## Ivano Ciardelli, Jeroen Groenendijk, and Floris Roelofsen

Print publication date: 2018

Print ISBN-13: 9780198814788

Published to Oxford Scholarship Online: December 2018

DOI: 10.1093/oso/9780198814788.001.0001

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# Questions

Chapter:
(p.77) 5 Questions
Source:
Inquisitive Semantics
Publisher:
Oxford University Press
DOI:10.1093/oso/9780198814788.003.0005

# Abstract and Keywords

Chapter 5 discusses how the meaning of various types of questions in English can be captured in the basic inquisitive semantics framework presented in the previous chapters. Several kinds of questions, including polar questions, alternative questions, and wh-questions, are given a formal analysis. Question coordination and conditional questions are also considered.

In Chapters 2–4 we laid out the basic architecture of inquisitive semantics. In the present chapter and the ones to follow we will discuss its applications to the analysis of natural language, and its relations to other semantic frameworks. In this chapter we discuss how and to what extent the semantics of various types of questions in English can be captured in InqB. We start in Sections 5.1–5.5 by examining a number of classes of natural language questions, and discussing the corresponding InqB-translations. In Section 5.6 we point out some features of the meaning of questions which are not captured by these translations, and we briefly discuss how InqB could be extended to capture these features, providing pointers to the literature in which such extensions are pursued.

Other important elements of the analysis of questions in inquisitive semantics will be put in place in the following chapters. In Chapters 6 and 7 we will see how the InqB-translation of certain classes of questions and statements can be built up compositionally. In Chapter 8 we will illustrate how the analysis of questions given here can be combined with suitable inquisitive entries for attitude verbs like know and wonder to obtain an analysis of question embedding. Finally, in Chapter 9 we will compare our approach to other influential approaches to question semantics.

# 5.1 Polar questions

Polar questions are questions that ask for the truth-value of a given proposition, as exemplified in (1).

(1)

The issue expressed by (1) is resolved in an information state s if it follows from the information available in s that Alice is married to Bob (i.e., if $s⊆|Mab|$) or if it follows that Alice is not married to Bob (i.e., (p.78) if $s⊆|Mab|¯$). This means that the issue expressed by (1) is precisely the issue expressed by the InqB-sentence ?Mab, which can thus be regarded as an InqB-translation of the English question in (1).1

(2)

# 5.2 Alternative questions

Alternative questions are questions that list a number of options, separated by disjunction, and ask for a choice among these. An example is given in (3), where the arrows and each mark the end of an intonational phrase and indicate whether the intonation is rising of falling at the end of that phrase (different intonation patterns for disjunctive questions will be briefly discussed below and in more detail in the next chapter).

(3)

The issue expressed by (3) is resolved in an information state s if it follows from the information available in s that Alice is married to Bob (i.e., if $s⊆|Mab|$) or if it follows that she is married to Charlie (i.e., $s⊆|Mac|$). This means that the issue expressed by (3) is the one that is expressed by the InqB-sentence MabMac.

(4)

Notice in particular that the disjunction word or occurring in (3) is translated as the connective ∨ in InqB.

One concern with translating (3) in this way is that, in our terminology, the formula MabMac is not only inquisitive, but also informative. Its informative content is that Alice is married to either Bob or Charlie. However, in uttering the question in (3), a speaker does not present the information that Alice is married to either Bob or Charlie as new information, but rather as something that she presupposes (see, e.g., Karttunen and Peters, 1976; Biezma and Rawlins, 2012). Properly capturing this requires an extension of the basic InqB (p.79) framework which, besides informative and inquisitive content, allows us to represent presuppositional content as well. We refer to AnderBois (2012), Ciardelli et al. (2012), and Roelofsen (2015a) for such an extension of the framework, and a refined representation of the meaning of alternative questions like (3).

A special case of an alternative question is obtained by disjoining a clause with its own negation, as in (5).

(5)

In this case, the translation is Mab ∨¬Mab, which is equivalent with the translation that we provided for the polar question in (1), ?Mab. This is expected, since the two questions indeed express the same issue.

Now consider the question in (6), which only differs from (3) in intonation: there is no intonational phrase boundary after the first disjunct, i.e., the two disjuncts are pronounced in a single intonational phrase, and the final pitch contour is rising rather than falling.

(6)

With this intonation pattern, the question is interpreted as a polar question, asking whether it is true or false that Alice is married to Bob or Charlie. That is, the issue expressed by (6) is resolved in an information state s if it follows from the information available in s that Alice is married to Bob or Charlie (i.e., if $s⊆|Mab∨Mac|$) or if it follows that she is not married to either Bob or Charlie (i.e., $s⊆|Mab∨Mac|¯$). This means that the issue expressed by (6) is precisely the one that is expressed by the InqB-sentence ?!(MabMac).

(7)

# 5.3 Open disjunctive questions

There exists yet another intonational variant of (3), given in (8) below.

(8)

(p.80) Questions of this kind are called open disjunctive questions (Roelofsen and van Gool, 2010; Roelofsen and Farkas, 2015). Note that the two disjuncts in (8) are pronounced in two separate intonational phrases, as in the alternative question in (3) and unlike in the polar question in (6). However, the final pitch contour is rising, as in the polar question in (6) and unlike in the alternative question in (3). Thus, the intonation pattern of open disjunctive questions differs both from that of alternative questions and from that of polar disjunctive questions.

The same holds for their resolution conditions. The issue expressed by (8) is resolved in an information state s if (i) it follows from the information available in s that Alice is married to Bob (i.e., if $s⊆|Mab|$), or (ii) it follows that she is married to Charlie (i.e., $s⊆|Mac|$), or (iii) it follows that she is not married to either Bob or Charlie (i.e., $s⊆|Mab∨Mac|¯$). This means that the issue expressed by (8) is the one expressed by the InqB-sentence ?(MabMac).

(9)

Note in particular that an information state in which it is established that Alice is married to either Bob or Charlie, but not to which of the two, does not contain enough information to settle the issue expressed by (8), while it does settle the issue expressed by the polar question in (6). Also note that (8) does not presuppose that Alice is married to either Bob or Charlie, unlike the alternative question in (3).2

# 5.4 Wh-questions

Besides polar questions, alternative questions, and open disjunctive questions, another major class of questions occurring in natural (p.81) languages consists of wh-questions. Below we will discuss several prominent kinds of wh-questions, exemplified in (10).

(10)

First, we will distinguish mention-all questions such as (10a) from mention-some questions such as (10b) and single-match questions such as (10c). Then we will turn to questions with multiple wh-words, such as (10d), and ones involving explicit domain restriction, such as (10e).

## 5.4.1 Mention-all wh-questions

Mention-all wh-questions ask for a complete specification of the individuals that have a certain property, i.e., for a specification of the complete extension of the property in the relevant domain of discourse. Under its most salient interpretation, (11) below is an example of a mention-all question.

(11)

The issue expressed by (11) is resolved in a state s if the information available in s determines exactly which individuals in the domain were invited to Alice’s party, that is, if any two worlds w, w′s agree on the set of individuals who were invited to the party. It is easy to check that this is equivalent to the requirement that for each individual dD, s should determine whether or not d was invited ($s⊆|Pad|$ or $s⊆|Pad|¯$). This shows that the issue expressed by (11) is precisely the one expressed by the InqB-sentence ∀x?Pax.

(12)

## 5.4.2 Mention-some wh-questions

Mention-some wh-questions just ask for an instance of a certain property. This is exemplifed in (13).

(13)

(p.82) The issue expressed by (13) is resolved in an information state s if the information available in s implies, for some object d, that Alice really likes d. This means that the issue expressed by (13) is the one expressed by the InqB-sentence ∃xLax.

(14)

It should be noted that the concern we mentioned above for alternative questions also arises here: in InqB, the sentence ∃xLax has non-trivial informative content, namely that there is at least one thing that Alice really likes. However, in asking the question in (13) a speaker does not present this information as new information, but rather presupposes it. Again, to capture this distinction, a presuppositional extension of InqB is required (see AnderBois, 2012; Ciardelli et al., 2012; Roelofsen, 2015a).

It is also worth remarking that, while mention-some wh-questions have received comparatively little attention in the literature (relative to mention-all wh-questions), they are extremely common in ordinary life as well as in scientific settings, as illustrated by the following examples.

(15)

Finally, while many mention-some questions involve existential expressions (e.g., something that Alice really likes, an Italian newspaper, a typical French dish, a number we can call), wh-questions without such expressions can also receive mention-some interpretations, as exemplified in (16).

(16)

## (p.83) 5.4.3 Single-match wh-questions

Single-match wh-questions ask for the unique individual having a certain property. This is exemplified in (17), under the assumption that nobody can be married to more than one person.

(17)

The issue expressed by (17) is resolved in an information state s if, for a specific individual d in the relevant domain of discourse, the information available in s implies that Alice is married to d. This means that the issue expressed by (3) is the one that is expressed by the InqB-sentence ∃xMax.

(18)

As is clear from this analysis, single-match wh-questions are a special case of mention-some wh-questions in which the relevant property can be satisfied by at most one individual. It is useful to explicitly consider single-match wh-questions, since they have some special logical properties, which are not shared by other mention-some wh-questions. In particular, the alternatives for single-match wh-questions always form a partition of a subset of the logical space. In this respect, they are more similar to mention-all questions than to other mention-some questions.

## 5.4.4 Questions with multiple wh-phrases

Wh-questions can contain multiple wh-phrases, as exemplified in (19). Under their most salient interpretation, multiple wh-questions like (19) are mention-all wh-questions: they ask for a specification of all the individuals that stand in a certain relation—here, the relation of being married. The arity of the relation equals the number of wh-phrases in the question—in this case there are two wh-phrases, so the relation whose extension needs to be specified is a binary relation.

(19)

The issue expressed by (19) is resolved in an information state s in case all worlds w, w′s agree on the extension of the relation M (i.e., Iw( M ) = Iw′( M )). This is equivalent to the requirement that (p.84) for every pair of individuals d, d′D, the state s determines whether d is married to d′ ($s⊆|Mdd′|$ or $s⊆|Mdd′|¯$). This shows that the issue expressed by (19) under its most salient interpretation is precisely the one expressed by the InqB-formula ∀xy?Mxy.

(20)

## 5.4.5 Explicit domain restriction

Sometimes, the wh-phrase in a wh-question involves an explicit domain restrictor, as exemplified in (21).

(21)

Several proposals have been put forward in the literature concerning the contribution of the explicit restrictor in such questions. Here, we will not argue for a specific proposal, but we will consider several options and describe how these analyses can be implemented in InqB.

According to Groenendijk and Stokhof (1984), (21) has two readings. Under the de dicto reading, (21) asks for a specification of the set of students who were invited by Alice. More precisely, the issue expressed by (21) under this reading is resolved in an information state s in case for every individual d, s determines whether or not d is a student who was invited by Alice. This is the issue expressed by the InqB-sentence ∀x?(SxPax).

(22)

Groenendijk and Stokhof also take (21) to have a second, de re reading, under which it asks the addressee to specify for each actual student d whether d was invited by Alice. More formally, if w0 is the actual world and $Iw0(S)={d1,…,dn}$, we have:

(23)

Notice that, under this reading, the issue expressed by (21) varies from world to world. Thus, it is not possible to give a single, world-independent translation in InqB, where formulas express issues whose resolution conditions do not depend on the world of evaluation. Of (p.85) course, it would be possible to refine the InqB system so as to allow for such world-dependency, but we will not pursue such a refinement in detail here.

Velissaratou (2000) puts forward a different analysis of which-questions. In her theory, (21) expresses an issue which is resolved if for every individual d, under the assumption that d is a student, it is known whether d was invited by Alice. More formally, an information state s counts as settling the relevant issue if for every d, the state $s∩|Sd|$ which results from assuming that d is a student settles whether or not d was invited by Alice (that is, $s∩|Sd|⊆|Pad|$ or $s∩|Sd|⊆|Pad|¯$). It is easy to check that this is precisely the issue expressed by the InqB-sentence $∀x(Sx→?Pax)$.

(24)

# 5.5 Question coordination and conditionalization

As we mentioned in Section 1.1.3, questions, just like statements, can be coordinated by means of conjunction and disjunction, and conditionalized by means of if-clauses. We will see that in each case, the relevant operation is matched by the corresponding logical operation in InqB.

## 5.5.1 Conjoined questions

A question like (25), which consists of two polar questions coordinated by means of the conjunction word and, asks for information which resolves both of the conjuncts.

(25)

That is, the issue expressed by (25) is resolved in an information state s just in case s resolves both the issue whether Alice likes Bob, and the issue whether Bob likes Alice. This is precisely the issue expressed by the conjunction ?Lab ∧ ?Lba in InqB.

(26)

(p.86) Notice that the English conjunction word and can simply be translated here as the logical connective ∧. This holds in general: given two questions Q and Q′ whose InqB-translations are μ‎ and μ‎′, the conjunctive question Q and Q′ can be translated as μ‎μ‎′.

(27)

## 5.5.2 Disjoined questions

A question like (28), consisting of two mention-some wh-questions which are coordinated by means of the disjunction word or, asks for information which resolves either one of the disjuncts.3

(28)

More precisely, the issue expressed by (28) is resolved in an information state s if s implies for some individual d that d can drive Alice to the party, or if s implies for some individual d that d can lend Alice a car. If the disjuncts of (28) are translated as ∃xDxa and ∃xLxa, respectively, then the issue expressed by (28) is precisely the issue expressed by the disjunction ∃xDxa ∨∃xLxa.

(29)

Notice that, as in the case of conjunction, the English disjunction word or can simply be translated here as the logical connective ∨.

## 5.5.3 Conditional questions

Conditional questions ask for a resolution of a question, specified by the main clause, under a certain assumption which is specified by an adjoined if-clause. As an example, consider (30), which is obtained by conditionalizing a single-match wh-question. (p.87)

(30)

The issue expressed by (30) is resolved in an information state s if restricting s to those worlds where Alice wins two tickets results in a state $s∩|Wa|$ which resolves the issue of who Alice will take with her, i.e., a state which implies for some individual d that Alice will take d with her.

(31)

Notice that the InqB-translation of (30) is a conditional whose antecedent is the translation of the if-clause, and whose consequent is the translation of the main clause. This is not a coincidence, but a result that holds generally for indicative conditional questions. Suppose that A is a statement whose InqB-translation is a non-inquisitive formula α‎, and suppose Q is a question whose InqB-translation is μ‎. The conditional question if A, Q is resolved in an information state s if restricting s to those worlds where A is true results in a state which resolves Q. Using the fact that α‎ is non-inquisitive, we have:

(32)

This ensures that if A, Q can be translated as α‎μ‎.

Besides indicative conditional questions, there are also counterfactual conditional questions, such as (33).

(33)

In order to translate (33), we need to extend InqB with an analysis of counterfactual conditionals. We will come back to this issue in Chapter 7.

# 5.6 Limitations and extensions

While we have illustrated above that InqB allows us to formally capture the resolution conditions of many kinds of questions occurring in natural language, there are also some aspects of the interpretation of questions that are beyond the immediate scope of this basic framework (p.88) and require suitable extensions. For instance, we already remarked in Sections 5.2 and 5.4 that, besides requesting information, questions may also presuppose certain information, and InqB as such is not equipped to encode such presuppositions. Below we will briefly discuss two other aspects of question meaning that are beyond the immediate reach of InqB, with pointers to the literature for further discussion of the required extensions.

## 5.6.1 Beyond resolution conditions: anaphora and bias

Compare the prototypical polar question in (34) with the somewhat less prototypical questions in (35) and (36).

(34)

(35)

(36)

An information state resolves the issue expressed by any of these questions if and only if it either implies that the door is open, or that the door is closed. Thus, these questions have exactly the same resolution conditions, and therefore they express exactly the same issue. This commonality is captured in InqB: (34), (35), and (36) all express the same proposition containing two alternatives, one consisting of all worlds where the door is open, and one consisting of all worlds where the door is closed.

However, despite the fact that the questions in (34)–(36) have exactly the same resolution conditions, they clearly differ in their overall conversational effects. For instance, (34) allows for yes/no answers and other anaphoric continuations, while (35) does not.

(37)

(38)

Moreover, while (34) can be felicitously uttered in a situation in which the speaker expects the door to be closed, the tag-question in (36) cannot. In other words, the latter conveys a bias on the part of the speaker that the door is open.

(39)

(40)

(p.89) The InqB framework as such is not designed to capture these differences. Dealing with yes/no answers and other anaphoric continuations requires an extension of the framework in which the semantics of a question does not only capture the resolution conditions of the issue that the question expresses, but also the antecedents that the question makes available for subsequent anaphoric expressions. For such an extension of InqB, as well as a detailed account of yes/no answers, we refer to Roelofsen and Farkas (2015).4

As for the bias conveyed by tag-questions like (36), this may be captured by integrating InqB with an explicit commitment-based model of discourse (e.g., Gunlogson, 2001; Farkas and Bruce, 2010), allowing for varying levels of speaker commitment. For such an approach we refer to Farkas and Roelofsen (2017).

## 5.6.2 Contextual parameters

Just like the information provided by a natural language statement, so also the issue expressed by a natural language question is rarely completely determined by grammar alone; rather, it depends on the conversational context in various ways. Some of the relevant contextual factors can be illustrated by considering the following examples.

(41)

A first important contextual parameter is the intended domain of quantification. For instance, the issue expressed by (41a) depends on the set of students which are relevant in a particular context.

A second contextual parameter manifests itself in (41b). The issue expressed by this question does not only depend on the intended (p.90) domain of quantification, but also on the intended method of identification (Aloni, 2005). Suppose that the question is asked in a situation in which there are two cards on the table, face down. If (41b) is asked by someone who wants to pick the winning card, it is resolved by any piece of information that conveys whether the winning card is the one on the left or the one on the right. On the other hand, if (41b) is asked by someone who does not know the rules of the game and wants a description of the winning card in terms of suit and number, then it is resolved by a piece of information that conveys, e.g., that the winning card is the six of hearts.

The issue expressed by (41c) depends, again besides the intended domain of quantification, also on the kind of goal that the questioner is trying to achieve in asking the question (van Rooij, 2003). For instance, she may be trying to identify someone who could give her a ride to the party, but she may also want to draw up a list of people driving to the party. In the first case, the question gets a mention-some interpretation: to resolve it, it suffices to specify one person who is driving to the party. In the second case, the question gets a mention-all interpretation: in this case, to resolve the question it is necessary to specify the complete set of people who are driving to the party.

Finally, the issue expressed by (41d) depends on the intended level of granularity (Ginzburg, 1995). In some contexts, the information provided by (42a) is sufficient to resolve the question. In other contexts, Mary’s location needs to be determined more precisely, for instance by providing the information in (42b).

(42)

Some sources of context-dependency are already taken into account in InqB. After all, an InqB-sentence expresses different issues in different information models. In this way, InqB captures the way in which the issue expressed by a question depends on the intended domain of quantification D, and on the set of worlds W which are considered possible in the given context.

On the other hand, some extra machinery would have to be added to InqB to model the influence of other contextual factors, such as the method of identification, the questioner’s goals, and the intended degree of granularity. In principle, it seems that the existing techniques (p.91) designed to deal with these contextual factors (Ginzburg, 1995; van Rooij, 2003; Aloni, 2005) can be combined with an inquisitive approach to question semantics. However, a concrete implementation of these techniques in the inquisitive setting has not been pursued yet.

# 5.7 Exercises

## Exercise 5.1 Disjunctive questions

Consider the following disjunctive question, in the given context:

(43)

Consider the following possible translations in InqB:

(44)

1. 1. What are the resolution conditions of the question according to these translations?

2. 2. Which translation is the most appropriate? Why?

## Exercise 5.2 Quantifying into questions

Consider the following question, with two possible translations into InqB:

(45)

1. 1. According to these two translations, what are the resolution conditions of the question?

2. 2. Do the two translations indeed correspond to two possible interpretations of the question?

## (p.92) Exercise 5.3 Which questions

Consider the which question in (46), the polar question in (47), and the statements in (48)[a–d], with the corresponding InqB-translations given on the right.

(46)

(47)

(48)

Recall that Groenendijk and Stokhof analyse (46) (on the de dicto reading) as ∀x?(SxAx), while Velissaratou (2000) analyses (46) as $∀x(Sx→?Ax)$.

1. 1. Which of the statements in (48) resolve (46) according to these analyses?

2. 2. According to these analyses, does (46) entail (47)?

3. 3. Discuss how well these predictions match your linguistic intuitions.

## Notes:

(1) We will use the following notation throughout this chapter: for any set of information states P, we will write P for the set of information states that are contained in some element of P, i.e., $P↓:={s∣s⊆tfor somet∈P}$.

(2) We refer to Roelofsen and Farkas (2015) for further examples of open disjunctive questions, and further discussion of how they differ from alternative and polar disjunctive questions. In particular, besides in intonation and in resolution conditions, the three question-types also differ in the extent to which they license yes/no responses.

(3) We should note here, as we also did in footnote 5 in Section 1.1.3, that disjunctions of questions are much less common in language than conjunctions of questions. Some authors have even claimed that questions cannot be disjoined at all (Szabolcsi, 1997; Krifka, 2001b). We are convinced by examples like (28) that disjoining questions is in principle possible. This point will be discussed in more detail in Section 9.2.2.

(4) Note that the contrast between (37) and (38) is parallel to the famous contrast between (i) and (ii) below (from Heim, 1982, with attribution to Barbara Partee).

((i))

((ii))

This contrast shows that truth-conditionally equivalent declarative sentences (such as the first sentences in (i) and (ii), respectively) can differ in their overall conversational effect, in particular in the antecedents that they make available for subsequent anaphoric expressions (here, the pronoun it in the second sentence). This observation has provided an important piece of motivation for the development of dynamic semantic theories (Kamp, 1981; Heim, 1982; Groenendijk and Stokhof, 1991, among others). Similarly, the framework of Roelofsen and Farkas (2015) can be seen as a first step toward a dynamic version of InqB.