# Dissertation

My dissertation, entitled Interpreting Questions with Non-exhaustive Answers'', expolores the semantics of questions. This dissertation begins by re-examining several fundamental issues, such as what a question denotes, how a question is composed, and what a wh-item denotes. It then tackles questions with complex structures, including mention-some questions, multi-wh questions, and questions with quantifiers. It also explores several popular issues, such as variations of exhaustivity, sensitivity to false answers, and quantificational variability effects.

## Chapter 1. A hybrid categorial approach

Over the past few decades, questions have been analyzed as λ-abstracts (as in categorial approaches), sets of propositions, or partitions. In the recent studies of questions, the categorial approaches are less commonly used due to their deficiencies in compositions and getting question coordinations. Nevertheless, a cross-linguistic observation due to Caponigro (2003) suggests that λ-abstracts are the most likely denotations of questions: any wh-word that can be used in free relatives can also be used in questions, but not the other direction. This observation suggests that free relatives are probably formed out of questions, and further that question denotations should be able to supply predicative and nominal meanings.

In chapter 1, I propose a hybrid categorial approach of question semantics, and define the root denotation of a question as a topical property (i.e., a function from the quantification domain of the wh-item to the Hamblin set). This approach makes the following improvements over traditional categorial approaches: it maintains the existential semantics of wh-words, avoids type-mismatch in composing multi-wh questions, and gets question coordinations by treating them as generalized quantifiers. Moreover, this approach carries forward the advantages of categorial approaches in tackling wh-constructions that admit only nominal or predictive readings, such as wh-free relatives and wh-conditionals in Mandarin. It can also comfortably capture the quantificational variability effects in cases where the quantification domain of the matrix adverb cannot be recovered from a Hamblin set.

## Chapter 2-3. Mention-some questions

It is commonly viewed that questions admit only mention-all (MA) (i.e., exhaustive) readings. Nevertheless, wh-constructions with weak modals (e.g. Where can we get coffee?) systematically admit mention-some (MS) readings. In the current dominant view, the availability of MS is mainly restricted by pragmatic factors, such as whether a non-exhaustive answer suffices for the conversational goal. This view, however, is too permissive to capture the characteristics of MS. For example, unlike the other non-exhaustive answers, a MS answer specifies exactly one possible choice, instead of a random list of possible choices.

In my opinion, the distribution of MS is primarily restricted by grammatical structures. In chapter 2, I adopt an answerhood from Fox (2013) which allows non-exhaustive answers to be complete, and propose a structural approach to capture the MS/MA ambiguity: this ambiguity comes from minimal structural variations within the question nucleus, including the scope ambiguity of the higher-order wh-trace, and the presence/absence of a pre-exhaustification exhaustifier.

Allowing non-exhaustive answers to be complete is a non-trivial move, because many semantic facts of questions are explained based on the assumption that questions must be interpreted exhaustively. For example, the uniqueness effects of singular wh-items are standardly explained by Dayal’s (1996) presupposition that a question must have a strongest true answer. In chapter 3, I provide a way to maintain the merits of Dayal’s presupposition based on internal type-shifts (Shan & Barker 2006).

## Chapter 4. Sensitivity to false answers

Knowing a question is traditionally defined as knowing the weakly exhaustive or strongly exhaustive answer of this question. But recent studies find these interpretations too weak or too strong. For example, for John knows Q, the most prominent reading requires (i) that John knows the complete true answer of Q, and (ii) that John has no false belief about Q. I call conditions (i) and (ii) “completeness” and “false answer (FA-)sensitivity,” respectively. The current dominant approach analyzes FA-sensitivity as a logical consequence of exhaustifying completeness (Klinedinst & Rothschild 2011, Uegaki 2015): John knows Q means that, among the potentially complete answers of Q, John only believes the true complete answer.

In chapter 4 of my dissertation, I argue that the reading predicted by the exhaustification-based approach is too weak: the predicted FA-sensitivity condition considers only false answers that are potentially complete, while the actual FA-sensitivity condition is also concerned with false answers that can never be complete. Hence, I propose to derive completeness and FA-sensitivity independently. In particular, completeness is defined based on a complete true answer, while FA-sensitivity is concerned with all relevant answers, recovered from the partition of the embedded question. This analysis uniformly accounts for indirect MA questions and indirect MS questions.

## Chapter 5. Pair-list readings of multi-wh questions

Pair-list readings of multi-wh questions and universal-questions have a lot of similarities in syntax and semantics. Hence, previous accounts attempt to derive them via similar LFs (e.g., Dayal 1996) or at least assign them with the same root denotation (e.g., Fox 2012). Nevertheless, in chapter 5, I show that these two pair-list readings are actually different: pair-list readings of universal-questions are subject to domain exhaustivity, while pair-list readings of multi-wh questions are not.

(1) (Context: 200 candidates are competing for three jobs.)
a.     Guess which candidate will get which job.   (multi-wh question)
b. # Guess which job each candidate will get.      (universal-question)

I propose a new function-based approach to derive the pair-list readings of multi-wh questions. For example, the root denotation of the multi-wh question in (1a) is a property that maps each function f ranging over atomic jobs to the conjunction of all the propositions of the form “candidate x will get f(x)”. The proposed approach makes the following improvements over earlier function-based approaches (e.g., Dayal 1996). First, assuming the domain of f to be unrestricted, it does not overly predict domain exhaustivity effects. Second, it does not involve any ad hoc assumptions or structure-specific operations. Third, it can also easily capture the quantification variability effects in interpreting quantified indirect multi-wh questions.

## Chapter 6. Quantifying into questions

Questions with quantifiers admit readings where the quantifiers seemingly scope out of the questions. For example, (2a/b) can be intuitively interpreted as ‘for one/each of the students x, who did x vote for?’. This reading is hard to derive compositionally, because quantifiers are defined in terms of propositions or truth values, while questions are not propositions or truth values.

(2) a. Who did one of the students vote for?
b. Who did each of the students vote for?

In chapter 6, I provide two compositional approaches to derive the quantification-into questions readings, including a higher-order question approach and a function-based approach. The higher-order question approach defines (2a/b) as a family of sub-questions: a max-informative set K such that for one/each student x, ''who did x vote for" is a member of K. Here the quantifier is nicely treated as a regular quantification into a memberhood relation. A question admits a choice reading only if it has multiple such K sets (as in universal-questions). A question admits a pair-list reading only if one of such K sets is non-singleton (as in existential-questions). The function-based approach uses the same techniques, except that it defines (2a/b) as a single question that takes a special functional reading

## Chapter 7. Semantics of the Mandarin particle dou 都

Variations of logical particles should be either non-existent or very limited, otherwise the logical system of human languages would be overly complex. Nevertheless, a number of functional particles in East Asian languages (e.g., Japanese ya and mo, Mandarin dou and ye) seemingly possess various logical uses. Take the Mandarin particle dou for example. Varying by the associated item and the prosody pattern, dou can trigger distributivity, license universal free choice (FC) items, or evoke an even-like inference. To maintain a simple logical system, it is crucial to figure out which functions are initial, what parameters are responsible for the switches, and when these switches are licensed.

In chapter 7 of my dissertation, I argue that the seemingly unrelated functions of dou share the same source. I define dou uniformly as a pre-exhaustification exhaustifier: it affirms the prejacent, negates the exhaustification of each sub-alternative, and presupposes the existence of a sub-alternative. In the initial state, sub-alternatives are alternatives that are not innocently excludable. The presupposition yields a distributivity effect, and the assertion is responsible for the FC inferences. In further development, grammatical factors (e.g., the presence of the focus-marker lian or stress on the associate of dou) license a weaker meaning of dou, under which sub-alternatives are defined in terms of likelihood, instead of logical strength. Under the weaker meaning, the presupposition of dou is equivalent to the existential presupposition of even