2.1 Cable (2010) on WhQs

Syntactically, all wh-phrases in Sinhala (and Tlingit) must be c-commanded by a Q-particle. Cable (2010) argues that the Q-particle heads a Q-particle phrase (QP) and that what looks like wh-movement is not movement of the WhP per se but of the QP [_QP [_WhP… wh…] də] containing the wh-phrase. The movement of QP is triggered by the need to check a syntactic feature in the left periphery of the clause: the interrogative Q-operator carries an uninterpretable feature that must be checked against the corresponding interpretable feature of the wh-phrase. More specifically, Cable proposes that the QP moves – overtly in Tlingit and covertly in Sinhala – to the specifier of a Focus Phrase (FocP) which is obligatorily selected by the Q-operator sitting in C⁰, as in (7). From this position, the intended syntactic feature is checked.

(7)

[Cable 2010, 78]

In simple WhQs, QP is often located immediately above the WhP and, thus, it solely contains the lexical material of the wh-phrase plus the Q-particle. This is exemplified in (8) for Tlingit, with overt movement of the QP [what Q], and in (1) for Sinhala, where the QP [what Q] appears in situ and moves to Spec-FocP only at LF:

However, syntactic considerations may enforce a higher attachment of the Q-particle. One such consideration concerns s(yntactic)-selection. In s-selection, a functional head selects a particular XP type and no extraneous projection is allowed to intervene between the two. This is the case, for example, when a postposition selects its complement DP. In such cases, the Q-particle cannot attach immediately above the interrogative XP but must, instead, attach higher up. This is illustrated in (9), where the QP cannot be located immediately above the interrogative DP [who] but must instead be placed above the PP [who with]:

Another syntactic consideration argued to force the Q-particle to attach higher up concerns islands. No syntactic dependency, including movement, can hold across an island. Now, recall that the entire QP needs to move – overtly or covertly – to Spec-FocP. What happens when our wh-phrase is buried within an island? If we attach the Q-particle over the wh-phrase but within the island, as in (10), the sentence is ungrammatical. This is because the movement of QP [what Q] to Spec-FocP is blocked by the island boundary. In contrast, as first noted by Gair (1983, 1998), if we attach the Q-particle above the wh-phrase and at the outer edge of the island, as in (11), the sentence becomes grammatical. This is because the QP [[_Island … what…] Q] can freely move and successfully reach Spec-FocP:

We turn now to the semantic side of Cable's analysis. Since, as we just saw, the Q-particle may syntactically c-command the wh-phrase at a short (1), medium (9a) or long distance (11), Cable adopts a flexible semantic analysis that allows for any distance between the Q-particle and the wh-phrase and even for an intervening island boundary between the two. Its tenets are the following, applied to example (9a) in (12) for illustration:

(12)

LF of example (9a):

First, in the spirit of Beck (2006), interrogative wh-words are inherently F(ocus)-marked and have a set of alternatives as their focus value ⟦.⟧^f, as illustrated in (13a). Second, each of the alternatives in the focus value ⟦.⟧^f composes pointwise with the meaning of the neighboring constituents via the Pointwise Functional Application rule in (14) (Rooth 1992), resulting in (13b). This composition process can continue at any distance and is insensitive to island boundaries. Third, at some point in the semantic derivation, we reach the Q-particle də, which bears an index i ranging over choice functions. The corresponding choice function f introduced by g(i) takes the Roothian focus value ⟦.⟧^f of its syntactic sister and selects an element of that set, as in (13c). Fourth, the resulting selected element keeps combining with the denotation of other constituents in the tree, as in (13d). Finally, the Q-operator heading ForceP existentially binds the choice function f introduced by the index of də, as in (13e). This derives the correct Hamblin-style denotation of the WhQ structure in (12):

In building our proposal in section 5, we will assume Cable's syntactic analysis of WhQs, we will maintain the lower, Roothian “leg” of his semantic dependency – which secures the connection between the wh-phrase and də at a short, medium and long distance across an island –, and we will liberalize the upper “leg” of the semantic dependency to account for PolQs.

2.2 Slade's (2011) extension to PolQs

Cable's (2010) analysis works beautifully for WhQs. However, extending Cable's choice function treatment of də to AltQs and PolQs is far from trivial.⁴ In this paper, we concentrate on the extension to PolQs.

Recall that, to form a PolQ, the Q-particle may attach broadly to the entire IP, as in (15), or narrowly to a specific focused constituent, as in (16). In the latter case, a naïve extension of Cable's choice function treatment of də would combine ⟦də⟧ with the Roothian set of focus alternatives ⟦Ranjit_F⟧^f – namely, {ranjit, chitra, alis…} – and select one element of it as the answer. Clearly, this does not correspond to the actual reading of (16): the PolQ asks the hearer to choose between ‘yes’ and ‘no’, not to choose among the alternatives in ⟦Ranjit_F⟧^f:⁵

To circumvent this challenge, Slade (2011) proposes to reduce PolQs – both with broad də and with narrow də – to the corresponding AltQs with a second elliptical negative disjunct. More concretely, what looks like a PolQ with broad də in (15) is argued to have the underlying AltQ-structure in (17), where the IP Ranjit came and an elided IP Ranjit did not come are disjoined. And what looks on the surface like a PolQ with narrow də in (16) is assigned the underlying AltQ-structure in (18), where the DP Ranjit and the elliptical DP not Ranjit are disjoined:⁶

Slade's rule for interpreting disjunction is given in (19):

This rule operates as follows. In the case of the PolQ structure (17) with broad də, the λx-slot in (19) will be filled with the proposition ‘that Ranjit did not come’ expressed by the second disjunct; the λf-slot will be saturated by the choice function variable f₂ introduced by də₂; and the λy-slot will be filled with the proposition ‘that Ranjit came’ expressed by the first disjunct. Once all the arguments of the Junction Interpretation Rule are saturated, we obtain the set in (20a), which – given that f₂ is choosing out of a singleton – boils down to the set {‘that Ranjit came’, ‘that Ranjit did not come’}. This set then serves as the argument of the choice function variable f₁ introduced by də₁. The result is the final question denotation in (20b):

The combinatorics for the PolQ structure (18) with narrow də are no different, except that now the disjuncts saturating the λx- and λy-slots are smaller. The λx-slot in (19) is filled with the generalized quantifier ‘not Ranjit’ denoted by the second disjunct; the λf-slot is saturated by the choice function variable f₂ introduced by də₂; and the λy-slot is filled with the generalized quantifier ‘Ranjit’ denoted by the first disjunct. The result of this composition is the set on (21a), which – similar to the case above – boils down to the set {‘Ranjit’, ‘not Ranjit’}. This set then acts as the argument of the choice function variable f₁ introduced by də₁, which delivers the final question meaning in (21b):

Importantly, the resulting meanings in (20) and (21) elicit the same answers ‘yes, Ranjit came’ and ‘no, Ranjit didn't come’ / ‘no, it wasn't Ranjit that came’ as bona fide PolQs. Hence, if the underlying structures in (17)–(18) can be maintained, the challenge to the choice function treatment of də could be evaded. Unfortunately, the novel island data in the next section will make the parse in (18) untenable.

4.1 The focus semantic value ⟦.⟧^h

Next to Rooth's (1992) focus framework with the focus value ⟦.⟧^f, Kratzer (1991), Wold (1996) and Beck (2006) develop a framework based on the focus value ⟦.⟧^h. As in Rooth, each expression has an ordinary semantic value ⟦.⟧ and a focus semantic value ⟦.⟧^h. But, contrary to the Roothian framework, in the Kratzerian framework the focus feature F is indexed and its index is interpreted via the assignment function h.

Let us see briefly how the ⟦.⟧^h-based focus framework works. We will follow Beck's (2006) version in this paper. Some basic lexical entries are provided in (26)–(29) for illustration.¹³ Note that, in Beck (2006), wh-words are inherently F-marked and provide the relevant alternatives via their focus semantic value (and do not have an ordinary semantic value):

Lexical entries combine via the Functional Application rule (30). The steps in (31b/b’) and (32b/b’) illustrate the result of this composition up to IP:

Next, we add Beck's (2006) interpretation rule for the ∼-operator in (33).¹⁴ This allows us to complete the derivation (31) as in (34):

Finally, we introduce Beck's (2006) interpretation rule for the Q-operator. With (35), we can complete the semantic derivation (32) as in (36):

In our proposal, we use Rooth's focus value ⟦.⟧^f for the lower leg of the dependency and Beck's version of ⟦.⟧^h for the upper leg of the dependency. The two legs will be connected by the Q-particle də.

4.2 Focus in PolQs and discourse structure

To model the contribution of F-marking in questions, we follow Roberts' (1996/2012) and take discourse structure to consist of a stack of hierarchically ordered (explicit or implicit) Questions Under Discussion (QUDs), as illustrated in (37). Hierarchically lower QUDs are subquestions of hierarchically higher QUDs, in that the complete answer to the lower QUD contextually entails a partial answer to the higher QUD (Roberts 1996/2012). For example, the complete answer to QUD (37.1.a.i) entails a partial answer to the hierarchically preceding QUD (37.1.a):

Importantly for us, explicit moves must obey congruence requirements with (explicit or implicit) hierarchically preceding moves. For declaratives, an explicit move m is congruent with its hierarchically preceding QUD in the stack if and only if the location of the foci in the uttered declarative corresponds to the location of the wh-phrase in the hierarchically preceding QUD. This is illustrated in the question-answer sequences in (38). Likewise, explicit PolQ moves are congruent with their hierarchically preceding QUD if and only if the location of the foci in the uttered question corresponds to the location of the wh-phrase in the hierarchically preceding QUD (Bäuerle 1979; Roberts 1996/2012; Biezma 2009). This is exemplified by the WhQ-PolQ sequences in (39):¹⁵

Formally, congruence is secured by computing the focus value of (the relevant constituent) of the current declarative or interrogative utterance and inserting the ∼-operator. This is illustrated in (40)–(41) using the focus value ⟦.⟧^h, as it will later be used in our proposal.¹⁶ The QUD corresponds to the value of the free variable C. In (40) with narrow focus on John, the resulting QUD in (40b) can be paraphrased as ‘Who left?’. In (41) with broad focus on the entire IP [_IP John left], the QUD obtained in (41b) can be paraphrased as ‘What happened?’:

As we will shortly see, the implication for Sinhala will be that, in PolQs with narrow and broad də, the ∼-operator will target the focus value ⟦.⟧^h triggered by the Q-particle in order to check discourse congruence à la Roberts (1996/2012).¹⁷

5.1 Application to WhQs

We start with WhQs. A sample syntactic structure is given in (49), where the Q-operator bears the same index as the Q-particle də c-commanding the wh-phrase:²⁰

The semantic derivation of this WhQ structure proceeds as follows. Next to the undefined ordinary semantic value of the wh-phrase in (50a), we have its focus semantic value in (50b), which in this first “leg” corresponds to the Roothian focus value ⟦.⟧^f. For the sake of concreteness, we will assume that the set of individuals {x: x ∈ D_e} equals the set {a(li), c(hitra), g(unapala)}. Then, the Q-particle də₁ combines with (its syntactic sister containing) the wh-phrase in (51). The resulting ordinary value is still undefined, as in (51a); the resulting focus value, now corresponding to the Kratzerian ⟦.⟧^h, is the constant individual concept [λw.h(1)], provided that h(1) is a member of ⟦whom_F⟧^f, i.e., of {a, c, g}. The QP combines via the Functional Application rule (30) with the rest of the constituents in the sentence up to the IP node, resulting in (52):

The final step in the semantic derivation adds the Q-operator, in (53). The Q-operator instructs us to build a set of propositions by manipulating the focus assignment h in ⟦IP⟧^h with respect to the targeted index 1, resulting in propositions of shape λw.SEE_w(a, h^x/1(1)) where x∈{a, c, g}. This gives us the set { λw. SEE_w(a, a), λw. SEE_w(a, c), λw. SEE_w(a, g) }, listed on the last line of (53a). Finally, the focus value in (53b) is equated to the ordinary value just computed:

In sum, as seen in this semantic derivation, the focus value ⟦.⟧^h triggered by the occurrences of də in WhQs is manipulated higher up by the Q-operator and, thus, it is used to generate the question meaning.

5.2 Application to PolQs

This subsection applies the proposed analysis to PolQs. We start with PolQs like (3) with narrow də and then show that the same rationale derives PolQs like (4) with broad də.

A sample PolQ structure with narrow də is provided in (54):

This PolQ LF differs from the WhQ LF above in two important respects. First, while the Q-operator in WhQs bears at least one index, the Q-operator in PolQs bears no index whatsoever. Indeed, since intuitively the question is not asking us to choose among alternatives to Chitra, there should be no interrogative link between the Q-operator and də and, thus, the two should not be co-indexed. This means that the Q-operator will have to operate on the ⟦.⟧^h of its syntactic sister without manipulating h's value for any index. Second, the ∼-operator has been inserted into the LF to secure Roberts' (1996/2012) discourse congruence on PolQs. As we will see, it will be the ∼-operator that manipulates (unselectively) the focus value ⟦.⟧^h triggered by də in PolQs.

The semantic derivation of this PolQ structure proceeds as follows. We start with the F-marked NP Chitra in (55), whose ordinary value is the individual c(hitra) and whose Roothian focus value is the domain of individuals, here again the set {a, c, g} for concreteness. The QP is composed in (56): The ordinary value is passed up unaltered in (56a); the focus value is transformed by də from the Roothian set of alternatives ⟦.⟧^f to the Kratzerian h-based focus value ⟦.⟧^h in (56b), exactly as in (51b) above. The two semantic values keep composing with the rest of the sentence up to the IP node to deliver (57):

Now the IP combines with the ∼-operator. The ∼-operator imposes a definedness condition. It instructs us to build the set of propositions that result from replacing h in ⟦IP⟧^h by a (total) focus assignment function h’ that may differ from the original h with respect to any index. In other words, in constructing this set of propositions, we are “closing off” the focus index 1 on də unselectively. The resulting set of propositions in (58a) is {λw. SEE_w(a, a), λw. SEE_w(a, c), λw. SEE_w(a, g)}:

As we saw in section 4, via the definedness condition imposed by the ∼-operator, this resulting set indicates the shape of ⟦C⟧, that is, the shape of the hierarchically preceding QUD in Roberts' discourse framework (Roberts 1996/2012; Biezma 2009). In this case, it indicates that the current PolQ Did Ali see [Chitra_F də]? is the daughter of the WhQ Who did Ali see?, as sketched in (59), and not e.g. of Who saw Chitra?:

The last step in the semantic derivation brings in the Q-operator, which, as pointed out, bears no index in the case of PolQs. Since there is no index on the Q-operator, in (60a) we build a set of propositions based on ⟦IP⟧^h without manipulating any index. The result will be a singleton set. More concretely, since the focus assignment h starts empty and no manipulation of h is operative in (60a), h(1) will default to the ordinary value of [Chitra_F də₁], i.e., to the individual c(hitra) in the third line of (60a).²¹ This gives us the final line in (60a), which corresponds to the correct singleton PolQ reading à la Roberts (1996/2012) and Biezma & Rawlins (2012).²² Finally, as we saw for WhQs, the focus value of [Q IP] is reset to the ordinary value of [Q IP], as in (60b):

We turn now to PolQs with broad də. A sample structure is given in (61). Instead of having narrow F-marking and də on a smaller constituent, we have broad F-marking on the entire IP and də attached to it:

The steps in the semantic derivation are parallel to the ones for PolQs with narrow də, modulo the size of the F-marked constituent and, thus, the shape of the Roothian focus value ⟦.⟧^f serving as argument of də. We start with the ordinary and Roothian focus values of the IP, in (62). The Roothian focus value in (62b) is the set of propositions {p: p∈D_<s,t>}. For the sake of concreteness, we will limit ourselves to sample propositions like ‘that Ali saw Chitra’, ‘that Chitra came’, ‘that Guna loves Ali’, …, as indicated in the last line of (62b):

Next, we add the Q-particle də. As before, the ordinary value in (63a) remains untouched. But the focus value is transformed from the Roothian format to the Kratzerian format in (63b):

In the next step, we check the definedness condition imposed by the ∼-operator. By cycling in different (total) h’ functions in (64a), we end up with the set of propositions {‘that Ali saw Chitra’, ‘that Chitra came’, ‘that Guna loves Ali’, …}. Via ⟦C⟧, the hierarchically preceding QUD in the discourse structure is indicated to be a subset of that set. In other words, broad də indicates that the current PolQ is the daughter of a general WhQ What happened?, as sketched in (68), and not of a more specific WhQ like Who saw Chitra? or Who did Ali see?:

Finally, we compose QP with the Q-operator in (66). As before, to construct the ordinary value in (66a), the Q-operator combines with the focus value ⟦QP ∼ Q⟧^h of its syntactic sister; but, since the Q-operator bears no index, it builds a set of propositions based on ⟦QP ∼ Q⟧^h without manipulating any index. The result is, again, a singleton set containing a single proposition for which each lexical entry has defaulted to its ordinary meaning. This is shown in the last line of (66a), which, again, corresponds to the correct singleton PolQ denotation à la Roberts (1996/2012) and Biezma & Rawlins (2012). Finally, the focus value of the entire PolQ is equated to its ordinary value in (69b):

In sum, as shown in the semantic derivations, the focus value ⟦.⟧^h triggered by də in PolQs is manipulated solely by the ∼-operator, and the goal of this manipulation is to situate the current PolQ in the discourse hierarchical structure. Note, furthermore, that the current analysis delivers the same denotation for narrow-focus PolQs and broad-focus PolQs. This is a desirable result, since the crucial difference between the two PolQ types is not semantic, but rather pragmatic: they are felicitous in different contexts, signaling the corresponding QUD.

With this treatment of PolQs, the problem faced by the choice function analysis of də has been solved. The Q-particle də uniformly turns the Roothian focus value ⟦.⟧^f into a Kratzerian focus value ⟦.⟧^h across WhQs and PolQs. The difference between the two, as we saw, lies simply on what operator will end up manipulating the focus value ⟦.⟧^h: the Q-operator in WhQs vs. the ∼-operator in PolQs.