist is only interested in those. However, imagine that John is specially educated on Novacek. Imaginethat the MOMA has a painting by this artist in a very hidden room. If the curator knew of John’s special interest in this painter hewould have offered it as an alternative (even though the curator may hate that artist and he has no interest whatsoever on anyonevisiting this painting), (ii).

(ii) Tim: Well, you can visit one of Anton Novacek’s paintings in room #13.

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that is not spelled out. (Of course, since they may not know the full range of epistemic options, they may notactually be in a position to do more than reject the positive alternative.) Thus the addressee of the questionin (71) can reject the offer of having coffee, and at the same time can request a tea (another epistemicallyavailable alternative that is typically available) with the result being a felicitous dialogue.

A final note on polar questions: on our account, a POLQ is still compatible with there being only oneother mentioned alternative. For example, in the above d-tree, the alternatives might be coffee or nothing.It is in this case that the analysis of POLQs converges to some degree with their classical account, and a“no” response will be fully resolving. Our claim is that this convergence happens at the level of discoursepragmatics, not semantics.

English ALTQs are different from POLQs and polar questions in general in two ways: (i) they mustinvolve disjunction with at least two disjuncts, and (ii) they involve list closure intonation, and the corre-sponding operator defined earlier in (48). In consequence they carry the presupposition that the alternativesspelled out are the only alternatives the speaker considers available, and that just one of those alternativesholds. (See §3.) That one of the alternatives in ALTQs hold is a corollary of the closure operator in com-bination with exhaustivity and exclusivity of the salient alternatives: if the world can only be in one ofthe alternatives put forward in the question (exhaustivity), and these alternatives do not overlap (mutualexclusivity), then one of them must hold. The overall effect can be seen in the following dialogue:

(73) A: Do you want coffee or teaH∗L−L%? [ALTQ]B: I want coffee, please.B′: I want tea, please.B′′: # I want a soda please

In (73), the questioner wonders what the addressee wants to drink, and the Big Question might well be thesame as in the earlier polar examples. A D-tree corresponding to the dialogue in (73) (assuming the whatBig Question) is in (74).

(74) (WHAT do you want to drink?)

1Do you want coffee or teaH∗L−L%?

2I want coffee, please/ 2′ I want tea, please

Effect of closure presupposition from H∗L−L%:

IQUD(1)={λw .you want coffee in w,λw .you want tea in w}(Where IQUD(1) is provided by the Big Question “WHAT...”)

When an ALTQ is used as strategy to answer the Big Question (“what do you want to drink?”), it blocksanswers that address an alternative besides those explicitly spelled out. This follows from the effect of theclosure operator, as described to the right of (74). The d-tree is well-formed (presuppositions are locallysatisfied in the d-tree) if the context makes salient an exhaustive/exclusive alternative set, and the closureoperator then enforces that the listed alternatives match the salient alternatives (the IQUD), and therefore areexhaustive/exclusive. The salient alternatives that form the input context in the ALTQ node are the outputalternatives from the constituent question, and therefore, the alternative question constrains these. Askingfor a soda would go outside the listed alternatives, leading to infelicity.

We have of course seen in §2.2 that there are ways of getting out of this alternative set: the ‘less-compliant’ responses. For example, someone could respond, “Actually, I don’t want anything to drink.” Toreiterate, our proposal is that these directly address the presuppositions of the preceding question. Here wesuggest a further constraint: they must still address (be part of a strategy for answering) the Big Question.(We assume that “nothing” is an alternative semantically present in constituent questions.) How could thisbe formalized in the d-tree account? We assume that this kind of response attaches as a sister to the ALTQ,and changes the assumptions about what IQUD(1) involves. (One concrete way of doing this and endingup with a consistent tree would actually be to cross out or eliminate move 1 from the tree, i.e. assume that

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the entire move is rejected by a presupposition denial.) In this example, for instance, a response like “well,do you have any soda?” at the same time attempts to deny the presupposition of the ALTQ and suggesta strategy for answer the Big (“what”) Question that is only viable if that presupposition in move 1 waswrong.

The general prediction is that alternative questions are often used as a tool for further specifying thesalient alternatives resulting from a prior constituent question (which does not specify the alternatives indetail), and this is a correct and important prediction.

In summary, polar and alternative questions embody two different kinds of strategies for addressinga Big Question. What they have in common is that each involves making explicit some alternative oralternatives that the questioner thinks are part of the Big Question. The difference is in what they makeexplicit: POLQs mention some such alternatives, and ALTQs mention all of them. In d-tree terms, POLQsallow for sister nodes, and ALTQs block implicit sisters that go outside the alternatives listed in the ALTQ.This discourse-structural difference between POLQs and ALTQs is the direct consequence of the differencein the semantics of the two types of questions: the presence/absence of exhaustivity operator signaled by afinal falling intonation, and the semantically underspecified nature of polar questions.

The power of this system is not just in understanding answers to polar and alternative questions, but re-sponses more generally. In the following sections we look at the properties of question-question sequences,arguing that they fall out naturally from this system. We focus on two core special cases: alternative ques-tions followed by narrowing polar questions, and polar questions followed by ALTQs, specifically “or not”ALTQs.

4.2.2 Question-Question sequences: POLQs and ALTQs Sometimes the questioner needs to appealto different strategies beyond letting the speaker answer and fill in implicit super-questions. For instance, asequence of polar questions can follow a bigger alternative question:

(75) A: Do you want coffee or tea?B: (silence and dubitative faces)A: Do you want coffee?B: No, I don’t want coffee...A: Do you want tea?B: Yes, thank you/No, thank you, I do not want tea either.40

The D-tree corresponding to the dialogue in (75) is in (76).

(76) (WHAT do you want to drink)

1Do you want coffee or teaH∗L−L%?

2Do you want coffeeL∗H−H%?

3No, thank you

4Do you want teaL∗H−H%?

5Yes, thank you

When asking the ALTQ, the speaker establishes that the only available alternatives are either that the ad-dressee wants coffee or tea (i.e. asks the speaker to accommodate that those are the only alternatives).However, since the addressee seems incapable of deciding between the offered alternatives the questioner

40Notice that the presupposition failure is dissolved here through the dialogue and does not come out as strong as a direct neitheranswer to an ALTQ. There is more to investigate here, but we speculate that it is the non-directness that licenses this “no” response.In particular, in this context A’s second polar question may actually signal a backing off of the exhaustivity presupposition.

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tries to help out by asking the POLQs corresponding to the alternatives spelled out in the ALTQ. Notice thatonce the first POLQ in (75) is answered, the questioner can still wonder about the other alternative madeavailable in the ALTQ and another POLQ can be uttered on this respect, until the questioner exhausts allthe alternatives put forward. Once the alternatives are made available, they remain available during the restof the dialogue. This can be observed in one of the felicitous responses in the dialogue in (77).

(77) A: Do you want coffee or tea?B: (silence and dubitative faces)A: Do you want coffee?B: Yes, thank you./Actually, I want tea.

In (77) one of B’s final responses, “Actually, I want tea” appeals to an alternative not spelled out in theimmediately dominating question, but that is epistemically and discursively available given the next super-question. This alternative is one of the two alternatives that the initial ALTQ puts forward, the other possiblesister of the question “do you want coffee?” The D-tree in (78) illustrates the dialogue in which the addresseeof the question chooses to answer by requesting a non-spelled out alternative.41

(78) (WHAT do you want to drink?)

1Do you want coffee or tea?

2Do you want coffee? (Do you want tea?)

3Actually, I want tea

The utterance “Actually, I want tea” answers affirmatively to one of the other (implicit) possible questions.We will get back to this issue below. Notice that an answer to “Do you want coffee?” in (77) can refer to theother alternative previously spelled out. However, as predicted, it is not possible to answer to this particularPOLQ by requesting something other than coffee or tea, (79).

(79) A: Do you want coffee or tea?B: (silence and dubitative faces)A: Do you want coffee?B: # Actually, I want a soda please

The question do you want coffee? in (79) is a POLQ, but the alternatives available have been previouslyestablished as being you want coffee and you want tea, and the set of alternatives cannot be expanded. Oncethe available alternatives are set up, we cannot introduce further alternatives. Thus even though a POLQis asked, it is still understood that the only possible alternatives from which the addressee can choose areeither wanting coffee or wanting tea. In our discourse representation, the infelicity in (79) is illustrated bythe absence of an (implicit) POLQ in which a soda is offered and thus Actually, I want a soda, please isnot a felicitous answer to any question (unlike Actually, I want tea in (77), which is a possible answer to animplicit question).

41Notice that “Actually, I want tea” is an answer to the question “Do you want coffee?”, via pragmatic enrichment we understandthat the answer to the question regarding coffee is negative and, furthermore, the speakers gives extra information, i.e. what theywant is tea.

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To summarize, ALTQs restrict the available alternatives to those mentioned in the question, as discussedin §3. However, POLQs regarding those alternatives independently are licensed. These POLQs only implythat the other possible alternatives available are the ones already provided by the previous ALTQ. Once theset of available alternatives has been closed, it cannot be widened, at least not without switching to a higherbranch in the d-tree and rejecting some previous discourse move(s).

4.2.3 Question-Question sequences: POLQs, ALTQs and ALTQVNs

In this section we turn to a special case where POLQs are followed by alternative “or not” questions.Consider the dialogue in (80).42

(80) A: Are you coming to the party?B: I don’t know.A: Are you coming to the party or not?

Speaker A wants to get some information: whether (or not) the addressee is coming to the party. Withthe purpose of obtaining that information, A utters a positive polar question. However, in uttering theresponse, the addressee B does not fulfill A’s expectations. B does not give/indicate a useful answer (afterB’s utterance, A does not know whether B is going to go to the party). Since A is not satisfied with theresponse, he/she utters a second question: an alternative question with “or not”. The final effect of thisquestion is that of cornering the addressee so that he/she will feel compelled to give/indicate a clear answerto the question (Biezma 2009).

What happens after cornering? The addressee could still resist and insist on that he/she does not knowyet about the matter (though such responses are marked). However, they will feel compelled to make adecision (or to reveal the truth, if the addressee was withholding information) and fulfill A’s expectations ofobtaining the requested information (either affirmative or negative). The effect of cornering the addressee isnot present if instead of using an ALTQVN, a PolQ is uttered again; compare (80) and (81).

(81) A: Are you coming to the party?B: I don’t knowA: # Are you coming to the party?

In fact A’s re-questioning here seems somewhat inappropriate. To the extent that the repeated POLQimposes some pressure on the addressee in (81), this is only the effect of insistence, and is not comparableto (80).43

42An open question is the precise role of “I don’t know” responses here. A response involving ignorance, i.e. I don’t know, ismore acceptable when a POLQ question is asked, than when an ALTQVN is asked. This contrast is shown in (i) and (ii).

(i) A: Are you coming to the party? B: I don’t know. A: Are you coming to the party or not? B: # I don’t know.(ii) A: Are you coming to the party? B: I don’t know A: Oh, c’mon! Are you coming to the party? B: I don’t know.

After a POLQ has been uttered the addressee can appeal to ignorance, (ii). However, when an ALTQVN has been asked, theappeal to ignorance in (i) is less acceptable. There is, of course a difference between cases in which the addressee of the questionis withholding information or is in a position in which he can make a decision and thus answer the question, as in (i), and cases inwhich the addressee really lacks the information or cannot make a decision and thus give an answer. Such cases are, for example,illustrated by questions regarding a third person: is John coming to the party?.

It is beyond of the scope of the paper to try to account for when a speaker can appeal to ignorance and avoid giving an answer.We leave further exploration of the topic for the future.

43“Cornering” certainly involves insistence. After all, asking an ALTQVN is a way of not letting go the issue and perseveringin getting an answer to a previously asked question. However, as the contrast between (80) and (81) shows, cornering is more than“insisting”.

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Sequences of POLQ+ALTQVN questions cannot be asked in the reverse order from the cornering dia-logue, (82).

(82) A: Are you coming to the party or not?B: (silence)A: # Are you coming to the party?

A POLQ is not felicitously asked after an alternative question on the same issue.What predictions does our system make about the kind of question-question sequence represented in

cornering? In particular, what does it say about the strategy embodied in the d-tree in (83)?

(83) Do you want coffee?

Do you want coffee or not?

Let us put the strategy in (83) in context, (84), and revisit the data.

(84) Scenario: B is paying a visit to A and B just walked through the door:A: Do you want some coffee?B: (silence and dubitative faces)A: Do you want coffee or not?B: No, maybe later/Yes, please

In this context, the questioner sees that the addressee is not quite decided, and wants to close up the issueby following his previous question with an ALTQVN. This can be a dialogue that is part of a d-tree like(85). As discussed above, the effect of the ALTQVN is that of forcing the addressee to give an answer withrespect to the coffee alternative.

(85) (WHAT do you want to drink?)

1Do you want coffee?

2Do you want coffee or not?

(Do you want tea?) (Do you want a soda?)

In the dialogue in (84), if the addressee answers “no” to the ALTQVN on coffee, the questioner couldfelicitously ask then whether the addressee wants some tea instead. This is a case in which the questionertries to help out the addressee to decide which drink he wants by discarding one by one all the alternatives,since evaluating all the alternatives at once seems to be overwhelming for the addressee. The ALTQVN is amove that is ultimately part of a strategy to answer the Big Question: what do you want to drink? Anotherway of putting the point is that the cornering effect is local: it does not permanently close off alternatives tocoffee, but just forces a local response regarding that alternative (see Stalnaker 2002).

As it stands our account needs a small amendment to handle this particular d-tree. Right now, ALTQscan’t have local effects, and the calculation of the IQUD for a move dominated by move 2 leads to the wrongpredictions. Intuitively, we want to allow the “or not” question to group all of the other alternatives into asingle one locally, and right now it has a global effect.

This can be seen more explicitly with discourse like the following:

(86) A1: Do you want coffee, tea, or soda? H∗L−L%

B2: ...

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A3: Well, do you want coffee?

B4: ...

A5: Do you want coffee or not? I have to decide how much to grind.

Here, move 5 seems to group the tea and soda alternatives together locally. This effect seems to be thatALTQs (so far) can be used to bundle existing alternatives together. Notice that move 5 here, as it stands,involves a presupposition failure (clash with the presuppositions introduced by move 1): there are threealternatives together. We will implement this bundling effect as a constrained kind of local accommodation,where we mean “accommodation” in the sense of Stalnaker 2002. The constraint is that we can take anexisting IQUD and locally disjoin alternatives, but never any other operation, as long as we keep the set ofworlds involved the same. We will implement this in terms of a partition (disjoint minimal cover) of theIQUD, and the notion of a ‘coarse extension’ of an alternative set below.

(87) Partition Given a set I, a partition of I is a set of sets P s.t. (e.g. Partee et al. 1993 p. 46)

a. For any A ∈ P, A⊆ I and A 6= /0.

b. For any A,B ∈ P. A∩B = /0

c.⋃

P = I

(88) Coarse extensions (/ ‘bundling’ of alternatives)For any set of sets of worlds Q, a set of sets of worlds Q+ is a coarse extension Q iff there is apartition P of Q such that for every A∈Q+, there is some A′ ∈P such that

⋃A′= A, and

⋃Q =

⋃Q+.

(89) Local accommodation of IQUDs to coarse extensionsIf M′ is a move with presuppositions on the IQUD that are not satisfied, locally allow accommoda-tion of IQUD(M′) to a new set Q+ that satisfies the presuppositions of M′, as long as Q+ is a coarseextension of the original IQUD(M′).

So, for example given the alternative set

{λw . sc wants coffee in w, λw . sc wants tea in w, λw . sc wants water in w},

there is a coarse extension that involves disjoining the latter two alternatives. This is exactly the kind ofalternative set that satisfies the presuppositions of the “or not” question above.44

Returning to the dialogue in (84), ALTQVNs are now predicted to be licit strategies for helping the ques-tioner to achieve the task of resolving the super-question question. How are they licensed? What we see hereis that the polar question occurred in a context with two alternatives in the scope of the closure operator, onecorresponding to the content proposition, and one corresponding to its negation. The answerer is thus morenarrowly restricted than what would result from the effect of the polar question alone, which only forces

44This predicts that bundling can be quite widespread, and we think this is right. The following question-question sequencesdemonstrate bundling in three more cases: a constituent-ALTQ sequence, a constituent-POLQ sequence, and an ALTQ-ALTQsequence (the latter involving multiple turns, similar to cornering).

(i) A: What do you want to eat? Do you want meat or something vegetarian?(ii) A: What do you want to eat? Do you want something vegetarian?

(iii) A: Would you like chicken, fish, tofu, or pasta with pesto sauce?

B: Hmm, not sure...

A: Well, do you want meat or something vegetarian?

These data also fall out under the account of bundling developed in the text. What would require further exploration in thesedialogues is what happens after the response to the bundling question, which presumably involves unbundling. One possibility isthat a further narrower (“Do you want chicken?”-type) question ends up as a sister to the bundling question.

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the salience of the content proposition as an alternative. The account we have developed straightforwardlypredicts this.

ALTQVNs can be strategies used to address a POLQ. Is there any strategy that could then be usedto obtain an answer for an ALTQVN? The answer is no. The effect of the ALTQVN on the set of salientalternatives means that there could be no licensed sister to the ALTQVN. There are not further questions thatcan be used to narrow down an ALTQVN. The only possible move, if this alternative question is acceptedby the addressee, is to give an answer to the ALTQVN. ALTQVNs are a cul de sac.

It is important to point out that the cornering effect is not just the result of the exhaustivity associatedwith falling intonation. The nature of the alternatives is important, as well. Notice that a regular alternativequestion indicates exhaustivity with respect to the alternatives available but there is not generally the samesense of cornering. This is because other questions can be used as strategies to answer the alternativequestion, (90).

(90) 1Do you want coffeeL∗H−or teaH∗L−L%?

2Do you want coffeeL∗H−H%?

3Do you want coffeeL∗H−or notH∗L−L%?

4Do you want teaL∗H−H%?

5Do you want teaL∗H−or notH∗L−L%?

Once the alternative question has been asked, the questioner can go on asking for the different alternativesspelled out (as a strategy to solve the question under discussion). It is when the question asks about oppositealternatives that we find the cornering effect. ALTQVNs are the last moves available to the questioner to tryto solve the Big Question.

The fact that ALTQVNs are the last question in a sequence of questions and that they do not havesisters explains the cornering effect. ALTQVNs are the best fitted and hence, not surprisingly, the preferredquestion to try to force the closure of open issues.

Let us briefly consider the even-more complicated case in (91).

(91) A: Do you want coffee?B: (silence)A: Do you want coffee or not?B: Actually I would like a soda instead

Many (though not all) speakers consider (91) an acceptable dialogue. The example illustrates that theaddressee can keep track of the alternatives opened (or implicitly accepted as available) in the previousutterances, and return to them. Once the implicit alternatives made salient by a polar question are availablein the discourse, they remain available if the local context can be escaped. (Speakers who do not accept thisdiscourse prefer more explicit means of escaping the local context.)

In structural terms there is a question as to how this kind of ‘escape’ response fits into the d-tree. Itdoes in a sense provide an answer to the local QUD, which is a bundled version of the Big Question withtwo alternatives, coffee and not coffee. But really it provides a complete answer to the Big Question.More complex (e.g. doubly linked) structures might be ideal in the long run, but in order to meet Buring’sminimality condition on d-trees (which basically says that a complete answer must be dominated directlyby a node providing the IQUD that it answers45), we will take the structure to involve the following tree.

45The full minimality condition, slightly amended to handle our treatment of questions that do not change the QUD:

(i) Minimality Condition (slightly amended)If m is a complete answer to Q (i.e., if JMK0 logically entails p or W − p for every p ∈ JQK0), some node providing thesame QUD as Q immediately dominates M and no other such node is dominated by M’s immedaite parent.

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(92) (WHAT do you want to drink?)

1Do you want coffee?

2Do you want coffee or not?

(Do you want tea?) (Do you want a soda?)

3Actually, I would like a soda (instead)

The slight oddity arising from the dialogue in (91) comes from the fact that when asking an ALTQVNon a particular proposition (in this case having coffee), all the questioner cares about is the resolution ofthat particular proposition. The ALTQVN carries the presupposition, possibly accommodated local to thispoint in the discourse, that the only available complete answers correspond to the coffee, or the no coffee,alternatives. The discourse at this point is about coffee, and nothing else is important. However, the globaldiscourse supports other alternatives, so as long as a response is appropriately marked, it can escape to theglobal level.

This is very similar to our analysis of non-compliant responses, and in fact we find similar marking forall responses that escape a local QUD to answer the Big Question, e.g. the presence of “actually”. Recallfrom earlier that we argued that “actually” in general marks denied expectations of all types (including butnot limited to presuppositions). Here it functions to deny the expectation (encoded as a presupposition) thatled the questioner into the cul-de-sac in move 2, i.e. to try a strategy with a ALTQVN as a sub-question.46

We leave open the larger question of whether the system should be amended to allow double linking ofmoves like 3 in the above d-tree to 2 in addition to its implicit parent.

We saw above that a question like Do you want coffee or not? cannot be followed by a POLQ, i.e.POLQs cannot be used as strategies to answer an ALTQVN. We also saw above that regular alternativequestions can be answered using strategies that do involve polar questions corresponding to the mentionedalternatives. The question now arises whether the “actually”-type reponses that were felicitous in (91) arefelicitous here as well. In fact the theory we have developed predicts that they are not, and this is the correctprediction:

(93) A: Do you want coffee or tea?B: (silence)A: Do you want coffee?B: # Actually, I want a soda.

In contrast to a response to an “or not” question, there is no expectation to deny here: the POLQ locallyleaves open other alternatives and thus has sisters in the d-tree.47

46Interestingly, it seems to be only able to deny fairly local expectations, and is thus usable as a diagnostic for what the localexpectations might be. For example, the B′ response in the following discourse, which attempts to locally deny a presuppositionarising from an ALTQ several nodes up, is not acceptable, even though it would be as a direct response to that question.

(i) A: Do you want coffee or tea? B: (silence) A: Do you want coffee? B: (silence) A: Do you want coffee or not?B: Actually, I want teaB’: # Actually, I want a soda.

47Notice that the (similar) question-question sequence in (i) is not felicitous at all.

(i) A: Do you want coffee or tea?B: (silence)A: # Do you want coffee or not?

This case is particularly interesting in that the negative alternative should actually already be restricted to the tea alternative, in

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While we will not go through examples in detail, nothing in our analysis is contingent on our use ofALTQs where the speaker is making an offer, they simply provide a convenient example type. Similarcornering effects occur with other types of questioning (e.g. information-seeking), and the analysis worksidentically. The main differences are (i) inferences about the way in which the Big Question is underspeci-fied, which are heavily domain-dependent, and (ii) differences in reasoning about why particular alternativesare the ones that overtly mentioned for POLQs. On our analysis both of these differences involve inferencesabout the discourse, not directly the discourse or semantic representations themselves.

In this section we have given an account of the pragmatics of question-answer sequences, a range ofquestion-question sequences, and especially for cornering dialogues. The summary is that cornering followsfrom the reduction in freedom to infer other salient alternatives that our system predicts when an ALTQVN(with a closure operator) follows a POLQ. This in turn follows from the semantics of alternative and polarquestions interpreted in the context of the QUD-based theory of discourse.

4.3 Interim conclusion

The proposal made in this paper explains the full distribution of responses to alternative questions, bothanswers and questioning responses. The general proposal is that the two types of questions have a differentalternative structure, which in turn leads to different pragmatics. Alternative questions involve presentingan exhaustive list of choices, but polar questions involve presenting a single alternative and leaving open topragmatic inference the nature of other alternatives (explicated in terms of the Question Under Discussionmodel of discourse; Roberts 1996; Buring 2003).

In the previous section we mentioned some ideas adopted from van Rooy and Safarova’s 2003 decision-theoretic analysis of the difference between polar and alternative questions, in particular that speakers willreason about why particular alternatives were chosen to make overt. In the following section we turn tothis proposal in more detail. We argue that van Rooy and Safarova’s (2003) theory as is does not make theright predictions, and moreover that our account provides an explanation of why POLQs and ALTQs invokethe kind of reasoning that the decision-theoretic account assumes they do, something not provided by thedecision-theoretic account.

4.4 ALTQVN vs. POLQ: the decision-theoretic account

As we saw earlier (6–7), Bolinger (1978) demonstrated empirically that polar questions and alternativequestions formed by two opposite alternatives (i.e. “or not” ALTQs) are not interchangeable. We haveexpanded on this by considering a range of question-question sequences where they do not subsitute.

Bolinger’s (1978) particular observations in particular have been taken up in later work. Recently,van Rooy and Safarova (2003) propose that many of Bolinger’s observations should be accounted for in adecision-theoretic framework. According to van Rooy and Safarova (2003), ALTQVNs and POLQs differ

terms of epistemic possibilities in a context, though the propositions are not matched (i.e. tea only is equivalent to not coffeerelative to some contexts). We will have to leave a full explanation for the future, but this actually seems to be a general propertyof alternatives, not specific to ALTQVNs – restating a single alternative using a different form is problematic. (In contrast to‘bundling’, where multiple alternatives can be restated at the same time.) For instance consider the following infelicitous variantof a cornering dialogue (see Pullum and Rawlins 2007 for a similar example using a species of unconditional adjunct; gnus are thesame species as wildebeests):

(ii) A: Did you see a gnu or an alpaca.

B: (silence)

A: # Did you see a wildebeest?

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in the “utility value” of their possible answers. A possible answer has a greater utility value than another ifthe answer is more in line with the questioner’s goals (e.g. involves more overlap with the possible worldscorresponding to those goals). For example, in the case of pleas like Do you know how to repair a puncturedtire? (van Rooy and Safarova 2003, 5:1) the speaker’s goal g, when asking ?q is for q to become true and,thus, a positive answer (a yes answer) would have greater utility value. In many cases the goal may verywell be merely to obtain information. Van Rooy and Safarova propose that using POLQ signals that theutility value of a positive answer is higher than the utility value of a negative answer. However, in the caseof alternative questions, the speaker does not prefer any one alternative over the other: the utility value of qis equal to the utility value of ¬q. In 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). This goes for a ALTQVNstoo, so for an alternative question ‘?(p∨¬p)’, UV(p)≈ UV(¬p), an entirely different relationship than ina positive polar question. Pragmatic differences should then fall out of the difference in the utility values ofpossible answers. With respect to (outer) negation polar questions (e.g. where negation appears on a raisedauxiliary; see §1.1), van Rooy and Safarova (2003) claim that the utility value of a negative answer is higherthan the utility value of a positive one. Thus, the proposal is to account for the distribution of negative andpositive polar questions in terms of the utility value of the answers: if the utility value of a positive answeris higher than the utility value of the negative answer, the speaker would utter a positive polar question, anda negative polar question otherwise.

While we think some version of this idea is on the right track, there are several problems with theproposal as formulated. First, van Rooy and Safarova 2003 do not give a compositional account of how toderive the utility values from the structure of the different types of questions. Second, the account does nothandle the full complexity of the response system, as discussed above in §2 (or the cornering data discussedin §4.2.3). While both a compositional account and an account of the rather large range of additional datawe have introduced were beyond the scope of their paper, they are of course desirable. Third, as we willshow in the remainder of this section, the decision-theoretic idea, formulated in terms of utility values, is toorestrictive in its predictions. The account developed in this paper allows for much more general reasoningabout why various alternatives might be included in the alternative structure of question, and suggests thatreasoning about the utility of possible answers to the questioner falls out as a special case, rather than beingthe case from which others are derived.

The upshot of the argument is that the decision-theoretic account makes the wrong predictions for posi-tive polar questions (though it is more succesful for negative questions, which we don’t discuss here). First,as a general point, we would not obviously expect POLQ-ALTQ or ALTQ-POLQ sequences on this kindof account, because they involve different commitments as to utility values. But such sequences are quitecommon and felicitous, as we have seen. This could perhaps be modeled by local adjustments of utilityvalues, or a change in the relevant notion of utility at various points in the discourse. We will leave open afull development of this idea, as we think a version of it follows from our account. We also would not expectorder to be crucial in cornering examples, but we have seen that something about ALTQVNs forces them tobe the last question in a strategy. Finally, a core prediction prediction is that for cases where a questionerbelieves two opposite answers to be equally likely, and is seeking information, there should be a (strong)preference to ask an ALTQVN question. We will show that in general in examples like this, there is no suchpreference, and in fact ALTQVNs are dispreferred.

Turning to a more specific example, let us consider (94).

(94) Last week John commented to Steve that he was considering the idea of going to Cancun for theSpring break or of staying home. Chances were 50%. Today they are having coffee in a cafeteria.Steve: Are you going to Cancun?

Intuitively, the scenario itself here sets up equally likely alternatives but is still most naturally addressed witha polar question. Let us consider this in more detail. The utility value of a positive answer to a POLQ should

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be higher than the value of a negative one on the decision-theoretic account. Hence, Yes, I am should havea higher utility value than a negative answer, No, I am not in (94). The scenario in (94) provides us with thesimplest case, the case in which the only goal of the inquiry is to obtain information. By default, van Rooyand Safarova (2003) assume positive statements are more informative than negative statements (see Givon1978), leading to a default higher utility for a positive answer. However, informativity needs to be checkedagainst the context and cannot be assumed by default. A standard (neo-Gricean) definition of informativitystates that a proposition p is more informative than a proposition q if by adding p to the common ground wenarrow down the context set more than when adding q. The cooperative principles tell us that one should beas informative as possible, and thus, more informative propositions are preferred. However, in (94), whenasking the POLQ question, Steve is agnostic regarding whether Steve is going to Cancun or not. For him,adding to his ground the positive answer q, Sam is going to Cancun for spring break, is as informative as¬q, Sam is not going to Cancun for Spring break. A positive answer is not more valuable than a negativeone, and thus in this case van Rooy and Safarova’s (2003) make the wrong predictions.

In fact, given that both the negative and the positive answer are equally informative in the scenario, theprediction according to van Rooy and Safarova (2003) would be that the question should be asked as analternative question with two opposite alternatives (where UV(p)≈ UV(¬p)), Are you going to Cancun ornot? However, such an ALTQVN is clearly inappropriate in the context in (94) or, at the very least, givesrise to an effect completely different from that of either negative or positive polar question.

On our account, an ALTQVN is not appropriate in (94) because “cornering” is simply not justified inthe local context in which it would appear.48

As noted earlier, on our account, speakers reason about why particular alternatives were made explicit.That is, the primary function of POLQs and ALTQs is to make explicit alternatives that have been implicit,not to actually change what question is currently under discussion. (The secondary function is to sometimesgroup together alternatives for the purposes of local discourse.) When a POLQ is used, it only makesexplicit a part of the alternative set, where as an ALTQ necessarily lists the entire set of (locally) salientalternatives. Thus each of these questions represents a choice about what (if any) alternatives to make clearto an interlocutor. In consequence, it is inevitable that the interlocutor will reason about why the speakermade these alternatives salient. We do not deny the importance of reasoning about the utility of variousalternatives (/ possible answers), or even of modeling them formally, but rather take this to be one specialcase of a kind of inference that happens as a consquence of the compositional semantics and pragmatics wehave developed. There is no direct mapping of question choice to utility values or probabilities.

Why do ALTQs tend to present probabilistically “balanced” choices? There are many reasons a speakermight present an exhaustive list, and several common ones lead to an inference along these lines. In anoffering context, the questioner may have no basis for guessing which options the recipient will prefer, soplays it safe and presents them all. In an information-seeking context, the questioner may not have anyinformation about which alternatives the interlocutor is aware of or will remember. They also may not have

48An anonymous reviewer points out that van Rooy and Safarova (2003) assume (following Bolinger 1978) that ALTQVNs canadditionally carry an “insistence” meaning. The reviewer further suggests that they could explain the infelicity of an ALTQVNin this context because insistence is not appropriate. First, this would not automatically explain why a POLQ can be used in thisscenario. But a decision-theoretic account of insistence, which they sketch, leads to other problems. In van Rooy and Safarova(2003) insistence is modeled by a rise in the utility values of the alternatives, but not the relation between them, which remainsUV (p) ≈UV (¬p). This rise is presumably given by world-knowledge. van Rooy and Safarova (2003) do not explicitly discusscornering, but their proposal consequently makes the prediction that we should be able to detach insistence (or cornering) fromALTQVNs altogether – any alternative question could potentially trigger the same effect. This is problematic, since we have arguedthat the effect triggered by ALTQVNs is not generally found in other ALTQs. Nevertheless, “insistence” never plays a role intheir explanation of why a POLQ may be preferred to an ALTQ or an ALTQVN, and it is always the relation between the utilityvalue of the answers that matters. Hence, on their account of insistence narrowly construed, the evaluation of examples like (94)would remain the same. Our proposal instead ties cornering to ALTQVNs in particular (we take this to be empirically correct) andprovides an explanation of why these particular questions trigger such effect. Furthermore, we have argued that cornering is morethan insistence; see fn. 43 and surrounding discussion.

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any expectations about which one is true, so can’t use a POLQ to focus in on one in particular. Thus ouraccount can be seen as a means of deriving inferences about utility values from the compositional semantics.

If reasoning about the utility value of the answers cannot fully predict the distribution of positive andnegative polar questions, what other tools are necesary? An idea we will adopt from previous literature onPOLQs vs. ALTQVNs is Buring and Gunlogson’s (2000) proposal that a POLQ, ?q, is felicitously utteredonly if there is no “compelling” evidence against q in the context. They do not discuss ALTQs (focusingon negative POLQs), but we can add to this that an alternative question requires that there be no compellingevidence against any alternative. In their system, this difference does not follow from anything. But inour system it does (though we will only briefly sketch the idea): a natural extension of the Maxim ofQuality into the domain of questions is that any alternative made explicit must be one the speaker considerspossible (or something stronger); we will call this constraint Viability. (A version of this idea is inherentin Hamblin’s Picture.) On the traditional view, a Viability-type constraint does not distinguish polar andalternative questions. But here, since polar questions only put forward their content alternative, they imposeno requirements on the negative alternative. An ALTQVN in contrast requires that both alternative satisfyViability. Therefore, an asymmetry in some cases (discussed below) is straightforwardly predicted.

We have seen that van Rooy and Safarova’s (2003) theory does not quite make the right predictionswith respect to positive polar questions. We have not fully resolved the issue of whether a decision-theoreticaccount could be amended to account for the problematic data, though it is clear that the account would needsome amendment. However, we have proposed that our account leads to a derivation of the same inferences,and can explain a full range of data, such as cornering. As such it provides an explanation of the inferencesvan Rooy and Safarova (2003) were interested in, not just a description of them. For the future we leave aformalization of exactly how inferences over utility values or probabilities might be derived.

4.5 Back to Bolinger’s data

On our account of alternative questions, any alternative question requires some fairly limited alternativescorresponding to the content of the disjuncts in the IQUD – presupposed to exist by the closure operator.(This presupposition is often accommodated.) Polar questions impose a much weaker requirement on the d-tree – they need just a single alternative matching the content proposition in the IQUD. We suggest that thisleads to an explanation for much of Bolinger’s data, showing a further range of contrasts between polar andalternative questions, mentioned at the start of the paper. The explanation is inspired by, but not the same as,van Rooy and Safarova’s 2003 account. Where they attempt to derive Bolinger’s contrasts from differencesin utility values implied by polar vs. alternative questions, we suggest that the difference follows from moregeneral reasoning about why alternatives would be presented in a particular way, i.e. a single non-exhaustivealternative vs. a list of exhaustive alternatives. Furthermore, we suggest that an understanding of corneringturns out to be crucial towards explaining several of the contrasts. Let us now return to this data, and seehow it works.

To understand Bolinger’s contrasts we will need three consequences of our analysis so far: (i) thefact that in asking a polar question ?p, the speaker favors the alternative p amongst the other contextuallyavailable alternatives by merely spelling it out, i.e. by putting forward p. Following Buring and Gunlogson(2000), (ii) we need to take into consideration that the polar question ?p is felicitously uttered only whenthe speaker assumes that there is no compelling evidence against p. The last ingredient we need to consideris that (iii) ALTQVNs are the last possible question in a discourse. The only possible move (without tryingto escape the local context) for a cooperative addressee after an ALTQVN, is an answer – i.e. the corneringeffect discussed earlier. All three of these points follow from our analysis, beginning with the proposal thatalternative questions present an exhaustive list but polar questions an open (and typically singleton) one.With these ingredients in hand, let us look at Bolinger’s (1978) data. Let us start by examining marriage

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proposals:It is worth highlighting for point (i) that often the reasoning involves considering why the speaker would

choose to ask an ALTQVN over a POLQ, or vice versa. This is exactly what our analysis predicts, becausenone of these questions actually change the alternative sets present in the QUD (though they may bundletogether some alternatives). That is, given a particular QUD, in principle a POLQ or ALTQ strategy isavailable, and therefore in competition.

(95) Requests: Marriage proposala. Will you marry me?b. # Will you marry me or not? [ALTQVN]

In the case of marriage proposals, such as (95), the utterance of a polar question is perfectly fine if thespeaker assumes that there is no compelling evidence against the addressee being willing to marry him/her.Also, if the speaker wants to marry the addressee, as is often the case when someone proposes marriage,it is best to put forward the desired alternative, i.e. the positive one. Therefore, a polar question is a goodstrategy for marriage proposals: it favors the speaker’s intentions. However, this does not explain why anALTQVN is not felicitous at all in this situation. We have seen above that ALTQVNs do not typically favorany of the alternatives. Further, when making a marriage proposal the proponent typically assumes that theaddressee is biased towards accepting. In those situations, ALTQVNs are not congruent with the context.But this isn’t enough. Speakers’ intuitions with respect to ALTQVN used as married proposals are not justabout them not being an efficient strategy to get acceptance; they are judged as “rude” or “aggressive” inthis use.

Bolinger’s invitations and conversation starters behave similarly:

(96) Invitations: Your friends just arrived at your housea. Do you want something to drink?b. # Do you want something to drink or not? [ALTQVN]

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

The fact that the speaker assumes that there is no evidence against p, and the fact that the speaker mightbe interested on p being true, explains the felicity of a polar question, but not the infelicity/rudeness of anALTQVN.

Under the current proposal, an ALTQVN is not felicitous in requests, invitations and conversationstarters because in these contexts it must act as a cornering question (forcing also hearers to infer implicitQUDs, something slightly tricky in these cases). It provides no room for the addressee to maneuver, and arigid structure to the kind of (compliant) responses they can give, and in particular allows no d-tree sisters.An ALTQVN is the last possible resort (besides an answer), not the first, and without substantial prior con-text leads to oddness and the impression of rudeness. In general, the “rudeness” effect for ALTQVNs, wesuggest, comes from their status as the strategy (among possible strategies) that always allows the answererthe least maneuverability. (Even with enough context to make such questions appropriate in discourse, theimpression of rudeness may still be conveyed.)

In the case of Bolinger’s inference drawing, (98), the context provides compelling evidence favoringp. In such situation, it is odd to mention both alternatives, and difficult to find a plausible reason whya questioner would choose to do so (e.g. the alternatives are not equally likely) over asking a POLQ.However, the flexibility of our account makes an interesting prediction, which is that it should be possibleto find reasons to mention both alternatives in inference-drawing contexts. This prediction is correct: if

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there are conflicting inferences, (appropriately marked) ALTQVNs may be licensed. An example is shownin (98).

(98) Drawing inferences: A conversation talking about DavidA: So, before I left David in Toronto to catch my plane, I invited him to a beer.B: Yeah..., having a beer with David is always fun.A: I agree, I just saw David and told him how much fun I had with him yesterday.

B2: Wait! Is David back from Toronto or not?

Here, B2’s ALTQVN response is licensed because both alternatives are equally salient, and in conflict, inthe discourse. (The “Wait!” is required because the ALTQVN represents a topic shift, which unfortunatelywe do not have space to fully explicate here.)

In the case of rhetorical questions, (99), the explanation is simpler.

(99) Rhetorical Questions: Your friend is telling you what he did last nighta. Are you crazy?b. # Are you crazy or not? [ALTQVN]

Rhetorical questions contribute information rather than truly raise an issue (we will not assume anythingspecific about how), i.e. the rhetorical question in (99) contributes the claim that the addressee is crazy.Rhetorical questions can only be uttered when there is compelling evidence for p. However, the ALTQVN istreating both alternatives, p and ¬p as equally worth mentioning (i.e. the speaker chose to use an ALTQVNover a POLQ). By considering both p and ¬p equally worth mentioning, no inferred assertion can be made,and thus ALTQVNs are not good rhetorical questions.

To sum up, the data in Bolinger (1978) concerning the differences in discourse between POLQs andALTQVNs find a very straightforward explanation on the account for POLQs and ALTQVNs argued for inthis paper. Crucial factors include the explanation of cornering, and reasoning about asking an ALTQVNinstead of a POLQ or vice versa.

5 CONCLUSION

In this paper we have given an articulated compositional semantics and pragmatics for both polar and alter-native questions. Together with a theory of discourse involving structured tree representations of a QuestionUnder Discussion, the proposal explains a range of new and old differences and similarities between the twokinds of questions: (i) the different types of responses one can give to polar and alternative questions, (ii)the different types of question-question sequences the two can appear in, and (iii) a range of contexts wherethe two types have a different felicity, including both Bolinger’s examples and the Cornering effect.

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 while at the same time mustaddress some larger (more general / structurally higher) Question Under Discussion in the discourse.

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 proposed

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that 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 identifyeither 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 tothe system proposed here, and shed light on further investigations on discourse models. The current papersupports a hierarchical theory of discourse, and gives a more articulated account of how the Question UnderDiscussion is updated in discourse, leading to a deeper understanding dynamics in discourse trees. However,more investigation is needed on when we can refer back to previous discourse moves and how; e.g. are dis-courses trees, or more highly connected graphs? Along the same lines, there is a range of phenomena notedin this paper that have not received much attention. For instance, in understanding the dynamics of discoursemodels and complex question-question sequences, we need to understand the phenomenon of ‘bundling’ ofalternatives (local accommodation of coarser-grained alternative structures) sketched in §4.2.3. It remainsto be seen how this kind of accommodation can be fully articulated – we expect that by studying this phe-nomenon, much can be learned about the semantics/discourse interface, and more generally about how weunderstand questions.

In summary, we have given an account of the compositional semantics and pragmatics of alternativeand polar questions, and in doing so have explained a large range of data: responses/answers to alternativequestions and their complicated distribution, question-question sequences, and the differences between AL-TQVNs and POLQs. The key insight is that ALTQs and POLQs have a different, opposed semantics, leadingto different interactions with discourse structure and complex interactions with each other – yet in the rightcontexts, the effects on discourse can be similar. This explains both their similarities and differences, andadditionally expands our knowledge of the division of labor between multiple levels of grammatical repre-

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