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# Proceedings of the 4th Workshop on Inquisitiveness Below and Beyond the Sentence Boundary

Valentin D. Richard, Floris Roelofsen

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## To cite this version:

Valentin D. Richard, Floris Roelofsen. Proceedings of the 4th Workshop on Inquisitiveness Below and Beyond the Sentence Boundary. 4th Workshop on Inquisitiveness Below and Beyond the Sentence Boundary (InqBnB4), Association for Computational Linguistics, 2023. hal-04358496

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InqBnB4

The 4th Workshop on
Inquisitiveness Below and Beyond the Sentence Boundary

Proceedings of the Workshop

June 20, 2023

Nancy, France

(hosted by IWCS 2023, SIGSEM)
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ISBN 978-1-959429-96-8
# Preface

This volume contains the 6 papers accepted and presented at the fourth edition of the workshop Inquisitiveness Below and Beyond the Sentence Boundary (InqBnB4). It was held in Nancy (France) on 20th June 2023, with the 15th International Conference on Computational Semantic (IWCS 2023).

https://iwcs2023.loria.fr/inqbnb4-inquisitiveness-below-and-beyond-the-sentence-boundary/

InqBnB is a workshop series bringing together researchers interested in the semantics and pragmatics of interrogatives. This series was originally organized by the Inquisitive Semantics Group of the Institute for Logic, Language and Computation (ILLC) from the University of Amsterdam. As such, the focus point mainly revolves around analyses using or related to inquisitive semantics. These interactions stimulated the creation of a small community around this topic.

The first edition was held in June 2017 in Broek in Waterland, close to Amsterdam, the Netherlands. It featured 20 invited speakers. The second edition was held in December 2017 in Amsterdam. Among 25 submitted papers, 11 were accepted, and 6 speakers were additionally invited. The third edition was held in June 2019, again in Amsterdam. It featured 20 invited speakers.

With InqBnB4, we aimed at bringing this community outside of its initial zone. First, by adjoining this workshop to a larger and international conference. Second, by changing the location and organizer affiliations. By doing so, we hoped to expose this research field to a wider audience, and at the same time we hoped to see more diversity in submitted study approaches.

InqBnB4 invited submissions on original and unpublished research focused on the properties of inquisitive content. We were mainly interested in theoretical questions, formal models and empirical works.

## Below the sentence boundary:

* Which operators (connectives, quantifiers, modals, conditionals) generate inquisitiveness?

* How do these operators project the inquisitive content of their arguments?

* How does inquisitive content interact with informative content in compositional semantics?

## Beyond the sentence boundary:

* How do conventions of use interact with inquisitive content?

* In which ways is pragmatics sensitive to inquisitive content?

* What kind of discourse anaphora are licensed by inquisitive expressions?
We thank everyone who submitted papers. We also thank everyone who accepted to be part of the program committee. The meeting was enriched by the inspirational talks from Wataru Uegaki and Todor Koev.

We are thankful to the NWO VICI grant "QuSign: Questions in sign language" (2021-2026) for financing invited speaker fees. We also thank the LORIA for hosting the website and the IDMC (Institut des Sciences du Digital, Management et Cognition) at Pôle Herbert Simon, the venue of the workshop. Finally, this workshop wouldn't have been possible without the help of IWCS 2023. We are very grateful to Maxime Amblard and Ellen Breitholtz, all the organizers and the sponsors of IWCS 2023 (CNRS, Inria, Université de Lorraine, University of Gothenburg, Erdil and Métropole du Grand Nancy).

Valentin D. Richard and Floris Roelofsen
**Organizing Committee**

Valentin D. Richard, Loria, Université de Lorraine, Nancy, France

Philippe de Groote, Loria, INRIA Nancy – Grand Est, Nancy, France

Floris Roelofsen, ILLC, Universiteit van Amsterdam, Amsterdam, The Netherlands

**Programme Committee**

**Local Chair:** Valentin D. Richard, Université de Lorraine

**Chair:** Floris Roelofsen, ILLC, Universiteit van Amsterdam

Maria Aloni, Universiteit van Amsterdam

Lucas Champollion, New York University (NYU)

Jakub Dotlačil, Universiteit Utrecht

Jonathan Ginzburg, Université Paris Cité

Philippe de Groote, INRIA Nancy – Grand Est

Todor Koev, Universität Konstanz

Reinhard Muskens, Universiteit van Amsterdam

Maribel Romero, Universität Konstanz

Wataru Uegaki, University of Edinburgh

Yimei Xiang, Rutgers Linguistics

**Invited Speakers**

Todor Koev, Universität Konstanz

Wataru Uegaki, University of Edinburgh
<figure><img src="image_4.png" /></figure>
Table of Contents

Short answers as tests: A post-suppositional view on wh-questions and answers
Linmin Zhang .................................................................................. 1

Referential Transparency and Inquisitiveness
Jonathan Ginzburg and Andy Lücking .................................................. 11

Uninquisitive questions
Tom Roberts .................................................................................... 21

mage as a bias particle in interrogatives
Maryam Mohammadi ........................................................................ 31

Dynamic Questions: Evidence from Mandarin Think–"Xiang"
Anshun Zheng .................................................................................... 40

The indefinite-interrogative affinity in sign languages: the case of Catalan Sign Language
Raquel Veiga Busto, Floris Roelofsen and Alexandra Navarrete González .................... 50
<figure><img src="image_5.png" /></figure>
Program of InqBnB4

9:00–9:30 Welcoming

9:30–9:40 Introducing words

9:40–10:35 Invited talk: *The MECORE database and the *whether-puzzle*
Wataru Uegaki

10:35–11:00 break

11:00–12:30 First session:

*Short answers as tests: A post-suppositional view on wh-questions and answers*
Linmin Zhang

*Referential Transparency and Inquisitiveness*
Jonathan Ginzburg and Andy Lücking

*Uninquisitive questions*
Tom Roberts

Lunch

12:30–14:00

14:00–15:30 Second session:

*mage as a bias particle in interrogatives*
Maryam Mohammadi

*Dynamic Questions: Evidence from Mandarin Think–"Xiang"*
Anshun Zheng

*The indefinite-interrogative affinity in sign languages: the case of Catalan Sign Language*
Raquel Veiga Busto, Floris Roelofsen and Alexandra Navarrete González

15:30–16:00 break

16:00–16:55 Invited talk: *Question Bias, Polarity Focus, and Salience*
Todor Koev (joint work with Cory Bill)

16:55–17:00 Final words
<figure><img src="image_6.png" /></figure>
Short answers as tests:
A post-suppositional view on wh-questions and answers

Linmin Zhang

NYU Shanghai, 567 West Yangsi Road, Shanghai, 200126, China

linmin.zhang@nyu.edu, zhanglinmin@gmail.com

**Abstract**

This paper explores a post-suppositional view on wh-questions and their answers with dynamic semantics. Inspired by Brasoveanu (2013); Charlow (2017); Bumford (2017), I propose a unified treatment of items like modified numerals, focus items, and wh-items: they (i) introduce a discourse referent (dref) in a non-deterministic way and (ii) impose definiteness tests (and additional tests) in a delayed, post-suppositional manner at the sentential / discourse level. Thus, with a question like who smiled, the (maximally informative) dref ‘the one(s) who smiled’ is derived. A short answer like ‘Mary and Max’ is considered another post-supposition-like, delayed test, checking whether the dref ‘the one(s) who smiled’ is identical to (or includes) the sum Mary⊕Max. I analyze various question-related phenomena to see how far this proposal can go.

# 1 Introduction

This paper explores a post-suppositional perspective on the semantics of wh-questions and (short) answers within a dynamic semantics framework.

In this introduction, I present the conceptual and technical motivations behind this project.

For a wh-question like (1), it is easy to see that the short answer in (1a) is guaranteed to be a complete true answer, and the corresponding propositional answer is actually tautological. However, despite its being true and complete, interlocutors usually don't accept such an answer, because it is derivable from the question and provides no new information. In contrast, (1b) illustrates what a typical acceptable short answer should look like.

(1) Who smiled?

a. The one(s) who smiled. **Short Ans.**
→ The one(s) who smiled smiled.

b. Mary and Max. **Short Ans.**
→ Mary and Max smiled.

The above observation suggests that a good short answer to a wh-question provides new information about **something definite** that has already been established and restricted by the wh-question.

This observation is reminiscent of existing literature on **post-suppositional** phenomena, i.e., delayed tests that (i) check definiteness or (ii) provide additional information about something definite.

Brasoveanu (2013) provides a post-supposition-based account for modified numerals in cumulative-reading sentences.<fnref n="1" />

(2) Exactly 3<u>u</u> boys saw exactly 5<u>v</u> movies.
**Cumulative reading** of (2):
$$ \underbrace{\sigma x \sigma y [\mathit{BOY}(x) \wedge \mathit{MOVIE}(y) \wedge \mathit{SEE}(x, y)]}_{\substack{\text{the mereologically maximal } x \text{ and } y \text{ satisfying these restrictions} \\ \wedge |y| = 5 \wedge |x| = 3}} \underbrace{\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \text{cardinality tests}} $$

(σ: maximality operator; for notation simplicity, cumulative closure is assumed.)

As sketched out in (2), the semantic contribution of modified numerals (i.e., the underlined parts) includes several layers:

First, modified numerals introduce, in a non-deterministic way, (potentially plural) discourse referents (drefs), *x* and *y* (assigned to *u* and *v* respectively).

Second, after various relevant restrictions are added onto these drefs (here BOY(*x*), MOVIE(*y*), and SEE(*x*, *y*)), modified numerals further contribute maximality tests and cardinality tests. Specifically, (i) the maximality operators σ pick out the mereologically maximal *x* and *y*, i.e., *x* that is equal to the sum of all boys who saw any movies, and *y* that is equal to the sum of all movies seen by any boys; (ii) these mereologically maximal drefs are finally checked for their cardinality.

<footnote n="1">¹Sentence (2) also has a distributive reading, which is not discussed in this paper (see also Brasoveanu 2013).</footnote>
Therefore, eventually, (2) addresses the cardinality of all the boys who saw any movies (which is 3) and the cardinality of all the movies seen by any boys (which is 5).

Conceptually, cumulative-reading sentences and wh-questions are parallel in at least two aspects, which motivate a similar underlying analysis:

1. **Relativized definiteness:** The meaning of cumulative-reading sentence (2) is about all the boys who saw movies and all the movies seen by boys, not all the boys or all the movies in context. For wh-question (1), evidently, the sentence is about all those who smiled, not all people in context. In both cases, definiteness is relativized by information beyond the immediate DP.

2. **Additional information about relativized definite items:** Cardinalities in sentence (2) bring additional information about the boys who saw movies and the movies seen by boys. The good short answer in (1b) also provides additional information with regard to all those who smiled. The lack of this kind of additional information would often result in triviality and thus degradedness (see (1a) and (3)).

(3) ??The boys saw the movies.

Intended: 'The boys who saw movies saw the movies seen by boys.'

Under the analysis of (2) by Brasoveanu (2013), relativized definiteness is realized via a global application of maximality operators. Essentially, the derivation starts with non-deterministic alternatives. Then, crucially, definiteness tests are not applied immediately at the local DP level, but as post-suppositions, delayed to a higher, sentential level, resulting in relativized definiteness. Thus a pseudo-wide-scope effect in interpreting modified numerals is achieved, via splitting their semantic contribution into an indefinite part and a definite part.

Technically, the spirit of this post-suppositional (or split) analysis of Brasoveanu (2013) can be realized in different ways: e.g., higher-order dynamic generalized quantifiers, update semantics, post-suppositions (see Charlow 2017 for a detailed discussion and comparison). To facilitate presentation, here I adopt the dynamic semantics formalism of Bumford (2017), which is based on the non-deterministic state monad developed by Charlow (2014). A re-engineering of (2) is shown in (4).

(4) Exactly $3^u$ boys saw exactly $5^\nu$ movies.

<figure><img src="image_7.png" /></figure>

**①:** Introducing drefs and restrictions:

$$ \textcircled{1} = [\text{some}^u \text{ boys saw some}^\nu \text{ movies}] = \lambda g. \left\{ g^{\nu \to y} | \text{MOVIE}(y), \text{BOY}(x), \text{SAW}(x, y) \right\} $$

**②:** Applying maximality tests:

$$ \textcircled{2} = \mathbf{M}_{u,\nu}(\textcircled{1}) = \lambda g. \left\{ g^{\nu \to y} | x = \Sigma x[\text{BOY}(x) \wedge \text{SEE}(x, y)], y = \Sigma y[\text{MOVIE}(y) \wedge \text{SAW}(x, y)] \right\} $$

**③:** Checking cardinalities:

$$ \begin{aligned} \textcircled{3} &= \mathbf{3}_u \bullet \mathbf{5}_\nu(\textcircled{2}) \\ &= \textcircled{2}, \text{ if } |x| = 3 \text{ and } |y| = 5 \end{aligned} $$

(5) Mereology-based maximality test:

$$ \mathbf{M}_u \stackrel{\text{def}}{=} \lambda m. \lambda g. \{h \in m(g) \mid \neg \exists h' \in m(g). h(u) \sqsubseteq h'(u)\} $$

(6) Cardinality test:

$$ \mathbf{3}_u \stackrel{\text{def}}{=} \lambda m. \lambda g. m(g), \text{ if } |g(u)| = 3 \quad \text{(if not, this returns } \emptyset \text{)} $$

Within this framework, as illustrated in (2), meaning derivation is a series of updates from one information state to another, and an information state $m$ (of type $g \to \{g\}$) is considered a function from an input assignment function to an output set of assignment functions. An update is true if the output set of assignment functions is not an empty set; an update is false if the output set of assignment functions is an empty set.

In (4), drefs are first introduced and various restrictions are added onto them (see ①). Maximality operators (see (5)) pick out the mereologically maximal drefs satisfying the restrictions (see ②). Finally, cardinality tests (see (6)) check the cardinalities of the maximal drefs (see ③). The cumulative-reading of (2) is true if the derivation does not return an empty set.

The rest of the paper is organized as follows. Section 2 presents the main proposal with this dynamic semantics formalism à la Bumford (2017). Section 3 explores further extensions of the proposal, analyzing various empirical phenomena hotly discussed in the existing literature on question semantics. Section 4 briefly compares the current work with recent related works. Section 5 concludes.
## 2 Proposal: Wh-questions and answers

(7) and (8) illustrate the core idea of the current proposal with a dynamic semantics implementation à la Bumford (2017).

<figure><img src="image_8.png" /></figure>

**①: Introducing drefs:**

① = [[who<sup>u</sup>] = [[some<sup>u</sup> (people)]
= λg. {g<sup>u→x</sup> | HUMAN(x)}]

**②: More restrictions are added:**

② = [[who<sup>u</sup> smiled]]
= [[some<sup>u</sup> (people) smiled]]
= λg. {g<sup>u→x</sup> | HMN(x) ∧ SML(x)}

**③: Applying maximality tests:**

③ = **Ans**<sub>u</sub>(②) =
λg. {g<sup>u→x</sup> | x = Σx[HMN(x) ∧ SML(x)]}

<figure><img src="image_9.png" /></figure>

**④: Checking additional information**

④ = Mary ⊕ Max<sub>u</sub>(③) =
λg. {g<sup>u→x</sup> | x = Σx[HMN(x) ∧ SML(x)]},
if x = Mary ⊕ Max (or x ⊑ Mary ⊕ Max)

<figure><img src="image_10.png" /></figure>

a. Mereological maximality as a special case: $\mathbf{Ans}_u \stackrel{\text{def}}{=} \lambda m. \lambda g. \{h \in m(g) | \neg \exists h' \in m(g). h(u) \sqsubseteq h'(u)\}$

(10) **Good short answer as another test:**

a. As a complete answer:

Mary ⊕ Max<sub>u</sub> def =
λm.λg.m(g), if g(u) = My ⊕ Mx
(if not, this returns ∅)

b. As a potentially partial answer:

Mary ⊕ Max<sub>u</sub> def =
λm.λg.m(g), if g(u) ⊑ My ⊕ Mx
(if not, this returns ∅)

In (7), who<sup>u</sup> first works like an indefinite and introduces a dref in a non-deterministic way. Given that the domain of this wh-item, who, is typically a set of human individuals, I also include the restriction HUMAN(x) here (see ① in (7)).

After other relevant restrictions are added (here SMILE(x), see ② in (7)), an operator **Ans**<sub>u</sub> is applied to ② (see ⑨ and ③ in (7)), picking out the definite dref that eventually leads to the maximally informative true answer to the wh-question.

Obviously, in this specific example (7), where the domain of the wh-item is a set of individuals and the predicate *smile* is inherently distributive, **Ans**<sub>u</sub> amounts to picking out the mereologically maximal dref, as shown in (9a). Essentially, ② means ‘someone that smiled (smiled)’, and ③ means ‘the one(s) who smiled (smiled)’. In some sense, the question meaning (i.e., here ③ in (7)) is equivalent to the meaning of its analytical answer – ③.

(8) illustrates how a good short answer works. As defined in (10), **Mary** ⊕ **Max**<sub>u</sub> plays the same role as cardinality tests do in a cumulative-reading sentence (see (6) and (4)). If **Mary** ⊕ **Max**<sub>u</sub> is a complete answer, this test checks whether the maximal dref in ③ is identical to the sum **Mary** ⊕ **Max**<sub>u</sub>. If **Mary** ⊕ **Max**<sub>u</sub> is a potentially partial answer, this test checks whether the sum **Mary** ⊕ **Max**<sub>u</sub> is part of the maximal dref in ③.

Basically, the above analysis shows (i) a compositional derivation of the meaning of a wh-question, (ii) the derivation of its (analytically) maximally informative true answer, and (iii) how a good short answer contributes information in addressing the wh-question. This analysis inherits many existing insights on question meanings.

### 2.1 Cross-sentential anaphora

Wh-items are parallel to indefinites in introducing drefs and supporting cross-sentential anaphora, as illustrated in (11) (see e.g., Comorovski 2013).

(11) a. Someone<sup>u</sup> laughed. They<sub>u</sub> are noisy.

b. Who<sup>u</sup> laughed? They<sub>u</sub> are noisy.

(12) a. λg. {g<sup>u→x</sup> | x = Σx[HMN(x) ∧ LG(x)]}
b. λg. {g<sup>u→x</sup> | NOISY(x)}

The analysis of the first and second sentence in discourse (11b) is sketched in (12). The parallelism between wh-items and indefinites are immediately explained: both introduce drefs that support cross-sentential anaphora. The only difference is that a wh-item also involves (relativized) definiteness.

<footnote n="2">²See further discussion below on degree questions (Section 2.5). See also Zhang (2023a) for more discussion on maximal informativeness.</footnote>
## 2.2 Short answers and the categorial approach

According to the categorial approach to wh-questions (Hausser and Zaefferer 1978), a wh-question denotes a function, which, when applying to its short answer, generates a (potentially complete true) propositional answer (see (13)).

(13) Categorial approach:
[who smiled] = $\lambda x$.SMILE(x)

a. Short answer: Mary and Max

b. Propositional answer:
[Mary and Max]_F smiled.

Similar to the categorial approach, the current analysis also composes a short answer with question meaning to derive the meaning of the corresponding propositional answer. As shown in (14), when the short answer $Mary \oplus Max_u$ (see (10)) is applied to the question meaning (see ③ in (7)), the meaning of the propositional answer (13b) is naturally derived (see also ④ in (8)).

<figure><img src="image_11.png" /></figure>

Thus under both the current analysis and the categorial approach, short answers are not derived from propositional analysis via ellipsis.

Jacobson (2016) also argues for the view that a short answer should not contain hidden, elided linguistic materials that would be part of a corresponding propositional answer. Actually Jacobson (2016) points out that for a wh-question like (7), a short answer like (8) is a genuine answer that addresses the wh-question, while a corresponding propositional answer is a derived reply. What a genuine answer really is is actually also reflected by the focus of a propositional answer.

The current analysis for short answers is in line with Jacobson (2016). A short answer as analyzed in (10) does not contain any ellipsis, and it only indicates (i) which dref in the wh-question the information $Mary \oplus Max_u$ is connected with and (ii) whether this connection is an identity relation or a part-whole relation. Sometimes the distinction between a complete and a potentially partial short

answer can be reflected by intonation.

There are two major differences between the current analysis and the categorial approach. First, the current analysis addresses the definiteness in interpreting a wh-question. Second, under the current analysis, a good short answer actually behaves as if it takes a pseudo-wide-scope over the wh-question.

The current analysis also overcomes a few issues that challenge the original categorial approach.

As pointed out by Xiang (2021), under the traditional categorial approach, a wh-item is considered a $\lambda$-operator, thus this analysis fails to show the parallelism between wh-items and indefinites, which is widely observed cross-linguistically. Under the current analysis, wh-items are analyzed in exactly the same way as indefinites (see Section 2.1).

Xiang (2021) points out that the traditional categorial approach also faces the issues of (i) composing multi-wh-questions and (ii) question coordination. Section 3 will show how the above analysis can be extended to handle these issues.

## 2.3 Karttunen (1977): A wh-question means its complete true answer

The current analysis of wh-questions is also in the same spirit as Karttunen (1977): A wh-question has the same meaning as its complete true answer. This can be seen from ③ in (7).

According to Dayal (1996)'s Maximal Information Presupposition, a question presupposes the existence of a maximally informative true answer. Thus as far as a wh-question meets this requirement, the operator $Ans_u$ (see (9)) is applicable to something like ② in (7), and ③ is derivable, which corresponds to the complete true answer. In other words, semantically, a wh-question is guaranteed to have an analytical complete true answer.

Different from Karttunen (1977), Hamblin (1973) analyzes the meaning of a wh-question as its possible propositional answers, instead of true propositional answers. Dependency data like (15) seem to support Hamblin (1973)'s view (see Dayal 2016), because according to our intuition, for (15), the interpretation of where is Mary seems a Hamblin set, i.e., a set of possible answers that address where Mary is. For this kind of dependency data, I'll account for them in Section 3.4 while maintaining a view in line with Karttunen (1977).

(15) What does John think? Where is Mary?
    ↦ Where does John think Mary is?
    (see, e.g., Dayal 2016)
## 2.4 The parallelism between wh-questions and wh-free-relatives

The current analysis also explains the parallelism between wh-questions and wh-free-relatives (see Caponigro 2003, 2004; Chierchia and Caponigro 2013). Essentially, a wh-free-relative can be considered the analytically true, definite, complete short answer to its corresponding wh-question.

As illustrated in (16), wh-free-relatives can be replaced by a definite DP, and (16a) and (16b) have the same truth condition. The analysis in (17) explains this truth-conditional equivalence. In (17), **Ans**<sub>u</sub> plays the same role as a mereological maximality operator, leading to the maximal sum of things cooked by Adam (see (9a)).

(16) a. Jie tasted *what*<sup>u</sup> *Adam cooked*.
(from Caponigro 2004)

b. Jie tasted *the*<sup>u</sup> things *Adam cooked*.

(17) [what<sup>u</sup> Adam cooked]
= **Ans**<sub>u</sub>(λg. {g<sup>u→x</sup>|COOK(Adam, x)})
= λg. {g<sup>u→x</sup> | x = Σx[COOK(Adam, x)]}
= [the<sup>u</sup> things Adam cooked]

A further issue is about mention-some questions.

(18) Who<sup>u</sup> can help her?

(19) Mary was looking for who<sup>u</sup> can help her.
= Mary was looking for *someone*<sup>u</sup> that can help her.
≠ Mary was looking for *all the*<sup>u</sup> *people* that can help her.

As illustrated in (18) and (19), in these examples, there is also a parallelism between mention-some wh-questions (see (18)) and mentions-some wh-free-relatives (see (19)). However, it seems that mereological maximality is not involved.

Actually, in (9), I consider **Ans**<sub>u</sub> a maximality operator that leads to the most informative answer. Maximal informativeness is not necessarily based on mereological maximality (see Zhang 2023a).

Thus for mention-some wh-questions and wh-free-relatives, the specific implementation of **Ans**<sub>u</sub> should be different from the mereology-based one defined in (9a). Presumably, the application of **Ans**<sub>u</sub> should involve (i) a context-relevant measurement of informativeness that takes into consideration the accessibility or availability of resources and/or (ii) some free-choice operator. I leave a detailed development of this idea for future research.

## 2.5 The parallelism between wh-questions and concealed questions

The current analysis also naturally captures the parallelism between wh-questions and concealed questions. Syntactically, a concealed question looks like a definite DP, but semantically, it works like a wh-question (see, e.g., Nathan 2006). In (20) and (21), the content of what Mary knows is expressed as a wh-question in (20) and as a concealed question in (21). (22) shows their parallel derivation.

(20) Mary know *how*<sup>u</sup> tall *John*<sup>ν</sup> is.
She thinks that Bill is shorter than that<sub>u</sub>.

<figure><img src="image_12.png" /></figure>

(21) Mary know the<sup>u</sup> height of John<sup>ν</sup>.
She thinks that Bill is shorter than that<sub>u</sub>.

<figure><img src="image_13.png" /></figure>

(22) $\textcircled{1} = \lambda g. \{g^{u \to I} | \text{INTERVAL}(I)\}$

$\textcircled{2} = \lambda I \lambda x. \text{HEIGHT}(x) \subseteq I$

(i.e., the height measurement of *x* falls into the interval *I*.)

$\textcircled{3} = \lambda g. \{g^{u \to I} | \text{HEIGHT}(x) \subseteq I, x = \mathbf{J}\}$

$\textcircled{4} = \mathbf{Ans}_u \stackrel{\text{def}}{=} \lambda m. \lambda g.$

$\{h \in m(g) \mid \neg\exists h' \in m(g). h'(u) \subseteq h(u)\}$

$$
\begin{align*}
\textcircled{5} \\
&= \mathbf{Ans}_u (\lambda g. \{g^{u \to I} | \text{HT}(x) \subseteq I, x = \mathbf{J}\}) \\
&= \lambda g. \{g^{u \to I} | I = \iota I [\text{HT}(\mathbf{J}) \subseteq I], x = \mathbf{J}\}
\end{align*}
$$

In both cases, the semantic contribution of *the* and *how* can be considered two-fold. They (i) first introduce a *dref* in the domain of degrees or intervals (which supports cross-sentential anaphora later)<fnref n="3" /> and (ii) then impose a definiteness test, lead-

<footnote n="3">³An interval is a convex set of degrees, e.g., [5', 5'], [5', 6'] (Schwarzchild and Wilkinson 2002; Zhang and Ling 2021).</footnote>
question coordination. For a sentence like (29), the
traditional approach predicts that it has the same
meaning as *Jenny knows who voted for Andy and
Bill* (see (30)), and this prediction is inconsistent
with our intuitive interpretation for (29).

(29) Jenny knows who$^{u1}$ voted for Andy and who$^{u2}$ voted for Bill. (see Xiang 2021)

(30) Traditional categorial approach:
[who voted for Andy and who voted for Bill]
= $\lambda x$.VOTE($x$, A) $\sqcap$ $\lambda x$.VOTE($x$, B)
= $\lambda x$.[VOTE($x$, A) $\wedge$ VOTE($x$, B)]
= [who voted for Andy and Bill]

Under the current analysis, for (29), the two
wh-items each introduce a dref and different re-
strictions are applied to the two drefs respectively.
Then two Ans operators are applied, selecting out
the maximal drefs (see (31)). Finally, (32) shows
that Jenny has the (weak) exhaustive knowledge
about these two maximal drefs. In her knowledge,
each dref is tracked separately.

(31) **Ans**<sub>u₁</sub>([who<sup>u1</sup> voted for Andy])
∧ **Ans**<sub>u₂</sub>([who<sup>u2</sup> voted for Bill])
= λg. {g<sup>u2&rarr;y</sup>|<sub>u₁&rarr;x</sub> x = Σx[HMN(x) ∧ VT(x, A)], y = Σy[HMN(y) ∧ VT(y, B)]}

(32) **Jenny knows**<sub>weak u₁,u₂,...</sub> ≜ **λm**·**λg**·**m**·(g)
if for each variable uᵢ ∈ {u₁, u₂, ...},
∀x'[x' ⊑ g(uᵢ) → ∃**now**<sub>⊤</sub>(x' ⊑ g(uᵢ))]

3.3 Wh-conditionals

The above idea on question coordination can be
further extended to sentences with multi wh-items.

(33) Who^u comes depends on who^v is invited.

(34) **depend-on**<sub>u,v</sub> def= λm·λg·m(g) if
∃f·f(g(v)) = g(u)

Sentence (33) addresses the correlation between
the answers to two wh-questions. The answer to the
question *who*<sup>*u*</sup> *comes* correlates with or depends
on the answer to the question *who*<sup>*v*</sup> *is invited*. As
proposed in (34), **depend-on**<sub>u,v</sub> works as a post-
suppositional test, checking whether there is a func-
tion *f* mapping the maximal dref assigned to *v*, i.e.,
*g*(*v*), to the maximal dref assigned to *u*, i.e., *g*(*u*).
Thus again **depend-on**<sub>u,v</sub> is like a short answer or
*Mary knows* in that their semantic contribution is
based on and added to existing definite items.

Wh-conditionals in Mandarin Chinese can be
accounted for in exactly the same way.

According to Liu (2017); Xiang (2021); Li
(2019, 2021), a wh-conditional sentence like (35)
includes two questions, here who^u loses and who^v
pays, and the short answer to the first wh-question
is equivalent to the short answer to the second one
(cf. Xiang 2021). As shown in (36) and (37), this
intuitive reading is naturally accounted for.

(35) Shéi^u shū-le, shéi^v (jiù) qǐngkè
who lose-ASP who (then) pay
‘For every person x, if x is the one losing
the bet, x is the one paying.’ (see Li 2021)

(36)

**Eq**<sub>u,v</sub>

**Ans**<sub>u</sub> shéi^u shū-le who^u loses u&rarr;x

**Ans**<sub>v</sub> shéi^v qǐngkè who^v pays

① = λg. {g<sup>ν&rarr;y</sup>|<sub>ν&rarr;x</sub> x = Σx[HMN(x) & LOSE(x)], y = Σy[HMN(y) & PAY(y)]}

(37) **Eq**<sub>u,v</sub> = λm·λg·m(g) if g(u) = g(v)

More general cases of wh-conditionals, includ-
ing those involving degree questions, can also be
accounted for. (38) means that the amount of food
you eat determines the amount of money you pay,
i.e., the answer to the first degree question deter-
mines the answer to the second one.

(38) chū duō-shǎo<sup>u₁,ν₁</sup>, fù duō-shǎo<sup>u₂,ν₂</sup>
eat how.much pay how.much
‘How much (you) eat, how much (money
you) pay.’ (see Liu 2017; cf. Xiang 2021)

(39) λg. {g<sup>u2&rarr;y,ν2&rarr;I2</sup>|<sub>u1&rarr;x,ν1&rarr;I1</sub> x = Σx[FD(x)], y = Σy[MN(y)], I₁ = AM(x), I₂ = AM(y)}

(40) **determine**<sub>ν₁,ν₂</sub> = λm·λg·m(g) if
∃f·f(g(ν₁)) = g(ν₂)

For (38), I assume that each degree question in-
troduces two drefs: one in the domain of *e* (here
*x* and *y*), and the other one in the domain of in-
tervals (here *I*₁ and *I*₂). (39) shows that the most
informative drefs are picked out: the mereologi-
cally maximal *x* and *y*, and the most informative
amount measurement of *x* and *y*, i.e., *I*₁ and *I*₂.
Obviously, *I*₁ and *I*₂ are the most informative an-
swers to the two wh-questions in (38). Similar
to (34), silent operator **determine**<sub>ν₁,ν₂</sub> works as a
test, checking whether there is a context relevant
function *f* that maps *g*(*ν*₁) to *g*(*ν*₂). The operator
**Eq**<sub>u,v</sub> (37) can be considered a special case of the
operator **determine**<sub>ν₁,ν₂</sub> in (40).
## 3.4 Question dependency (44)

Syntactically, there are two subtypes of question dependency: **direct dependency** (see (41)) and **in-direct dependency** (see (42)). Semantically, they have the same meaning. Based on their syntactic differences, Dayal (1994, 2016) advocate distinct analyses to derive their meaning. Here I follow this desideratum to address question dependency.

(41) Where$^u$ does John think Mary is?

(42) What$^v$ does John think? Where$^u$ is Mary?

As shown in (43), the derivation of direct dependency is straightforward. Wh-item where$^u$ introduces a dref (which is a location), and the application of the definiteness test $Ans_u$ is delayed until the matrix sentence level. Due to the selection requirement of think, roughly speaking, the embedded question should be something of type $\langle st \rangle$, and $\llbracket \text{John thinks} \rrbracket$ is of type $\langle st, t \rangle$, restricting items of type $\langle st \rangle$. Eventually, (41) denotes the most informative dref $x$ such that John thinks Mary is in $x$. Obviously, this dref $x$ does not necessarily satisfy the restriction 'IN(Mary, $x$, $w$)' (in which $w$ is a free variable). Thus the intensionality of attitude-reporting predicate think is captured.

<figure><img src="image_14.png" /></figure>

$$① = \lambda g. \{g^{u \to x} | \begin{array}{l} \text{LOCATION}(x), \\ \text{JOHN-THINKS}(\lambda w. \text{IN}(\text{Mary}, x, w)) \end{array}\}$$

$$② = \lambda g. \{g^{u \to x} | x = \iota x[\text{LCT}(x) \wedge \text{JOHN-THINKS}(\lambda w. \text{IN}(\text{Mary}, x, w))]\}$$

Then as shown in (44), for (42), I propose that what$^v$ introduces a dref of type $\langle st \rangle$, and where$^u$ introduces a dref of type $e$. As shown in ⑤, the part of the what$^v$ question denotes the most informative proposition $p$ satisfying JOHN-THINKS($p$). Then as shown in ©, the where$^u$ question works as a test and provides further information on $p$, introducing a dref $x$ and checking whether this most informative $p$ entails a propositional that addresses Mary is somewhere. The rest is similar to the case of direct dependency. Eventually, (42) also denotes the most informative dref $x$ such that John thinks Mary is in $x$, i.e., the same meaning as (41).

<figure><img src="image_15.png" /></figure>

$$④ = \lambda g. \{g^{v \to p} | \text{JOHN-THINKS}(p)\}$$

$$⑤ = \mathbf{Ans}_v(④) = \{g^{v \to p} | p = \cap p[\text{JOHN-THINKS}(p)]\}$$

$$⑥ = \llbracket \lambda w. \mathbf{Mary \ is \ where}^u \text{ in } w \rrbracket_v = \lambda m. \lambda g. m(g) \text{ if } g(u) \mapsto x \text{ s.t. } \text{LCT}(x) \wedge$$

$g(v) \subseteq \lambda w. \text{IN}(\text{Mary}, x, w)$

$$① = \lambda g. \{g^{v \to p} | \begin{array}{l} \text{LC}(x), p = \cap p[\text{J-T}(p)], \\ \text{JOHN-THINKS}(\lambda w. \text{IN}(\text{Mary}, x, w)) \end{array}\}$$

$$② = \lambda g. \{g^{v \to p} | p = \cap p[\text{J-T}(p)], x = \Sigma x[\text{LCT}(x) \wedge \text{J-T}(\lambda w. \text{IN}(\text{Mary}, x, w))]\}$$

The current analysis of question dependency is still in line with Karttunen (1977): A wh-question denotes its complete true answer, not its possible answers (see Section 2.3). With this dynamics semantics implementation, the derivation always starts with non-determinate alternatives, and it is the application of $Ans$ operators that results in relativized definite items that constitute complete true answers. In (44), $Ans_u$ is not applied on ©, but delayed until discourse level. thus the derivation never yields a Hamblin set for where$^u$ is Mary.

## 3.5 Multi-wh-questions

A multi-wh-question has two readings, e.g.,

(45) Which girl read which book?

a. **Single-pair reading:**
Anna read *Anna Karenina*.

b. **Pair-list reading:** Anna read *Anna Karenina*; Emma read *Madame Bovary*; Jane read *Jane Eyre*.

The single-pair reading (45a) is easy to derive. In (46), atomic drefs $x$ and $y$ are introduced, and the operator $Ans_{u,v}$ checks whether they are unique.

<figure><img src="image_16.png" /></figure>
(drefs *x* and *y* are atomic here.)

**Single-pair reading:** $\mathbf{Ans}_{u,\nu} =$
$\lambda m. \lambda g.m(g)$ if $|\{g(u) | g \in m(g)\}| = 1$
and $|\{g(\nu) | g \in m(g)\}| = 1$.

(i.e., there is a unique girl-reader and a
unique book read by a girl.)

② = λg. {g<sub>ν→y</sub>|x = ιx[GL(x) ∧ RD(x, y)], y = ιy[BK(y) ∧ RD(x, y)]} (Anna<sub>u</sub>, AK<sub>ν</sub> bring more tests on drefs.)

For the pair-list reading (45b), its short answer
can be considered a function written as a set of or-
dered pairs: i.e., $f = \{\langle A, AK \rangle, \langle E, MB \rangle, \langle J, JE \rangle\}$
(see Schlenker 2006; Brasoveanu 2011; Bumford
2015). Another observation is that pair-list reading
is different from single-pair reading in supporting
cross-sentential anaphora (see (47) vs. (48)).

(47) Which<sup>u</sup> girl read which<sup>ν</sup> book? Does she<sub>u</sub>
like it<sub>ν</sub>? ✓ single-pair; # pair-list

(48) Which<sup>u</sup> girl read which<sup>ν</sup> book? Do they<sub>u</sub>
like their<sub>u</sub> book / # it<sub>ν</sub>? ✓ pair-list

Thus the pair-list reading of (45) amounts to
'what is the function *f* s.t. for each girl *x*′ who read,
*f*(*x*′) is all the books *x*′ read and |*f*(*x*′)| = 1'. In
(49), which<sup>u</sup> girl introduces a (potentially plural)
dref *x*, and which<sup>ν</sup> (book) introduces a functional
dref *f*, mapping each atomic *x*′ to the book-sum *x*′
read. I assume that a hidden distributivity operator
DIST is responsible for the singularity of girl. Ans<sub>u</sub>
selects out the maximal sum of girl-readers. Ans<sub>ν</sub>
checks the singularity of book, i.e., whether for
each *x*′, |*f*(*x*′)| = 1. If so, *f* is the short answer.<fnref n="5" />

(49)

<figure><img src="image_17.png" /></figure>

① = λg. {g<sub>ν→f</sub>|G(x), ∀x'<sub>ATM</sub> ⊑ x[f(x')
= Σf(x')|BK(f(x')) ∧ RD(x', f(x'))]}
Ans<sub>ν</sub> = λm.λg.m(g) if ∀x'[x'<sub>ATM</sub> ⊑ g(u)
→ |g(ν)(x')| = 1]

4 Comparison with recent works

Among recent works, there are heated discussions
on how to represent the drefs introduced by wh-

items, how to have access to short answers, etc.
These issues motivate new approaches to questions,
incorporating insights from dynamic semantics or
categorial approaches (e.g., Krifka 2001; Xiang
2021; Li 2019, 2021; Dotlačil and Roelofsen 2019,
2021). The current work joins this trend of research
and has a similar empirical coverage.<fnref n="6" />

Compared to other recent works, the current
work is distinguished in at least two aspects. First,
conceptually, it provides a new perspective on an-
swerhood, teasing apart the analytically invariant,
definite part and the part that contributes new in-
formation. New information is considered tests
at another layer, providing further description for
the analytically invariant part. Thus even though a
wh-question might be answered with different infor-
mative short answers in different possible worlds,
the analytical definite dref remains stable. Con-
sequently, in analyzing question phenomena, we
can just start with this complete true answer, and
various phenomena address what/how additional
information is related to this analytical answer.

Second, empirically, the current approach brings
a more unified treatment for wh-questions raised
on different domains (e.g., entities, scalar values
like degrees or intervals). Specific implementation
of definiteness tests is based on the same idea of
maximizing informativeness. We never need to
loop over possible answers in the domain of wh-
items, which is difficult for domains of non-entities.

5 Summary

This paper explores a post-suppositional view on
wh-questions and answers. I analyze wh-items
along with items like modified numerals: their se-
mantic contribution all involves dref introduction
and definiteness tests. Based on this, for answers
to wh-questions, we can separate the invariant, an-
alytical part, and the new information part. The
new information part further serves as tests on the
invariant part. This papers also sketches out how a
series of related phenomena are analyzed. Further
development and refinement is left for future work.

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Referential Transparency and Inquisitiveness

Jonathan Ginzburg

Université Paris Cité, CNRS

Laboratoire de Linguistique Formelle

yonatan.ginzburg@u-paris.fr

Andy Lücking

Université Paris Cité, CNRS

Laboratoire de Linguistique Formelle

and

Goethe University Frankfurt

luecking@em.uni-frankfurt.de

Abstract

The paper extends a *referentially transparent* approach which has been successfully applied to the analysis of declarative quantified NPs to *wh*-phrases. This uses data from dialogical phenomena such as clarification interaction, anaphora, and incrementality as a guide to the design of *wh*-phrase meanings.

# 1 Introduction

An alternative to Generalized Quantifier Theory (GQT) has recently been developed in terms of *Referential Transparency Theory* (RTT; Lücking and Ginzburg, 2022). RTT draws its main motivation from data of natural language use as observed in dialogical interactions, where higher-order denotations postulated by GQT do not seem to be confirmed. Hence, RTT pursues a witness-based approach to quantification, which arguably simplifies the representation of quantification phenomena.

In this paper, we extend this to questions. This is *prima facie* tricky because in contrast to QNPs *Wh*-phrases (WhPs) are never referential.¹ Indeed a crucial difference between declarative and interrogative quantified meaning is that the former involves *predication*—giving rise to descriptive potential, whereas the latter involves *abstraction*—giving rise to predicational potential. Phenomena we discuss includes the following:

**Clarificational potential:** Data from clarification allows for a considerable strengthening of compositionality, the classical syntax-semantics interface desideratum. This via the Reprise Content Hypothesis (RCH) due to (Purver and Ginzburg, 2004) They distinguish different kinds of reprise fragments, including *intended meaning* requests, that is, reprise fragments that follow the template “A: ...u₁... B: u₁?” exemplified in (2). Purver and Ginzburg (2004) show further that reprise fragments of the *intended meaning* type, at least when they address a non-sentential constituent, do not query pragmatically inferred material but are restricted to direct semantic content. On the basis of this they posit the *Reprise Content Hypothesis* whose strong version is given in (1):

(1) **Reprise Content Hypothesis:** A reprise fragment question queries exactly the standard semantic content of the fragment being reprised.

Whereas non-interrogative QNPs allow for clarification questions relating to their witnesses (but not to properties of properties, as would be expected in GQ accounts), *wh*-phrases allow only for clarification of their restriction property (not to any propositional entities, as might be expected by GQ accounts of interrogatives common in Type-driven Categorial Grammar (Vermaat, 2006; Mihaliček and Pollard, 2012)).²

(2) a. A: Most students came to the party.
B: Most students? A: Yes, all but
Tristan and Isolde.

¹Of course there are languages where the same form, albeit with distinct intonation, plays a double or even triple role such as Hebrew ‘eyze’ which serves as a quantificational, interrogative and exclamative determiner:

(i) eyze yeladim azvu(./?/!)
Some/Which/what child-pl left
Some children left./Which children left?/What children
left!

Our account will enable us to capture the core similarities between these uses, but crucially also the differences, as we demonstrate in an extended version of this paper.

²See (Purver, 2004) for corpus examples of clarification exchanges concerning *wh*-phrases, though he does not discuss examples like our (constructed) (2c,d).
b. A: Everyone supports the proposals.

B: Everyone? A: All the ministers.

c. A: Who should we contact for help? B: Who? A: A lawyer or a psychologist?/#Everyone except Tristan and Isolde.

d. A: When are you leaving? B: When?

A: What day./#Saturday.

A similar point can be made for intensional argument roles of verbs, which allow for clarification without expectation of witnesses (Cooper, 2013b):

(3) A: Sam is looking for the trainset.

B: What trainset?

A: The one he was promised for Christmas (Cooper, 2013b),

**Anaphoric potential:** wh-phrases allow for discourse anaphora, though without a referential commitment:

(4) a. A: Who will support the proposal? Will they reveal themselves before the vote? B: No one. A: Yeah that makes sense.

b. A: Where are you going? Can we contact you there?

The same holds for intensional argument roles of verbs:

(5) a. Charlie wants a train for her birthday. Ideally it should be light blue.

**Incremental potential:** input is processed word by word (and indeed at a higher, sub-lexical latency). Utterances with QNPs are understood incrementally (Urbach et al., 2015), as exemplified also in (6a,b). Although we are not aware of similar empirical studies for wh-phrases, (6c,d) suggests that this is the case as well:<fnref n="3" />

(6) a. A: Everyone ... B: Who?

b. A: [enters class] No students ... Oh, they're hiding.

c. A: Who... B: What are you going to ask me now?

d. A: Which student... B: In what class?

Approaches which treat wh-phrases as mediated via an operation like Quantifier Raising, where a quantifier is moved out of its syntactic surface position into another position in logical form or more generally involve long-distance binding (Xiang, 2021), seems to be a serious obstacle to this empirical fact.

**Answerhood:** the substantive semantic contribution of wh-phrases is the answerhood conditions they give rise to, the details of which are discussed in section 2.

**Response space:** any dialogical theory of meaning needs to account for the class of responses a given utterance type gives rise to. In the case of questions there exists detailed empirical and formal work we build on (Ginzburg et al., 2022), briefly summarized in section 2.

An example that combines these aspects of wh-phrase meaning is in figure 1, where the exophoric context triggers the bare wh-clarification question, which give rise to the short answer.

<figure><img src="image_18.png" /><figcaption>Figure 1: (Context: Harden gets called for a foul) Harden: Who, me?</figcaption></figure>

In section 2, we sketch a theory of questions, answerhood, and responses. In section 3, we develop our account of wh-phrase meaning, which is applied to the initial data in section 4.

## 2 A KoS-TTR theory of questions

Our explication is formulated using the frameworks of Type Theory with Records (TTR; Cooper and Ginzburg, 2015; Cooper, 2023) (for the semantic ontology) and KoS (Ginzburg, 2012; Ginzburg et al., 2022) (for the theory of dialogue context).

### 2.1 Basic semantic notions

We will assume a view of questions as propositional functions, a view apparently initiated by Ajdukiewicz (1926), developed significantly in Kucinski (1960), and subsequently shared and further

<footnote n="3">³For an interesting discussion of incremental interpretation of wh-questions, though not in a dialogical setting see (Hopmans, 2019).</footnote>
developed by a number of different approaches,
e.g., Krifka (2001).

We adopt an implementation of this view within
the framework of TTR. The starting point, hence,
is the notion of a proposition in TTR. Propositions
are construed as typing relations between records
(situations) and record types (situation types), or
Austinian propositions (Austin, 1961; Barwise and
Etchemendy, 1987); more formally:

(7) a. Propositions are records of type

$$
\text{Prop} = \begin{bmatrix} \text{sit} & : \text{Rec} \\ \text{sit-type} & : \text{RecType} \end{bmatrix}.
$$

b. $p = \begin{bmatrix} \text{sit} = s \\ \text{sit-type} = T \end{bmatrix}$ is true iff $p.\text{sit} : p.\text{sit-type}$

i.e., *s* : *T* —the situation *s* is of the type
*T*.

Similarly, we will model questions as records
comprising two fields, a situation and a function
(Ginzburg et al., 2014). The role of wh-words on
this view is to specify the domains of these func-
tions; in the case of polar questions there is no
restriction, hence the function component of such a
question is a constant function. (8) exemplifies this
for a unary ‘who’ question and a polar question:

(8) a. Who = $\begin{bmatrix} x_1 : Ind \\ c1 : person(x_1) \end{bmatrix}$;

b. *Whether* = *Rec*;

c. ‘Who runs?’ ↦→

$$
\left[
\begin{array}{l}
\text{sit} = r_1 \\
\text{abstr} = f:Who([c : run(r_1.x_1)])
\end{array}
\right];
$$

d. ‘Whether Bo runs?’ ↦→

$$
\left[
\begin{array}{l}
\text{sit} = r_1 \\
\text{abstr} = f:Whether([c : run(b)])
\end{array}
\right]
$$

Austinian questions can be conjoined and dis-
joined though not negated. We view this as an
advantage over inquisitive approaches which over-
generate in allowing interrogatives to be negated.
The definition for con-/disjunction is as follows:

$$
(9) \quad \left[
\begin{array}{lcl}
\begin{array}{lcl}
\text{sit} & = & s \\
\text{abstr} & = & f : T_1 (T_2)
\end{array}
& \quad & \wedge \quad (\forall) \\
\\
\left[
\begin{array}{lcl}
\text{sit} & = & s \\
\text{abstr} & = & f : T_3 (T_4)
\end{array}
\right] \\
\\
\left[
\begin{array}{l}
\text{sit} = s \\
\text{abstr} = f : \begin{bmatrix} \text{left} : T_1 \\ \text{right} : T_3 \end{bmatrix} \\
\quad (q_1(\text{s.left}) \wedge (\forall) q_2(\text{s.right}))
\end{array}
\right]
\end{array}
\right]
$$

<figure><img src="image_19.png" /><figcaption>Figure 2: Proposed response space of questions</figcaption></figure>

2.2 Response Space

We assume the following theory of the response
space of queries, due to Ginzburg et al. (2022).
This amounts to the following general types of
responses (see Figure 2):

1. Question-Specific: DirectAnswers (DA), In-DirectAnswers (IND) and Dependent Questions (DP):

(a) Answerhood

(b) Dependent questions (A: Who should we invite? B: Who is in town?)

2. Metacommunicative Responses:

(a) Clarification Responses (CR)

(b) Acknowledgements (ACK)

3. Evasion responses:

(a) Ignore (address the situation, but not the question)

(b) Change the topic (CHT; ‘Answer *my* question’)

(c) Motive ('Why do you ask?')

(d) Difficult to provide a response (DPR).

The basic notion of context we adopt is via each
participant’s view of publicized context, the dia-
logue gameboard (DGB), whose basic make up is
given in (10):

$$
\begin{equation}
\left[
  \begin{array}{@{}l@{\quad}l@{}}
    \begin{array}{@{}l@{}}
      \text{spkr} : \text{Ind} \\
      \text{addr} : \text{Ind} \\
      \text{utt-time} : \text{Time} \\
      \text{c-utt} : \text{addressing}(\text{spkr},\text{addr},\text{utt-time}) \\
      \text{facts} : \text{set}(\text{Prop}) \\
      \text{vis-sit} = [\text{foa} : \text{Ind} \lor \text{Rec}] : \text{RecType} \\
      \text{pending} : \text{list}(\text{LocProp}) \\
      \text{moves} : \text{list}(\text{IllocProp}) \\
      \text{qud} : \text{poset}(\text{Question})
    \end{array} &
    \left[
      \begin{array}{@{}l@{}}
        \text{sit} = s \\
        \text{abstr} = f : T_1 (T_2) \\
        \text{sit} = s \\
        \text{abstr} = f : T_3 (T_4) \\
        \text{sit} = s \\
        \text{abstr} = f : \begin{bmatrix} \text{left} : T_1 \\ \text{right} : T_3 \end{bmatrix} \\
        (q_1(\text{s.left}) \land (\forall) q_2(\text{s.right}))
      \end{array}
    \right]
  \end{array}
\right]
\end{equation}
$$

Here *facts* represents the shared assumptions of the
interlocutors—identified with a set of propositions.

Dialogue moves that are in the process of being
grounded or under clarification are the elements
of the *pending* list; already grounded moves are moved to the *moves* list. Within *moves* the first element has a special status given its use to capture adjacency pair coherence and it is referred to as *LatestMove*. The current question under discussion is tracked in the QUD field, whose data type is a partially ordered set (*poset*). *Vis-sit* represents the visual situation of an agent, including his or her visual focus of attention (*foa*), which can be an object (*Ind*), or a situation or event. We call a mapping between DGB types a *conversational rule*—Conversational rules are the means for specifying how DGBs evolve. The types specifying its domain and its range we dub, respectively, the *pre(conditions)* and the *effects*, both of which are subtypes of DGBType: they apply to a subclass of records that constitute possible DGBs and modify them to records that constitute possible DGBs. Conversational rules are written here in a form where the preconditions represent information specific to the preconditions of this particular interaction type and the effects represent those aspects of the preconditions that have changed.

The first conversational rule we formulate relates to the basic effect a query has on the DGB—as a consequence of a query a question becomes the maximal element of QUD:

(11) Ask QUD-incrementation: given a question *q* and Ask(A, B, *q*) being the LatestMove, one can update QUD with *q* as MaxQUD.

$$ \text{pre : } \left[ \begin{array}{l} \text{q : Question} \\ \text{LatestMove = Ask(spkr, addr, q) : LocProp} \end{array} \right] \\ \text{effects : } \left[ \begin{array}{l} \text{QUD = } \langle \text{q, pre.QUD} \rangle : \text{poset(Question)} \end{array} \right] $$

Before we consider how question-specific responses get accommodated, we turn to a discussion of answerhood.

## 2.3 Answerhood

Descriptively the *simple* answers to questions are the range of the propositional abstract, plus their negations.

(12) a. SimpleAns($p$?) = {$p, \neg p$};

b. SimpleAns($\lambda x.P(x)$) = 
$\{P(a), P(b), \dots, \neg P(a), \neg P(b) \dots\}$

More formally, an *atomic answer* *p* is a proposition for which there is a record *r* such that *p* is a proposition whose *sit* is identical to the question's

*sit* and such that applying the question's *abstr* to *r* yields *p*'s *sit-type*:

(13) AtomAns =

$$ \begin{bmatrix} p & : \text{Prop} \\ q & : \text{Question} \\ p.sit = q.sit & : \text{Rec} \\ p.sit-type = q.abstr(p.sit) & : \text{RecType} \end{bmatrix} $$

A negative atomic answer *p* is a proposition for which there is a record *r* such that *p* is a proposition whose *sit* is identical to the question's *sit* and such that negating the application of the question's *abstr* to *r* yields *p*'s *sit-type*:

(14) NegAtomAns =

$$ \begin{bmatrix} p & : \text{Prop} \\ q & : \text{Question} \\ p.sit = q.sit & : \text{Rec} \\ p.sit-type = \neg q.abstr(p.sit) & : \text{RecType} \end{bmatrix} $$

To exemplify:

(15) a. Take $r_1 : Who$ (cf. (8a)), e.g., $r_1 =$

$$ \begin{bmatrix} x_1 = a \\ c_1 = \text{PersObs1} \\ \dots \end{bmatrix}, \text{ then} $$

$$ p_1 = \begin{bmatrix} \text{sit} = r_1 & : \text{Prop} \\ \text{sit-type} = \text{abstr}(r_1) = [c : \neg \text{run}(a)] & : \text{Question} \end{bmatrix} \text{ (a does not run')} $$

is a negative *atomic* answer to the question 'who runs'.

b. Take any record $r_1$, then $p_1 =$

$$ \begin{bmatrix} \text{sit} = r_1 \\ \text{sit-type} = \text{abstr}(r_1) = [c : \neg \text{run}(b)] \end{bmatrix} \text{ is the only negative atomic answer to the question 'whether B runs'}. $$

The type of negative answers, however, will be slightly revised in adopting answerhood to RTT in section 3.

A *simple* answer is an answer that is either atomic or negative atomic: *p* is a simple answer to *q* if $r_0 : AtomAns$ and $p = r_0.p$ and $q = r_0.q$ or $r_0 : NegAtomAns$ and $p = r_0.p$ and $q = r_0.q$:

(16) SimpleAns =

$$ \begin{bmatrix} r_0 : \text{AtomAns} \lor \text{NegAtomAns} \\ p = r_0.p : \text{Prop} \\ q = r_0.q : \text{Question} \end{bmatrix} $$

In fact, *simple answerhood*, though it has good coverage in practice, is not sufficient. It does not accommodate conditional, weakly modalized, and quantificational answers, all of which are pervasive in actual linguistic use (Ginzburg and Sag, 2000).
Thus, we suggest that the semantic notion relevant to direct answerhood is the relation aboutness—a relation between propositions and questions that any speaker of a given language can recognize, independently of domain knowledge and of the goals underlying an interaction.

The most detailed discussion of Aboutness we are aware of is (Ginzburg and Sag, 2000, pp. 129–149), which offers (17a) (reformulated here in TTR as Austinian questions). This requires the situational type component of the proposition to be a subtype of the join of the situational type of the question’s simple answer set. As it stands, this definition allows in principle very informationally strong types as direct answers, since nothing bounds the proposition from above. Plausible upper bounds for direct answerhood familiar in the semantics of questions from the classic proposal of (Karttunen, 1977) are the meets of the question’s atomic and negative atomic answer set.<fnref n="4" /> This condition is formulated in (17b):

$$ (17) \quad \begin{aligned} & \text{For } p = \begin{bmatrix} \text{sit} = s_1 \\ \text{sit-type} = T_1 \end{bmatrix} : \text{Prop}, \\ & q = \begin{bmatrix} \text{sit} = s_1 \\ \text{abstr} = r : T_2(T_3) \end{bmatrix} : \text{Question} \end{aligned} $$

a. About($p, q$) holds iff $T_1 \subseteq \forall \{T | \exists p'[p' : \begin{aligned} & \text{Prop} \wedge \text{SimpleAns}(p', q) \wedge T = \\ & p'.\text{sit-type}] \end{aligned}}$

b. DirectAns($p, q$) holds iff About($p, q$) and either

(i) $\neg AtomAns(q) \sqsubseteq T_1$ or

(ii) $\neg NegAtomAns(q) \sqsubseteq T_1$

For reasons of space, we omit discussion here of indirect answers and dependent questions, which figure in the following conversational rule, which is the main engine in driving question-specific responses:

(18) a. Given $r : Question \lor Prop, q : Question, dgb : DGBType, QSpecific(r, q, dgb) \iff DirectAns(r, q) \lor IndirectAns(r, q, dgb) \lor Depend(q, r)$

b. QSPEC =

$$ \left[ \begin{array}{l} \text{pre : } \left[ \begin{array}{l} \text{QUD} = \langle q, Q \rangle : \text{poset}(\text{Question}) \end{array} \right] \\ \text{effects : } \left[ \begin{array}{l} \text{spkr} = \text{pre.spkr} \lor \text{pre.addr} : \text{Ind} \\ \text{addr} : \text{Ind} \\ \text{caddr} : \neq(\text{addr,spkr}) \\ \text{p} : \text{Prop} \lor \text{Question} \\ \text{c1} : \text{QSpecific}(\text{p,q,pre}) \end{array} \right] \end{array} \right] $$

Ginzburg and Cooper (2004); Purver (2004); Ginzburg (2012) show how to account for the main classes of clarification requests using rule schemas of the form “if *u* is the interrogative utterance and *u*<sub>0</sub> is a constituent of *u*, allow responses that are co-propositional<sup>5</sup> with the clarification question CQ<sup>i</sup>(*u*<sub>0</sub>) into QUD.”, where ‘CQ<sup>i</sup>(*u*<sub>0</sub>’) is one of the three types of clarification question (repetition, confirmation, intended content) specified with respect to *u*<sub>0</sub>.

For instance, responses such as (2) can be explained in terms of the schema in (19):

(19) if A’s utterance *u* is yet to be grounded and *u*<sub>0</sub> is a sub-utterance of *u*, QUD can be updated with the question *What did A mean by u*<sub>0</sub>?

More formally: the issue $q_0$, *What did A mean by u*<sub>0</sub>?, for a constituent $u_0$ of the maximally pending utterance, A its speaker, can become the maximal element of QUD, licensing follow up utterances that are CoPropositional with $q_0$.<fnref n="6" />

(20) Parameter identification:

$$ \left[ \begin{array}{l} \text{pre : } \left[ \begin{array}{l} \text{MaxPENDING} = \begin{bmatrix} \text{sit} = u \\ \text{sit-type} = T_u \end{bmatrix} : \text{LocProp} \\ \text{A} = u.dgb-params.spkr : \text{Ind} \\ u_0 : \text{Sign} \\ c1 : \text{member}(u_0,u.\text{constits}) \end{array} \right] \\ \text{effects : } \left[ \begin{array}{l} \text{MaxQUD} = \lambda x.\text{Mean}(A,u_0,x) : \text{Question} \\ \text{LatestMove} : \text{LocProp} \\ \text{c1} : \text{CoPropositional}(\text{LatestMove.\text{cont, MaxQUD}}) \end{array} \right] \end{array} \right] $$

(21) a. $\lambda x.\text{Mean}(A, u_0, x)$

<footnote n="4">⁴For a polar question *p*? the meets of the question's atomic and negative atomic answer set are respectively *p* and *¬p*, whereas for a wh-question λx.P(x) (e.g., ‘who left’) they are respectively ∧P(*a*<sub>i</sub>) (‘Bo left and Millie left . . . ’), whereas ∧¬P(*a*<sub>i</sub>) (‘Bo did not leave and Millie did not leave . . . , i.e., equivalent to ‘No one left’”).</footnote>

<footnote n="5">⁵Here CoPropositionality for two questions means that, modulo their domain, the questions involve similar answers: for instance ‘Whether Bo left?’, ‘Who left?’, and ‘Which student left?’ (assuming Bo is a student) are all co-propositional. More precisely, two questions $q_1$ and $q_2$ are copropositional iff there exist a record $r$ such that $q_1(r) = q_2(r)$.</footnote>

<footnote n="6">⁶Assuming a propositional function view of questions, CoPropositionality allows in propositions from the range of Range($q_0$) and questions whose range intersects Range($q_0$). Since CoPropositionality is reflexive, this means in particular that the inferred clarification question is a possible follow up utterance, as are confirmations and corrections, as exemplified in (21).</footnote>
b. ?Mean(A,u₀,b) ('Did you mean Bo')

c. Mean(A,u₀,c) ('You meant Chris')

The formulation of this rule is based on the existence of a feature **CONSTITS** which tracks all the constituents of an utterance and therefore licences clarification of all constituents down to the word level. It presupposes the existence of a relation *Mean* that holds between the speaker of an utterance, the utterance, and the intended content. In general, this has been identified with the value instantiated by dgb-params (on a distinguished label 'x') for that utterance:

(22) Mean(A,u,c) iff $u.dgb-param.spkr = A$ and $u.dgb-param.x = c$

This definition was motivated by the assumption that what gets queried in **intended content** CRs is the intended instantiation of contextual parameters.

### 3 An RTT theory of WhP meaning

As we have suggested, building on much past work, QNPs have more duties than merely contributing to truth conditions: QNPs act as antecedents for anaphoric expressions, they supply verbal affiliates of co-speech gestures, and they are objects of discourse dynamics which becomes apparent in terms of acceptance or clarification requests (we restrict attention here to nominals, but the conditions generalize cross-categorially):

(23) **Referential Transparency**: a semantic representation for an NP is *referentially transparent* if

a. it provides antecedents for pronominal anaphora;

b. it provides the semantic type required by a clarification request;

c. it provides an attachment site for co-verbal gestures;

d. its content parts can be identified and addressed.

Recall from section 1 that the Reprise Content Hypothesis provides a stronger claim than Fregean compositionality: more complex contents are not just systematically combined from their parts, but the contributions from the parts have to be traceable within the complex content. This we achieve in

virtue of the feature **CONSTITS** mentioned above, whereas potential clarifiability arises from the update rule **parameter identification**, formulated above as (20)

The “QNP anatomy” (a phrase due to Cooper, 2013a), which will be an important basis for satisfying these desiderata, is based on a set triplet:

$$ (24) \qquad \left[ \begin{array}{rcl} \text{q-params :} & \left[ \begin{array}{l} \text{refset : Set(Ind)} \\ \text{compset : Set(Ind)} \\ \text{maxset : Set(Ind)} \\ \text{c1 : } \mathbf{\overrightarrow{\text{PType}(\text{maxset})}} \\ \text{c2 : } \text{union(\text{maxset,refset,compset})} \end{array} \right] & \mathbf{\overrightarrow{\text{Rel}(|\text{q-params.refset}|, |\text{q-params.compset}|)}} \\ \text{q-cond :} & \mathbf{\overrightarrow{\text{Rel}(|\text{q-params.refset}|, |\text{q-params.compset}|)}} \end{array} \right] $$

The arrow indicates a plural predicate type (*PType*), that is, a predicate that expects a set-valued argument. Condition c2 simply states that refset and compset add up to the maxset. The value of condition c1 is donated by the head noun and distributed over all maxset members (and thereby over refset and compset). The quantificational workhorse is the quantifier condition “q-cond”: it captures what can be called the descriptive meaning of a QNP. For instance, the q-cond of *most* states that the refset is larger than the compset (|refset| > |compset|). Hence, q-cond not only expresses NP-internal quantification (i.e., quantification without a scope set from the VP), it also implements quantifiers as “sieves”, a metaphor due to Barwise and Cooper (1981).

Singular is seen as a special case of plural which just adds the following constraint:

$$ (25) \qquad \left[ \text{q-params :} \left[ \begin{array}{l} \text{refind : Ind} \\ \text{c3 : in(\text{refind, refset})} \end{array} \right] \right] $$

RTT involves a twist in predication: the compset gives rise to “two-headed” propositions. For example, the propositional structure for the simple sentence *Most squirrels sleep* is given in (26), where sit-type is of type *RecType*:

$$ (26) \qquad \left[ \begin{array}{l} \text{sit}=s_1 : \text{Rec} \\ \text{q-params :} \left[ \begin{array}{l} \text{maxset : Set(Ind)} \\ \text{refset : Set(Ind)} \\ \text{compset : Set(Ind)} \\ \text{c0 : squirrel(maxset)} \\ \text{c1 : union(maxset,refset,compset)} \end{array} \right] \\ \text{q-cond : } |\text{q-params.refset}| > |\text{q-params.compset}| \\ \text{nucl : } \mathbf{\overrightarrow{\text{sleep}(\text{q-params.refset})}} \\ \text{anti-nucl : } \mathbf{\overleftarrow{\text{sleep}(\text{q-params.compset})}} \end{array} \right] $$

Hence, there are several ways to form a propositional abstract from RTT propositions—namely
over refset, compset, or refind. Two remarks are in order:

* Since refind is a special case of refset, we do not distinguish those cases and subsume refind to refset abstractions.

* In principle, the refset/compset distinction allows us to semantically distinguish positive and negative WhPs: positive ones ("Who PRED?") target the refset, negative ones ("Who does not" PRED?) can be seen to target the compset of the situational abstract of the question. However, in line with the distinction of negative and positive propositions in TTR-KoS, we treat negative questions as involving a negated nucl (and a double negated (equivalent but distinct from positive) anti-nucl).

The basic contribution of a wh-phrase to an interrogative meaning is the domain from which a propositional function will be constructed. It is this domain clarification for which can be sought. Hence, we add additional structure in abstr with a label wh-dom, which also gets projected as the dgb-params.x value of that sub-utterance.<fnref n="7" /> Hence, the basic “anatomy” of WhP meaning in RTT is: The situation types of propositions on the RTT account factor out referential parameters in terms of q-params—see (24) and (26). Hence, questions and answers are constructed in terms of these parameter sets.

$$ (27) \quad \left[ \begin{array}{l} \text{wh-dom} = \left[ \begin{array}{@{}l@{}} \text{refset : Set(Ind)} \\ \text{c1} : \overrightarrow{\text{PType}(\text{refset})} \end{array} \right] : \text{RecType} \\ \text{cont} : [x = \text{wh-dom}.\text{refset}] \\ \text{dgb-params} : [x = \text{wh-dom} : \text{RecType}] \end{array} \right] $$

A question's abstr now works as follows:

$$ (28) \quad \left[ \begin{array}{l} s = r_1 \\ \text{abstr} = f : T_1(T_2.\text{sit-type}.\text{q-params}.\text{refset}) \end{array} \right] $$

which yields contents as in (29):

(29) a. Who sleeps? $\mapsto$

$$ \left[ \begin{array}{l} \text{sit} = r : \text{Rec} \\ \text{abstr} = \left[ \begin{array}{@{}l@{}} \text{wh-dom} = \left[ \begin{array}{@{}l@{}} \text{refset : Set(Ind)} \\ \text{c1} : \overrightarrow{\text{person}(\text{refset})} \end{array} \right] : \text{RecType} \end{array} \right] \\ \text{f} = \text{wh-dom}(\left[ \begin{array}{@{}l@{}} \text{refset} = r.\text{refset} : \text{Set(Ind)} \\ \text{nucl} : \overrightarrow{\text{sleep}(\text{refset})} \end{array} \right]) \end{array} \right] $$

b. Who does not sleep? $\mapsto$

$$ \left[ \begin{array}{l} \text{sit} = r : \text{Rec} \\ \text{abstr} = \left[ \begin{array}{@{}l@{}} \text{wh-dom} = \left[ \begin{array}{@{}l@{}} \text{refset : Set(Ind)} \\ \text{c1} : \text{person}(\text{refset}) \end{array} \right] : \text{RecType} \end{array} \right] \\ \text{f} = \text{wh-dom}(\left[ \begin{array}{@{}l@{}} \text{refset} = r.\text{refset} : \text{Set(Ind)} \\ \text{nucl} : \overrightarrow{\text{sleep}(\text{refset})} \end{array} \right]) \end{array} \right] $$

Note that refset abstraction accommodates both singular and plural answers. Note further that the compset provides a straightforward link for maintaining situational identity between questions and answers in case of negative answers. For instance, answering "Who sleeps?" with "Not the squirrel" can be straightforwardly understood in an Austrian manner as being about the same situation since the NP negation indicates compset membership (cf. Lücking and Ginzburg, 2019).

* SimpleAns($p$?) =

$$ \left\{ \left[ \begin{array}{l} \text{sit} = s0 \\ \text{sit-type} = [\text{nucl} : p] \end{array} \right] , \left[ \begin{array}{l} \text{sit} = s0 \\ \text{sit-type} = [\text{nucl} : \neg p] \end{array} \right] \right\} $$

* SimpleAns($\lambda x.P(x)$) =

$$ \left\{ \left[ \begin{array}{l} \text{sit} = s1 \\ \text{sit-type} = \left[ \begin{array}{@{}l@{}} \text{nucl} : \text{P(s1.refset)} \\ \text{anti-nucl} : \neg \text{P(s1.compset)} \end{array} \right] \end{array} \right] , \\ \left[ \begin{array}{l} \text{sit} = s2 \\ \text{sit-type} = \left[ \begin{array}{@{}l@{}} \text{nucl} : \text{P(s2.refset)} \\ \text{anti-nucl} : \neg \text{P(s2.compset)} \end{array} \right] \end{array} \right] , \\ \dots $$

SimpleAns($p$?) is answer to polar question ("whether Bill is running?" "No, he's not"/"Bill is not running"), SimpleAns($\lambda x.P(x)$) involves Not NP ("Who is running?" "Not Bill").

* AtomAnsRTT = answer given in terms of nucl

* NegAtomAnsRTT = answer given in terms of anti-nucl

* StrongExhaustiveAns =

$\bigwedge \{\text{AtomAnsRTT}, \text{NegAtomAnsRTT}\}$ (i.e., an answer that enumerates all refset and compset members)

# 4 Accounting for the data

## 4.1 Putting together wh-meanings

In order to develop our account we need to appeal to a grammar for interrogatives. We assume the HPSG-TTR grammar developed in (Ginzburg

<footnote n="7">⁷We think that a similar account can be developed for intensional argument roles used with QNPs. Such cases are analyzed in RTT, following (Cooper, 2005), as the verb composing with a QNP's type value. Hence all that is required is to ensure also that this value is projected as the dgb-params.x value.</footnote>
and Sag, 2000) and refined in (Ginzburg, 2012; Lücking et al., 2021). We start by exemplifying three constructions: sentential wh-interrogatives and two types of non-sentential wh-interrogatives ('sluicing'), one direct and the other used for clarification questions. In the case of sentential wh-interrogatives the filler daughter (specified as having a non-empty value for the feature wh) contributes the domain for the question; the range is identified with the content of the head daughter, with a substitution of filler daughter variable for gap variable. In the case of direct sluicing content is composed in an analogous way, save for the fact that the queried proposition is supplied by context—it is the nucleus of a quantified proposition that constitutes MaxQUD—and the substitution is the sluice WhP daughter for the focus establishing constituent variable: see Figure 3 (i) and (ii).<fnref n="8" /> Finally for reprise sluicing (as well as other uses (Ginzburg, 2012, p. 258)), it allows a bare wh-phrase to denote MaxQUD given that the domain of the wh-phrase is the same as the domain of MaxQUD: see Figure 3 (iii).

## 4.2 Clarificational potential

The clarificational potential of wh-phrases is captured since the dgb-params.x value of the wh-phrase is the type specified by the label wh-dom; since the value specified is a type rather than an individual, there is no possibility of responding to such a clarification question with a witness (set).

## 4.3 Anaphoric potential

The anaphoric potential of wh-phrases in questions is subtle and requires a more detailed discussion, not least of the data, than we can offer here. All NPs provide antecedents via their content.x value. Intrasententially this is available subject to certain binding theory constraints. For discourse anaphora, available antecedents are sub-utterances in active moves (Ginzburg, 2012, p. 335) (essentially moves which address QUD or are PENDING). The restricted possibilities of wh-phrases and QNPs in intensional argument roles are due to a basic horror vacui, meaning that they avoid empty antecedent denotations, hence the need for accommodation in such cases. The basic idea we sketch for the wh-phrase case is this: via the accommodation rule in (30) (Ginzburg, 1997), the querier increments her

Topical FACTS with a positive resolution of the wh-question;<fnref n="9" /> this in turn provides an antecedent for the anaphor.

(30) Positive Resolution Accommodation

$$ \left[ \begin{array}{l} \text{pre : } \left[ \begin{array}{l} \text{QUD} = \langle q, Q \rangle : \text{poset(Question)} \\ \text{f : Prop} \\ \text{c1 : } \sqrt{\text{AtomAns}(q) \sqsubseteq f} \end{array} \right] \\ \text{effects : } [\text{TOPICAL-FACTS} := \text{TOPICAL-FACTS} \cup \{f\}] \end{array} \right] $$

## 4.4 Incrementality

Following Ginzburg et al. (2020), QUD gets modified incrementally, that is, at a word-by-word latency. Technically, this is implemented by adopting the predictive principle of incremental interpretation in (31). This says that if one projects that the currently pending utterance (the preconditions in (31)) will continue in a certain way (pending.proj in (31)), then one can actually use this prediction to update one's DGB, concretely to update Latest-Move with the projected move; this will, in turn, by application of the existing conversational rules, trigger an update of QUD:

(31) Utterance Projection :=

$$ \left[ \begin{array}{l} \text{preconditions : } [\text{pending.sit-type.proj} = a : \text{Type}] \\ \text{effects : } \left[ \begin{array}{l} \text{e1 : Sign} \\ \text{LatestMove} = \left[ \begin{array}{l} \text{sit} = \text{e1} \\ \text{sit-type} = a \end{array} \right] : \text{LocProp} \end{array} \right] \end{array} \right] $$

Our proposed treatment of interrogative clauses in conjunction with our treatment of interrogative sluices is quasi-incremental (Schlesewsky and Bornkessel, 2004). That is, it allows to explain why an interrogative clause can already be (partially) understood as soon as the wh-phrase is uttered—there is already at that point an initial specification of a propositional function, namely its domain. More specifically, after processing 'wh-phrase ...', one can postulate a content where the projected but as yet unuttered constituent u1 contributes its content in an existentially quantified form, as in (6c), with a content as in (32a). Equally, this can give rise to a clarification request concerning the initial wh-phrase, as in (6d).

<footnote n="8">⁸'fec' (focus establishing constituent) is the antecedent utterance whose scope builds up MaxQUD—in the case of sluicing it is the quantified NP in the antecedent utterance.</footnote>

<footnote n="9">⁹Topical FACTS are, roughly, those facts that are About some question currently in QUD; see (Ginzburg, 2012, pp. 311–313). These play a role somewhat analogous to the right frontier constraint in discourse-tree based theories such as SDRT (Hunter et al., 2015).</footnote>
<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /><figcaption>Figure 3: (i) Head-Filler Construction, for ex situ wh-sentences such as (2c.A): Who should we contact __ for help?, (ii) Sluice clause, for elliptical, non-reprise wh-questions such as A: A student left. B: Who? (iii) wh-anaphoric clause, for reprise or “echo” wh-phrases such as Fig. 1: Who?</figcaption></figure>

<figure><img src="image_23.png" /></figure>

(reference: ANR-10-LABX-0083). It contributes to the IdEx Université Paris Cité - ANR-18-IDEX-0001.

## 4.5 The Harden example

Finally, we return to the example from Figure 1. This involves an initial utterance or gesture directed at James Harden. Using *parameter identification* targeting the addressee contextual-parameter, this leads to a context in which a reprise sluice (Figure 5) can be used, giving rise to the reading ‘Who do you mean by this pointing gesture’.

## 5 Summary and conclusions

In this paper we have sketched an extension of a recent theory of quantification to wh-phrases and questions. We have applied this account to several dialogical phenomena which we believe have not been addressed in previous work.

## Acknowledgments

We thank the InqBnB referees for helpful comments and Robin Cooper for a useful discussion. This work is supported by a public grant overseen by the French National Research Agency (ANR) as part of the program ‘Investissements d’Avenir’

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# Uninquisitive questions

Tom Roberts

University of Amsterdam

t.roberts@uva.nl

## Abstract

The sort of denotation a sentence is assigned is typically motivated by assumptions about the discourse function of sentences of that kind. For example, the notion that utterances which are *functionally* inquisitive (asking a question) suggest denotations which are *semantically* inquisitive (expressing the multiple licit responses to that question) is the cornerstone of interrogative meaning in frameworks like Alternative Semantics (Hamblin, 1973) and Inquisitive Semantics (Ciardelli et al., 2018).

This paper argues that at least some kinds of questions systematically do not involve utterances with inquisitive content, based on novel observations of the Estonian discourse particle *ega*. Though *ega* is often labeled a ‘question particle’, it is used in both assertions and questions with sharply divergent discourse effects. I suggest that the relevant difference between assertive and questioning uses of *ega* is not semantic or sentence type-related, but rather reflects an interaction between a unified semantics for declaratives *ega*-sentences and different contexts of use. I then show that if we assume that *ega* presupposes that some aspect of the discourse context implicates the negation of *ega’s* prejacent, and that it occurs only in declarative sentences, we can derive its interpretation across a range of contexts: with the right combination of ingredients, we can ask questions with semantically uninquisitive sentences.

## 1 Introduction

A fundamental question in Inquisitive Semantics (Ciardelli et al., 2018) is what sorts of linguistic items generate semantic inquisitivity, in the sense of raising multiple mutually non-entailing alternatives. Polar interrogative clauses, for example, are a paradigmatic example of an inquisitive object, characterized by an inquisitive operator INT which is responsible for contributing inquisitivity, reminiscent of influential analyses of questions as denoting

sets of answers to those questions (e.g. Hamblin,
1973; Karttunen, 1977; Groenendijk and Stokhof,
1982).

How can we tell what linguistic objects are in-
quisitive? In the case of interrogatives, their char-
acteristic inquisitivity correlates with the fact that
they canonically raise issues with multiple possi-
ble resolutions. This can be formally cashed out
in various ways. For example, Farkas and Roelof-
sen (2017) propose a general-purpose utterance
function that applies equally to both declaratives
and interrogatives; the ‘questioning’ effect of in-
terrogatives comes from an interaction between
their inquisitive denotation and this utterance func-
tion. The difference between declaratives and inter-
rogatives in this view comes from the assumption
that declarative sentences denote a singleton set of
propositions, and therefore raise issues with only a
single maximal resolution.

But we cannot always straightforwardly link in-
quisitive denotations to inquisitive speech act func-
tions. For instance, English rising declaratives
(You're in London?) seem to ask questions, de-
spite their declarative form. This pragmatic obser-
vation has motivated analyses of rising declaratives
as having a (possibly compositionally determined)
inquisitive denotation à la interrogatives (Roelof-
sen and Farkas, 2015; Farkas and Roelofsen, 2017;
Jeong, 2018), but many others aim to derive their
question-asking pragmatic function from the in-
teraction between non-inquisitive declarative se-
mantics *per se* and rising intonation (Truckenbrodt,
2006; Gunlogson, 2008; Krifka, 2015; Malamud
and Stephenson, 2015; Westera, 2017, 2018; Rudin,
2022, to name but a few).

Whatever the right analysis of rising declaratives
is, they raise the much larger issue of what path(s)
languages make use of to get from denotations
to pragmatic functions. To put a finer point on
it: Do question-y pragmatics point to inquisitive
denotations, or can pragmatic ‘inquisitivity’ arise
via other means? And if the latter is true, what are
those means?

This paper aims to shed light on the sentential
denotation-speech act mapping through the lens of
the Estonian left-periphery discourse particle *ega*.
*Ega* is an interesting case from this perspective be-
cause it occurs in both questions (1) and assertions
(2), but makes sharply different interpretive con-
tributions in each case.<fnref n="1" /> Also strikingly, *ega* only
occurs in sentences with sentential negation (with
some rare exceptions, see §4).

(1) *Context: Discussion diagnosing warning lights on a car dashboard*

Ega see pilt punasest kollaseks ei
EGA this picture red.ELA yellow.TRA NEG
vahetu?
change.NEG
‘Does the icon not change from red to yel-
low?’

*(etTenTen 2021)²*

(2) *Context: Speaker is sure that Russia would advance in the tournament, but they lost. They describe their reaction to this state of affairs:*

Ega ma eriti kurb ei olnud.
EGA I especially sad NEG was.neg
‘I wasn’t especially sad.’

*(etTenTen)*

In questions, *ega* conveys a ‘checking’ function
similar to tag questions, though it also is used in po-
lite requests. By contrast, in assertions, *ega* offers
a sense of ‘epistemic reinforcement’ that its preja-
cent is true, in contrast to some prior assumption.
Despite this apparent duality of function, much
more attention has been paid to the former use of
*ega*, and it is often explicitly described in both for-
mal and descriptive work as a ‘negative question
particle’ (e.g. Metslang, 1981, 2017; Erelt et al.,
1995).

The two guises of *ega* seem to be at odds
with one another: *Ega*-assertions convey epistemic
certainty, but *ega*-questions solicit addressee re-
sponses in a similar manner to interrogatives. We
could reconcile these facts by assuming that there
are two distinct versions of *ega* in the lexicon, one
for declaratives, and one for interrogatives. This
approach might well be sufficient for a description
of *ega’s* discourse effects in various contexts, but it
also leaves any similarities between the two com-

pletely accidental, such as their tendency to occur
alongside sentential negation.

In this paper, I propose a different approach:
we have the same *ega* in both questions and asser-
tions, but its divergent behavior arises from inter-
actions between this unified meaning and general
pragmatic principles. I argue that *ega*-sentences
are never inquisitive in the formal sense—they do
not denote non-singleton sets of propositions—but
they do come with a presupposition that generates
a pragmatic clash with their preajacent in most dis-
course contexts, giving the sense that the addressee
in fact has an issue to resolve. In this way, the appar-
ent ‘inquisitivity’ of *ega*-questions is epiphenom-
enal, adding to a body of literature which teases
apart semantic and pragmatic inquisitivity, and sug-
gesting that questions can be derived pragmatically
from the interaction between uninquisitive building
blocks.

## 2 A profile of ega

I will first lay out the pragmatic profile of *ega* by describing its distribution. As mentioned, *ega* occurs almost exclusively in negative sentences, an observation I will revisit in §4. Here, ‘negative’ means marked by *sentential* negation, a combination of the negative particle *ei* and a special con-negative form of the verb.<fnref n="3" /> Thus, in this section, I will describe the three kinds of discourse functions *ega*-sentences of the form *ega not-p* may have.

### 2.1 Ega in questions

Canonically, *ega* occurs in two main types of ques-
tions. The first is polite requests, which can be
naturally uttered in both informal and formal con-
texts, such as asking a stranger for directions or
interacting with customer service over the phone.
Generally, the speaker in these cases presents an
obliging tone, similar to rough English paraphrases
like *I don’t suppose that...* or *Do you happen to...:*

(3) Ega sa ei oska öelda, kus
EGA you NEG can.NEG say where
asub Eesti Pank?
is.located Bank of Estonia
‘I don’t suppose you could tell me where
the Bank of Estonia is?’

(4) Ega sul ratas ei ole?
EGA you.ADE bike NEG be.NEG

<footnote n="1">¹In fact, *ega* has yet another life as a coordinating conjunc-
tion. I set this version of *ega* aside here.</footnote>

<footnote n="3">³*Ei* can in fact be omitted in *ega*-sentences so long as the
connegative verb is still present and thus the sentence is still
identifiably negative-marked (Tamm, 2015).</footnote>
‘Do you happen to have a bike?’

The second class of *ega*-questions function like tentative assertions that *¬p*, while additionally seeking confirmation from the addressee whether this is in fact the case (Metslang, 2017). This profile is reminiscent of tag questions (see e.g. Reese and Asher 2007).

(5) Ega jaanipäeva viktoriin liiga raske EGA Midsummer.GEN quiz too difficult ei olnud? NEG was.NEG ‘The quiz about Midsummer wasn’t too difficult, right?’ (Tamm 2015:411)

(6) Ega sa midagi pole unustanud? EGA you anything be.NEG forgot.NEG ‘You haven’t forgotten anything, right?’ (Sign after airport security checkpoint)

While *ega*-questions of the confirmation sort are felicitous if the speaker seems to reasonably expect that *p* is false ((7) in Context 1), they are infelicitous if the addressee is neutral with respect to the truth or falsity of *p* (Context 2) or biased towards the truth of *p* (Context 3):

(7) A doctor asking a patient a standardized series of questions to make a diagnosis:

Ega sul ei ole valu seljas? EGA you.ADE NEG be.NEG pain back.INE ‘You don’t have back pain, right?’

**Context 1:** Patient burned their hand on a stove. (7)✓

**Context 2:** Doctor has no information about patient’s status. (7)#

**Context 3:** Patient fell off a ladder. (7)#

What both of these species of questions have in common is that the speaker presents themselves as committing (at least contingently) to **¬p**, but solicits a response from the addressee to either agree with or refute **¬p**.

## 2.2 Ega in assertions

In contrast with its questioning uses, *ega* has a life as an ‘adversative’ particle in assertions. Informationally, it indicates that the speaker is committed to the truth of **¬p**, in contrast with some existing evidence for *p*. As Keevallik and Habicht (2017) put it, *ega* ‘challenges something that has been assumed by the prior speaker’. This assumption can come from many sources, including implicatures of previous speech acts (Keevallik, 2009) or even

the addressee’s (even non-linguistic) behavior (8).

(8) A left dirty dishes in the sink and asks B to clean them. B responds:

Ega ei ole sinu ema! EGA NEG be.NEG your mother ‘I’m not your mother!’

In (8), B is not challenging a literal assertion of motherhood, but rather the apparent implication of A's behavior. Importantly, however, *ega*-assertions are not licensed in cases of bald-faced disagreement, i.e. in responses to assertions of *p* itself (note that B's response in (9) is similarly infelicitous without the polarity particle *ei* ‘no’):

(9) A: Ma võitsin mängu. I won game ‘I won the game.’
B: #Ei, ega sa ei võitnud! no EGA you NEG win.PAST.NEG ‘(No), you didn’t win!’

## 2.3 Summary

Though *ega*-questions and *ega*-assertions differ fundamentally in whether they seem to be requesting information or providing it, both convey that the speaker believes **¬p** and that there is some reason to believe that *p*.

## 3 Ega as a context update modifier

In this section, I will motivate the central analytical claim of this paper: despite often being used to ask questions, *ega*-sentences are always declarative, and the interrogative uses are derived by means of a crucial interaction between the meaning of *ega* and its contexts of use. Throughout this section, I will only examine *ega*-sentences are always negative (that is, having the form *ega not-p*), since positive *ega*-sentences are rare; the polarity restriction itself will be addressed in §4.

### 3.1 Ega-questions are declarative

In order to obtain a unified analysis of *ega*, we must contend with the apparent heterogeneity of discourse functions of *ega*-claims. On the basis of the discourse effects of *ega*-questions, we might assume they are in fact interrogative clauses. However, there is good reason to believe that *ega*-questions are in fact declarative.

In terms of core sentence structure, declaratives and interrogatives are identical in Estonian; there
is no obvious syntactic difference between a declarative and its corresponding polar interrogative, and there has been argued to be no reliable prosodic difference between them either (Keevallik, 2003; Asu, 2006; Salveste, 2015). Rather, neutral polar questions are typically characterized by adding a left-periphery particle *kas* to a corresponding vanila declarative.

(10) a. Liis on kodus.
Liis is home
‘Liis is home.’
b. Kas Liis on kodus?
Q Liis is home
‘Is Liis home?’

Absent a syntactic signature of clause type, we
can only argue that *ega*-sentences are interrogative
indirectly, but in fact, two additional pieces of evi-
dence point toward a declarative analysis. First, as
Keevallik (2009) points out, *ega* often co-occurs
with epistemic particles that are incompatible with
bonafide interrogatives, such as *vist* ‘probably, I
assume’. This is even the case in *ega*-sentences
whose apparent discourse function is to request
information (11):

(11) Ega sul ei köeta vist.
EGA you.ADE NEG heat.PASS.NEG probably
‘I assume that your place is not heated?’
(Keevallik 2009: 152)

Second, both *ega*-assertions and checking ques-
tions require the speaker to be biased toward the be-
lief that **¬p** (as opposed to *p*), which is entirely un-
surprising if *ega*-sentences are declaratives, since
uttering a declarative sentence **¬p** (absent special
intonation) typically commits the speaker to **¬p**.
We will revisit this notion in more detail below. It
might seem at first glance that polite requests like
(3) run counter to this line of reasoning, since the
speaker in such cases clearly does not believe **¬p**.
I will propose that this is an artifact of the polite
reasoning contexts: in fact, speakers of such *ega*-
questions are presenting themselves as believing
**¬p** for politeness reasons; I spell this out more
concretely in §3.4.1.

I take these pieces of evidence to jointly tip
the scales in favor of a declarative analysis of
*ega*. One possible issue is that on their face, *ega*-
sentences can be embedded under anti-rogative
verbs—those which permit interrogative but not
declarative complements—like küsima ‘ask’ and
uurima ‘investigate’ in the following examples

from blogs.

(12) Nancy isa küsib, et ega teil
Nancy.GEN father asks that EGA you.ADE
ju seal Eestis kartuleid et
after.all there Estonian.INE potatoes NEG
kasvatata.
grow.INF
‘Nancy’s father asks whether you really
don’t grow potatoes there in Estonia.’<fnref n="4" />

(13) Praamil tuleb kohe onu
ferry.ADE comes immediately uncle
kandikuga ja uurib, et ega sa
tray.COM and investigates that EGA you
teed ei taha.
tea NEG want.NEG
‘On the ferry, the waiter comes right away
with a tray and asks whether you would
like some tea.’<fnref n="5" />

To my knowledge, *ega* occurs embedded under
anti-rogative predicates only when those predicates
have a quotative reading. For instance, (12) and
(13) both exhibit obligatory indexical shift: sec-
ond person pronouns in the embedded clause refer
to the addressee in the reported discourse context
rather than the reader of the blog, characteristic of
quoted, rather than indirectly reported, speech in
Estonian (Teptiuk and Hirvonen, 2021). Thus, I
follow Rudin (2019) in assuming that these are not
instances of bonafide clause embedding, but rather
mere quotation, in which *ega* is part of the reported
speech (for ways of working this out more con-
cretely, see a.o. Lahiri 2002 and Davidson 2015).

One final issue I will note is that if *ega*-sentences
are declaratives, we might expect that they could be
composed with *kas* to make a polar interrogative,
but *ega* cannot co-occur with clausemate *kas* (14).

(14) *{Kas ega/ega kas} sul ratas ei
Q EGA/EGA Q you.ADE bike NEG
ole?
be.NEG
Intended: ‘Don’t you have a bicycle?’

I suggest that this is likely to be a fact about
syntax—*kas* and *ega* both occur somewhere in the
left periphery of a clause, above the canonical sub-
ject position and below the complementizer. If *kas*
and *ega* are both competing for the same syntactic
slot, their inability to co-occur is expected.<fnref n="6" />

<footnote n="4">⁴ http://marikatom.blogspot.com/2010/05/ukس-harilik-kartulivotu-paev.html</footnote>

<footnote n="5">⁵Abridged from https://lillelaps.blogspot.com/2013/01/tsivilisatsioonide-kokkuporke-koht.html</footnote>

<footnote n="6">⁶A reviewer points out that this competition story requires</footnote>
## 3.2 Ega in the Table model

In assertive contexts, ega often serves the purpose of canceling an implicature, that is, ega ~~p~~ is uttered in contexts in which the addressee might have some 'good reason' in principle to believe p. We could equally characterize questioning uses of ega in a similar way, roughly that the addressee is presenting themselves as believing ~~p~~, despite such evidence, but additionally requiring some input from the addressee to settle the matter. I will treat the evidential requirement as the core contribution of ega:

(15) **Licensing conditions on ega, informal version**

Ega ~~p~~ is licensed iff there exists a body of evidence jointly available to the speaker and the addressee which could lead the addressee to form the belief that p.

To make my assumptions about components of discourse more precise, I adopt a version of the Table model of discourse Farkas and Bruce (2010). In a nutshell, the Table model distinguishes three main parts of utterance meaning: semantic denotation, the commitments it places upon speakers, and how the utterance guides potential futures of the conversation.

The Table model consists of four main components:

* A Stalnakerian **common ground** cg consisting of all propositions all discourse participants are publicly committed to, which describes a **context set** cs of all worlds compatible with $cg (cs = \bigcap cg)$

* The **Table**, a set of issues to be jointly resolved in the discourse<fnref n="7" />

* A set of **discourse commitments** DC<sub>X</sub> for every discourse participant X consisting of propositions X has publicly committed to

* A **projected set** ps of possible common

grounds enhanced by resolutions of the current QUD

In this model, discourses are assumed to be driven by a cooperative goal to shrink cs. This is achieved by making utterances which raise and resolving **issues**. Issues are sets of classical propositions (i.e., sets of sets of worlds), which are raised by being put on the Table, and resolved by a context set that entails one of its constituent propositions. Uttering a declarative sentence contributes an assertion, as follows:

(16) **ASSERTION:** Uttering a declarative sentence which expresses proposition p in context i yields an output context o s.t. (Farkas and Bruce 2010: Ex. 9)<fnref n="8" />

a. $T_o = T_i + \{p\}$

b. $DC_{Sp,o} = DC_{Sp,i} + p$

c. $ps_o = \{cg_i + p\}$

d. $c_o = c_i$ in all other respects

An assertion does three things: puts the singleton issue {$p$} on the Table, commits the speaker to the truth of p, and adds an enhancement of the common ground with p to the projected set, intuitively specifying that the addressee should resolve the issue {$p$} by adding p to the common ground.

I propose that uttering ega *not-p*, contributes the normal discourse effects of asserting ~~p~~ and additionally carries two presuppositions, contributed lexically by ega. I frame these presuppositions for the moment as licensing conditions on uttering negative ega-sentences rather than giving a lexical entry for ega itself due to complications about how ega interacts with polarity, which will be revisited in §4.

(17) **Licensing conditions on ega, final**

ega *not-p* can be uttered in context c iff:

a. $p \notin DC_{Ad}$

b. There is a body of evidence E accessible to Sp and Ad in c such that $E \models p$

The condition in (17a) states that it is not already common ground that the addressee believes p, which ensures that ega is not utterable in contexts where the addressee has asserted p themselves. and

<footnote>the assumption that kas and ega both belong to the same syntactic category. This is not in principle a problem for the treatment of ega-sentences as uniformly declarative if kas is in a category which correlates to sentence type, as is commonly assumed for question particles cross-linguistically (see Bailey 2012), rather than interrogativity *per se*.</footnote>

<footnote n="7">⁷In Farkas & Bruce's original formulation, the Table is a stack. In this paper I will only consider Tables which have only one issue on them at a time, so treating it as a set is adopted for simplicity.</footnote>

<footnote n="8">⁸One could equally adopt the definition of assertion which assumes Inquisitive Semantics, i.e., that declarative sentences denote a singleton set of propositions, as in Farkas and Roelofsen (2017). Because I treat ega-sentences as uniformly uninquisitive, this complication is not necessary.</footnote>
the condition in (17b) that the speaker believes that
there is some contextually available evidence that
entails that *p*. Taken together, *ega* expresses an
estimation of the addressee’s information state: it
doesn’t yet have *p* in it, but there is mutually avail-
able evidence that could lead them in that direction.

At this stage, the presupposition is still modeled
somewhat informally. For the purposes of this pa-
per, I will abstract away from how to model this
presupposition more precisely, while acknowledg-
ing it raises interesting questions for future work;
the important point of the subsequent analysis will
be how this licensing condition at an intuitive level
interacts with context.

3.3 Ega-assertions

Recall that in assertive cases, an *ega*-claim typically
is taken to straightforwardly assert the prejacent,
but indicates there was nevertheless reason to dis-
believe that prejacent. Moreover, an *ega*-assertion
is ‘epistemically strong’ as Keevallik (2009) puts
it: it conveys a sense that the speaker is especially
committed to the truth of **¬p**. I propose that *ega*
sentences take on this assertive flavor when ut-
tered in contexts in which the speaker has a greater
*epistemic authority* with respect to *p* than the ad-
dressee, in the sense of Northrup 2014. Roughly,
*AUTH<sub>X</sub>(*p*) indicates the degree to which *X* is a
reliable source about the truth (or falsity) of *p*:

(18) *Ega not-p* is interpreted as an assertion iff:
    a. *AUTH<sub>Sp</sub>(*p*) > *AUTH<sub>Ad</sub>(*p*)

A plain assertion of ¬p commits the speaker to the
truth of ¬p with the reasonable assumption of the
Gricean maxim of Quality, namely that people only
assert propositions they believe to be true (Grice,
1975). The strengthening effect in ega-assertions
comes from the contrast between a speaker's ut-
tering ¬p in a context in which they are a greater
authority on it than the addressee—performing a
canonical assertion—and ega's presupposition re-
quiring the context to be such that there is good
reason for the addressee to believe p.

In other words, the speaker is demonstrating
their commitment to **¬p** *despite evidence to the*
*contrary*, and *ega* explicitly signals to the addressee
not to be fooled by the evidence for *p*. This tension
naturally gives rise to the sense that *ega*-assertions
are especially forceful: a sincere assertion of **¬p** in
the fact of evidence for *p* requires the speaker to be
so certain that they override any ambient evidence

for *p*.

3.4 Ega-questions and addressee authority

Unlike *ega*-assertions, *ega*-questions seem to so-
licit information from the addressee. While the two
types of *ega*-questions (polite requests and check-
ing questions) seem nevertheless distinct on the
surface, they have a common core in that they both
suggest that the speaker is a lesser epistemic au-
thority on *p* than the addressee. If the speaker is
unlikely to believe **¬p**, we get the polite request
reading; if the speaker is likely to believe **¬p**, we
get the checking reading.

3.4.1 Polite requests

One prototypical use of *ega*-questions is to make a
polite request of the addressee. Given our declar-
ative semantics, and the assumption that uttering
declarative sentences adds their propositional con-
tent to the speaker’s discourse commitment, this
might seem an odd function. I propose that it can
be understood by considering the interaction be-
tween the semantics of *ega* and general constraints
on *politeness*. Consider (19):

(19) Context: Telephone call to an information line.

Ega te ei oska öelda Võru
EGA you.PL NEG can.NEG say Võru.GEN
bussijaama telefoninumbrit?
bus station.GEN phone number.PRT

‘I don’t suppose you can tell me the phone
number of the Võru bus station?’

(Keevallik and Habicht 2017: ex. 33)

Polite request interpretations of *ega* arise when it
is common ground both that the speaker believes
*p*, and that the speaker believes that the addressee
has greater authority than them with respect to the
truth of *p*:

(20) *Ega not-p* is interpreted as a polite request iff:
    a. *B*<sub>sp</sub>(*p*)
    b. *AUTH*<sub>Sp</sub>(*p*) < *AUTH*<sub>Ad</sub>(*p*)

The story goes like this: the speaker presents her-
self as committing to **¬p**—in (19), that the ad-
dressee cannot provide the bus station’s phone num-
ber. In this particular discourse context, it is implaus-
ible that the speaker actually believes **¬p**, since
they would not be calling otherwise. In the terms
of Rudin (2022), the caller makes an INSINCERE
(and thus pragmatically marked) discourse move
by committing themselves to $\neg p$, while assuming
that the addressee has evidence for $p$.

The act of making a commitment which is
known to be insincere to all discourse participants
can only be cooperative if being insincere is a way
for the speaker to avoid committing a more egre-
gious pragmatic violation, as in Optimality The-
oretic approaches to pragmatics (e.g. Dekker and
van Rooy, 2000).

In the case of *ega*, I propose that the competing
pragmatic constraints at play are SINCERITY (com-
mitting oneself only to that which they believe to
be true, Rudin 2022) and POLITENESS.<fnref n="9" /> The idea
is this: the presupposition of *ega* requires the caller
in (19) to believe the addressee has good reason to
believe they *can* report the number—in this case,
the evidence being their job in a call center.

If we consider a plausible alternative utterance
to (19) the speaker could have asked instead which
is a bonafide interrogative (e.g. *What is the phone
number of the bus station?*), such an utterance is
preferable in terms of SINCERITY, since uttering
an interrogative does not commit the speaker to
any one particular answer to the question it de-
notes (Farkas and Bruce, 2010; Farkas and Roelof-
sen, 2017). However, the *ega*-request is more PO-
LITE because it gives the addressee a chance to
save face—maintain a positive social image—in
the sense of Brown and Levinson (1987).

In Brown & Levinson's view, disagreeing with
a preceding assertion is a face-threatening move.
If the addressee has to decline the speaker's *ega*-
request, itself socially undesirable, they can do so
by agreeing with the speaker's presented commit-
ment **\neg p**. In other words, the speaker sacrifices
sincerity to mitigate the addressee's possible loss
of face by letting them 'agree their way out' of a
potentially face-endangering situation should they
have to give the speaker an answer they don't want.
If the addressee was asked directly for the phone
number and couldn't provide it, they would incur
a double-whammy of social violations: being un-
able to answer a question, and being unable to help
the speaker. By saying an *ega*-sentence instead,
the speaker presents themselves as believing the
addressee can't help them, giving the addressee a
way to decline the request while saving face.

Given a choice between being insincere and be-

ing impolite, then, the proposal is that speakers
are opting for the former when they make a polite
request using *ega*. (In OT terms, we could say that
the goal of being POLITE *outranks* that of being
SINCERE.)

### 3.4.2 Checking questions

Recall that checking *ega*-questions—requests for
the addressee to validate the truth of **\neg p**—convey
that the speaker is fairly sure that **\neg p** is the case, but
nevertheless wants some validation about this from
the addressee. I formalize the felicity conditions as
follows:

(21) *Ega not-p* is interpreted as a checking
question iff:

a. $\neg B_{sp}(p)^{10}$

b. $AUTH_{Sp}(p) < AUTH_{Ad}(p)$

Normally, making assertions in a context where the
addressee is assumed to be a greater authority about
the truth of the asserted proposition is infelicitous:

(22) #You're hungry. (Northrup 2014: ex. 129)

This can be again be attributed to the Gricean
maxim of Quality: the speaker's evidence is not
sufficient to make their claim. With *ega not-p*, the
tension between apparently asserting **\neg p** on one
hand and presupposing evidence for *p* on the other
poses a natural conflict that demands resolution.
Uttering *ega not-p* emphasizes this mismatch. If
the speaker is taken to be an authority on *p*, the ad-
dressee has no reason not to take them at their word
that **\neg p**. But if the *addressee* is an assumed author-
ity, highlighting the conflict between the speaker's
epistemic state and contextual evidence can only
serve the function of asking the addressee to make
the call between them.

For instance, in the forum post in (23), the
speaker follows up a question about whether it is
potentially problematic to forget taking antidepress-
sants with an *ega*-sentence about specific repercus-
sions:

(23) Can constantly changing antidepressants
and forgetting to take them have a negative

<footnote n="9">⁹This is of course a gross oversimplification, since polite-
ness itself involves many competing constraints, but I leave
the formulation fairly general here for purposes of space.</footnote>

<footnote n="10">¹⁰Note that this condition requires merely that the speaker not believe *p*, rather than the stronger condition that they believe **\neg p**. I make this formal choice to allow for the fact that the speaker's bias for **\neg p** might fall short of what we would want to call 'belief'. I assume that the fact that *ega* is incompatible with contexts where the speaker is neutral about *p* comes from the infelicity of asserting **\neg p** in such a context.</footnote>
effect?...

Ega sellest ei teki epsilepsiat või
EGA this NEG cause. NEG epilepsy or
šõsofreniat[sic]?
schizophrenia?

‘This doesn’t cause epilepsy or schizophrenia?’

*(etTenTen)*

In this advice-seeking situation, the speaker puts forward **¬p** as their ‘best guess’ for what is true, while signaling to the addressee that they would like confirmation. Had they asserted **¬p** directly, they would have conveyed that there was no reason to believe otherwise than **¬p**, a nakedly odd conversational move to make if the addressee knows more about the truth of *p*.

## 3.5 Analytical summary

In this section, I proposed that three kinds of *ega*-sentences—assertions, polite requests, and checking questions—arise from a unified denotation of such sentences being uttered in contexts with different configurations of speaker belief and relative authority between speaker and addressee.

In particular, the sense of *questioning* in the latter two cases arises from the use of *ega*-statements in contexts where the speaker has relatively low epistemic authority about the truth of the prejacent. In effect, *ega* serves to highlight a contrast between the assertion that **¬p** and some available evidence for *p*, and uttering it in contexts where the addressee is in a better position than the speaker to resolve this tension gives rise to the ‘inquisitive’ function of *ega*-questions.

# 4 Whence the polarity generalization

One outstanding issue given the analysis of *ega* thus far is its allergy to positive sentences:

(24) \*Ega sul on valu seljas.
EGA you.ADE is pain back.INE
‘You EGA have back pain.’<fnref n="11" />

After all, the intuitive characterization of *ega*-sentences is that they presuppose there was good reason to believe *p*, but this presupposition does not in and of itself derive the polarity restriction on *ega*-sentences.

To probe the polarity constraint, we must first make explicit what *ega* itself contributes to interpretation, rather than just its discourse effects in full

utterances. There are two plausible logical forms for *ega*-sentences with negation if we treat *ega* as a propositional operator. One is that *ega* takes the prejacent **¬p** as an argument (*ega* (**¬p**))<fnref n="12" /> and presuppose there is evidence for the negation of the argument, *p*. The other is that *ega* takes the positive prejacent as an argument, but occur itself within the scope of negation (**¬**( *ega* *p*)), and presuppose that there is evidence for that argument *p*.

These LFs make different predictions for what *ega* should mean in non-negated contexts. If *ega* takes widest scope, we expect *ega* *p* to have an analogous reading to *ega* not-*p*: that is, *ega* *p* should **assert** *p* and presuppose evidence for **¬p**. On the other hand, if *ega* scopes below negation, *ega* in a positive sentence should reinforce the alignment of the speaker’s assertion that *p* with evidence for *p*.

In fact, *ega* does show up in positive sentences, albeit rarely (25). Such cases only exhibit the former reading, suggesting that *ega* takes wide scope:

(25) *A comment on a newspaper article about cat rabies with a picture of a cat claimed to be unrelated to the story:*

Ega see pildil olev kass on ka
EGA this picture.ADE be.PCP cat is also
kahtlase näoga...
suspicious face.COM

‘In fact the cat in this picture looks suspicious too...’

*(Keevallik and Habicht 2017, ex. 27)*

The author of (25) asserts a positive *p* (*The cat has a suspicious face*), but indicates this is contrary to a contextually-supported assumption that the cat does not have rabies. Keevallik and Habicht (2017) take examples like (25) to indicate that *ega* in assertive contexts is not limited to negative sentences, and note that similar examples occur more commonly in spoken language.

But if *ega* *p* is in fact *possible*, we have a conundrum: why is it nevertheless so rare in non-negated contexts? Because the polarity restrictions on *ega* are not categorical, we don’t want to derive its negative tendencies by all-or-nothing constraints, such as by stipulating that *ega* is a negative polarity item.

A full account of the polarity sensitivity of *ega* is outside the scope of this paper, but I suggest that the paucity of positive *ega*-sentences could be a

<footnote n="11">¹¹I use an asterisk here to indicate systematic unacceptability rather than ungrammaticality *per se*.</footnote>

<footnote n="12">¹²We might also think *ega* operates at the level of illocutionary force and instead takes an utterance or a sentence as an argument; for present purposes what matters is whether or not negation is inside whatever argument is fed to *ega*.</footnote>
distributional artifact arising from an asymmetry
in the pragmatics of uttering positive and negative
declaratives.

It is a longstanding observation that negative
assertions are pragmatically marked: uttering **not p**
often presupposes (in a weak, defeasible sense)
that there was reason to believe that *p* or that *p* was
under discussion, where uttering *p* has no analo-
gous implications (Givón, 1978, et seq.). Given
independently-motivated pressures to presuppose
as much as possible (perhaps analogous to a princi-
ple like Maximize Presupposition, e.g. Heim 1991),
we might expect that negative sentences are pre-
ferred utterances over logically equivalent positive
sentences (e.g. *John is not married* vs. *John is a
bachelor*) in contexts where there is evidence to
believe that these sentences are false (i.e. that John
is married).

Of course, *ega* itself also presupposes the exis-
tence of evidence which conflicts with a prejacent
proposition, so the explanation could be that *ega*
requires the exact kind of input contexts which
would lead one to prefer a negative sentence over
a positive alternative, so we expect the negative
version to be used unless there is some special in-
dependent pressure to pick the positive alternative
specifically, whatever this pressure might be. This
story generates the testable hypothesis that positive
*ega*-sentences are generally less acceptable than
interpretively equivalent negative *ega*-sentences.
For example, we might expect that (25) would be
less acceptable in the same context than a similar
version where the prejacent of *ega* is a negative
proposition, e.g., *This cat isn't healthy*. I leave
exploration of this hypothesis for future research.

5 Conclusion

A major project at the semantics-pragmatics in-
terface is understanding the relation between the
denotation of a sentence and the function of utter-
ing that sentence in context. This paper brings new
data from Estonian to bear on this task. I have ar-
gued that the discourse particle *ega*, despite having
a seemingly expansive range of potential discourse
effects, can receive a single unified denotation if
we make sensible assumptions about the way its
semantics interacts with contexts of use. The appar-
ent ‘inquisitivity’ of *ega* in some contexts, rather
than being a result of inherently inquisitive seman-
tics, comes from the tension inherent in making
assertions that presuppose there is evidence to the

contrary in contexts where the addressee is better
equipped to adjudicate between these conflicting
sources.

The role that discourse particles have in deter-
mining discourse function remains a fertile ground
for cross-linguistic exploration. Just as interroga-
tive sentences can serve many different kinds of
communicative functions besides just asking ques-
tions (Lauer and Condoravdi, 2012), there are like-
wise multiple pathways to generating questioning
speech acts, and this paper represents an attempt to
chart a new part of this underexplored terrain. A
broader view of the typology of inquisitive prag-
matics may help us get closer to understanding the
ur-question: What *is* a question, anyway?

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*mage* as a bias particle in interrogatives

Maryam Mohammadi

University of Konstanz

maryam.mohammadi@uni-konstanz.de

**Abstract**

This paper investigates Farsi particle *mage*
in interrogatives, including both polar and
constituent/Wh questions. I will show that
*mage* requires both contextual evidence and
speaker's prior belief in the sense that they
contradict each other. While in polar ques-
tions (PQs) both types of bias can be straight-
forwardly expressed through the uttered propo-
sition (cf. Mameni 2010), Wh-questions
(WhQs) do not provide such a propositional
object. To capture this difference, I propose
*Answerhood* as the relevant notation that pro-
vides the necessary object source for *mage*
(inspired by Theiler 2021). The proposal es-
tablishes the felicity conditions and the mean-
ing of *mage* in relation to the (contextually)
restricted answerhood in both polar and con-
stituent questions.

# 1 Introduction

Discourse particles are useful tools for organiz-
ing conversations by fitting an utterance into the
context. The small words (usually) do not con-
tribute to the core propositional content but con-
vey expressive meaning. They indicate informa-
tion that would otherwise need to be described by
the speaker or inferred by the addressee. There-
fore, many studies investigate the intended mean-
ing expressed by these particles, as well as the fe-
licity conditions that capture the necessary proper-
ties of the discourse or the interlocutors.

Zimmermann (2011) introduces three semantic
core functions for discourse particles (in German):
(i) marking the expression as part of the Common
Ground (e.g., *ja*), (ii) indicating that the expression
is not activated with one of the discourse partici-
pants (e.g., *doch*), and (iii) weakening the commit-
ment to the expression (e.g., *wohl*). More recently,
Theiler (2021) provides examples of the particle
denn being felicitous in WhQs but not in PQs,

which could not be explained neither by the ex-
pressive meaning nor by the felicity conditions of
denn. Theiler claims that for certain particles, such
as denn, we also need to consider which notion of
semantic content are linked to them. She argues
that while discourse particles are usually relevant
to the informativity notion in declaratives (mod-
eled as a proposition), this notion becomes more
tricky in questions that seek information. Fol-
lowing Roelofsen and Farkas (2015), she suggests
highlighting as the relevant notion in questions. In
her proposal, particle denn indicates that learning
the highlighted proposition is a necessary precon-
dition for the speaker to proceed the discourse.

Particle *mage* in Farsi seems to require a sim-
ilar consideration. It is worth noting that *mage*
literally means ‘unless’ in non-interrogatives (see
Section 5 for some examples), however, this pa-
per focuses only on its discursive function in in-
terrogatives. Like many other discourse particles
that have double lives (e.g., *ja* and *denn* in Ger-
man Lindner 1991, Theiler 2021), I consider parti-
cle *mage* in interrogatives as a homonymous with
the conditional *mage* in non-interrogatives. I leave
the discussion about its conditional *mage* for fu-
ture studies.

A comparison between minimal pairs of polar
and constituent questions with and without *mage*
reveals that the particle carries additional informa-
tion about both speaker's prior belief and contex-
tual evidence in the given context. Example (1)
presents a canonical polar question in Farsi (in
the form of a rising declarative), simply asking
whether or not Ali came to the party (*p*?). Exam-
ple (2), which asks the same question, not only sig-
nals the speaker's prior belief/expectation against
the uttered proposition *p*, that Ali didn't come
(Mameni, 2010), but also requires contextual ev-
idence for *p*.
(1) Ali mehmuni umad?
Ali party came
'Did Ali come to the party?'

(2) mage Ali mehmuni umad?
MAGE Ali party came
'Did Ali come to the party?'

(3) ki mehmuni umad?
who party came
'Who did come to the party?'

(4) mage ki mehmuni umad?
MAGE who party came
'Who did come to the party?'

On the other hand, examples (3) and (4) are minimal pairs of WhQs in Farsi, both seeking the list of people at the party. While in PQs, the meaning of *mage*, as the speaker's contrary expectation, has been interpreted in relation to the uttered proposition, it cannot be reconstructed in WhQs as in (4). To understand the exact function of *mage* in WhQs, further discourse analysis is required.

In the next section, I will present examples of *mage* in PQs, arguing that it necessarily requires contextual evidence. Then, we will see examples of *mage* in WhQs, and I will demonstrate that *mage* perform the same function in both types of questions (with respect to their alternative set of answers). In Section 3, I propose a unified analysis based on the *answerhood* notation for the meaning of the discourse particle *mage* in both polar and constituent questions. Section 4 introduces further issues about *mage*. We will have a look at the previous studies about *mage* in Section 5. Finally, the conclusion will be presented in Section 6.

## 2 The Data

A large and growing body of literature has investigated the questions that require *original bias* (OB) as speaker's prior (epistemic) belief (Ladd 1981, Romero and Han 2004), or *contextual bias* (CB) as evidence mutually available to all participants in a conversation (Büring and Gunlogson 2000) or their combinations (Domaneschi et al. 2017).

Particle *mage*, which can appear in both positive and negative polar questions, expresses speaker's prior belief (OB) contrary to the uttered proposition in the question (cf. *really*-questions in Romero and Han 2004). In positive polar questions, such as in (5), the speaker has the prior belief that Ali didn't come to the party, while in negative polar questions like (6), it signals the reverse belief that Ali came.

(5) mage Ali mehmuni umad?
MAGE Ali party came
'Did Ali come to the party?'

(6) mage Ali mehmuni na-yumad?
MAGE Ali party NEG-came
'Did Ali not come to the party?'

Regarding the implication of the speaker's belief, Mameni (2010) shows that *mage* is felicitous in contexts that carry the speaker's prior expectation. Thus, since example (7) implicates that the speaker didn't expect Ali went to the party, it is truly predicted to be infelicitous (#) in Context 1 (as well as in out-of-the-blue contexts).

(7) A: mage Ali mehmuni umad?
MAGE Ali party came
'Did Ali come to the party?'

\# Context 1: A calls B to know about the guests who went to the party last night.

\# Context 1.1: ...A doesn't think that Ali went to the party.

✓ **Context 1.2:** ...B says that she had a nice conversation with Ali at the party. A didn't think Ali went to the party.

Although the OB is implemented in the continuation as in Context 1.1, it is still infelicitous (#). In other words, the suggested implicature (of the speaker's belief) is not enough to predict the infelicity of Context 1.1. When Context 1 is continued as in Context 1.2, it provides the proper setting (✓) for example (7). Therefore, the felicitous context for *mage* requires both CB and OB.

Furthermore, particle *mage* can be used in different WhQs as in examples (8)-(11) (the negative forms are omitted for brevity).

(8) mage ki umade?
MAGE who came
'MAGE who did come?'

(9) mage či xaridi?
MAGE what bought
'MAGE what did you buy?'

(10) mage koja rafti?
MAGE where went
'MAGE where did you go?'

(11) mage kei rafti?
MAGE when went
'MAGE when did you go?'
Let's focus on the first example with *ki* 'who' and find a felicitous context. In the given context in (12), *mage* indicates that the speaker did not expect any celebrities to be at the party and is now inquiring about which celebrities were there. That implies that although question (12) does not explicitly state a specific proposition as the speaker's belief, the context suggests that the speaker held a contrary belief regarding the restriction of the guests who were celebrities over all of the guests who went to the party.

(12) **Context:** A calls B to know about the guests who went to the party last night. B says that it was fun to see some celebrities there. A didn't expect that there were any celebrities at the party.

A: *mage ki-à umadan?*
MAGE who-PL came
'MAGE who did come?'

To figure out the meaning of *mage* in WhQs, we need to investigate the domain of the Wh-phrase, which is somehow restricted by *mage*. Assume that we have the following list of professors in context (13): {Valeria, Wolfgang, Xavier, Yara, and Zachary}, where only {Yara and Zachary} are the famous ones. Semantically, the same question *Who did you invite?* is asked in (A1) and (A2). Considering the context, both answers in (B1) and (B2) are acceptable in response to (A1), albeit with different preference order. However, only (B2) is the felicitous answer to (A2).

In other words, the speaker in (A1) would be looking for either all the invited professors or just the famous ones. Therefore, both (B1) and (B2) are felicitous responses, respectively. It is worth noting that prosody, such as an enthusiastic intonation, and/or expressives like *awesome*, could help guide the interpretation towards the contextually restricted set of famous professors rather than all guests. For instance, if speaker A expresses *âlie!* 'Awesome!' at the beginning of the question in (A1) and/or asks the question with an enthusiastic intonation, then (B2) is more likely to be the answer rather than (B1).

(13) A and B and C are the organizers of a conference. A wants to finalize the list of the invited guests.

A: Let's make a list. Who did you invite?

B: I invited some professors, two of them

are so famous.

A1: *ki-à ro davat kardi?*
awesome who-PL ACC invite did?
'Who did you invite?'

A2: *mage ki-à ro davat kardi?*
MAGE who-PL ACC invite did?

'Who did you invite?'
→ The speaker didn't expect any famous professors.

B1: I invited Valeria, Wolfgang, Xavier, Yara and Zachary

B2: I invited Yara and Zachary

The question in (A2) implies that the speaker didn't expect any famous professors and further restricts the question to only the famous ones. Hence, if B starts listing all the invited professors as in (B1), speaker A would complain and explicitly mention that she meant which famous professors. Consequently, only (B2) is the appropriate answer to question (A2). It is important to note that any expressive term like *awesome* or prosody, whether usual or enthusiastic intonation, does not affect the acceptability of the answers to (A2). It is worth emphasizing that while both answers are somewhat acceptable in response to (A1), in the case of (A2), it is not a matter of answer preference but rather a matter of felicity.

Overall, the mandatory presence of contextual evidence in *mage* questions introduces a certain semantic object, which then becomes available as an anaphoric reference. The context restricts the question under discussion by narrowing down the alternative set of answers. More specifically, in *mage*-PQs, the uttered proposition in the question indicates the restriction over the contextual evidence. Similarly, the evidence in *mage*-WhQs obligatorily restricts the alternative set of answers to a subset list. In both types of questions, *mage* refers to the restricted set object, indicating that the speaker did not expect such a restriction. In the next section, I will propose an account based on the answerhood of the questions.

## 3 Proposal

The discursive function of *mage* in both polar and constituent questions can be formulated based on
the *Answerhood* notation (instead of the uttered proposition in *mage*-PQs). According to the literature, the denotation of a question is a set of propositions that correspond to the possible answers (Hamblin 1973, Karttunen 1977). In the case of polar questions (PQs) ($\phi?$), the denotation returns a binary set {$\phi$, $\neg\phi$}, including the positive and negative answers. On the other hand, for WhQs ($wh_x P?$), the denotation may generate multiple members {$P(x)|x \in D_e$}, where each member represents a possible answer to the question.

The alternative set of answers can be contextually restricted, meaning that the restricted set is a subset of all possible alternatives (cf. contextual variables in Martinez 2003). These (evidential) restrictions, particularly in WhQs, introduce specific semantic objects that can be referred to anaphorically using *mage* (cf. Theiler 2021). In this context, the restriction generates a proper subset from the alternative set. Based on this understanding, the denotation of *mage* can be formulated as follows:

(14) $[mage \ \phi?] = [\phi?]$, provided that there is a proper subset $Q'$ of $[\phi?]$ such that for all $q$ in $Q'$:
- $q$ is supported by the contextual evidence, and
- the speaker did not expect $q$.

Following (14), the contextual evidence captures the discourse anaphoricity of *mage* to the subset answerhood, while the particle expresses that the speaker didn't expect such a restriction to hold. Now, let's go through the examples and see if the account can explain the data.

Starting with polar questions as in (7), which is repeated here in (15), the denotation of the question is the alternative set of answers, as shown in (a). The context implies *that Ali came*, as in (b). Regarding the (semantic) alternative set in (a) and the (contextually) restricted set in (b), the required proper subset condition is satisfied in (c) and (d), where *mage* indicates that the speaker didn't expect the restriction to hold.

(15) MAGE did Ali come?

a. $[mage \ did \ Ali \ come?] = \{come(a), \neg come(a)\}$

b. Contextual Evidence for {come(a)}

c. {come(a)} ⊂ {come(a), \neg come(a)}, and

d. The speaker didn't expect that Ali came.

Moving on to WhQs as in example (13), repeated here in (16), the non-restricted set of alternatives results in a list of all invited professors, as shown in (a). However, the context suggests that there is a restricted list of famous invited professors, which narrows down the answerhood to a subset list, as illustrated in (b). In such cases, *mage* can felicitously appear since the subset condition is supported by the context in (c), and the particle signals that the speaker did not expect the restriction.

(16) MAGE who did you invite?

a. $[mage \ who \ did \ you \ invite] = \{invited(x) | Professor(x)\}$

b. Contextual Evidence for
$Y = \{invited(y) | Professor(y) \land famous(y)\}$

c. Taking $X$ the set in (a), $Y \subset X$

d. The speaker didn't expect any famous prof.

In summary, *mage* is felicitous in both polar questions with a binary set of alternatives, as well as in WhQs with a multiple member set, when the context indicates a restriction for a proper subset of the possible answers. In PQs, the evidence signals a single proposition, while in WhQs, it can result in a subset of multiple members. The contextual evidence provides the subset answerhood object, and particle *mage* implies that the speaker did not expect such restrictions to hold.

Lastly, it is worth noting that the proposal predicts that *mage* is not felicitous in alternative questions (AltQs) like those in (17) and (18).

(17) # mage Ali mehmuni umad ya na?
MAGE Ali party came or no

(18) # mage Ali mehmuni umad ya na-yumad?
MAGE Ali party came or NEG-came

≈ ‘Did Ali come to the party or not?’

AltQs, as unbiased questions, express a symmetric interest of the speaker in either of the alternatives offered disjunctively, for example, *Do you come or not?* (Bolinger 1978, Biezma 2009). Therefore, they are not felicitous in settings where either the speaker or the context indicates a bias towards a proposition rather than its alternative.

Roughly speaking, the intended meaning of examples (17) and (18), presented in (19), is the set of answers similar to PQs, as shown in (a). While
the question without *mage* is felicitous in neutral contexts (b), we have no subset object as in (c), and the contextual support condition fails. Furthermore, in AltQs, the speaker is open to either of the answers, i.e., she has no idea whether or not Ali came (d). Thus, the speaker's prior expectation of *mage* contradicts the felicitous context for AltQs. In other words, none of the bias conditions of *mage* would be met in contexts that are felicitous for AltQs.

(19) # MAGE did Ali come or not?

a. [[mage did Ali come or not]] =
{come(a), ¬come(a)}

b. No contextual evidence is allowed in AltQs.

c. There is no subset object.

d. There is no speaker's prior expectation.

## 4 Further Issues

It is worth mentioning two outstanding points about *mage*. First, while I have characterized *mage* as anaphoric to the contextual evidence, it can also be used deictically and pick up non-linguistic contextual information as its antecedent. That is, the variable that shrinks the alternative set could be implemented by either being anaphoric to a piece of contextual evidence or deictic to extralinguistic information. The speaker can felicitously use *mage* if she can reasonably assume that the addressee can identify the intended referent. Otherwise, the use of *mage* is infelicitous. For instance, in example (20), the information that they might have an important guest is perceived through extralinguistic evidence, i.e. A and B know that they only clean the house when they have important guests.

(20) **Context:** B begins cleaning the house and asks A for help. Normally, they wouldn't bother cleaning the house unless they were hosting someone important. A was not expecting to have any special guests.

A: *mage ki miyâd?*

MAGE who comes

‘Who does come?’

~~The speaker didn't expect any important guests~~

Thus, I follow the intentional view, on which reference resolution of the restriction is a prag-

matic process that succeeds if the addressee can correctly recognize speaker's referential intention.

Second, the negative expectation in *mage* implicature doesn't need a strong belief/expectation. Regarding the negative raising constructions, the interpretation of negation in the embedded clause, e.g. *Sara expected that Ali doesn't come*, can have a stronger reading in which the speaker is opinionated about the complement proposition. While it feels weaker in the matrix clause, e.g. *Sara didn't expect that Ali comes*, in the sense that the speaker could be unopinionated and the complement clause was not simply in her (active) mental state. In *mage*-Qs, it is possible that either the speaker has some opinion about the restriction or she did not expect the restriction simply because it was not in her mental state.

## 5 Previous Accounts

Surprisingly, there is little published research on *mage*. Here, I will review Mameni (2010), who introduces *mage* as a genuine interrogative morpheme, similar to *âyâ* ‘whether’, which only differs in the not-at-issue content. The claim for a genuine interrogative function brings up discussions about *mage* in non-interrogatives and the types of sentences in Farsi.

Let's start with *mage* in non-interrogatives as a conditional operator. *mage* morphologically means ‘not if’, consisting of *ma-* as an allophone of the negative prefix *na-* and the conditional operator *age* ‘if’ in Farsi. Hence, it is close enough to translate it as ‘unless’ in English. Examples (21) and (22) are minimal pairs with the same truth-value meaning: $\neg \text{Study}(ali) \rightarrow \text{Fail}(ali)$.

(21) age Ali dars na-xune, miofte.
if Ali lesson NEG-read fails
‘If Ali doesn’t study, he fails.’

(22) Ali miofte, *mage* dars bexune.
Ali fails unless lesson read
‘Ali fails, unless he studies.’

The difference between the examples above is that (22) has an exceptional reading (von Fintel 1992). Roughly interpreting, it indicates ‘*Except if Ali studies, he doesn’t fail*’. In this paper, I focused only on the role of *mage* in interrogatives. Regarding the distinct function and (surface) forms of *mage* in non-interrogatives versus interrogatives, I proposed its second role as a discourse particle.
However, I would not be surprised if we can extend the account to cover both interrogative and non-interrogative conditionals.<fnref n="1" />

Mameni (2010) was aware that the non-interrogative use of *mage* could be an objection against his claim for *mage* as a genuine question morpheme. Although I consider it to be a significant objection, the author briefly addresses it in a footnote by suggesting that if we assume question particles to be morphemes that operate over a proposition and result in multiple possibilities, the objection may not hold (cf. *inquisitive* proposition in Groenendijk and Roelofsen 2009).

Mameni argues that conditionals like (23) (adopted from Mameni 2010:p. 13) proposes two possibilities: the one in which it rains and the one in which it doesn't rain. Thus, truth-conditionally, the sentence denotes both possibilities, including 'Milad comes if it doesn't rain' and 'Milad doesn't come if it rains'.

(23) Milad miad, mage (inke) bârun biâd
Milad comes !Q COM rain comes
'Milad will come only if it doesn't rain.'

He then argues that since *mage* can only scope over irrealis predicates, the speaker does not commit to either of the possibilities. Hence, the conditional meaning is similar to questions, both of which introduce the set of alternatives/partitions.

The discussion about conditionals and and their discourse commitments is beyond the scope of this study. However, in (23), the speaker committs to the consequent *that Milad will come* under the specific circumstance *that it doesn't rain*. That is, if it doesn't rain and Milad doesn't come, he has to retract his commitment. Neither Mameni nor I fully consider the non-interrogative use of *mage* in our studies. However, he underestimates such a role without delving into its properties, and I consider it to be polysemous. While I leave the study of conditionals for future research, I argue that it is a crucial objection for claiming *mage* is *genuinely* a question morpheme.

Let's move on to *mage* in interrogatives. Farsi is an SOV language in which falling (↓) and rising (↑) intonations are required for declarative and interrogative sentences, respectively. Examples (24) and (25) are minimal pairs, where the former is a declarative (assertion) sentence, and the latter is an interrogative (question).

(24) Ali mehmuni miyâd. ↓
Ali party comes
'Ali comes to the party.'

(25) Ali mehmuni miyâd? ↑
Ali party comes
'Does Ali come to the party?'

Mameni claims that in Farsi, the presence of a (polar) question morpheme is optional. He introduces *âyâ* and *mage* as genuine question operators with different implicatures, and he argues that the default reading of non-morpheme questions is the one with *âyâ*. Thus, (25) has the same meaning as (26).<fnref n="2" /> I follow his coding for *Q* and !*Q* as the question operators for *âyâ* and *mage*, respectively.

(26) âyâ Ali mehmuni miyâd?
Q Ali party comes

(27) *mage* Ali mehmuni miyâd?
!Q Ali party comes
≈‘Does Ali come to the party?’

Mameni proposes that both examples (26) and (27), similar to (25), ask whether or not Ali comes to the party, while they express different not-issue contents. *âyâ* in (26) expresses the speaker's ignorance about the answer, while *mage* in (27) signals that the speaker has a (tentative) commitment against the uttered proposition.

Now, let's delve into his argument for proposing *mage* as a genuine question operator. Mameni examines the environments that only select questions and preclude other types of sentences like assertions and commands. He uses the "let me ask you a question" test (Gunlogson 2001) to identify

<footnote n="1">¹There are some syntactic and semantic limitations between *age* and *mage*. For instance, (i) sentence (21) can maintain the conditional reading by the use of intonation without *age*, while this is not possible for *mage*, (ii) the order of the antecedent and consequent clauses generally does not affect *age*-sentences, but it affects the scope of negation in *mage*-sentences, (iii) there are constraints on indicative and subjunctive clauses with *mage*. A comprehensive study is required to capture all differences before arguing for any unified analysis of *mage* in both non-interrogatives and interrogatives.</footnote>

<footnote n="2">²Although Mameni (2010) didn't mention it, (25) and (26) greatly differ in style. That is, *âyâ*-question is very formal and it is often used in written forms, while the rising-question is the canonical form used in usual/colloquial settings. As a Farsi speaker, I hardly remember if I have ever used *âyâ*, even in formal contexts. Furthermore, following his claim for the default reading of (rising) non-morpheme questions with *âyâ*-operator, the ignorant implicature of *âyâ* in (26) is expressed in (25) as well, which I am not sure about. The discussion about the difference between rising polar questions and *âyâ* questions is beyond the scope of this paper.</footnote>
the questions from other types. Example (28) is
adopted from Mameni (2010): p. 14.

(28) azat ye soâl beporsam, ...
from one question ask

Let me ask you a question,...

a. âyâ Milâd raft?
Q Milad left
≈‘Did Milad leave?’

b. mage Milâd raft?
!Q Milad left
≈‘Did Milad leave?’

c. # Milâd raft.
Milad left
‘Milad left.’

d. # boro!
leave
‘Leave!’

Regarding the unacceptability of the declarative
in (c) and the imperative in (d) compared to (a) and
(b), Mameni concludes that âyâ and *mage* are gen-
uine interrogative morphemes. He did not provide
further explanation or argument for this (crucial)
claim. He only challenges the critics, stating that if
*mage* is not a question morpheme, it is almost im-
possible to explain why declarative sentences with
*mage* are necessarily interpreted as questions. No-
tice that Mameni provides sentences with *mage* in
falling intonation and claims that such sentences
have a question reading. Overall, the argument
presented by the author for *mage* as a question
morpheme is based on its presence in interroga-
tives, and in order to support this argument, he
stipulates conditional sentences as inquisitive.

I start with his examples of questions with
falling intonation. In Farsi, rising intonation is nec-
essary for polar questions, regardless of the pres-
ence of a question marker such as âyâ or *mage*. None of his examples with falling intonation on *mage*-questions were considered felicitous by my native speaker informants, including the author (some informants interpreted them as conditionals, with an elided antecedent).

Furthermore, while multiple Wh-words can
form a single WhQ as in (29), using a dou-
ble polar question marker shouldn't be felicitous,
as claimed by Mameni in examples (30)-(31)
(adopted from Mameni 2010: p. 12).

(29) ki či xarid?
who what bought
‘Who bought what?’

(30) ??âyâ mage Milad raft?
Q !Q Milad left

(31) *mage âyâ Milad raft?
!Q Q Milad left

Mameni footnoted that the judgments were in-
accurate since many speakers reject (31), but find
(30) possible. The author suggests two hatches
for the judgment variation.<fnref n="3" /> He, however, rejects
these hatches as they could not explain why the
acceptability of (30) is degraded, in addition to
why the movement of *mage* is restricted when it is
preceded by *âyâ*. Therefore, he considers the sen-
tences unacceptable and claims that the two mor-
phemes cannot co-occur.

I share the intuition with the informants in
which (30) sounds better than (31). What is irri-
tating and degrades the acceptability of the combi-
nation of âyâ and *mage* is more about their style
difference. That is, while âyâ is used in very for-
mal and literary settings, *mage* is a colloquial par-
ticle. A native speaker might find the examples
better in a context where the speaker should be po-
lite and formal, but also wants to be friendly and
informal. In such cases, it is widely common for
the speaker to use elements from different styles
to express both formal politeness (e.g., âyâ) and
informal friendliness (e.g., *mage*). It seems weird
but is practically common.

For instance, speaking with grandparents, on
one hand, the grandchild wants to be polite regard-
ing the age difference. On the other hand, she has
a friendly relationship with her grandparents that
allows her to speak in a friendly/informal style. In
such cases, as in (32), the grandchild sometimes
uses the pronoun šomâ plural PL-you (instead of
to singular SG-you), but she conjugates the verb
in singular. Syntactically, the structure is ungram-
matical, but pragmatically it is commonly used.

(32) šomâ mehmuni miya-i?
you-PL party comes-SG
‘Do you come to the party?’

In the context of (33), we can also see that
the mother uses šomâ PL-you to treat her kid po-

<footnote n="3">³(i) He said that regarding the fact that *mage* is free to occur sentence-medially and sentence-finally, he assumes that if *mage* precedes *âyâ*, it cannot move. Thus, (31) is ungrammatical according to the informants compared to the better form in (30). (ii) It could be the case that since the meaning of *âyâ* questions is distinct from the meaning of *mage*, in marginal cases like (30), the question is interpreted as *mage*-meaning. This is possible by hypothesising that there is a covert *âyâ* morpheme in every *mage* question.</footnote>
litely, while she conjugates the verbs in singular, as they have an informal/friendly mother-child relationship. Now, using formal *âyâ* and informal *mage* sounds reasonable. While the order (*âyâ* *mage*) and (*mage* *âyâ*) don't matter here, the former is generally preferred because the default position of *âyâ* is sentence-initial.

(33) **Context:** In child psychology, it is suggested to speak politely with children to show that the parents respect their character. A is a young mother following this comment. She and her kid are at a party. She told the kid that he is allowed to have two cookies. She sees that the kid starts eating the fourth cookie...

A: *âyâ* *mage* man be šomâ na-goftam
Q MAGE I to you-PL NEG-tell
faqat dota širini mitun-i boxor-i?
only two cookie can-SG eat-SG
'Didn't I tell you that you can only
have two cookies?'

If *mage* is genuinely a question morpheme, its co-occurrence with *âyâ* shouldn't be possible, specifically because they express implicatures that conflict with each other. Finally, while polar question operators like *âyâ* cannot occur with other Wh-words as in (34), *mage* can be easily used in WhQs as in (35).

(34) # *âyâ* ki miad?
Q who comes

(35) *mage* ki miad?
MAGE who comes
'MAGE who does come?'

Note that Mameni did not work on WhQs, and he left it for future studies to extend his account to WhQs. I am not sure what exactly a question might ask, carrying both polar and constituent question operators. Thus, taking *mage* as a question morpheme could not explain the data in (35).

## 6 Conclusion

In this paper, I investigated the discursive function of particle *mage* in interrogatives. While the literature reported that *mage* in polar questions, [*mage* φ?], implicates speaker's prior belief against the uttered proposition φ, I presented that the felicitous context for the particle requires con-textual evidence towards φ. I then extended the

analysis to *mage* in WhQs, where the required con-textual evidence restricts the alternative set of an-swers. Therefore, I proposed the meaning and felicity condition of particle *mage* based on the *anserhood* notation in interrogatives.

The proposal for the role of two types of biases, including speaker's bias and contextual bias, in *mage*-questions could explain the data in both polar and constituent questions. Furthermore, it provides a natural explanation for the unacceptability of *mage* in alternative questions, as AltQs cannot be used in biased contexts. While the literal meaning of *mage* in conditionals is far-fetched from its bias-sensitive function in interrogatives, I leave the discussion about *mage* in non-interrogatives for future studies.

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Mameni, M. (2010). *Epistemic Implicatures and Inquisitive Bias: a Multidimensional Semantics for Polar Questions*. Ma dissertation, Simon Fraser University.

Martinez, M. L. M. (2003). *Contextual Variables*. Phd dissertation, University of Connecticut.
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# Dynamic Questions: Evidence from Mandarin Think–“Xiang”

Anshun Zheng

School of Philosophy Psychology and Language sciences
University of Edinburgh

A.Zheng-3@sms.ed.ac.uk

## Abstract

This paper investigates the clausal embedding pattern of the Mandarin verb “xiang” (think) and reveals its internal anti-interrogative nature, with the possibility of “xiang Q” in certain cases. Through various stativity tests, I establish that the results are consistent with the generalization proposed by Özyıldız (2021), with “minor” deviations observed in the stativity of “xiang P” and the correlation with neg-raising. Additionally, I employ a semantic shift perspective to explain instances of neg-raising failure. Overall, this study sheds light on the unique characteristics of the verb “xiang” and contributes to a better cross-linguistic understanding of CP selection.

## 1 Introduction

Predicates are able to embed different types of clausal complements. For example, “think” usually selects the declarative clauses while “wonder” takes interrogative ones only. Traditionally, this selection was attributed to syntactic factors, but since Grimshaw (1979), it has been viewed as more of a semantic choice. A series of works have been devoted to revealing the role of semantic factors in complement selection including factivity and veridicality hypotheses (Hintikka, 1975; Egré, 2008), reductive approach (Q-to-P reduction: Karttunen 1977; Lahiri et al. 2002; Spector and Egré 2015, P-to-Q reduction: Uegaki 2015), uniform approach (inquisitive semantics: Theiler et al. 2018, 2019, a systematic review see Uegaki 2019) and the stativity hypothesis (Özyıldız, 2021). Given most of the studies attended to English exclusively, the present investigation into Mandarin aims to provide more cross-linguistic evidence to the issue. In Mandarin, predicates taking CP can be classified as responsives (±Wh), anti-rogatives (-Wh), and rogatives (+Wh) as in English. Canonical examples are given below.

(1) Ask, Rogative (+Wh)
Wo wen ni mali zai na
I ask you Mary exist where
'I ask you where Mary is.'

(2) Know, Responsive (±Wh)
a. Wo zhidao mali zai na
I know Mary exist where
'I know where Mary is.'
b. Wo zhidao mali zai jia
I know Mary exist home
'I know Mary is at home.'

(3) Think, Anti-rogative (-Wh)
Wo renwei mali chi-le fan
I think Mary eat-perf rice
'I think Mary has eaten.'

Among these predicates, “think” is particularly intricate in many ways. The English word “think” can have several counterparts in Mandarin including “renwei”, “juede”, “ganjue”, “yiwei”, “xiang” and “sikao”<fnref n="1" />. Despite a little nuance, all of them can be used to report thoughts. However, they differ in terms of their CP selection pattern. For example, “renwei” and “xiang” are canonically anti-rogative in bare form (4a,4b), while “sikao” is rogative (4c) <fnref n="2" />.

(4) “xiang”, “renwei” cf. “sikao”
a. *Wo xiang zenme zuo ti
I think how do question

<footnote n="1">¹Glass (2020) gave translations to some of these terms: renwei(neutral think), xiang(believe/want), juede(feel that), and she also discussed the false belief think, “yiwei”. “Ganjue” is similar to “juede” with the nuance of “sensual”. “Sikao” is a more formal way to say think, closer to “ponder”.</footnote>

<footnote n="2">²This bare form “sikao” plus Q in (4c) sounds not good to some informants, and an aspect marker like “zai(-prog)” will make it work better. Since it is acceptable to some informants, I suggest it may be regional. However, there is a consensus that “xiang” is less natural with an embedded Q than “sikao”.</footnote>
b. *Wo renwei zenme zuo ti
I think how do questions

c. Wo sikao zenme zuo ti
I think how do questions

‘I’m thinking how to solve questions.’

To make matters worse, the selection pattern is not fixed (cf. 4a, 5), as was observed in Özyıldız (2021)'s analysis of “think Q”.

(5) Wo zai xiang zenme zuo ti
I -prog think how do questions

‘I’m thinking how to solve questions.’

The instability in Özyıldız’s account is due to stativity. I will call it the stativity hypothesis. He showed that embedding types are correlated to stativity of the event structure, so the selection is not purely lexical but is highly dependent on the environment (Table 1, see also Roberts 2019). For instance, he claimed the availability of “think Q” is from a dynamic environment<fnref n="3" />. His account works smoothly with English “think”, but will it be safe and sound in Mandarin as well? For many reasons, this paper selects “xiang” as its primary object of study. Unlike some other equivalents (e.g., “renwei”), “xiang” shows an aspectual alternation, which is crucial, since we will use the compatibility with certain aspects to test for stativity. Additionally, “xiang” does not appear to allow for a neg-raising reading, which deviates from the correlation suggested in Özyıldız’s account. Finally, “xiang” shows a very complex lexical semantics, which may reveal more intricacies and interactions for future research to consider

<table><caption>Table 1: Özyıldız’s idea of correlation between stativity, question embedding and neg-rasing</caption><thead><tr><th></th><th>Embedded Q</th><th>Neg-raising (with P)</th></tr></thead><tbody><tr><th>Stative</th><td>-</td><td>+</td></tr><tr><th>Dynamic</th><td>+</td><td>-</td></tr></tbody></table>

There are mainly two goals of this paper. Firstly, it seeks to provide empirical evidence and tests to examine the embedded question compatibility of “xiang”. Secondly, it aims to probe how much the stativity hypothesis accommodates this Mandarin equivalent of *think*.

The structure is organised as follows. §2 provides a brief overview of the various meaning entries of “xiang” in Mandarin and explains how its

meaning might be determined. §3 presents an analysis of the lexical selectional pattern of “xiang” <fnref n="4" />, while §4 and §5 examine how the stativity hypothesis can be applied to explain the occurrences of “xiang Q” and how neg-raising is problematic in the case of “xiang”.

## 2 Lexical semantics and pragmatics of “xiang”

“Xiang” can have several interpretations in different linguistic contexts. There are roughly four interpretations: (1) think and assume (2) hope and want (3) pine for, and (4) recall and remember<fnref n="5" />. Sometimes, the boundary between these entries are not clear-cut. (6) shows the same phrasing can lead to different readings under different contexts, namely asking for opinions and imperatives<fnref n="6" />.

(6) Ni xiang zenme zuo
you think how do
‘how do you **want** to do.’
‘you **think** how to do.’

The interpretation of “xiang” is highly dependent on the its environment. Some potential factors that can trigger the semantic shift include: (1) modals and aspect markers in the embedded clause<fnref n="7" /> (2) the presence of negation (see §5), and (3) status as an imperative (6). However, the details of these triggers are beyond the scope of this paper<fnref n="8" />. In the following sections, I endeavor to control for these

(7) a. Wo xiang ta chifan
I think he eat
‘I **want** him to eat.’

b. Wo xiang ta chi-le-fan
I think he eat-perf
‘I **think** he has eaten.’

<footnote n="3">³However, Özyıldız also admitted it remains unclear where the dynamicity comes from. The reason he thinks a structure is dynamic is because it passes several dynamicity tests.</footnote>

<footnote n="4">⁴By bare form, I mean there are no extra aspect markers or collocations so it is not in a sense of inflection.</footnote>

<footnote n="5">⁵A summary of usages of “xiang” mentioned in (Lü, 1999).</footnote>

<footnote n="6">⁶In (6), “xiang” combines with a phrase that contains the wh-word “zenme” (how), which seems to contradict with my claim that it is anti-rogative. I will explain it in §3, where I will present evidence of the question not being an embedded Q.</footnote>

<footnote n="7">⁷</footnote>

<footnote>(7a) and (7b) manifest the aspect marker being a trigger.</footnote>

<footnote n="8">⁸Presenting these factors is to make readers aware that there are more interactions happening than what is described in the paper. For readers who are interested, check Xiao and McEnery (2004) and He (1992) on Mandarin aspects and Biq (1991) on second person pronoun influence to get a flavor of the details. However, in terms of selection, it is still understudied.</footnote>
factors and focus on situations where “xiang” is
used to mean “think”<fnref n="9" />.

## 3 Plain “Xiang” does not take Q

“Xiang” alone shows significant incompatibility
with question embeddings (4a). The following ex-
amples further confirm this.

(8) a. \*Wo/ta xiang ta shi shei
I/He think he is who
‘I/He am/is thinking who he is.’

b. \*Wo/ta xiang ta hui chi shenme
I/He think he will eat what
\#‘I/He think(s) what he will eat.’

You may be wondering why I did not provide
examples in the second person. That is because “xi-
ang” seems to be compatible with questions when
used with second person subjects (6, 9). Does it
mean “xiang” is not anti-rogative but responsive?
Probably not. I posit that in these second person
cases, the question is not an embedded clause, but
rather a root question, which is possible because
Mandarin is a wh-in-situ language. Therefore, we
need to first differentiate between embedded ques-
tions and root questions<fnref n="10" />.

(9) Ni xiang ta hui chi shenme
you think he will eat what
‘what do you think he will eat?’

### 3.1 -Ne test as a test for matrix Q

“-Ne” is a particle that is compatible with wh-
questions and shares the scope with the wh-phrase
in Mandarin (10a, 10b). Canonical wh-questions
usually do not need “-ne” and it turns out “-ne” can
serve as a matrix clause scope marker to distinguish
root questions from embedded questions. Apart

from the question reading, “-ne” can also lead to
“emphatic” reading and “imperfective” reading.

(10) a. Ta zai na (ne)
He exist where (-ne)
‘where is him?’

b. Ta zai gan shenme (ne)
He -prog do what (-ne)
‘what is he doing?’

Dong (2018) pointed out that this particle is not able to take a scope of embedded questions. Rogative predicates like “wen”(ask) usually force an embedded question reading. Hence, they do not co-occur with “-ne”, which is incompatible with the embedding scope. For example, (11) is ungrammatical if it intends to give an embedded question reading, while it still can have an emphatic interpretation—“Zhangsan even asked the question!”<fnref n="11" />, or an imperfective reading—“Zhangsan is asking me the question, don’t bother me”.

(11) Ask (Dong, 2018, 29)
\*Zhangsan wen wo shei mai-le shu ne
Zhangsan ask me who buy-perf books -ne

‘Zhangsan asked me who bought books.’

According to Dong’s account, anti-rogatives are
limited to having only matrix clause scope, making
them compatible with the “wh-ne” structure (12).

(12) Believe (Dong, 2018, 30)
Zhangsan xiangxin shei mai-le shu ne
Zhangsan believe who buy-perf books -ne

‘who does Zhangsan believe bought
books?’

However, in the case of responsives, which can
have both matrix and embedding scope, Dong
claimed that as long as the matrix clause scope
is available, the structure remains well-formed<fnref n="12" />.

In summary, “wh-ne” construction can be
utilised to test for whether an in-situ question is
embedded or not. As (13) shows, the second per-
son “xiang + Q” passes the test, leading to a root
question reading, indicating (13) at least has a read-
ing as a matrix question, even though it looks on
the surface like it embeds a question.

<footnote n="9">⁹One intriguing question that remained to be considered is why conceptually similar words associated with psychoactivity encompass vastly different meanings. While this paper does not thoroughly address the question, one approach is to examine it through prototype theory. For instance, words like “recall” and “miss” can be seen as prototypical of “xiang”, but not of “think”. Some accounts, such as Xu et al. (2013), view this issue as a distinction between cognition, emotion, and motivation (another decompositional approach see also Bondarenko (2020)). According to Xu et al.’s account, the difference between “xiang” and “think” can be attributed to a division difference between these elements.</footnote>

<footnote n="10">¹⁰Note that (8a) and (8b) are not considered well-formed, no matter the question is embedded or not. The purpose of contrasting them with (9) is to demonstrate that in second person cases, a question interpretation is feasible. The subsequent discussion in section 3.1 aims to unravel whether “xiang” can inherently take a question complement with a person that allows for a question interpretation.</footnote>

<footnote n="11">¹¹The reading is possible under contexts where the speaker is surprised or acts mean to the subject.</footnote>

<footnote n="12">¹²There is a minor point to mention regarding Dong’s account of responsives. It is possible that his examples of responsives being ungrammatical could be due to factive islands. However, this matter is not directly pertinent to the main focus of this paper, so I won’t delve into it extensively.</footnote>
(13) 2nd person + “xiang”

Ni xiang ta hui chi shenme ne
you think he will eat what -ne

‘what do you think he will eat?’

It is important to highlight that the root question reading with “xiang” plus “wh-ne” is not valid in other persons (e.g., *adding “-ne” to 8a,8b), implying there possibly exists a person effect that does not exist in English, but unfortunately, this paper will not address what this effect could be<fnref n="13" />. A detailed “-ne” test result is shown as in Table 2. Apart from the findings on question readings, I noticed the emphatic reading is more compatible with predicates that allow for [+Wh]. This implies that Mandarin wh-phrases may also be tinted with [+Excl] even if it is not used in an exclamtive construction like English.

<table><caption>Table 2: The available interpretations of predicates of different selectional types in “wh-ne” environment. Several trends revealed here are: (1) anti-rogatives can have root question readingª (2) only predicates allowing (+WH) can be emphatic.</caption><thead><tr><th>Predicates</th><th>Root Question</th><th>Emphatic</th><th>Imperfective</th></tr></thead><tbody><tr><td>Renwei(think, -Wh)</td><td>+</td><td>-</td><td>#</td></tr><tr><td>Xiang(think, -Wh)</td><td>+</td><td>#</td><td>+</td></tr><tr><td>Sikao(think, +Wh)</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Zhidao(know, ±Wh)</td><td>#</td><td>+</td><td>-</td></tr><tr><td>Wen(ask, +Wh)</td><td>-</td><td>+</td><td>+</td></tr></tbody></table>

## 3.2 Evidence from question-response pairs

The “-ne” test identifies that what are in the idiosyncratic second person cases are matrix questions, rescuing my claim that “xiang” does not take question complements. Here in this section, I intend to provide further evidence to show that the embedded scope is actually not available.

Matrix questions and matrix statements with question-complements differ in their ability to elicit responses. The former is designed to seek new information, while the latter has the capability to prompt a simple yes/no response. For instance, a sentence like “What do you think he will eat?” can elicit a response like “(I think he will eat) cake.” (cf. (12)), whereas a sentence like “She knows

what he will do.” can elicit a response like “No, she doesn’t.” (cf. (11)).

According to (14), even without a particle that specifically triggers a matrix scope interpretation, the reading of the sentence still remains as a matrix question. This implies that the availability of an embedded scope is not possible, thereby supporting my argument that the bare form “xiang” does not accept wh-complements.

(14) Ni xiang ta hui chi shenme
you think he will eat what
‘what do you think he will eat?’

a. *‘dui, wo xiang.’ (Yes, I am.)

b. ‘wo xiang ta hui chi yu.’ (I think he will eat fish.)

## 4 Influences from the environment: stative or dynamic

However, there exist certain scenarios in which the verb “xiang” can take embedded questions as its complement. These situations include imperatives, verbs that imply force, and certain aspect markers<fnref n="14" />, which roughly mirrors what Özyıldız (2021) observed in English “think+Q”.

(15) Imperatives

Ni xiang zhe ti zenme zuo (*-ne), wo
you think this question how do (*-ne), I
xiang xia yi ti
think next one question

‘You think how to solve this question, I’ll think about the next one.’

(16) Force

Wo ba rang wo xiang zenme zhuan
my father make me think how earn
qian (*-ne)
money (*-ne)

‘My father makes me think how to make money.’

(17) Some aspect markers

Wo zai-/xiang/-le/-guo xia yi bu qi
I think-prog/-perf/-exp next one step chess
zenme zou (*-ne)
how walk (*-ne)

<footnote>ªResponsives (e.g., tell) “can” have root question reading as well but most of them are under restrictions of factive islands.</footnote>

<footnote n="13">¹³This is in contrast to English matrix clause questions with “think”, which can be formed in all persons given the appropriate context (e.g., what does he think we should do?).</footnote>

<footnote n="14">¹⁴Some informants, including the author, found “sikao” (the possibly rogative “think”) is more natural with verbs of force type. When “xiang” is under force, it just means “sikao”. “Xiang” with durative marker, most informants felt, is more acceptable with declaratives such as “wo xiang-zhe ni mingtian youkong, women keyi yiqi qu guangjie” (I think-dur you are available, so we can go shopping together.).</footnote>
‘I am/have thinking/thought what is the next move.’

According to Özyıldız’s analysis, this alternation is determined by the event structure, the environment in which the verb is used. The alternation occurred at the lexical level (e.g., within the vP) by taking different arguments (Q or P), but the effect is observed at a higher level (e.g., the AspP). This observation also applies in Mandarin. For example, the verb “wang” (forget) requires an obligatory perfective marker “le” when used alone (Figure 1), but the marker becomes optional when there is a VP complement (Figure 2). Thus, the aspectual nature of the vP could be determined by analyzing higher-level structures.

<figure><img src="image_24.png" /><figcaption>Figure 1: “Mary forgot.”</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>Figure 2: “Mary forgot to take the key.”</figcaption></figure>

In Özyıldız (2021), several tests were employed to examine the stativity of the vP (e.g., present simple and progressive interpretations, and narrative progression) to show that the resulting event description of “think Q” is dynamic while that of “think P” is either stative or dynamic. In the upcoming section, we will explore whether this generalisation holds in the case of “xiang”.

**Generalisation** (Özyıldız, 2021, 43)

a. when ‘think’ composes with a question, the resulting description must be dynamic.

b. when ‘think’ composes with a declarative, the resulting description may be stative or it may be dynamic.

## 4.1 Stativity tests

**-Zhe test** “-Zhe” is a durative aspect marker in Mandarin. It usually combines with a dynamic verb such as “xiao”(smile) and “zou”(walk). However, the resulting situation is stative. For example, (18a-18b) describe how a person eats and enters the room, namely, the manner. Thus, there is no clear temporal contour of the events without a clear reference to the initial or the ending point.

(18) a. Ta xiao-zhe chi fan
He/she smile-dur eat rice
‘He/she is eating with a smile/while smiling’

b. Ta zou-zhe jinru-le yige fangjian
He/she walk-dur enter-perf one room
‘He/she entered into a room by walking’

According to He (1992), “-zhe” denotes an exclusive stative situation. He observed that “-zhe” co-occurs with some stative predicates or with action verbs to express manner or background so that the situation as a whole is stative regardless of the innate temporality of the verb itself <fnref n="15" />. Even if “-zhe” is not helpful in distinguishing the stativity of the lexical aspect, it hints the stativity of the situation as a whole, which is sufficient for our purpose.

(19) “Xiang-zhe + Q/P”
a. *Wo xiang-zhe xia yi bu qi
I think-dur next one step chess
zenme zou
how walk
‘I am thinking what is the next move.’

b. Wo xiang-zhe women mingtian keyi qu
I think-dur we tomorrow can go
guangjie
shopping
‘I think we can go shopping tomorrow.’

<footnote n="15">¹⁵Xiao and McEnery (2004) has a slightly different take on “-zhe”. They mentioned the same phrase “chuan-zhe” (put on/wear-zhe) can describe both dynamic and stative situation: “he is wearing the body armour all day long” (stative) and “he rushed towards the room while he was still putting on his overcoat” (dynamic). They claimed the stative situation is an extension of dynamic event. But the resulting event description is stative after all.</footnote>
According to (19a), it is evident that the structure “xiang Q” cannot coexist with “-zhe”, which results in a constrained stative context. This suggests that “xiang Q” may require a dynamic environment and possess the trait of non-stative. Conversely, the structure “xiang P” (see 19b) exhibits a strong compatibility with “-zhe”, indicating that it can be internally stative. These findings align with the generalization in terms of stativity.

## 4.2 Dynamicity

In addition to looking at stativity, there are also a variety of diagnostics to test whether a sentence is dynamic, for instance, progressive, pseudo-cleft and agentive adverbials (Dowty, 1979; Olsen, 1994; Özyıldız, 2021). All of these three tests will be utilised.

**Progressive -Zai** In English, dynamic predicates are usually able to combine with progressives to express an on-going event (e.g., be running) and do not usually coexist with typical stative predicates (e.g., *be liking). In Mandarin, the progressive marker “-zai” also usually occurs in dynamic situations. Xiao and McEnery (2004) conducted a corpus study and found that out of 88 instances (not necessarily “zai-xiang”) with “-zai”, 86 of them are describing a dynamic situation<fnref n="16" />. From examples (17, 20a), we can roughly confirm that “xiang Q” is compatible with progressive aspect, indicating it may require a dynamic environment. On the contrary, “xiang P” resists suffixing “-zai” (20b), implying that “xiang P” may not be dynamic, which differs from English, where “think P” can be dynamic.

(20) “Zai-xiang + Q/P”

a. Wo zai-xiang ruhe zuo fan
I think-prog how make rice
‘I am thinking how to cook.’

b. *Wo zai-xiang ta chi-guo fan-le
I think-prog he eat-exp rice-LE
‘I am thinking he has eaten.’

**Pseudo-clefting** According to Dowty (1979), structures such as “what he did was...” can only be used with non-stative verbs. For instance, “what he did was run” is grammatical, whereas “what he did was like” is not. This same pattern may also exist in Mandarin, as demonstrated in examples

(21a,21b). The literal translation of the original construction in (21a,21b) is “the thing that he/she did was”, which differs from the English pseudo-cleft. This difference could be due to the fact that free relatives and wh-phrases are distinct in Mandarin. However, despite the structural differences, these constructions should have a similar function.

(21) What he did was...

a. Ta zuo-le de shiqing shi
He/she do-perf -relative thing is
paobu
run
‘What he/she did was run.’

b. *Ta zuo-le de shiqing shi
He/she do-perf -relative thing is
xihuan mao
like cat
‘what he/she did was like cats.’

Example (22a) is acceptable under a context like checking against a to-do list, while example (22b) is unacceptable under any circumstances. The results, again, show “xiang Q” is dynamic and “xiang P” is not.

(22) Clefting + “xiang + Q/P”

a. Ta zuo-le de shiqing shi
He/she do-perf -relative thing is
xiang wanfan chi shenme
think dinner eat what
‘what he/she did was think what to eat
for dinner.’

b. *Ta zuo-le de shiqing shi
He/she do-perf -relative thing is
xiang mali chi-le wanfan
think Mary eat-perf dinner
‘what he/she did was think Mary has
had dinner.’

**Agentivity tests** Agentivity is another feature that is considered closely related to dynamicity. Diagnostics includes “force/persuade” type verbs, imperatives, agent-oriented adverbs (Lakoff, 1966; Dowty, 1979). We have seen the compatibility of the first two in (15,16)<fnref n="17" />. Here, we will test against agentive adverbials. The equivalents of the agentive adverbials used in English are “jiaojide(worriedly)”, “zixide”(carefully), and “guyide”(deliberately) in Mandarin.

(23) Worriedly, carefully, intentionally + “xiang + Q/P”

<footnote n="16">¹⁶The rest two are stage-level stative words such as “hungry”, and “happy”, in contrast with individual-level stative words like “clever”.</footnote>

<footnote n="17">¹⁷I should also note here “xiang P” shows ungrammaticality in these two situations.</footnote>
a. Wo jiaojide/zixide/?*guyide

I worriedly/carefully/intentionally
xiang ta zai na
think he exist where

‘I am worriedly/carefully/intentionally
thinking where he is.’

b. Wo \*worriedly/\*zixide/\*guyide

I worriedly/carefully/intentionally
xiang ta chi-le fan
think he eat-perf rice

‘I worriedly/carefully/intentionally think he has eaten.’

Examples (23a) and (23b) demonstrate that “xi-
ang Q” can be used with some selected adverbials,
while “xiang P” cannot be used with the same ad-
verbials. This suggests that “xiang Q” involves
some degree of agency, while “xiang P” does not.
This conclusion is in line with the results of the
other two tests, which indicate that “xiang Q” is
dynamic while “xiang P” is stative. However, this
agentive adverbial test is not reliable in a few ways:
(1) The acceptability of the result sentences de-
pends on how natural the collocation is rather than
the stativity. (2) They can appear with some stative
words (i.e., asleep). But, essentially, all three tests
lead to the same conclusion about the nature of
“xiang Q” and “xiang P”.

4.3 Eventive contexts

Narrative progression Before coming to the end, I would like to discuss the deviation from English “think P” that “xiang P” is not dynamic under tests in §4. In fact, there is a possibility where “xiang P” is dynamic. Under the theory of temporal dis- course representation (Dowty 1986; Abusch 2014 and references therein)<fnref n="18" />, a sequence of situations can be constructed as : Given a sequence of sen- tences S<sub>1</sub>...S<sub>n</sub> with respective described situations as σ<sub>1</sub>...σ<sub>n</sub>, if a sentence S<sub>i</sub> is stative, then tempo- rally σ<sub>i</sub> and σ<sub>i-1</sub> is overlapping (σ<sub>i</sub> ○<sub>t</sub> σ<sub>i-1</sub>), oth- erwise, for any sentence S<sub>t</sub>, its situation σ<sub>t</sub> should show progression (σ<sub>t-1</sub> ≤<sub>t</sub> σ<sub>t</sub>). That is, if “xiang P” by any chance is dynamic, the utterance contain- ing “xiang P” should successfully show narrative progression, without showing overlapping or an oddity from overlapping<fnref n="19" />.

(25) Zhangsan zoujin-le shitang. Ta xiang ta Zhangsan enter-perf restaurant. He think he yingai hui chi yu. Ta dian-le yi probably will eat fish. He order-perf one fen yu.
-CLS fish

'Zhangsan entered a restaurant. He thought
he probably would eat fish. He ordered
fish.'

(25) shows a valid progression in narration time without oddity<fnref n="20" />, indicating “xiang P” is possibly eventive. However, I also found out that the pro- gression also works for “know”(zhidao), a canoni- cally stative verb. This opens several possibilities, if the test is effective in Mandarin: (1)“Xiang P” is dynamic. (2) The canonical stative “zhidao(know)” is also potentially dynamic like “xiang”. (3) The incompatibility between progressive marker and potential dynamic “xiang P” suggests “-zai” may be special.

¬ think P One argument put forth by Özyıldız (2021) in favor of the dynamic “think P” is based on the observation that the negation of this expression can be used to describe an activity in which the attitude holder is not involved at the topic time. Through examples provided in Özyıldız (2021, 43), it is shown how “think P” can resist being interpreted as a background belief when negated, thereby implying an eventive interpretation.

(26) a. When Esra knocked, I was thinking that she was in Mexico. [Background belief]

b. When Ersa knocked, I wasn't think that she was in Mexico. [As activity]

However, in our analysis (see also §5), we do not
observe such a change due to negation because

a succession is inferred in an eventive situation followed by
stative situation, there will be an oddity (24).

(24) An example adapted from Lascarides and Asher (1993)

#Zhangsan yin-le bisai. Ta zai jia.
Zhangsan win-perf competition. He at home.

'Zhangsan won the race. He was at home.'

<footnote n="18">¹⁸Özyıldız (2021) also used a similar narrative progression test, which works by identifying whether an inserted simple past event advances the narrative time. Since Mandarin does not have “simple past”, I reckon this test requires a bit more work.</footnote>

<footnote n="19">¹⁹The resulting oddity was pointed out by and Lascarides and Asher (1993) and further explained by Abusch (2014). If</footnote>

<footnote n="20">²⁰This test is not straightforward, as we can see a sentence like “when he entered the restaurant, he already knew/thought that he should order fish, then he ordered fish” can pass the progression test as well.</footnote>