1 Introduction

It is cross-linguistically common for a single particle to participate in the formation of indefinites, questions and disjunction. Languages in which this type of particle—henceforth the Q-particle—occurs at least in questions and indefinites include Sinhala (Kishimoto 1992; Hagstrom 1998; Slade 2011), Malayalam (Jayaseelan 2001), Tlingit (Cable 2010), Japanese (Kuroda 1965; Hagstrom 1998) and Shuri Okinawan (Hagstrom 1998). Table 1 from Slade (2011) summarizes the distribution of the Q-particle in these languages.

Sinhala Malayalam Tlingit Japanese

Y/N-question -oo ka
wh-question -oo (Old Malayalam) ka
indefinite (aff.),
hari (aff.), -oo ka
vat (neg.),
declarative disjunction hari (aff.) -oo khachu ka
vat (neg.)
alternative question -oo gé, gwáa ka

Table 1

Summary of the distribution of Q-particles from Slade (2011).

The observation that the same particle appears in at least a subset of questions, indefinites and disjunctions across languages has stimulated discussions on the proper semantic analysis of these semantic categories. More specifically, researchers have tackled the following closely related questions:

(1) a. What is shared by the semantic representations of indefinites, questions and disjunctions?
  b. What is the semantic contribution of the Q-particle in indefinites, questions and disjunctions?
  c. How are the different syntactic environments in which the Q-particle occurs mapped to the interpretations of indefinites, questions and disjunctions?

In the last decade or so, investigations on these questions have provided insights into the theoretical nature of the relevant semantic categories (e.g., Hagstrom 1998; Shimoyama 2006; Cable 2010; Slade 2011; Szabolcsi 2015b).

Research into these questions should also take into account the fact that not all languages in Table 1 express the five semantic categories using exactly the same particle. In particular, Sinhala and Tlingit use different particles for indefinites/questions and declarative disjunction, while Japanese and Malayalam appear to use the same particles in all categories. There are two analytic possibilities for dealing with this non-perfect parallel between languages. One is to take the Sinhala and Tlingit patterns as the starting point and analyze the Malayalam and Japanese patterns as involving homophony. The other is to analyze the different semantic categories as sharing a core compositional element, and to assume that there is a cross-linguistic variation in how this shared compositional element is lexicalized with other elements. According to the latter approach, Malayalam and Japanese lexicalize the shared element by a single particle while Sinhala and Tlingit lexicalize the element differently, depending on the presence of other elements contributing to the difference within the five semantic categories. For example, the core element contributing the semantics of disjunction could be lexicalized differently depending on whether it appears in a clause headed by the declarative complementizer or in a clause headed by the interrogative complementizer in languages like Tlingit and Sinhala (Slade 2011).

In order to investigate the feasibility of the latter approach and address the questions in (1), it is necessary as a first step to investigate whether the unified analysis of the particle is indeed possible in languages like Malayalam and Japanese. The goal of this paper is to demonstrate that this is in fact possible in the Japanese case. I will provide a comprehensive and concrete semantics for the Japanese Q-particle ka that properly accounts for its use in questions, indefinites and disjunctions in a unified fashion. The Japanese particle ka is also interesting in the context of questions (1b) and (1c) above since its interpretation is tightly connected with the syntactic environments in which it occurs. As exemplified in (2a), when ka directly attaches to a wh-item and forms a DP, it functions as an indefinite. On the other hand, as seen in (2b), when ka is in the final position of a clause containing a wh-item, the clause ending with ka forms a wh-question.

    1. (2)
    1. a.
    1. [DP
    2.  
    1. dare-ka
    2. who-KA
    1. ]
    2.  
    1. -ga
    2. -NOM
    1. hashitta.
    2. ran
    1. ‘Someone ran.’                                              (∃-statement)
    1.  
    1. b.
    1. [CP
    2.  
    1. dare-ga
    2. who-NOM
    1. hashitta-ka
    2. ran-KA
    1. ]
    2.  
    1. oshiete.
    2. tell
    1. ‘Tell me who ran.’                                        (Wh-Question)

A number of proposals have been proposed to capture this pattern (e.g., Hagstrom 1998; Shimoyama 2006; Slade 2011). However, as I will argue later in the paper, none of the current compositional semantic analysis of ka can successfully capture the fact that the semantic contribution of ka is conditioned by its syntactic position in its disjunction use in a way parallel to how its semantic contribution is conditioned in the wh+ka construction. That is, the form α-ka β-ka receives an interpretation of a disjunction without a question force (what is dubbed as declarative disjunction in the table above) when the ka-phrases are syntactically smaller than a CP. On the other hand, the form receives an interpretation of an alternative question (AltQ) when the ka-phrases themselves form a CP. This is exemplified in the following sentences.

    1. (3)
    1. a.
    1. [DP
    2.  
    1. Hanako-ka
    2. Hanako-KA
    1. Jiro-ka]-ga
    2. Jiro-KA-NOM
    1. hashitta.
    2. ran.
    1. ‘Either Hanako or Jiro ran.’                               (declarative disjunction)
    1.  
    1. b.
    1. [CP
    2.  
    1. [Hanako-ga
    2. Hanako-NOM
    1. hashitta-ka]
    2. ran-KA
    1. [Jiro-ga
    2.  Jiro-NOM
    1. hashitta-ka]]
    2. ran-KA
    1. oshiete.
    2. tell
    1. ‘Tell me which is true: It seems that Hanako ran or it seems that Jiro ran?’                   (AltQ)

This paper argues that this parallel pattern straightforwardly falls out from the combination of (a) an extension of the Hamblin-semantic analysis of in-situ wh-questions and Q-particles (Beck 2006; Shimoyama 2006; Kotek 2014) and (b) the analysis of the disjunction structure as schematized in the following (den Dikken 2006; Mitrovič & Sauerland 2014; Szabolcsi 2015b):

    1. (4)

Adopting a two-tier alternative semantics, I will propose that the role of the ka-particle is always to project a set of alternatives introduced by the wh-item in the “alternative-semantic” dimension to the “ordinary-semantic” dimension. This ensures that a ka-ending clause as in (2b) denotes a set of propositions, i.e., the semantic value of a question according to Hamblin (1973) and Karttunen (1977). This part of the proposal simply preserves the existing analysis of in-situ wh-questions (Beck 2006; Shimoyama 2006; Kotek 2014). What sets the current analysis apart from the existing analyses is that it maintains the same analysis of ka for its clause-internal occurrences. Thus, the ordinary-semantic meaning of dare-ka ‘who-KA’ in (2a) would be a set of individuals. I will claim that such a set in the ordinary-semantic dimension faces a type-mismatch when embedded clause-internally, and that it has to be type-shifted by a (cross-categorial) existential closure, which turns a set into an existential quantifier having the set as its domain. This provides us with the contrast in (2): (2b) is a question since there is no existential closure, and (2a) is an existential statement since the set denoted by dare-ka is type-shifted into an existential quantifier due to a type-mismatch.

This mechanism can be extended to the disjunction case in (3), as the structure in (4) is compositionally analyzed as denoting the set consisting of (the denotations of) α and β. When each disjunct is a clause, as in (3b), the set expresses an alternative question. On the other hand, when the whole disjunction is in a clause-internal position, as in (3a), the set denoted by the disjunction is type-shifted into an existential quantifier, resulting in a declarative disjunctive interpretation.

The rest of the paper is structured as follows: In §2, I will review the distributions and interpretations of ka in wh+ka constructions and ka-disjunctions, and show how the semantic contribution of ka is conditioned by its syntactic environment both in wh+ka and ka-disjunctions. The empirical parallelism between wh+ka and ka-disjunctions that I suggested above is discussed here in detail. §3 lays out the basic analysis in terms of two-tier alternative semantics. I will begin by proposing an analysis following previous analyses of wh+ka constructions by Beck (2006); Shimoyama (2006) and Kotek (2014). I will illustrate how the proposed analysis explains the effect of the syntactic environment on the interpretation of ka by (a) maintaining the analysis of Q-particles sentence-internally, and (b) adopting the mechanism of (cross-categorial) existential closure as a repair of type-mismatch. This analysis is then extended to ka-disjunctions, employing the syntax for disjunctions following den Dikken (2006). In §4, I will discuss a potential problem of the proposal concerning the (im)possibility of existential closure at the clausal level. A solution to this problem is proposed on the basis of the observation that wh+ka constructions trigger existential presuppositions. §5 is a brief note on how the particle mo—which has been treated as the universal counterpart of the existential ka in the previous literature (Shimoyama 2006)—would fit in the picture. Three prominent compositional-semantic analyses of ka, i.e., Hagstrom (1998), Shimoyama (2006) and Yatsushiro (2009), are discussed in §6, where it will be argued that the parallel between wh-ka and ka-disjunctions cannot be correctly accounted for under these analyses, even with plausible extensions to disjunctions, employing recent theories such as Slade (2011). The paper concludes by discussing implications for the cross-linguistic semantics of Q-particles.

2 The position of ka and its semantic contribution

2.1 wh+ka

As discussed in the introduction, the interpretation of a Japanese sentences involving a wh-item and ka depends on the syntactic position of ka (Kuroda 1965; Hagstrom 1998). When ka directly attaches to the wh-phrase, the wh-ka complex functions as an indefinite. On the other hand, when ka is in a sentence-final position, the sentence constitutes a wh-question. This can be seen in the following examples:

    1. (5)
    1. a.
    1. [DP
    2.  
    1. Dare-ka
    2. who-KA
    1. ]
    2.  
    1. -ga
    2. -NOM
    1. hashitta.
    2. ran
    1. ‘Someone ran.’                           (∃-statement)
    1.  
    1. b.
    1. [CP
    2.  
    1. Dare-ga
    2. who-NOM
    1. hashitta-ka
    2. ran-KA
    1. ]
    2.  
    1. (oshiete).
    2. tell
    1. ‘(Tell me) who ran.’                   (Wh-Question)
    1. (6)
    1. a.
    1. Taro-ga
    2. Taro-NOM
    1. [DP
    2.  
    1. nani-ka
    2. what-KA
    1. ]
    2.  
    1. -o
    2. -ACC
    1. mita.
    2. saw
    1. ‘Taro saw something.’                   (∃-statement)
    1.  
    1. b.
    1. [CP
    2.  
    1. Taro-ga
    2. Taro-NOM
    1. nani-o
    2. what-ACC
    1. mita-ka
    2. saw-KA
    1. ]
    2.  
    1. (oshiete).
    2. tell
    1. ‘(Tell me) who ran?’                   (Wh-Question)

Here, the embedding verb oshiete ‘tell me’ is added in (5b) since the clause-final ka is most natural in embedded contexts for stylistic reasons. In an unembedded clause, no is used instead of ka in informal speech.1 In an unembedded formal speech, ka is attached to the polite form of the verbal complex (mi-mas-ita ‘see-POL-PAST’ in the case of mita ‘saw’).

For some speakers, the wh-item and ka can be separated within a DP that functions as an indefinite. The following example from Yatsushiro (2009) illustrates this:

    1. (7)
    1. [
    2.  
    1. Dare-o
    2. who-ACC
    1. hihanshita
    2. criticized
    1. gakusei
    2. student
    1. ]
    2.  
    1. -ka-ga
    2. -KA-NOM
    1. taihosareta.
    2. be.arrested
    1. ‘A student or other who had criticize someone was arrested.’

In this example, ka is separated from the wh-item dare itself, and the subject DP ending with ka receives an interpretation as an existential quantifier over students who criticized someone.

It is also observed in the literature that wh+ka indefinites behave like epistemic indefinites like German irgendein and Spanish algún (Sudo 2010; Kaneko 2011; Alonso-Ovalle & Shimoyama 2014). That is, they convey the speaker’s ignorance about the identity of the individual serving as the witness of the existential statement. For example, (5a) conveys that the speaker does not know who ran. The semantic and pragmatic nature of this implication is still under debate, but evidence suggests that they can be treated as an implicature, as argued by Alonso-Ovalle & Shimoyama (2014). As shown below, the ignorance implication disappears in a downward-entailing environment (a conditional antecedent in (8a)). Also, it is compatible with both cancellation of the ignorance implication (as in (8b)) and can be non-redundantly followed up by an explicit statement of the ignorance (as in (8c)).

    1. (8)
    1. a.
    1. Dare-ka-ga
    2. who-KA-NOM
    1. hashitta-ra
    2. ran-COND
    1. oshie-masu.
    2. tell-POL
    1. ‘I will tell you if anyone runs.’
    2. *‘I will tell you if someone runs but I don’t know who.’
    1.  
    1. b.
    1. Dare-ka-ga
    2. who-KA-NOM
    1. hashitta.
    2. ran.
    1. Sorede,
    2. And,
    1. boku-wa
    2. I-TOP
    1. sore-ga
    2. it-NOM
    1. dare-da-ka
    2. who-COP-KA
    1. shitteiru.
    2. know
    1. ‘Someone ran, and I know who that is.’
    1.  
    1. c.
    1. Dare-ka-ga
    2. who-KA-NOM
    1. hashitta.
    2. ran.
    1. Sorede,
    2. And,
    1. boku-wa
    2. I-TO
    1. sore-ga
    2. it-NOM
    1. dare-da-ka
    2. who-COP-KA
    1. shira-nai.
    2. know-NEG
    1. ‘Someone ran, and I don’t know who that is.’

These data suggest that the ignorance implication is an implicature rather than an entailment (see Alonso-Ovalle & Shimoyama (2014) for further arguments for the implicature analysis). Since I will focus on the semantic aspect of the wh+ka constructions and their compositional derivation in this paper, I will leave aside their characteristics as epistemic indefinites in the rest of the paper.2

2.2 ka-disjunctions

Another empirical domain in which ka appears is disjunction. Example (9) shows that ka can attach to each disjunct in a disjunction (optionally to the second disjunct).3 I will call this construction ka-disjunction. In ka-disjunctions, an additional coordinator (in this case matawa) can be inserted between the two disjuncts marked by ka.

    1. (9)
    1. Taro-ga
    2. Taro-NOM
    1. [DP
    2.  
    1. Hanako-ka
    2. Hanako-KA
    1. (matawa)
    2.  or
    1. Jiro-ka]-o
    2. Jiro-KA-ACC
    1. mita.
    2. saw
    1. ‘Taro saw Hanako or Jiro.’

I will discuss more on the additional coordinator between ka-phrases in the Section 2.4. Unless noted otherwise, the data I describe in this section and the following sections are that of ka-disjunctions with a phonologically null coordinator. Later, the description will be made more precise by taking into account the role of different phonologically explicit coordinators.

One of the empirical contributions of this paper is to establish that the interpretation of ka in ka-disjunctions is similarly dependent on the syntactic position of ka in each disjunct. In fact, it turns out that we can state a unified generalization that applies to both wh+ka construction and ka-disjunctions. The generalization that I am going to submit is stated in the following:

(10) Generalization: When the ka-phrase is syntactically smaller than a CP, its semantic contribution is an existential quantifier (without the question force); when it syntactically forms a CP, its semantic contribution is to form a question involving alternatives expressed by the wh-item/disjunction.

Table 2 summarizes how this generalization is instantiated in the wh+ka construction and α-ka β-ka construction. Below, I elaborate this empirical claim in some detail.

the ka-phrase is… smaller than a CP CP

wh+ka existential quantifier wh-question
α-ka β-ka declarative disjunction alternative question

Table 2

The dependence of the interpretation of a ka-phrase on its syntactic size.

First of all, the dependence of the interpretation of wh+ka on the syntactic position of ka, exemplified in (5) above, can be described as in the first row of Table 2. The syntactic category of the wh+ka phrase is a DP in (5a), where ka attaches to the wh-phrase dare directly and dare-ka serves as the subject of the verb hashitta ‘ran’. This wh-ka phrase functions as an indefinite/existential quantifier. On the other hand, the wh+ka phrase in (5b) is a whole CP which by itself expresses a question (modulo stylistic anomaly) and can be embedded under clause-embedding predicates such as oshiete ‘tell me’. In this case, the wh-phrase functions as a wh-word in a wh-question.

Turning now to ka-disjunctions, it is known that ka-disjunctions can coordinate (at least) DPs, TPs as well as CPs (Kishimoto 2013; Uegaki 2014; Miyama 2015), as exemplified below.4 Each of the examples also indicates whether the sentence has a reading as a disjunctive statement (∨-statement) or an alternative question (AltQ).

    1. (11)
    1. [DP
    2.  
    1. Hanako-ka
    2. Hanako-KA
    1. Jiro-ka]-ga
    2. Jiro-KA-NOM
    1. hashitta.
    2. ran
    1. ‘Either Hanako or Jiro ran.’                          (✓∨-statement)
    2. *‘Which is true: Hanako ran or Jiro ran?’                   (*AltQ)
    1. (12)
    1. a.
    1. [TP
    2.  
    1. [Hanako-ga
    2. Hanako-NOM
    1. hashitta-ka]
    2. ran-KA
    1. [Jiro-ga
    2.  Jiro-NOM
    1. hashitta-ka]]
    2. ran-KA
    1. mitai-da.
    2. seem-COP
    1. ‘It seems that Hanako ran or Jiro ran.’                             (✓∨-statement)
    1. *‘Which seems to be true: Hanako ran or Jiro ran?’                       (*AltQ)
    1.  
    1. b.
    1. [TP
    2.  
    1. [Hanako-ga
    2. Hanako-NOM
    1. hashitta-ka]
    2. ran-KA
    1. [Jiro-ga
    2.  Jiro-NOM
    1. hashitta-ka]]
    2. ran-KA
    1. daroo.
    2. may.well.be
    1. ‘It might well be that Hanako ran or Jiro ran.’                         (✓∨-statement)
    2. *‘Which might well be true: Hanako ran or Jiro ran?’                           (*AltQ)
    1. (13)
    1. a.
    1. [CP
    2.  
    1. [Hanako-ga
    2. Hanako-NOM
    1. hashitta-mitai-ka]
    2. ran-seem-KA
    1. [Jiro-ga
    2.  Jiro-NOM
    1. hashitta-mitai-ka]]
    2. ran-seem-KA
    1. (oshiete).
    2. tell
    1. ‘(Tell me) which is true: It seems that Hanako ran or it seems that Jiro ran?’                   (✓AltQ)
    2. *‘(Tell me) it seems that Hanako ran or it seems that Jiro ran.’                             (*∨-statement)
    1.  
    1. b.
    1. [CP
    2.  
    1. [Hanako-ga
    2. Hanako-NOM
    1. hashitta-daroo-ka]
    2. ran-may.well.be-KA
    1. [Jiro-ga
    2.  Jiro-NOM
    1. hashitta-daroo-ka]]
    2. ran-may.well.be-KA
    1. (oshiete).
    2. tell
    1. ‘(Tell me) which is true: Hanako might well have run or Jiro might well have run.’               (✓AltQ)
    2. *‘(Tell me) Hanako might well have run or Jiro might well have run.’                         (*∨-statement)

Following Kishimoto (2013), I take the positioning of mood items such as mitai ‘seem’ and daroo ‘might well’, which are in functional projections outside TPs, as indicating the syntactic category of ka-disjunctions. When the mood is outside the ka-disjunction involving tensed predicates, as in (12), its syntactic category is TP. On the other hand, when the mood is inside the ka-disjunction, as in (13), or when there is no overt mood item in the sentence as in (14) below, its syntactic category is CP.

    1. (14)
    1. [CP
    2.  
    1. [Hanako-ga
    2. Hanako-NOM
    1. hashitta-ka]
    2. ran-KA
    1. [Jiro-ga
    2.  Jiro-NOM
    1. hashitta-ka]]
    2. ran-KA
    1. oshiete.
    2. tell
    1. ‘Tell me which is true: Hanako ran or Jiro ran?’                   (✓AltQ)

Crucially, the interpretation of a ka-disjunction is a disjunctive statement in both (11) and (12) whereas it is an AltQ in (13) and (14). In other words, α-ka β-ka becomes a question with α and β as alternatives only when it is a CP coordination. That sub-CP ka-disjunction does not introduce alternatives remains to be true even when an additional ka as a question particle is added to the sentence-final position (Uegaki 2014). This is shown in the following examples:

    1. (15)
    1. [[DP
    2.  
    1. Hanako-ka
    2. Hanako-KA
    1. Jiro-ka]-ga
    2. Jiro-KA-NOM
    1. hashitta-ka]
    2. ran-KA
    1. oshiete.
    2. tell.
    1. ‘Tell me whether or not Hanako ran or Jiro ran.’                   (✓YNQ)
    2. *‘Tell me which is true: Hanako ran or Jiro ran.’                     (*AltQ)
    1. (16)
    1. [[TP
    2.  
    1. [Hanako-ga
    2. Hanako-NOM
    1. hashitta-ka]
    2. ran-KA
    1. [Jiro-ga
    2.  Jiro-NOM
    1. hashitta-ka]]
    2. ran-KA
    1. mitai-ka]
    2. seem-KA
    1. (oshiete).
    2. tell
    1. ‘Tell me whether or not it seems to be that Hanako or Jiro ran.’                   (✓YNQ)
    2. *‘Tell me which is true: Taro saw Hanako or he saw Jiro.’                            (*AltQ)

The only interpretation (15–16) can get is the Yes/No Question (YNQ) interpretation which embeds a disjunctive statement, i.e., the question of whether or not ‘Taro saw Hanako or Taro saw Jiro’ is true. Establishing the unavailability of the AltQ reading in (15–16) is not so straightforward since the possible answers to the AltQ, i.e., ‘Hanako (ran)’ and ‘Jiro (ran)’ would also be (over-informative but) acceptable answers to the YNQ. The following examples, however, make it clear that the AltQ interpretation is indeed unavailable.

    1. (17)
    1. (Context: I know that either Hanako or Jiro ran, but I don’t know which.)
    1. Watashi-wa
    2. I-TOP
    1. [[DP
    2.  
    1. Hanako-ka
    2. Hanako-KA
    1. Jiro-ka]-ga
    2. Jiro-KA-NOM
    1. hashitta-ka]
    2. ran-KA
    1. shir-anai.
    2. know-NEG
    1. ‘I don’t know whether or not either Hanako or Jiro ran.’                (✓ YNQ)
    2. ‘I don’t know which is true: Hanako ran or Jiro ran.’                        (*AltQ)
    1. (18)
    1. (Context: I know that it seems that either Hanako or Jiro ran, but I don’t know which.)
    1. Watashi-wa
    2. I-TOP
    1. [TP
    2.  
    1. [Hanako-ga
    2. Hanako-NOM
    1. hashitta-ka]
    2. ran-KA
    1. [Jiro-ga
    2.  Jiro-NOM
    1. hashitta-ka]]
    2. ran-KA
    1. mitai-ka]
    2. seem-KA
    1. shir-anai.
    2. know-NEG
    1. ‘I don’t know whether or not it seems that either Hanako or Jiro ran.’               (✓YNQ)
    2. ‘I don’t know which seems to be true: Hanako ran or Jiro ran.’                          (*AltQ)

The examples would be true under the given context if the embedded clauses had the AltQ interpretation although they would be false in the YNQ interpretation. Intuitively, the sentences sound false in the context. This indicates that the AltQ interpretation is unavailable for these sentences.

This fact is in parallel with the behavior of a wh-ka DP in a ka-clause, which only serves as an indefinite and not as a wh-phrase introducing alternatives. For example, the embedded clause in the following sentence involving dare-ka can only have a YNQ interpretation, and not a wh-question interpretation.

    1. (19)
    1. (Context: I know that Taro met someone, but I don’t know who.)
    1. Watashi-wa
    2. I-TOP
    1. [Taro-ga
    2.  Taro-NOM
    1. [DP
    2.  
    1. dare-ka]-o
    2. who-KA-ACC
    1. mita-ka]
    2. saw-KA
    1. shira-nai.
    2. know-NEG
    1. ‘I don’t know whether Taro saw someone.’                   (✓ YNQ)
    2. ‘I don’t know whom Taro saw.’                                     (*whQ)

The fact that the embedded clause in (19) lacks a wh-question interpretation is evidenced by the fact that the sentence is intuitively false under the given context.

In contrast to ka-disjunctions with sub-CP disjuncts, ka-disjunctions with CP disjuncts are interpreted as AltQs and not as disjunctive statements, as shown in (13) above. This is confirmed in the following example under the context similar to the ones in (17–18). (Note that (17–18) involve negation in the matrix clause whereas the following example doesn’t).

    1. (20)
    1. (Context: I know that either it seems that Hanako ran or it seems that Jiro ran, but I don’t know which.)
    1. Watashi-wa
    2. I-TOP
    1. [CP
    2.  
    1. [Hanako-ga
    2. Hanako-NOM
    1. hashitta-mitai-na-no-ka]
    2. ran-seem-COP-GEN-KA
    1. [Jiro-ga
    2.  Jiro-NOM
    1. hashitta-mitai-na-no-ka]]
    2. ran-seem-COP-GEN-KA
    1. shitteiru.
    2. know
    1. ‘I know which is true: it seems that Hanako ran or it seems that Jiro ran.’                     (✓AltQ)
    2. ‘I know that it seems that Hanako ran or it seems that Jiro ran.’                           (*∨-statement)

This sentence would be true if the embedded clause had an interpretation as a disjunctive statement. However, the sentence is intuitively false. In fact, it would be true only if I know which of Hanako and Jiro ran. This means that the embedded clause in (20) only has an AltQ interpretation. Again, this is in parallel with the behavior of wh+ka. The wh+ka phrase as a CP only receives an interpretation as a wh-question and not as an existential statement.

In sum, ka-disjunctions are interpreted as disjunctions without the question force when they are sub-CP-coordinations while they are interpreted as AltQs with each disjunct as alternatives when they are CP-coordinations. This parallels the behavior of wh+ka constructions as summarized in Table 2. In section §3, I will propose a unified semantics of ka in wh+ka and disjunctions which can naturally account for these data in a compositional fashion.

2.3 CP-sized ka-disjunctions are syntactically coordinations

In this subsection, I address a potential worry about the nature of CP-coordination sentences in (13, 20). One might wonder if ka-disjunctions with CP-disjuncts should be analyzed as sequences of two speech acts rather than a single question involving coordinated CPs (see e.g., Kishimoto 2013 for this view). However, there are at least three reasons to believe that the sentences can be analyzed as involving a single question. The first reason concerns the embedding of the CP-disjunction under clause-embedding predicates, something that we have already seen in (20). Embedding under a clause-embedding predicate would be impossible if the two clauses didn’t have a single clausal status. The second reason is that there can be an across-the-board (ATB) extraction (Williams 1978) from inside each disjunct, suggesting that the structure as a whole is a coordination. This is exemplified in the ATB extraction of the constituent sono paati-e-wa ‘to the party’ in the following examples:

    1. (21)
    1. a.
    1. [Sono
    2.  the
    1. paati-e-wa
    2. party-to-TOP
    1. [Hanako-ga
    2.  Hanako-NOM
    1. ________
    2.  
    1. itta-mitai-na-no-ka]
    2. went-seem-COP-GEN-KA
    1. [Jiro-ga
    2.  Jiro-NOM
    1. ________
    2.  
    1. itta-mitai-na-no-ka]]
    2. went-seem-COP-GEN-KA
    1. (oshiete).
    2. tell
    1. ‘Tell me which is true: it seems that Hanako went to the party or it seems that Jiro went to the party.’
    1.  
    1. b.
    1. [Sono
    2.  the
    1. paati-e-wa
    2. party-to-TOP
    1. [Hanako-ga
    2.  Hanako-NOM
    1. ________
    2.  
    1. itta-daroo-ka]
    2. went-may.well.be-KA
    1. [Jiro-ga
    2.  Jiro-NOM
    1. ________
    2.  
    1. itta-daroo-ka]]
    2. went-may.well.be-KA
    1. (watashi-ni-wa
    2.  I-DAT-TOP
    1. wakara-nai).
    2. know-NEG
    1. ‘I don’t know which is true: Hanako may well have gone to the party or Jiro may well have gone to the party.’

Finally, ka-disjunctions with CP disjuncts are associated with an exclusivity presupposition typically associated with AltQs. It is well known that English AltQs are associated with the presupposition that only one of the alternatives is true (Karttunen 1977; Biezma & Rawlins 2012). For example, the following AltQ presupposes that Hanako or Jiro went to the party, but not both.

(22) Is it Hanako or Jiro who went to the party?

The same presupposition is observed in AltQs in the embedded clauses in (21). They presuppose that only one of ‘it {seems/may well be} that Hanako went to the party’ and ‘it {seems/may well be} that Jiro went to the party’ is true. This presupposition is unexpected if the two clauses are independent question speech acts. For, a sequence of two questions wouldn’t have such a presupposition. For instance, the following sequence of two YNQs is compatible with situations where neither or both Hanako and Jiro went to the party.

(23) Did Hanako go to the party? Did Jiro go to the party?

2.4 The coordinator between ka-marked disjuncts

Before finishing the section, I note on different coordinators that can appear between ka-marked disjuncts. There are at least four such coordinators in Japanese: soretomo, matawa, soreka and the phonologically null ∅. They differ in syntactic distributions as summarized below:

(24) Distributions of different coordinators
  a. soretomo: appears only in CP-sized ka-disjunctions.
  b. matawa: appears in sub-CP-sized ka-disjunctions. Also, it appears in CP-sized ka-disjunctions when the disjunction is embedded under the sentence-final copula particle da.
  c. soreka: no restriction.
  d. ∅: no restriction.

If we disregard the role of the copula da for now, the first two coordinators soretomo and matawa are in complementary distribution with each other. The other two coordinators, soreka and ∅, have no restriction on their occurrences. These syntactic distributions are exemplified in the following examples:

    1. (25)
    1. Taro-ga
    2. Taro-NOM
    1. [DP
    2.  
    1. Hanako-ka
    2. Hanako-KA
    1. {matawa/*soretomo/soreka/∅}
    2.  or
    1. Jiro-ka
    2. Jiro-KA
    1. -o
    2. -ACC
    1. mita.
    2. saw.
    1. ‘Taro saw Hanako or Jiro.’
    1. (26)
    1. [TP
    2.  
    1. [
    2.  
    1. Hanako-ga
    2. Hanako-NOM
    1. hashitta-ka ]
    2. ran-KA
    1. {matawa/*soretomo/soreka/}
    2.  or
    1. [Jiro-ga
    2.  Jiro-NOM
    1. hashitta-ka] ]
    2. ran-KA
    1. mitai-da.
    2. seem-COP
    1. ‘It seems that Hanako ran or Jiro ran.’
    1. (27)
    1. [CP
    2.  
    1. [
    2.  
    1. Hanako-ga
    2. Hanako-NOM
    1. hashitta-mitai-ka ]
    2. ran-seem-KA
    1. {*matawa/soretomo/soreka/}
    2. or
    1. [ Jiro-ga
    2.  Jiro-NOM
    1. hashitta-mitai-ka ]].
    2. ran-seem-KA
    1. ‘Which is true: It seems that Hanako ran or it seems that Jiro ran?’

In other words, the environments in which matawa and soretomo can appear mirror the ones in which a ka-disjunction with the null coordinator is interpreted as a declarative disjunction and an AltQ.

The situation is a bit different when a ka-disjunction with CP disjuncts are embedded under the copula da. This is shown in the following example:

    1. (28)
    1. [[
    2.  
    1. Hanako-ga
    2. Hanako-NOM
    1. hashitta-mitai-ka]
    2. ran-seem-KA
    1. matawa
    2. or
    1. [
    2.  
    1. Jiro-ga
    2. Jiro-NOM
    1. hashitta-mitai-ka]
    2. ran-seem-KA
    1. -da].
    2. COP
    1. ‘It seems that Hanako ran or it seems that Jiro ran.’                   (∨-statement)

The coordinator matawa is possible in this environment, and is interpreted as a declarative disjunction. Although this special behavior of the copula da will be taken up again in later sections, the analysis proposed in this paper will focus on cases where da is absent, and the extension of the analysis to the cases where da is present will have to be left for future studies.

The three phonologically explicit markers are in fact morphologically complex. Both soretomo and soreka consist of the third person inanimate pronoun sore and one or more additional particles. The other marker matawa is possibly a combination of the conjunctive marker mata and the topic marker wa. However, here I will not try to derive the semantic functions and syntactic distributions of these particles from their morphological parts since finding out the correct morphological analysis of these items is beyond the scope of the current paper.

This being said, soreka has a plausible morphological analysis that explains its syntactic distribution: soreka can be analyzed as an additional (redundant) ka-disjunct involving a pronoun referring back to the first disjunct. If this is the case, α-ka sore-ka β-ka is syntactically a three-way disjunction involving the null marker ∅. This analysis would then reduce the syntactic distribution of soreka to that of ∅, explaining the fact that they share the distributional property. In the following, I will treat ka-disjunctions with soreka as a sub-case of ka-disjunctions with the null coordinator.

3 An analysis in two-tier alternative semantics

Our proposal employs two-tier alternative semantics (Rooth 1985) for in-situ wh-questions (Beck 2006; Kotek 2014). The gist of the analysis is the following: ka introduces a set of alternatives in its ordinary-semantic value, but only specific predicates—which I will call set-compatible predicates—semantically combine with such a set. Set-compatible predicates include predicates embedding interrogative CPs, such as oshier ‘tell’, and the disjunctive coordinators ∅ and soretomo. As a result, a semantic composition of a ka-phrase and a set-incompatible predicate requires that the set denoted by the former be “flattened” into an existential meaning. This is what happens when ka is introduced below CPs. A predicate or operator embedding a ka-phrase below the CP level are always set-incompatible except for the disjunctive coordinators. Thus, when ka-phrases are smaller than CPs, they are “trapped” inside a set-incompatible predicate and receive an existential meaning. Formally, the flattening effect is implemented with a cross-categorial existential closure ∃.

3.1 wh+ka

Below, I illustrate this system using a simple fragment that captures the basic data discussed in the previous section. First, let us consider the case of the wh+ka construction, repeated below.

    1. (5)
    1. a.
    1. [DP
    2.  
    1. dare-ka]-ga
    2. who-KA-NOM
    1. hashitta.
    2. ran.
    1. ‘Taro saw someone.’                   (∃-statement)
    1.  
    1. b.
    1. [CP
    2.  
    1. dare-ga
    2. who-NOM
    1. hashitta-ka].
    2. ran-KA
    1. ‘(Tell me) who ran?’                   (Wh-Question)

In the two-tier alternative-semantic analysis of in-situ wh-questions developed by Beck (2006) and Kotek (2014), lexical items have ordinary and alternative-semantic values (hereafter o-values and alt-values). For instance, the semantic values of ka, dare ‘who’ and hashitta ‘ran’ look like the following:

(29) a. α ka⟧o = ⟦αalt
  b. α ka⟧alt = {⟦αalt}

(30) a. ⟦dare⟧o = undefined
  b. ⟦dare⟧alt = {x | xhuman}

(31) a. ⟦hashitta⟧o = λxe λws.ran(x,w)
  b. ⟦hashitta⟧alt = {λxe λws.ran(x,w)}

Here, ka is defined as an operator that simply “copies” the alt-value of its prejacent to the o-value. A wh-item like dare has an undefined o-value while it introduces a set of alternatives in the alt-value.5 A set-incompatible predicate like hashitta has a standard denotation as a function from individuals to truth values in the o-value while its alt-value is the singleton set consisting of the o-value.

Except for ka, which has a syncategorematic definition, semantic values are composed according to either one of the following two rules, depending on whether it is an o-value or an alt-value:

(32) a. Functional Application (FA)
    If the node α has {β,γ} as the set of its daughters and ⟦βoDσ and ⟦γoD⟨σ,τ⟩, then ⟦αo is defined only if both ⟦αo and ⟦βo are. In this case, ⟦αo = ⟦γo (⟦βo).
  b. Point-wise Functional Application (PWFA) (Hamblin 1973)
    If the node α has {β,γ} as the set of its daughters and ⟦βaltDσ and ⟦γaltDσ,τ, then ⟦αalt = {a | ∃f ∈ ⟦γaltb ∈ ⟦βalt [a = f(b)]}.

3.1.1 Wh-questions

Given this setup adopted from Beck (2006) and Kotek (2014),6 we can already account for the interpretation of the wh-question in (5b). Below is a simplified LF tree for (5b) with annotation of the two kinds of semantic values for each node. The notation ⟨a,b⟩ indicates that the node’s o-value is a while its alt-value is b.

    1. (33)

What is crucial above is that the alternatives introduced by dare is passed up via an application of PWFA in the alternative-semantic dimension, until the top-level ka returns it as the o-value (Beck 2006). As a result, the sentence receives the standard proposition-set denotation for wh-questions (Hamblin 1973; Karttunen 1977) as its o-value.

3.1.2 Excursion: Yes/No-questions and the semantics of complementizers

It is important to note at this point that ka defined in (29) is also the one that appears as the sentence-final particle in Yes/No-questions (YNQs), as exemplified below.

    1. (34)
    1. Hanako-ga
    2. Hanako-NOM
    1. hashitta-ka?
    2. ran-KA
    1. ‘Did Hanako come?’

The analysis predicts the following o-value for the YNQ in (34) above.

(35) ⟦(34)⟧o = {λw.ran(h,w)}

The singleton-set denotation for YNQs as exemplified above is different from the more standard bipolar denotation (Hamblin 1973; Karttunen 1977), which would be the following two-membered set in the case of (34).

(36) w.ran(h,w), λwran(h,w)}

Versions of the singleton analysis of the semantics of YNQs are maintained by authors such as Roberts (1996/2012); Abels (2006); Pruitt & Roelofsen (2011); Biezma & Rawlins (2012); Roelofsen & Farkas (2015), and its empirical motivations come from biased polar questions, the interpretation of response particles and the selectional property of dubitative predicates, among others. In many of these analyses, the singleton denotation is mapped to the corresponding bipolar denotation by an extra operation in order to capture the fact that polar questions license negative responses. In this paper, I formulate the mapping using the following type-shifting operator, similar to the polar-question operator in Hamblin (1973: 50) and the non-informative closure in Ciardelli et al. (2015).

(37) ?o := λQ{p}.Q⋃ {¬∪Q} (Hamblin 1973: 50)

(38) ?o (⟦(34)⟧o) = {λw.ran(h,w), λwran(h,w)}

An issue that comes with positing an operator like (37) is that its application has to be somehow constrained to avoid unwanted consequences of its application to wh-questions. For example, when (37) is applied to the o-value of the wh-question dono gakusei-ga hashitta-ka ‘Which student ran?’, we get the following denotation:

(39) ?o ({λws.ran(x,w) | xstudent})
  = {λws.ran(x,w) | xhuman} ⋃ {λws.¬∃x[xstudentran(x,ws)]}

This is problematic since, empirically, ‘No student ran’ is not a possible response to the question. In fact, the intuition is that the question presupposes that some student ran (see §4.1 for the analysis of the existential presupposition in wh-questions). Thus, we need a way to constrain the application of (37) so that it does not apply to wh-questions.

As a solution to this problem, I argue that the application of the type-shifting operation in (37) is possible only in cases where the LF without the operator would result in uninterpretability. That is, I posit the following constraint:

(40) Application of ? as a repair strategy
  Let φ be an LF containing ? and φ′ be an LF just like φ except that it does not contain ?. Then, φ is licensed only if φ′ is uninterpretable.

This account assumes that a ka-ending non-wh clause without the ?-operator is uninterpretable while a ka-ending wh-clause without the the ?-operator is interpretable. If we mark uninterpretability with #, the situation can be exemplified below:

    1. (41)
    1. Interpretability without ?
      1. a.
      1. #Hanako-ga
      2.   Hanako-NOM
      1. hashitta-ka.
      2. ran-KA
      1. b.
      1. ✓Dare-ga
      2.     who-NOM
      1. hashitta-ka.
      2. ran-KA

Why, then, is there such a contrast between polar questions and wh-questions? Intuitively, it is because (41a) without the ?-operator would denote a “defective” question with only a single possible answer while (41b) without the ?-operator would denote a non-defective question with multiple answers. The requirement for multiple alternatives in an interrogative clause is implemented in the denotation of the interrogative complementizer as a presupposition, as in (42):

(42) ⟦Cinto = λQ{p} : |Q| > 1.Q (cf. Biezma & Rawlins 2012: 392)

Given that the interrogative complementizer requires multiple alternatives, (41a) without the ?-operator would necessarily result in a presupposition failure. This situation is avoided by the insertion of the ?-operator. On the other hand, (41b) without the ?-operator already satisfies the presupposition encoded by (42).78

A ka-ending non-wh-clause is uninterpretable also as a declarative clause since the declarative complementizer selects for a proposition, as given below:

(43) ⟦Cdeclo = λpp.p

Since type-mismatch results in uninterpretability, (41a) without ? would be uninterpretable even as a declarative clause.

It is worth noting at this point that the type-shifter ∃ to be introduced in the next section would not cause a problem for this account. The type-shifter would convert a singleton set of a proposition into the unique proposition in the singleton set. Although it might appear that the presence of this type-shifter would make a ka-ending non-wh-clause compatible with Cdecl in the structure exemplified in (44a), such a structure would be blocked by a simple declarative clause without ka, as in (44b), which would have an equivalent interpretation.9

(44) a. [ [ [ Hanako-ga hashitta-ka] ∃ ] Cdecl ].
  b. [ [ Hanako-ga hashitta] Cdecl ].

3.1.3 Indefinites

Let us now turn to how we derive the existential statement in (5a). The first thing to note is that, without any additional mechanisms, the semantic composition does not go through due to type-mismatch. This is so since neither FA nor PWFA can combine the semantic values of hashitta with the semantic values of dare-ka. This can be seen in the following uninterpretable LF tree.

    1. (45)

Here, the operation of existential closure that I mentioned above comes into play. Specifically, I propose that there is a following operator that turns a set in the o-value dimension into the corresponding existential quantifier.10

(46) a. ⟦∃⟧o = λQ{σ}.    
    • λws.∃pQ[p(w)] if σ = p (p := ⟨s,t⟩)
    • λPσ,pλws.∃xQ[P(x)(w)] otherwise  
  b. ⟦∃⟧alt = {⟦∃⟧o}  
  c. σ is any type, and {σ} is the type for the set of σ-type objects. I assume a formal distinction between sets and characteristic functions. Thus, {σ} is a distinct type from ⟨σ,t⟩.11

This operator can be applied to dare-ka in (45). As a result, we derive the existential statement as in the following LF:

    1. (47)

Thus, we can capture the fact that (5a) is an existential statement rather than a wh-question. The only way in which the semantic composition of dare-ka ‘who-KA’ and hashitta ‘ran’ goes through is to turn the the o-value of the former into an existential quantifier by ∃. The same mechanism applies to other cases where a set-incompatible predicate combines with a ka-phrase.12

Note, however, that the introduction of ∃ creates a potential problem. The wh-question interpretation of (5b) itself could now be turned into an existential statement if ∃ is freely available and applied to the whole sentence. This problem can be straightforwardly solved once we assume that the constraint on the application of ? posited in (40) above also applies to ∃. The assumption is that the application of ∃ is subject to the following slightly generalized version of (40):

(48) Application of ? and ∃ as a repair strategy
  Let O be a type-shifting operator ? or ∃. Also, let φ be an LF containing O and φ′ be an LF just like φ except that it does not contain O. Then, φ is licensed only if φ′ is uninterpretable.

This generalized version of the constraint on type-shift prohibits the application of ∃ to the whole sentence of (5b). Since the LF (33) of (5b) does not involve any type-mismatch and is interpretable, unlike the uninterpretable (45), the application of ∃ is disallowed. Hence, the sentence lacks an interpretation as the existential statement.

This analysis also extends to cases where (5b) is embedded under question-embedding predicates since there would be no type-mismatch between question-embedding predicates and (5b). I analyze all question-embedding predicates as a set-compatible predicate, i.e., as selecting for a set of propositions, both in the o-value and in the alt-value. For instance, the semantic values of oshier(u) ‘tell/teach’ look like the following:

(49) a. ⟦oshier⟧o = λQ{p} λxλw.tell(x,Q,w)
  b. ⟦oshier⟧alt = {λQ{p} λxλw.tell(x,Q,w)}

Thus, the set of propositions in the o-value and the alt-value of an interrogative CP can be combined with the question-embedding predicate via FA and PWFA. Hence, there is no type-mismatch and the existential closure by ∃ does not occur. I claim that there is no set-compatible predicate in Japanese other than interrogative-CP-embedding predicates like (49), disjunctive coordinators such as soretomo (which I will discuss in detail below) and ∃ itself.13 Thus, any case in which a ka-phrase combines with items other than these operators at LF involves existential closure.

Thus, the constraint in (48) seems to account for the lack of existential interpretation for ka-ending wh-clauses in both matrix and embedded contexts. However, it does not account for the behavior of ka-ending wh-clauses when they are embedded under proposition-embedding predicates, such as shinjiteiru ‘believe’ or mitai ‘seem’. Empirically, ka-ending wh-clauses are ungrammatical under these predicates, as exemplified below:

    1. (50)
    1. a.
    1. *Hanako-wa
    2.   Hanako-TOP
    1. [
    2.  
    1. dare-ga
    2. who-NOM
    1. hashitta-ka
    2. ran-KA
    1. (da) -to
    2. COP Cdecl
    1. ]
    2.  
    1. shinjiteiru.
    2. believe
    1.     Intended: ‘Hanako believes that someone ran.’
    1.  
    1. b.
    1. *[
    2.  
    1. dare-ga
    2. who-NOM
    1. hashitta-ka ]
    2. ran-KA
    1. mitai
    2. seem
    1. da.
    2. COP
    1.     Intended: ‘It seems that someone ran.’

This is unexpected in the account described above since (48) predicts that ∃ would be allowed in (50), which would otherwise involve a type-mismatch between the proposition-embedding (set-incompatible) predicates and the set of propositions denoted by the complements. Therefore, the constraint in (48) cannot account for all of the relevant data. In §4 below, I will revisit this problem and propose an account of the ungrammaticality of examples in (50), based on the analysis of presuppositions inherent in the wh+ka construction, whether it is clausal or not.

Summing up the section, the system can be described in the following way. One can conceive of the o-value dimension as the “foreground” and the alt-value dimension as the “background”. A wh-word like dare introduces a set of alternatives in the background. As long as these alternatives are kept in the background, they can be semantically combined with alt-values of other constituents via PWFA. The job of ka is to bring the alternatives in the background into the foreground. Once this is done, the situation differs depending on whether the constituent combining with the ka-phrase (if there is any) is compatible with a set or not. If it is, or if the ka-phrase is the matrix CP, there is no existential closure. Otherwise, the set of alternatives would have to be flattened into an existential meaning.

This system captures the fact that the position of ka conditions the interpretation of a wh+ka construction that we saw in the previous section. When the ka-phrase together with Cint form a whole CP, it would receive the interpretation as a set of propositions, i.e., a question, whether or not it is embedded by a question-embedding predicate. For, there would be no type-mismatch in the semantic composition. On the other hand, when the ka-phrase forms a DP, the set of alternatives it denotes in the o-value cannot participate in the semantic composition unless it is flattened into a non-set. For, as I claimed above, there is no set-compatible predicate that can syntactically combine with a DP.

3.2 ka-disjunctions

In this section, I will argue that the generalization about the effect of the position of ka on the interpretation of ka-disjunctions can be captured as a natural extension of the system outlined above, once we take into account an appropriate syntax for disjunctions. Following the structure of complex coordinations adopted in the literature on the cross-linguistic syntax and semantics of coordinations (den Dikken 2006; Slade 2011; Mitrovič & Sauerland 2014; Szabolcsi 2015b) I assume that ka-disjunctions involve a Junction head (hereafter J) with ka-phrases both in its internal argument position and in the specifier. The structure is schematized as follows:

    1. (51)

The disjunctive J head is realized either as matawa or soretomo, or is phonologically null. In the following, I will define a uniform semantics for the J head, based on the behavior of the phonologically null coordinator. In the next section, we will extend the treatment to phonologically explicit coordinators by adding assumptions about their syntactic features. I treat the coordinator head J as denoting the set-union operation in the o-value, as given in (52a) below, while its alt-value is defined in terms of generalized disjunction (Partee & Rooth 1983).

(52) a. ⟦J⟧o = λX{σ}λY{σ}.XY
  b. ⟦J⟧alt = {λX{σ}λY{σ}.{ιXιY}}14
  c. ιX is defined only if X is a singleton set. If defined, ιX is the unique member of X.
  d. XY =
      • XY         if X and Y are of type t
      • λZσ.X(Z) ∨ Y(Z) if X and Y are of type ⟨σ,t

As concrete examples, we have the following semantic derivations of two ka-disjunctions: the DP disjunction Hanako-ka Jiro-ka and the clausal disjunction Hanako-ga hashitta-ka Jiro-ga hashitta-ka. As one can see from the following LFs, the analysis derives two-membered sets consisting of (the o-values of) its disjuncts (i.e., α and β in the schema in (51)) as the semantic values of a ka-disjunction as a whole.15

    1. (53)
    1. a.
    1.  
    1. b.

We have now already accounted for the AltQ interpretation for clausal ka-disjunctions. As can be seen in (53b), a clausal ka-disjunction receives as its o-value a set of two propositions, each contributed by the clausal disjuncts. This is precisely the standard semantic denotation for AltQs (Karttunen 1977; Biezma & Rawlins 2012).16 In other words, the AltQ interpretation is analyzed as the union of the singleton interpretations of the question nucleus of two YNQs (Uegaki 2014). Similar analyses of AltQs are maintained by Pruitt & Roelofsen (2011) for English, Gračanin-Yuksek (2016) for Turkish and Mayr & Zuchewicz (2015) for Polish.

Furthermore, given the mechanism of semantic composition and the repair of the type-mismatch in terms of ∃, described in the previous section, we can also account for the fact that ka-disjunctions syntactically smaller than the complement of C17 end up receiving an existential/declarative disjunctive interpretation. The explanation is exactly parallel to that of the existential interpretation of wh+ka. The gist is the following: when a ka-disjunction is smaller than the complement of C, it has to be semantically combined with a sub-CP predicate/operator. Given the assumption that any such sub-CP operator (other than the J head and ∃) is set-incompatible, the o-value of a ka-disjunction cannot be directly combined with them. It would result in a type-mismatch.

For example, when the DP-disjunction in (53a) appears in a sentence such as the following repeated from the previous section, ∃ repairs the type-mismatch between the disjunction and the verb hashitta.

    1. (11)
    1. [DP
    2.  
    1. Hanako-ka
    2. Hanako-KA
    1. Jiro-ka]-ga
    2. Jiro-KA-NOM
    1. hashitta.
    2. ran
    1. ‘Either Hanako or Jiro ran.’

Below is the LF structure of this example illustrating how the existential/disjunctive interpretation is derived:

    1. (54)

Finally, it is also a natural consequence of the current system that when ka attaches to a sentence containing a sub-clausal ka-disjunction, it receives an interpretation as a YNQ embedding a declarative disjunction, not as an AltQ. This is the case in the following examples again repeated from the data section.

    1. (15)
    1. [[DP
    2.  
    1. Hanako-ka
    2. Hanako-KA
    1. Jiro-ka]-ga
    2. Jiro-KA-NOM
    1. hashitta-ka]
    2. ran-KA
    1. (oshiete).
    2. tell
    1. ‘Tell me whether or not Hanako ran or Jiro ran.’                   (✓YNQ)
    2. *‘Tell me which is true: Hanako ran or Jiro ran.’                     (*AltQ)
    1. (16)
    1. [[TP
    2.  
    1. [Hanako-ga
    2. Hanako-NOM
    1. hashitta-ka]
    2. ran-KA
    1. [Jiro-ga
    2.  Jiro-NOM
    1. hashitta-ka]]
    2. ran-KA
    1. mitai-ka]
    2. seem-KA
    1. (oshiete).
    2. tell
    1. ‘Tell me whether or not it seems to be that Hanako or Jiro ran.’                (✓YNQ)
    2. *‘Tell me which is true: Taro saw Hanako or he saw Jiro.’                       (*AltQ)

In these examples, ka operates on the disjunctive statement derived in the above LF (54). Since ka is defined as returning the alt-value of its prejacent, the analysis predicts the following semantic value for (15).

(55) ⟦(15)⟧o = {λw.ran(j,w) ∨ ran(h,w)}

Thus, the analysis predicts that (15–16) denote a singleton set consisting of a proposition. These denotations are mapped to bipolar denotations of polar questions by the ?-operator, defined in (37).

4 Existential closure at the clausal level?

As discussed in previous sections, one of the predictions of the analysis developed so far is that clauses ending with ka would receive an existential meaning under proposition-embedding predicates, as the existential closure would kick in to rescue the type-mismatch. In fact, this is not what we see empirically. Clauses ending with ka are ungrammatical under proposition-embedding predicates like shinjiru ‘believe’ and mitai ‘seem’, as previewed in §3.1.3. In this section, I will detail the data of ka-ending clauses embedded under proposition-embedding predicates, and offer an explanation of the pattern based on a presuppositional behavior of ka-ending constituents.

The analysis presented up to this point has problems with the following examples, where clauses (specifically CPs and TPs) ending with ka are embedded under the proposition-taking predicate shinjiru ‘believe’ and mitai ‘seem’. The sentences are ungrammatical although the analysis predicts an existential interpretation of the complements.18

    1. (56)
    1. a.
    1. *Hanako-wa
    2.  Hanako-TOP
    1. [
    2.  
    1. dare-ga
    2. who-NOM
    1. hashitta-ka
    2. ran-KA
    1. (da)
    2. COP
    1. -to/∅
    2. Cdecl/Cint
    1. ]
    2.  
    1. shinjiteiru.
    2. believe
    1. Intended: ‘Hanako believes that someone ran.’
    1.  
    1. b.
    1. *[
    2.  
    1. dare-ga
    2. who-NOM
    1. hashitta-ka ]
    2. ran-KA
    1. mitai
    2. seem
    1. da.
    2. COP
    1. Intended: ‘It seems that someone ran.’

What makes the problem puzzling is the fact that the following sentence is grammatical with the same existential interpretation as predicted for (56).

    1. (57)
    1. a.
    1. Hanako-wa
    2. Hanako-TOP
    1. [
    2.  
    1. dare-ka-ga
    2. who-KA-NOM
    1. hashitta-to
    2. ran-Cdecl
    1. ]
    2.  
    1. shinjiteiru.
    2. believe
    1. ‘Hanako believes that someone ran.’
    1.  
    1. b.
    1. [
    2.  
    1. dare-ka-ga
    2. who-KA-NOM
    1. hashitta
    2. ran
    1. ]
    2.  
    1. mitai
    2. seem
    1. da.
    2. COP
    1. ‘It seems that someone ran.’

The only difference would be when the existential closure is applied. In (57a), it is at the DP level while in (56a), it is at the CP/TP level.

A possible solution to this issue can be given by invoking the notion of economy, as suggested by Takahashi (2002) and pursued in an earlier version of this paper (Uegaki 2016). Takahashi (2002) argues that particles ka and mo are base-generated in the sister position of a wh-word and undergo head-movement to the surface position, which also determines their scope position. Crucially, according to Takahashi, this movement is constrained by scope economy (Fox 2000). That is, the movement of ka/mo is allowed only if it results in an interpretation that differs from what is predicted by the particles’ original position. If we follow this story, the ungrammaticality of (56) can be accounted for. The sentences in (56) are analyzed as being derived from (57), but the movement of ka in (56) violates the scope economy since the sentences would have the same interpretations as (57).

Although our account is not based on the overt movement of ka, the economy-based explanation can be adapted to it, along the following lines: (a) the lowest position is the default position for ka; (b) ka cannot be placed in a non-default position unless it leads to a distinct interpretation from what is predicted by its default position. Uegaki (2016) implements this idea employing the notion of blocking (e.g., Aronoff 1976; Atlas & Levinson 1981; Horn 1984).

This economy-based analysis however faces an empirical problem. It predicts that a ka-ending clause can be embedded by a proposition-embedding operator, such as shinjiteiru ‘believe’, if there is an intervening operator between the wh-word and the proposition-embedding operator, so that there would be a difference between the interpretations resulting from the two positions of ka. This prediction is not borne out, as shown in the following:

    1. (58)
    1. a.
    1. Hanako-wa
    2. Hanako-TOP
    1. [
    2.  
    1. dare-ka-ga
    2. who-KA-NOM
    1. hashira-nakerebanaranai-to ]
    2. run-mustdeon-Cdecl
    1. shinjiteiru.
    2. believe
    1. ‘Hanako believes that someone must run.’
    1.  
    1. b.
    1. *Hanako-wa
    2.  Hanako-TOP
    1. [
    2.  
    1. dare-ga
    2. who-NOM
    1. hashira-nakerebanaranai-ka
    2. ran-mustdeon-KA
    1. (da) -to/∅]
    2. COP Cdecl/Cint
    1. shinjiteiru.
    2. believe
    1. Intended: ‘Hanako believes that there is someone who must run.’

In these sentences, the deontic necessity modal nakerebanaranai intervenes between the wh-word and the proposition-embedding predicate shinjiteiru ‘believe’. The economy-based account thus predicts that (58b) would be grammatical as it would lead an interpretation where the existential closure takes scope over the modal, which is distinct from the interpretation of (58a). Despite this prediction, (58b) is ungrammatical.

I take this to be a strong argument against the economy-based account of the unacceptability of ka-ending clauses embedded by proposition-embedding operators. Below, I propose an alternative solution to this issue.

4.1 An account based on the existential presupposition

The key to the solution of the problem described above lies in the existential presupposition of wh+ka constructions, which can be observed whether it is clausal or clause-internal. The gist of the solution is the following. A wh+ka clause presupposes that there exists a true proposition in the set of proposition that ka projects. When the existential closure ∃ is applied to such a clause, we end up with a meaning that asserts exactly what is presupposed, i.e., that there exists a true proposition in the set of alternatives. This systematic triviality leads to ungrammaticality (Gajewski 2002). Below, I empirically demonstrate the presence of the existential presupposition in wh+ka constructions, and provide a formal implementation of it. The solution to the problem of existential closure at the clausal level will then be illustrated using the formal implementation of the presupposition.

A number of authors, including Karttunen & Peters (1979); Comorovski (1989) and Dayal (1996), have argued that English wh-questions presuppose existence of a true answer in their Hamblin denotation, as exemplified in the following:

(59) a. Who ran? (presupposes) Someone ran.
  b. Which student ran? (presupposes) Some student ran.

The same judgment holds for Japanese wh-questions:

    1. (60)
    1. a.
    1. Dare-ga
    2. who-NOM
    1. hashitta-no-desu-ka?
    2. ran-NMNL-POL-KA?
    1. ‘Who ran?’          ⇒   (presupposes)   Someone ran.
    1.  
    1. b.
    1. Dono
    2. which
    1. gakusei-ga
    2. student-NOM
    1. hashitta-no-desu-ka?
    2. ran-NMNL-POL-KA?
    1. ‘Which student ran?’      ⇒    (presupposes) Some student ran.

In the current setup, there are at least two ways to analyze the source of this presupposition in the Japanese case. One is to associate it with the interrogative complementizer, Cint (see §3.1.3), and the other is to associate it with wh+ka-constructions in general, whether it is a question or not.

The presuppositional behavior of wh+ka indefinites suggests that the existential presupposition is a phenomenon general to wh+ka constructions, and thus the latter approach is more suitable. The existential presupposition of wh+ka indefinites can be observed in the following examples, where the presence of a wh+ka indefinite in a conditional antecedent or a polar question leads to infelicity if the context allows the domain of the indefinites to be empty.

    1. (61)
    1. Context: One of Taro’s books is missing. It is not known by the interlocutors whether Taro misplaced it himself or someone stole it.
    1.  
    1. a.
    1. #Dono-hannin-ka-o
    2.  which-culprit-KA-ACC
    1. mitsuke-tara
    2. find-if
    1. oshiete
    2. tell
    1. kudasai.
    2. POL
    1. ‘If you find a culprit, please tell us.’ (Intended)
    1.  
    1. b.
    1. #Dono-hannin-ka-ga
    2.  which-culprit-KA-NOM
    1. gakusei-no
    2. students-GEN
    1. naka-ni
    2. among-LOC
    1. i-masu-ka?
    2. be-POL-KA
    1. ‘Is there a culprit among the students?’ (Intended)
    1. (62)
    1. Context: the same as (61).
    1.  
    1. a.
    1. #[
    2.  
    1. Sono
    2. the
    1. hon-o
    2. book-ACC
    1. nusunda ]
    2. steal
    1. dare-ka-o
    2. who-KA-ACC
    1. mitsuke-tara
    2. find-if
    1. oshiete
    2. tell
    1. kudasai.
    2. POL
    1. ‘If you find a person who stole the book, please tell us.’ (Intended)
    1.  
    1. b.
    1. #[
    2.  
    1. Sono
    2. the
    1. hon-o
    2. book-ACC
    1. nusunda ]
    2. steal
    1. dare-ka-ga
    2. who-KA-NOM
    1. gakusei-no
    2. students-GEN
    1. naka-ni
    2. among-LOC
    1. i-masu-ka?
    2. be-POL-KA
    1. ‘Is there anyone who stole the book among the students?’ (Intended)

The above Japanese examples are infelicitous in the given context, unlike the English translations. This indicates that existence of a culprit who stole the book is presupposed by the sentences. This fact suggests that the wh+ka indefinites presuppose existence of an individual in the relevant domain.

The existential presupposition of wh+ka constructions in general can be analyzed as resulting from a semantic contribution of ka. Roughly speaking, it presupposes that the alt-value of its prejacent has a non-empty extension. This can be formally implemented in the following revised entry for ka:19

(63) a. α ka⟧o
    ={λw: [∃a′ ∈ ⟦αalt[a′(w) is defined ∧ a′(w) ≠ 0]].a(w)| a ∈ ⟦αalt}
  b. α ka⟧alt = {⟦αalt}

The existential presupposition of ka is implemented as partiality of each proposition in the o-value of α-ka. Below, I illustrate how this analysis of ka interacts with other elements in the semantic composition. We first look at the case where the prejacent of ka is clausal, and then move on to the case where the prejacent is non-clausal.

In the case where the prejacent of ka is clausal, ⟦α-kao effectively presupposes that some of the propositions in ⟦αalt is true. Suppose that the alt-value of the wh-clause dare-ga hashitta ‘who ran’ is {p1,p2,…,pn}. Then, we have the following o-value for dare-ga hashitta-ka:

(64) ⟦dare-ga hashitta ka⟧o
  = {λw: [∃p′ ∈ {p1, p2,…, pn} [p′(w) is defined ∧ p′(w) ≠ 0]].p(w)
                                                                              | p ∈ {p1, p2,…,pn}}

All propositions in this denotation have the same presupposition: that at least one of {p1,p2,…,pn} is true. Thus, at an evaluation world w, the possible answers to this question have truth values only if the presupposition is satisfied in w, i.e., that at least one of {p1,p2,…,pn} is true in w. This is how the existential presupposition of a wh+ka question described above is captured.

Crucially, we derive a trivial statement if we apply the existential closure ∃ to (64). The definition of ∃ is repeated below:

(46) a. ⟦∃⟧o = λQ{σ}.    
          • λws.∃pQ[p(w)] if σ = p
          • λPσ,pλws.∃xQ[P(x)(w)] otherwise
  b. ⟦∃⟧alt = {⟦∃⟧o}

In (65) below, we see the result of applying (46a) to (64). As one can see, the presupposition of the resulting proposition is equivalent to its assertive content, assuming existential presupposition projection out of a existential quantification/disjunction (Beaver 2001; Chemla 2009).20 This means that the proposition in (65) is true whenever its presupposition is satisfied.

(65) ⟦[dare-ga hashitta ka] ∃⟧o
  = λw.∃p
  w′: [∃p′ ∈ {p1, p2,…, pn}[p′(w′) =1]]. p(w′)| p ∈ {p1, p2,…, pn}} [p(w)]
  ≡ λw.(    [λw′ : [p1(w′) ∨ p2(w′) ∨…∨ pn(w′)].p1(w′)](w)
          ∨ [λw′ : [p1(w′) ∨ p2(w′) ∨…∨ pn(w′)].p2(w′)](w)
          ∨…
          ∨ [λw′ : [p1(w′) ∨ p2(w′) ∨…∨ pn(w′)].pn(w′)](w))
  ≡ λw: [p1(w) ∨ p2(w) ∨…∨ pn(w)].p1(w) ∨ p2(w) ∨…∨ pn(w)
           (Given the existential presupposition projection out of disjunction)

Hence, applying the existential closure to a wh+ka clause results in a trivial statement that can only be true if it is defined at all. Following Barwise & Cooper (1981) and Gajewski (2002), I assume that systematic triviality arising from logical vocabulary results in ungrammaticality. This accounts for the ungrammaticality of wh+ka clauses under proposition-embedding predicates, as in (56) above. The type-mismatch between a set-incompatible predicate and a wh+ka clause forces existential closure to the embedded clause, but it would necessarily result in triviality, which in turn would lead to ungrammaticality.21

Next, let us look at the case where wh+ka is non-clausal, as in (61–62). As we will see, our presuppositional denotation for ka in (63) accounts for the existential presupposition, but the resulting sentential meaning involving the existential closure ∃ is non-trivial, unlike the clausal case. I will show this by compositionally deriving the denotation of the sentence dono hannin-ka-ga hashitta ‘which-culprit-KA ran’.

First, the alt-value of a wh-phrase with a restriction like dono hannin ‘which culprit’ is analyzed as a set of individual concepts that presuppose that the individual satisfies the restriction, as follows:22

(66) a. ⟦dono hannin⟧o = undefined
  b. ⟦dono hannin⟧alt = {λw: culprit(x)(w). x | xDe}

Applying the presuppositional version of ka to (66) gives us the following denotation in (67) as the o-value. The denotation is simplified, with the assumption that De = {d1, d2, …, dn}.23

(67) ⟦[dono hannin] ka⟧o =
  w: [∃c ∈ {λw′: culp(x)(w′). x | xDe}[c(w′) is def. ∧ c(w′)≠ 0]]. c′(w)
                                                        | c′ ∈ {λw″: culp(x′)(w″). x′| x′ ∈ De}}
  ≡{λw′: culp(d1)(w′). d1w′: culp(d2)(w′).d2,…,λw′: culp(dn)(w′). dn}

Applying the existential closure in (46) to this set of individual concepts gives us (68), which can then be applied to the revised denotation of the verb in (69) to derive the (partial) propositional denotation in (70).

(68) ⟦[[dono hannin] ka] ∃⟧o
  = λP⟨se,p⟩λw.(Pw′: culp(d1)(w′).d1)(w) ∨
                       Pw′: culp(d2)(w′).d2)(w) ∨
                       …∨
                       Pw′: culp(d3)(w′).d3)(w))

(69) ⟦hashitta⟧o = λcs,e λw.ran(c(w))(w)

(70) ⟦[[dono hannin] ka ∃] hashitta⟧o
  = λw.(ran([λw′: culp(d1)(w′).d1](w))(w) ∨
             ran([λw′: culp(d2)(w′).d2](w))(w) ∨
             …∨
             ran([λw′: culp(dn)(w′).dn](w))(w))

The resulting proposition in (70) is defined for w only if there is some culprit (of the relevant incident) in w (again assuming the existential presupposition projection), and asserts that at least one of the culprits in w ran. Thus, this analysis captures the existential presupposition for the non-clausal wh+ka observed above. Furthermore, unlike the clausal case, the resulting sentential meaning including the existential closure ∃ is non-trivial since the presupposition states the non-emptiness of the restriction (the set of culprits) while the assertion states the non-emptiness of the intersection of the restriction and the scope (the set of culprits who ran). This captures the grammaticality of non-clausal wh+ka.

4.2 ka-disjunction under proposition-taking predicates

The account for the ungrammaticality of ka-ending clauses under proposition-embedding predicates discussed above also applies to ka-disjunctions. For example, the ungrammaticality of (71) is accounted for as the result of the triviality arising from the combination of the existential presupposition of the wh+ka clauses and the existential closure.

    1. (71)
    1. *Taro-wa
    2.   Taro-TOP
    1. [Hanako-ga
    2. Hanako-NOM
    1. hashitta-ka
    2. ran-KA
    1. or
    1. Jiro-ga
    2. Jiro-NOM
    1. hashitta-ka
    2. ran-KA
    1. Cint ∃]
    2.  
    1. shinjiteiru.
    2. believe
    1. Intended: ‘Taro believes that either Hanako ran or Jiro ran.’

Given the presuppositional denotation of ka in (63), the o-value of the embedded alternative question in (71) would look like the following:

(72) ⟦[Hanako-ga hashitta-ka ∅ Jiro-ga hashitta-ka] Cinto
  ={λw : ran(h)(w).ran(h)(w), λw : ran(j)(w).ran(j)(w)}

Applying the existential closure to (72) results in the following proposition, again, assuming the existential presupposition projection.

(73) ⟦[Hanako-ga hashitta-ka ∅ Jiro-ga hashitta-ka] Cint ∃⟧o
  = λw : [ran(h)(w) ∨ ran(j)(w)].
  p ∈ {λw : ran(h)(w′).ran(h)(w′), λw : ran(j)(w′).ran(j)(w′)}[p(w)]

Just as in the wh+ka case, this proposition is true whenever its presupposition is met. Thus, we have systematic logical triviality leading to ungrammaticality.24

On the other hand, when the existential closure is applied at the non-clausal level, we get a non-trivial meaning, as exemplified in the following.25

(74) a. ⟦[Hanako-ka ∅ Jiro-ka]⟧o = {λw′.h, λw′.j}
  b. ⟦[Hanako-ka ∅ Jiro-ka] ∃⟧o = λPse,stλw.[Pw′.h)(w) ∨ Pw′.j)(w)]
  c. ⟦[[Hanako-ka ∅ Jiro-ka] ∃] hashitta⟧o = λw.[ran(h)(w) ∨ ran(j)(w)]

Thus, the parallelism between wh+ka and ka-disjunctions manifests itself here as well.

4.3 Accounting for the behavior of coordinators

In §2.4 above, I introduced phonologically explicit disjunctive coordinators that can appear between ka-phrases. In particular, I discussed the restricted distributions of matawa and soretomo. Below is the summary of the behaviors of these two coordinators.

(75) a. matawa appears in sub-clausal ka-disjunctions. It also appears in clausal ka-disjunctions when embedded under the copula da. A ka-disjunction with matawa is always interpreted as a declarative disjunction.
  b. soretomo appears only in clausal ka-disjunctions. A ka-disjunction with soretomo is always interpreted as an AltQ.

We now have necessary ingredients to account for these different behaviors of coordinators, except for the case involving the copula da. Given the current analysis, they can be accounted for as consequences of different syntactic features of these operators while they share the semantics of the J-head introduced in the previous section, i.e., (52) repeated below.

(52) a. ⟦J⟧o = λX{σ}λY{σ}.X⋃Y
  b. ⟦J⟧alt = {λX{σ} λY{σ}.{ιXιY}}

Specifically, I will treat matawa as requiring an agreement with the declarative complementizer Cdecl while soretomo as requiring an agreement with the interrogative complementizer Cint.26 What is also crucial in the account is the semantic denotations of the declarative and interrogative complementizers, repeated below from Section 3.1.2:

(76) a. ⟦Cdeclo = λpp.p
  b. ⟦Cinto = λQ{p}: |Q| > 1.Q

In the following, I will illustrate how these assumptions lead to an account of the behaviors of the coordinators summarized in (75).

First, the fact that soretomo can only appear in clausal ka-disjunctions follows from the requirement that it has to agree with Cint. Since Cint selects for a set of propositions in the o-value, a clause involving a ka-disjunction with soretomo has to denote a set of proposition. Given the mechanism of existential closure introduced in the previous section, this can only happen when the ka-disjunction is clausal. Also, it is a natural consequence of this that a ka-disjunction with soretomo denotes an AltQ.27

If we set aside the copula da for now, the fact that matawa only appears in sub-clausal ka-disjunctions is also expected from the agreement requirement. The agreement ensures that a ka-disjunction with matawa is in a CP headed by Cdecl, which requires its complement to denote a proposition. This requirement is satisfied by an application of ∃ to the set of alternatives denoted by the ka-disjunction. If the disjunction has a sub-clausal size, then ∃ is applied before it is combined with a set-incompatible predicate. If the disjunction is clausal, then ∃ has to be applied at the clausal level before it is combined with Cdecl. However, the latter is impossible due to the reasons described in the previous subsections. Therefore, the fact that the interpretation of a ka-disjunction with matawa is always that of declarative disjunction follows from the need for the existential closure.

As for the phonologically null coordinator ∅, I will treat it as having an underspecified agreement specification. Thus, it can appear in CPs headed by Cdecl or Cint. In the former case, an existential closure is required somewhere in the sub-clausal domain, and this leads to a declarative disjunction interpretation. The latter case leads to an AltQ interpretation with clausal disjunction.

As discussed in §2.4, the empirical pattern is in fact more involved if we look closely at the case where the copula da is present in the sentence-final position. For example, we find cases where a clausal ka-disjunction with matawa functions as a declarative disjunction when there is a sentence-final copula da:

    1. (77)
    1. Hanako-ga
    2. Hanako-NOM
    1. hashitta-ka
    2. ran-KA
    1. matawa
    2. or
    1. Jiro-ga
    2. Jiro-NOM
    1. hashitta-ka
    2. ran-KA
    1. *(da).
    2.     COP
    1. ‘Hanako ran or Jiro ran.’

The particular behavior of da in (77) can be accounted for if da involves a presupposition accommodation operator (Beaver & Krahmer 2001), as in the following:

(78) After Beaver & Krahmer (2001)
  ⟦da⟧o = λpp. (p)
  where (p) : = λws.1 iff p(w) is defined ∧ p(w) = 1

Given the accommodation of the presupposition, the triviality predicted by the application of ∃ to the clause embedded by da in (77) is obviated, and the interpretation of the sentence comes out as a simple disjunctive statement:

(79) ⟦da⟧o (⟦Hanako-ga hashitta-ka matawa Jiro-ga hashitta-ka ∃⟧o)
  = λw.ran(h)(w) ∨ ran(j)(w)

Nevertheless, this account does not explain why a ka-ending wh-clause with da at the end of the sentence is ungrammatical as an existential statement.28

    1. (80)
    1. *Dare-ga
    2.   who-NOM
    1. hashitta-ka
    2. ran-KA
    1. da.
    2. COP
    1. ‘Someone ran.’ (Intended)

Thus, the cases involving the copula da remains to be a puzzle, and addressing this puzzle will probably require a more thorough investigation of the semantics of da in contexts other than wh+ka constructions and ka-disjunction, which might lead us too far afield. In order to keep the scope of the current paper manageable, I would like to leave this issue for future studies.

4.4 Apparent existential interpretation of wh+ka clausal adjuncts

In an earlier version of this paper (Uegaki 2016), it was claimed that there are cases where clausal adjuncts involving wh+ka can receive existential interpretations, and that they have to be analyzed as involving existential closure at the clausal level. The relevant examples are the following:

    1. (81)
    1. a.
    1. [ Dare-ga
    2.     who-NOM
    1. kita-kara-ka
    2. came-because-KA
    1. ]
    2.  
    1. Taro-wa
    2. Taro-TOP
    1. yorokondeita.
    2. was.happy
    1. ‘For some person x, because x came, Taro was happy, but I don’t know who it is.’
    1.  
    1. b.
    1. [ Dare-ni
    2.     who-DAT
    1. au-tame-ka
    2. meet-in.order.to-KA
    1. ]
    2.  
    1. Taro-wa
    2. Taro-TOP
    1. hayaku
    2. early
    1. daigaku-ni
    2. university-GOAL
    1. kita.
    2. came
    1. ‘For some person x, to meet x, Taro came, but I don’t know who it is.’

In the present paper, I instead follow Tomioka & Kim (2014) and treat these data as involving a wh-question rather than an existential statement in the adjunct position. That is, the adjuncts in (81) do not involve existential closure. One piece of evidence for the fact that we are dealing with questions rather than existential statements in (81) is that the examples have obligatory ignorance implication. This is in contrast to examples with clear wh-indefinites such as those in (82), which constitute minimal pairs with (81).

    1. (82)
    1. a.
    1. [ Dare-ka-ga
    2. who-KA-NOM
    1. kita-kara
    2. came-because
    1. ]
    2.  
    1. Taro-wa
    2. Taro-TOP
    1. yorokondeita.
    2. was.happy
    1. ‘Because someone came, Taro was happy.’
    2. ⇏ The speaker does not know who made Taro happy.
    1.  
    1. b.
    1. [ Dare-ka-ni
    2. who-KA-DAT
    1. au-tame
    2. meet-in.order.to
    1. ]
    2.  
    1. Taro-wa
    2. Taro-TOP
    1. hayaku
    2. early
    1. daigaku-ni
    2. university-GOAL
    1. kita.
    2. came
    1. ‘John came early to the university to meet someone.”
    2. ⇏ The speaker does not know who Taro came early to see.

The obligatory ignorance implication in (81) is straightforwardly accounted for under Tomioka & Kim’s (2014) analysis, which treats the wh+ka clauses in (81) as conventionally implicating an unembedded wh-questions. On the other hand, the data call for further explanation if the wh+ka clauses are existential statements on a par with those in (82). The existential import in (81), on the other hand, can be accounted for in terms of the existential presupposition of the conventionally implicated wh-questions.

Thus, I conclude that the cases in (81) do not pose a challenge to the claim made in the previous sections, i.e., that existential closure at the clausal level is impossible. This does not mean that the current account is already equipped with necessary ingredients for a proper compositional analysis of (81). In particular, it remains to be seen how the wh-question in the adjunct position can be semantically combined with the main clause in the current setup. Although I would like to leave this question for future research, I expect no principled obstacle in incorporating Tomioka & Kim’s (2014) compositional analysis in terms of (a modification of) Potts’s (2005) Comma into the current setup.

4.5 Summary

To summarize §4, existential closure at the clausal level is impossible because the combination of the existential presupposition associated with a wh+ka clause and the existential closure would result in necessary triviality, which in turn would lead to ungrammaticality. The same problem does not arise in the case of non-clausal wh+ka since the existential presupposition and the statement resulting from existential closure would be distinct: existential presupposition amounts to non-emptiness of the restriction of the wh-phrase while the existential closure amounts to non-emptiness of the intersection of the restriction and the scope. The existential presupposition of ka also accounts for the ungrammaticality of existential closure of clausal ka-disjunctions. Finally, although there are cases where ka-ending clausal adjuncts appear to have existential interpretation, they are more straightforwardly accounted for as wh-questions, following Tomioka & Kim (2014).

The reader might have noticed that the presupposition-based account of the impossibility of existential closure at the clausal level proposed in this section obviates the need to call for the constraint in (48) discussed in §3.1.3, which states that ∃ is allowed only if it is necessary to resolve grammatical conflicts like a type-mismatch. This is so since the presupposition-based account explains the impossibility of existential closure at the clausal level in general while the account based on (48) only explains the impossibility in an unembedded clause. It is an open question whether there are independent motivations for the constraint in (48).

5 Note on mo

In the literature on Japanese indeterminate pronouns, wh+mo has often been discussed in parallel to wh+ka. In Shimoyama (2006), in particular, mo is treated as a universal quantifier over the alternatives introduced by the wh-item, forming a dual with the local ka, which is treated as an existential quantifier. This analysis of mo can be preserved in the current account. That is, we have the following denotations for mo.

(83) a. α mo⟧o = λP⟨e,t⟩.∀x ∈ ⟦αalt [P(x)]
  b. α mo⟧alt = {λP⟨e,t⟩.∀x ∈ ⟦αalt[P(x)]}

An interesting consequence of this analysis is that mo now wouldn’t be a dual with ka: mo is a universal quantifier while ka is an operator that copies the alt-value to the o-value. It is worth noting that a non-parallel analysis of mo and ka has already been proposed by Yatsushiro (2009), based on detailed distributional differences between the two particles.

The particle mo can also be used in a coordination structure with a conjunctive interpretation, as in the following example.

    1. (84)
    1. Taro-mo
    2. Taro-MO
    1. Jiro-mo
    2. Jiro-MO
    1. hashitta.
    2. ran
    1. ‘Both Taro and Jiro ran.’

Also, when used in isolation, it functions as an additive particle:

    1. (85)
    1. Taro-mo
    2. Taro-MO
    1. hashitta.
    2. ran
    1. ‘Taro ran, too.’

In the literature, it is debated whether the mo in universal wh+mo construction is the same morpheme as the mo in (84–85). Hagstrom (1998) argues that the fact that mo is used both as a universal quantifier and an additive particle is a case of accidental homophony. On the other hand, Mitrovič & Sauerland (2014) provide evidence for the view that mo in two constructions are identical. In this paper, I will limit the focus to the semantics of ka, and stand neutral with respect to whether and how the analysis in (83) should be extended to the coordination and the additive use. See Mitrovič & Sauerland (2014) for a unified semantics for all of the uses of mo based on the Shimoyama-style analysis in (83), employing the Junction structure and exhaustification.

6 Problems for previous accounts

In this section, I review three previous analyses of wh+ka in the previous literature: a choice-functional analysis by Hagstrom (1998) and Slade (2011), a Hamblin-semantic analysis by Shimoyama (2006) and another choice-functional analysis by Yatsushiro (2009). I have already pointed out that the existential interpretations of ka-ending clauses are problematic for these analyses since they associate clause-final ka with a question interpretation. In this section, I focus on how the analyses deal with the other empirical focus of the current paper: the parallel between wh+ka and ka-disjunctions.

6.1 ka as an existential quantifier over choice-functions (Hagstrom 1998; Slade 2011)

Hagstrom (1998) analyzes wh+ka in Japanese, Sinhala and other related languages, employing the idea that ka is an existential quantifier over choice-functions (Reinhart 1997). According to this analysis, ka in wh-ka is always base-generated in the sister position of the wh-word. Both in wh-questions and wh-indefinite constructions, this ka undergoes either overt or covert movement to the periphery of C, as a result of which the choice-functional variable left in the base position of ka is existentially bound. Here, the choice-functional variable (given an assignment) simply picks out a member of the denotation of the wh-word in its sister position, e.g., people in the case of dare. More specifically, when the (phonologically null) C has the feature [+int], ka overtly moves and forms a complex C. Due to the denotation of C[+int]29 and the existential quantification over the choice-functional variable, we derive the following Karttunen-style denotation for the wh-question dare-ga hashitta-ka.

(86) ⟦ [ [ dare ti ] hashitta ] [ C[+int] kai ] ⟧ = {p | ∃f [p = ran(f (people))]}

On the other hand, a non-interrogative C does not attract ka. However, ka still has to be moved covertly in order to resolve the type-mismatch. As a result, we derive an existential interpretation for the declarative sentence dare-ka-ga hashitta, as follows:

(87) ⟦ [ [ [ [ dare ti ] hashitta ] C[–int] ] kai ] ⟧ ⇔ ∃f [ran(f (people))]

In sum, Hagstrom (1998) attributes the difference in interpretations between a wh-questions and wh-indefinite constructions in terms of the different syntactic and semantic properties of C. The difference in the overt syntactic position of ka is another consequence of the different properties of C: when C is [+int], ka moves overtly moves to the sentence-final position; when C is [–int], ka covertly moves, but stays in the base-position in the overt syntax. In other words, there is no direct relationship between the position of ka and interpretations; the two are distinct consequences of the different properties of C. This is in contrast to my analysis, where the position of ka directly influences the interpretation of the sentence assigned by the compositional semantic derivation.

Although Hagstrom (1998) does not offer an analysis of ka-disjunctions, Slade (2011) extends the choice-function analysis to a similar disjunctive construction in Sinhala, having the form α-də β-də. According to Slade (2011), a disjunction involving α and β as disjuncts have the following structure, involving multiple adjunctions to JP:

    1. (88)

Here, Q1 and Q2 are Q-particles such as the Japanese ka and the Sinhala , and are interpreted as variables over choice functions, which would be bound by existential quantifiers introduced by C. It is also assumed that the clitic alignment mechanism called Lowering appends a Q-particles to each disjunct at PF. In Sinhala, surfaces in the base position both in wh-indeterminates and disjunctions. This fact is captured in Slade (2011) by the fact that itself (rather than its trace, as in Hagstrom 1998) denotes the choice functional variable, which would eventually be bound by C. In AltQs, the binding of the choice functions by C[+int] results in the Karttunen-style denotation, i.e., the set of alternative propositions.

As we extend this analysis to Japanese ka-disjunctions, the null hypothesis would be that the ka and C[±int] behave in the same way as in wh+ka. That is to say that kas in a disjunction are attracted by C[+int] and undergoes an overt movement while they undergo a covert movement under C[–int]. It is furthermore natural to assume that the movement of kas is an ATB movement since a sentence with multiple occurrences of ka in a sentence-final position is ungrammatical:

    1. (89)
    1. *[
    2.  
    1. Hanako
    2. Hanako
    1. matawa
    2. or
    1. Jiro ]-ga
    2. Jiro -NOM
    1. hashitta-ka-ka.
    2. ran-KA-KA
    1. ‘Hanako or Jiro ran.’

This analysis correctly captures the disjunctive interpretation of the declarative sentence in (90), which would be derived by the covert ATB movement of ka. However, the problem arises with (91), which would be derived by the overt ATB movement of ka.

    1. (90)
    1. [ Hanako-ka
    2.   Hanako-KA
    1. (matawa)
    2. or
    1. Jiro-ka ]-ga
    2. Jiro-KA -NOM
    1. hashitta.
    2. ran
    1. ‘Hanako or Jiro ran.’
    1. (91)
    1. [ Hanako
    2.   Hanako
    1. (matawa)
    2. or
    1. Jiro ]-ga
    2. Jiro -NOM
    1. hashitta-ka.
    2. ran-KA
    1. ‘Is it the case that either Hanako or Jiro ran?’

The problem is that the analysis predicts an AltQ interpretation for (91), i.e., {ran(h), ran(j)}, despite the observation that the sentence only receives a YNQ interpretation.

The problem persists even if ka in ka-disjunctions do not overtly move, i.e., ka-disjunctions behave in the same way as -disjunctions in Sinhala. In this case, there wouldn’t be a problem with (91) since it wouldn’t be analyzed as being derived by the overt ATB movement of ka. However, the problem arises with (90). We would expect (90) to allow an AltQ reading since it can involve C[+int], which is phonologically null, and does not attract the overt movement of ka by assumption. This is contrary to fact: (90) cannot be interpreted as an AltQ however it is pronounced.

6.2 Hamblin-semantic analysis (Shimoyama 2006; Beck and Kim 2006)

Another influential analysis of wh-indeterminates in Japanese is the Hamblin-semantic analysis offered by Shimoyama (2006). The analysis proposed in this paper, too, is an extension of Shimoyama’s (2006) system. In this section, I illustrate in what respect the current analysis has advantages over a simple extension of Shimoyama’s (2006) analysis to disjunctions. In Shimoyama (2006), wh-words introduce Hamblin alternatives which pass up the structure via PWFA. The sentence-final question particle ka in a wh-question simply returns the set of alternatives at the sentence level. On the other hand, when there is an existential particle ka (which Shimoyama 2006 distinguishes from the question particle ka) or a universal particle mo in a syntactic position that is more local to the wh-word, the alternatives denoted by the sister constituent of these particles serve as the restrictor of the quantifiers the particles denote.

Shimoyama (2006) does not discuss ka-disjunctions explicitly, but a natural way to extend her analysis to them would be to employ the alternative-semantic analysis of disjunctions (Kratzer & Shimoyama 2002; Alonso-Ovalle 2006; Beck & Kim 2006). The basic idea of such an analysis would be to treat α-ka β-ka as introducing alternatives, as in the following schema:

(92) α-ka β-ka⟧ = {⟦α⟧,⟦β⟧}

This analysis certainly captures the AltQ interpretation of CP-sized ka-disjunctions, as in the following examples:

    1. (13)
    1. a.
    1. [CP
    2.  
    1. [Hanako-ga
    2.  Hanako-NOM
    1. hashitta-mitai-na-no-ka]
    2. ran-seem-COP-GEN-KA
    1. [Jiro-ga
    2.  Jiro-NOM
    1. hashitta-mitai-na-no-ka]].
    2. ran-seem-COP-GEN-KA
    1. ‘Which is true: It seems that Hanako ran or it seems that Jiro ran?’
    1.  
    1. b.
    1. [CP
    2.  
    1. [Hanako-ga
    2.  Hanako-NOM
    1. hashitta-daroo-ka]
    2. ran-may.well.be-KA
    1. [Jiro-ga
    2. Jiro-NOM
    1. hashitta-daroo-ka]].
    2. ran-may.well.be-KA
    1. ‘Which is true: Hanako might well have come or Jiro might well have come?’

However, this analysis would incorrectly predict an AltQ interpretation for the following examples involving ka-disjunctions smaller than CPs:

    1. (15)
    1. [[DP
    2.  
    1. Hanako-ka
    2. Hanako-KA
    1. Jiro-ka]-ga
    2. Jiro-KA-NOM
    1. hashitta-ka]
    2. ran-KA
    1. (oshiete).
    2. tell
    1.   ‘Tell me whether or not Hanako ran or Jiro ran.’            (✓YNQ)
    2. *‘Tell me which is true: Hanako ran or Jiro ran.’                (*AltQ)
    1. (16)
    1. [[TP
    2.  
    1. [Hanako-ga
    2. Hanako-NOM
    1. hashitta-ka]
    2. ran-KA
    1. [Jiro-ga
    2. Jiro-NOM
    1. hashitta-ka]]
    2. ran-KA
    1. mitai-ka]
    2. seem-KA
    1. (oshiete).
    2. tell
    1.   ‘Tell me whether or not it seems to be that Hanako or Jiro ran.’            (✓YNQ)
    2. *‘Tell me which is true: Taro saw Hanako or he saw Jiro.’                      (*AltQ)

Of course, one could syntactically distinguish the ka in CP-sized disjunctions and in sub-CP-sized disjunctions. In fact, Shimoyama (2006) does distinguish the question particle ka in the complementizer position and the existential particle ka in syntactically more local positions. Distinguishing two kinds of ka-disjunctions in a similar fashion, we would have the following distinct interpretations for CP-sized ka-disjunctions and DP/TP-sized ka-disjunctions:

(93) a. ⟦[α-ka]CP [β-ka]CP⟧ = {⟦α⟧,⟦β⟧}
  b. ⟦[α-ka]DP/TP [β-ka]DP/TP⟧ = ⟦α⟧ ⊔ ⟦β

CP-sized disjunctions introduces alternatives, but DP/TP-sized disjunctions are interpreted as generalized disjunction, which does not introduce alternatives. As a result the former is interpreted as an AltQ while an interrogative embedding the latter is interpreted as an YNQ.

This analysis would be descriptively adequate. However, the analysis would not offer principled answers to the following two questions: (i) why the syntactic size of the disjunction affects interpretations of disjunctions in the way sketched in (93); and (ii) why there is a parallel between wh-indeterminates and disjunctions. That is, why the way in which the syntactic size of ka-phrases affects interpretations is the same in wh-indeterminates and disjunctions. Syntactically distinguishing the two kinds of ka-disjunctions as in (93) does not offer an answer to the first question. Also, it is not straightforward how the distinction in (93) follows from the distinction between the question particle ka and the existential particle ka, at least without adopting the JP-based analysis described in 3.2.

In the current analysis, these two questions are answered in principled ways. The particle ka has a unified analysis, encompassing both the “question particle” use and the “existential particle” use in both wh-indeterminates and disjunctions. The effect of the syntactic size of ka-phrases on interpretations is a consequence of the fact that ka-phrases denote sets (in their o-value) and that they have to be flattened in order to enter the semantic composition in the sub-CP level. Also, the effect is parallel between wh-indeterminates and disjunctions because both wh+ka and ka-disjunctions introduce alternatives which by themselves are interpreted as questions in the CP-level but are flattened into existential meaning in the sub-CP-level.

6.3 ka as a free variable over choice-functions (Yatsushiro 2009)

In this section, I review Yatsushiro’s (2009) analysis of wh+ka. I will first discuss Yatsushiro’s (2009) empirical claim that ka does not take scope at the surface position, and then move on to how the analysis can be extended to ka-disjunctions.

Yatsushiro (2009) proposes that ka in wh-indefinites is a free variable over choice-functions, which is bound by an existential closure inserted at vP, TP or CP. The primary evidence for this claim comes from the following contrast:

    1. (94)
    1. a.
    1. [ Dare-ka-no
    2.   who-KA-GEN
    1. dono-kaban
    2. which-bag
    1. ] -mo
    2. -MO
    1. tsukue-no
    2. desk-GEN
    1. ue-ni
    2. top-LOC
    1. aru.
    2. be
    1. ‘Someone’s every bag is on the desk.’          (✓∃ > ∀, *∀ > ∃)
    1.  
    1. b.
    1. [[ Dare-ka-o
    2.   who-KA-ACC
    1. hihanshita
    2. criticized
    1. hito
    2. person
    1. ] -no
    2. -GEN
    1. dono-kaban
    2. which-bag
    1. ] -mo
    2. -MO
    1. tsukue-no
    2. desk-GEN
    1. ue-ni
    2. top-LOC
    1. aru.
    2. be
    1. ‘Every bag of a person who criticized someone is on the desk.’          (✓∃ > ∀, ✓∀ > ∃)

Yatsushiro (2009) observes that (94a) lacks an interpretation in which the universal quantifier dono-kaban-mo ‘every bag’ takes scope over the indefinite dare-ka, and that it only receives an interpretation in which the indefinite takes the higher scope. On the other hand, (94b) can receive an interpretation in which the universal takes the higher scope.

This is surprising, under the view that ka takes scope at the surface position, assuming the following structure for (94a):

    1. (95)

Yatsushiro (2009) argues that this puzzle can be resolved if we view ka as a free variable over choice functions that is bound by an existential closure at a clausal projection. In (95), the existential closure will be applied to the TP, and thus the existential quantification has to take scope over the universal quantification by mo. On the other hand, since (94b) involves a TP node within the subject, the existential closure can be applied there scoping below the universal quantification by mo.

Although the analysis proposed in the current paper also employs existential closure, it would predict that the indefinite can take scope below the universal in a structure like (95) since the existential closure ∃ in the current system can be applied at sub-clausal positions. Thus, if the pattern reported by Yatsushiro (2009) is systematic, it would be problematic for the current analysis. However, I claim that the contrast in (94) stems from pragmatic rather than from syntactic differences. In the following, I will explain the reasoning behind this claim.

The universal over existential interpretation of (94a) would be represented as follows:

(96) x[bag(x) ∧ ∃y[human(y) ∧ own(y,x)] → on-desk(x)]

This is contextually equivalent to the interpretation of the following sentence, under the normal context in which every bag is owned by someone.

    1. (97)
    1. Dono-kaban-mo
    2. which-bag-MO
    1. tsukue-no
    2. desk-GEN
    1. ue-ni
    2. top-at
    1. aru.
    2. be
    1. ‘Every bag is on the desk.’

Thus, under this normal context, a speaker who would like to convey (96) would use (97) instead of (94a), according to the Gricean principle of brevity (Grice 1975). Accordingly, a cooperative interlocutor who hears (94a) would infer that the speaker does not intend the meaning in (96), but rather the other meaning with the wide-scope indefinite.

Turning now to (94b), we see that its interpretation with the universal-over-existential scope configuration, (98), is not contextually equivalent to (97) under the normal context.

(98) x[bag(x) ∧ ∃yz[human(y) ∧ human(z) ∧ criticize(y,z) ∧ own(y,x)] → on-desk(x)]

Under the normal context, not all bags are owned by someone who criticized some other person. Thus, there is no reason for the interlocutor to infer that the speaker of (94b) is intending another construal.

If the contrast in (94) is pragmatic in nature, as I suggest above, we should be able to construct an example that allows a narrow-scope indefinite interpretation, without recourse to a clausal structure within the subject. This is indeed the case. In the following example, the indefinite can take either wide or narrow scope with respect to the universal quantifier mo.

    1. (99)
    1. [
    2.  
    1. Gakubusei
    2. undergrads
    1. dare-ka-no
    2. who-KA-GEN
    1. dono-sensei
    2. which-teacher
    1. ] -mo
    2. -MO
    1. kaetta.
    2. went.home
    1. ‘Some undergrad’s every teacher went home.’

To see that (99) has a narrow-scope indefinite interpretation consider the following context:

(100) Context: There is a university in Tokyo with a linguistics program, with 20 professors and 30 graduate students. There are also only three undergraduates in the program. Their names are Hanako, Ken and Takashi. Each undergraduate is taking classes from the following professors:
  • • Hanako: Professor Suzuki, Professor Takada
  • • Ken: Professor Wilson, Professor Terasawa
  • • Takashi: Professor Suzuki, Professor Sato

Keiko, one of the graduate students, will be TAing for a class open to undergraduates next semester, and she needs some general advices on undergraduate teaching. So, she wants to talk to some professor or other who currently has an undergraduate in their class. Keiko asks Taro if any of the professors who teaches some undergraduate is still around the department. Taro answers by (99).

Under this context, (99) can convey that all of the five professors who has any undergraduate in their class, i.e., Professors Suzuki, Takada, Wilson, Terasawa and Sato, have already left the department. This indicates that the sentence has an interpretation in which the indefinite takes a narrow scope with respect to the universal quantifier. If only the wide-scope indefinite interpretation is possible, the sentence would only mean the following:

(101) Both Professors Suzuki and Takada left, or both Professors Wilson and Terasawa left, or Both professors Suzuki and Sato left.

This is certainly a possible construal of (99), but, crucially, the stronger interpretation mentioned above is also possible.

The possibility of the narrow-scope indefinite in (99) makes sense under the pragmatic account sketched above. Since not all professors teach undergraduates, the narrow-scope indefinite interpretation of (99) does not end up contextually equivalent to ‘Every professor left’. Hence, the interpretation does not get excluded on pragmatic grounds. On the other hand, the syntactic account in Yatsushiro (2009) has difficulty explaining the availability of the narrow-scope indefinite in (99) since there is no clausal projection below mo in (99) such that the existential closure can be applied to it.

The fact that wide-scope indefinite is possible in (94, 99) might seem puzzling for the current account since the current basic setup would predict the indefinite to take scope below mo. However, Schwarzchild (2002) has shown that an interpretation predicted by a wide-scope indefinite can be achieved by a narrow scope singleton indefinite. That is, for example, if the domain of undergraduates in (99) is contextually restricted to be the singleton set of a certain student, the reading predicted by a wide-scope indefinite and the reading predicted by a narrow-scope indefinite would be truth conditionally indistinguishable. This gives rise to the appearance that the indefinite has a wide scope even with respect to the universal quantifier even if it is structurally below the universal quantifier at LF.30

Next, let us move on to how Yatsushiro’s (2009) analysis can be extended to ka-disjunctions. If ka in ka-disjunctions is also analyzed as a free variable over choice functions that is bound by an existential closure at some clausal projection, a disjunctive statement such as (102) would receive an interpretation along the lines of (103) below.

    1. (102)
    1. Hanako-ka
    2. Hanako-KA
    1. or
    1. Jiro-ka-ga
    2. Jiro-KA-NOM
    1. hashitta.
    2. ran
    1. ‘Hanako or Jiro ran.’
(103) f[ran(f (⟦Hanako⟧)) ∨ ran (f (⟦Jiro⟧))]

Assuming that names can denote singleton sets, and that a choice function applied to a singleton set always returns its unique member, (103) does capture the interpretation of (102). However, what is problematic is that a parallel analysis can be made for CP-sized ka-disjunctions, which empirically expresses an AltQ, such as the following.

    1. (104)
    1. [ Hanako-ga
    2.   Hanako-NOM
    1. hashitta-ka
    2. ran-KA
    1. or
    1. Jiro-ga
    2. Jiro-NOM
    1. hashitta-ka ]
    2. ran-KA
    1. (oshiete).
    2. tell
    1. ‘Tell me which is true: Hanako ran or Jiro ran.’

Again, assuming that the sister of ka is analyzed as denoting a singleton set, we would derive the following reading for (104), if we maintain the same semantics for ka in (104):

(105) f[f ({ran(h)}) ∨ f ({ran(j)})]

This interpretation would be equivalent to (103), i.e., that Hanako ran or Jiro ran. This is empirically incorrect: (104) only receives an AltQ interpretation unless it is embedded under proposition-embedding operator. Hence, the precise interpretation of ka-disjunctions cannot be captured by the extension of Yatsushiro (2009).

7 Conclusions and cross-linguistic prospects

This paper started out with mentioning the following three research questions currently discussed in the semantics of Q-particles.

  • What is shared by the semantic representations of indefinites, questions and disjunctions?
  • What is the semantic contribution of the Q-particle in indefinites, questions and disjunctions?
  • How are the different syntactic environments in which the Q-particle occurs mapped to the interpretations of indefinites, questions and disjunctions?

The proposed unified analysis of the Japanese Q-particle ka in questions, indefinites and disjunctions offers clear answers to these questions, from a language-specific point-of-view.

  • Indefinites, question and disjunctions all involve a set of alternatives at some point in the compositional semantic derivation. These alternatives are introduced (in the alt-dimension) by a wh-item in questions and indefinites while they are introduced in the JP structure in disjunctions.
  • The semantic contribution of the Q-particle is to bring the set of alternatives in the alt-dimension to the o-dimension.
  • The phrase denoting the set of alternatives in the o-dimension is interpreted differently depending on whether its syntactic environment is set-compatible or not. If it is, then the phrase is interpreted as a question (i.e., wh-question or AltQ). Otherwise, it is interpreted existentially (i.e., as an indefinite or as a declarative disjunction) through the mechanism of existential closure.

As mentioned in the introduction, note that this proposal is a conservative extension of existing proposals, which have been argued for from independent grounds. The unified analysis of indefinites and questions in terms of alternatives has been extensively defended at least since Kratzer & Shimoyama (2002), and the extension of this program to the JP structure is undertaken by Mitrovič & Sauerland (2014) and Szabolcsi (2015b). The role of Q-particle as an operator that brings the alt-value of the prejacent to the o-value is proposed by Beck (2006) and Kotek (2014), and is shown to have further positive consequences for independent empirical problems such as the interpretation of multiple wh-questions. There are two features of the current proposal that set it apart from previous proposals: (i) the adoption of the above semantics for the Q-particle for its clause-internal use, not only for its clause-final use; and (ii) the employment of type-compatibility and existential closure in the account of the interpretations of ka-ending phrases. Throughout the body of the paper, I have argued that addition of these two claims have far-reaching consequences, including a unified analysis of indefinites and wh-questions and an account of the parallelism between wh+ka and ka-disjunctions.

Finally, I will conclude by speculating on the cross-linguistic implications of the analysis. Although the primary aim of the current paper has been a language-specific one, the analysis can be potentially extended to the distribution of the Q-particle common in languages such as Sinhala and Shuri Okinawan. In these languages, the Q-particle itself is located in the vicinity31 of the wh-item both in indefinites and wh-questions while the wh-question comes with a specific morphology in the clause-final verb: the E-suffix in Sinhala and the ra-suffix in Shuri Okinawan. The following Sinhala pair from Hagstrom (1998: 23) exemplifies this:

    1. (106)
    1. a.
    1. mokak
    2. what
    1. Q
    1. wætuna.
    2. fell
    1. ‘Something fell.’
    1.  
    1. b.
    1. mokak
    2. what
    1. Q
    1. wætune?
    2. fell-E
    1. ‘What fell?’

Under the current analysis, the existential interpretation of (106a) follows from the basic setup, without assuming a movement of the Q-particle (contra Hagstrom 1998). On the other hand, the analysis cannot be directly extended to the question in (106b). Under the current analysis, the sub-CP position of in (106b) would entail an existential closure, contrary to fact. One way to extend the analysis to this case is to posit a covert movement of the Q-particle to the clause-edge position marked by the E-suffix. The structure after such a covert movement would look exactly like that of modern Japanese, and the current analysis for wh-questions can be directly applied to it.

In fact, a covert movement of to the clause-edge position in Sinhala is something that is extensively argued for based on island data (Kishimoto 1992; Hagstrom 1998). However, the analysis sketched above calls for a different semantic implementation of the movement from the one proposed in the existing literature. That is, the covert movement of has to be semantically vacuous under the current analysis, rather than being interpreted as creating a variable-binding configuration as in Hagstrom (1998). The cross-linguistic difference between Japanese on the one hand and Sinhala and Shuri Okinawan on the other (with respect to the grammar of Q-particles) would then boil down to the absence/presence of this semantically-vacuous covert movement of the Q-particle to the clause-edge position. Given that Premodern Japanese exhibits similar association between the wh-item and a verb-suffix morphology (the so-called “kakari-musubi”), the diachronic variation in the Japanese Q system might also consist in the presence and absence of this semantically-vacuous covert movement. Evaluating the full cross-linguistic and diachronic prospects of the current analysis requires further data collection and research.