2.1 PolQPs are mandatory

The first major difference between PolQPs and particles like Japanese ka and Hindi-Urdu kya: is that in contrast to the latter, PolQPs are mandatory (see Holmberg 2014 on Finnish -kO and Kamali & Krifka 2020 on Turkish mI and references therein). Example (5) shows that in Japanese and in Hindi-Urdu, the particles ka and kya: are optional in a question. In contrast, example (6) shows that when in Finnish and Turkish, the particles -kO and mI are not realized, the resulting polar questions are not well-formed.

2.2 PolQPs are restricted to polar and alternative questions

As mentioned in the introduction, particles like Japanese ka can also form disjunctions and/or indefinites in declaratives. This is not a property shared by particles like Hindi-Urdu kya: and PolQPs, which are all restricted to interrogatives.²

As far as their occurrence in interrogatives is concerned, the three types of particles can appear in polar and alternative questions. This is illustrated in example (7) for Japanese ka, in example (8) for Hindi-Urdu kya: and in examples (9) and (10) for PolQPs (see Holmberg 2014, a.o., on Finnish -kO; and Kamali 2011, Atlamaz 2015, Özyıldız 2015 and Kamali & Krifka 2020 on Turkish mI for further examples)

Just like in polar questions, the use of PolQPs is mandatory in alternative questions. In Turkish, both instances of mI are obligatory.

Particles like Japanese ka and PolQPs also differ in their ability to participate in the formation of wh-questions. While Japanese ka can participate in the formation of these questions (12), PolQPs cannot (see Kamali & Krifka (2020) on Turkish mI) as illustrated in (13).³

As for Hindi-Urdu kya:, while it does not occur in who-questions, it participates in the formation of what-questions (Biezma & Butt & Jabeen 2018; Bhatt & Dayal 2020). Specifically, it functions as the wh-word meaning ‘what’, as shown in (14).

Biezma & Butt & Jabeen (2018) have shown that kya: used as an interrogative particle in polar and alternative questions and kya: used as a wh-word do not share the same prosody. Based on this, previous studies investigating this particle have focused on its use in polar and alternative questions (Biezma & Butt & Jabeen 2018; Bhatt & Dayal 2020). As mentioned by Bhatt & Dayal (2020) however, it might be that the two instances of kya: are accidentally homophonous or that these two have a deeper connection – especially in light of the fact that other languages with presumably the same type of interrogative particles like Bangla and Odia (Syed & Dash 2017), and Italian and Slovenian (Bhatt & Dayal 2020), show the same homophony. This issue which requires further research would deserve a paper on its own. What is important for the current discussion is that PolQPs – in contrast to particles like Hindi-Urdu kya: – cannot act as the wh-word meaning ‘what’ in wh-questions.

2.3 PolQPs can be embedded

Another difference between Hindi-Urdu kya: and PolQPs concerns their ability to be embedded. Specifically, while kya: can only be embedded under a subset of question-embedding predicates, PolQPs do not show the same restrictions. For instance, example (15) shows that kya: can be embedded under the rogative predicate pu:ch ‘ask’, but cannot be embedded under the responsive predicate ja:n ‘know’.⁴

In contrast, PolQPs can be embedded under both kinds of question-embedding predicates, as illustrated in (16) and (17) for Finnish and Turkish respectively.⁵

As far as embedding is concerned, PolPQs resemble particles like Japanese ka which can be embedded under both rogative and responsive predicates as well.

2.4 PolQPs are focus-sensitive

To my knowledge, interrogative particles like Japanese ka have not been claimed to show focus-sensitivity. In contrast, Biezma & Butt & Jabeen (2018) and Bhatt & Dayal (2020) show that the interrogative particle kya: is focus-sensitive and can associate with material to its right. As illustrated in example (19), only expressions that follow kya: can be negated and thus targeted for correction. For further evidence in favor of the focus-sensitivity of kya:, I refer the reader to Biezma & Butt & Jabeen (2018) and Bhatt & Dayal (2020).

Similarly, PolQPs have been shown to be focus-sensitive (Holmberg 2014; Kamali 2011; Atlamaz 2015; Kamali & Krifka 2020, a.o.). In all the Finnish and Turkish examples discussed up to now, PolQP -kO attached to the predicate, and PolQP mI occurred right after the object – these constitute the unmarked case. However, the distribution of these particles is more flexible than what these previous examples suggest. Specifically, Finnish -kO can attach to other elements in the question, as in (20), as can Turkish mI (21). In both languages, varying the position of the interrogative particle affects the interpretation of the question.

In what follows, I adapt Bhatt & Dayal’s (2020) diagnostics to Finnish and Turkish to show that the two PolQPs usually associate with the constituent they follow. For a discussion of other kinds of focused expressions (e.g., verbs, adjectives) or more complex constituents focused (e.g., PPs, VPs) whereby PolQPs can associate with a constituent that contains a focused expression (see Section 4.2), I refer the reader to Holmberg (2014) for Finnish -kO and Kamali (2011) and Özyıldız (2015) for Turkish mI. The first diagnostic is about the formation of alternative questions. Examples (22)–(25) show that alternative questions can only be formed on phrases that precede PolQPs -kO and mI, wether the interrogative particles follow the subject of the question, the object or the adverb.

As of now, I will add brackets to the examples to highlight the interrogative particle and the constituent it associates with.

The second diagnostic is about negative responses. Examples (26)-(29) show that expressions that precede PolQPs are the only ones that can be negated and thus targeted for correction in both Finnish and Turkish. Again, this is the case whether the interrogative particles follow the subject of the question, the object or the adverb.

2.5 Presence of an existential presupposition

With this section ends our discussion of the characteristic properties of PolQPs and of the questions where they occur. Polar questions involving PolQPs differ from polar questions in languages like English for instance – and to my knowledge, from polar questions in languages like Japanese – in that they come with an existential presupposition (see e.g. Atlamaz 2015 on Turkish). For instance, the questions in (30) and (31), in Finnish and Turkish respectively, both presuppose that someone left.⁶

Although to my knowledge it has not been discussed explicitly in previous literature, some polar questions involving Hindi-Urdu kya: seem to come with an existential presupposition as well. For instance, example (32) suggests that the two questions in (a) and (b) differ in the presuppositions they come with. The first question is unfelicitous in the given context because its presupposition (i.e., there is something that John gave to Amra) is not satisfied, whereas the second question is felicitous because its presupposition (i.e., there is someone whom John gave a toy to) is satisfied. Whether polar questions involving particles like Hindi-Urdu kya: indeed come with an existential presupposition will need to be carefully investigated in future work.

In what follows, I adapt some well-known tests to diagnose the presence of the existential presupposition in polar questions involving PolQPs. First, when the speaker does not take for granted that someone left, the two polar questions given above are unfelicitous, as shown in (33) and (34). This provides evidence in favor of the presence of a presupposition of the form ‘Someone left.’.

Another well-known diagnostic for presuppositions is the ‘Hey, wait a minute’ test. von Fintel (2004) claims that if a sentence S presupposes P, one can respond ‘Hey, wait a minute. I didn’t know that P.’ In examples (35) and (36), I adapt this test to Finnish and Turkish respectively. These examples show that the two polar questions come with an existential presupposition of the form ‘Someone left.’ and ‘Someone kissed Dilara.’ respectively.

To sum up, I have shown in this section that the differences between particles like Japanese ka and PolQPs are the following:

1. Unlike ka, PolQPs are mandatory;

2. Unlike ka, PolQPs are restricted to interrogatives;

3. Unlike ka, PolQPs cannot participate in the formation of wh-questions;

4. Unlike ka, PolQPs are focus-sensitive;

5. Unlike polar questions involving ka, polar questions involving PolQPs come with an existential presupposition.

And the differences between particles like Hindi-Urdu kya: and PolQPs are the following:

1. Unlike kya:, PolQPs are mandatory;

2. Unlike kya:, PolQPs cannot function as the wh-word meaning ‘what’ in a wh-question;

3. Unlike kya:, PolQPs can be embedded under all kinds of question-embedding predicates.

Table 1 summarizes the uses of the three types of interrogative particles. As illustrated in this table, Finnish -kO and Turkish mI pattern alike.

Drawing from data found in previous literature as well as novel data in Finnish and Turkish, I have established in this section the signature properties of PolQPs. I have further shown that PolQPs differ from interrogative particles well-studied in the semantic literature, and thus that we need to draw a distinction between (at least) three types of interrogative particles cross-linguistically: (i) particles like Japanese ka, (ii) particles like Hindi-Urdu kya:, and (iii) PolQPs. Although I limited my discussion to Finnish -kO and Turkish mI, PolQPs are presumably more widely spread across languages than one may have previously thought. For instance, other possible candidates are Bulgarian li (Rudin 2012), Quechua chu (Juan Carlos Romero Ventura, p.c.) and Russian li (King 1993 and references therein, Lena Borise, p.c.).⁷ To determine whether these particles are truly PolQPs or rather belong to the second type of interrogative particles, further work is required.

3.1 A baseline semantics for polar questions

There are two main approaches to the semantics of questions which differ with respect to what a question denotes. On the approach adopted in this paper, questions denote a set of propositions (Hamblin 1973; Karttunen 1977). As far as polar questions are concerned, it has been argued in the past decade that these questions do not denote a set containing both of their possible answers, but rather denote a singleton set which only contains the proposition out of which the question is formed (Biezma & Rawlins 2012; Roberts 2012; Roelofsen & Farkas 2015: a.o.). Empirical arguments in favor of such an analysis come from the distinct behavior of polar questions and alternative questions, biased polar questions, the interpretation of response particles, among others. On this proposal, the polar question in (37) can be analyzed as in (38). That is, it denotes the singleton set which contains the proposition that Zoe left.

The question whether polar questions denote singleton sets or sets containing both of their possible answers is outside the scope of this paper. For the sake of consistency with the recent literature on polar questions, I adopt the singleton analysis. However, my proposal for questions involving PolQPs which will be presented in the next section does not rely on this analysis.

As is well-known, presuppositions triggered within declaratives survive in polar questions. That is, the polar question in (39a), just like the declarative Zoe brought the cake., presupposes that there is a unique contextually relevant cake. To capture the projection of presuppositions in polar questions, I adopt Guerzoni’s (2003) proposal according to which the interrogative C_[+Q] head denotes a function that inherits the definedness conditions of its argument. The new interrogative C_[+Q] head is defined in (40c). Once we combine C_[+Q] with the proposition in (40b), we obtain the interpretation in (40d) for the question in (39a). This question as a whole presupposes that there is exactly one contextually relevant cake. We thus derive the presupposition given in (39b) that this question comes with.

With this baseline analysis for polar questions and their presuppositions in hand, I turn to my proposal for questions involving PolQPs in the next section.

3.2 Analysis of PolQPs-questions

On the syntactic side, building on Holmberg’s (2014) proposal for Finnish -kO I propose that PolQPs can be merged anywhere in a tree as long as they c-command a [Foc] feature. They carry a [uFoc] feature which needs to enter in an Agree-relation with a valued [Foc] feature. In addition, PolQPs carry an interrogative [uQ] feature which needs to agree with an interrogative C_[Q] head. To illustrate that the Agree-relation between C_[Q] and the PolQP has taken place, I will rewrite the interrogative C-head C_[+Q] in the remainder of this paper. Languages differ in whether the PolQP together with the constituent it associates with moves to the specifier of FocP or not. While in Turkish, the mI-phrase (i.e., the phrase made of mI and the constituent it associates with) can remain in situ, in Finnish, the kO-phrase (i.e., the phrase made of -kO and the constituent it associates with) moves to Spec,FocP on the surface.⁸

On the semantic side, I build on Atlamaz (2015) and Kamali & Krifka (2020) and analyze PolQPs as focus markers which are interpreted within the proposition out of which the question is formed. In other words, I claim that PolQPs are interpreted below the interrogative C_[+Q] head. These particles can combine with constituents of any semantic type as long as these constituents contain a focused expression. When α is a focused expression (or contains a focused expression), the contribution of PolQPs is vacuous, as shown below.

I adopt a two-tier alternative semantics analysis of focus (Rooth 1985; 1992) according to which the function of focus is to evoke alternatives. On this analysis, expressions come with both an ordinary (o-value) and a focus-semantic value (f-value). The f-value of an expression which does not carry any F-feature is the singleton-set that contains its ordinary semantic value, as illustrated in (42). In contrast, the f-value of an F-marked expression corresponds to the set of objects of the same semantic type. As for its o-value, it is the same as its regular semantic value without an F feature, as illustrated in (43).

The focus alternatives combine in a compositional manner, via a rule known as pointwise functional application, until they get factored into meaning via some operator.

In particular, the focus alternatives triggered by the constituent PolQPs combine with at LF project all the way to the focus-sensitive ~ -operator. Rooth’s (1992) ~ -operator is defined in (45).⁹ This operator evaluates all foci in its scope unselectively and neutralizes their contribution by resetting the f-value to the o-value (Beck 2006).

Let us now turn to the denotation of the interrogative C_[+Q] head. I propose that in languages with PolQPs, C_[+Q] is a focus operator which triggers an existential presupposition, as defined in (46).

The set Γ is identical to the set provided by the ~ -operator, which is moreover dependent on the focus value of the sister node of ~.

To illustrate this analysis, let us consider again the polar question involving Finnish -kO in (47a) and the polar question involving Turkish mI in (49a). The step-by-step composition of the Finnish question in (47a) is given in (48) and the step-by-step composition of the Turkish question in (49a) is given in (50). Both questions denote partial functions from worlds to sets of propositions, which are only defined in worlds in which one proposition in the alternative set g(Γ) is true. That is, the question in (47a) is only defined in worlds in which someone left, and the question in (49a) is only defined in worlds in which someone bought Sessizev.

As a result, this analysis captures the existential presupposition questions involving PolQPs come with. Presuppositions which come with PolQPs-questions involving other kinds of focused expressions will be discussed in Section 4.2.

The astute reader may wonder whether the existential presupposition coming with PolQPs-questions is not triggered by the interrogative particle itself or by the constituent it associates with. The following example from Turkish suggests that this is not the case. The polar question in (51a) which involves PolQP mI and the universal quantifier herkes ‘everyone’ cannot be uttered in a context in which everyone is going to a different place. For it to be felicitously uttered, there needs to be a place where everyone is going to, showing that the question in (51a) comes with the presupposition in (51b).

Section 5.1 will show that Turkish shows scope-rigidity and that the linear order between herkes and [Ankara-ya mı] determines their relative scope. As a result, the universal quantifier outscopes the mI-phrase in (51). This example thus shows that the existential presupposition PolQPs-questions come with is not triggered by mI or the expression it associates with but is triggered higher in the structure, above the universal quantifier in (51). In the proposed account, this existential presupposition is triggered by the interrogative C_[+Q] head defined in (46) which is available in languages with PolQPs like Finnish and Turkish.

4.1 PolQPs are mandatory

Recall that when PolQPs are not realized in a polar question, the resulting question is not well-formed, as shown again for Turkish below.

The role of PolQPs together with the constituent it combines with is to satisfy the non-singleton requirement of the ~-operator that co-occurs with C_[+Q]. When they are absent in a question, the presupposition is not sastified, and as a result, the question not well-formed. To illustrate, consider the step-by-step composition of the question in (52) in (53). The set of focus alternatives of the proposition that combines with ~ is a singleton-set. Thus, the presupposition of this operator is not satisfied and the question is undefined.

Questions like (54) which involve a stressed expression are not well-formed polar questions in Turkish either. Underlyingly, I propose that these questions involve a covert exhaustification operator EXH which co-occurs with the ~-operator. EXH is defined in (55). Given a sentence φ and a set of alternatives Δ of φ, EXH φ asserts the conjunction of φ and the negations of all alternatives that are not entailed by the assertion.

The step-by-step composition of the question in (54) is given in (56). The ~-operator which comes with EXH evaluates the F-marked expression in its scope and resets its focus semantic value to its ordinary semantics value. Thus, the set of focus alternatives of the proposition that combines with the ~-operator that comes with C_[+Q] is a singleton. As a result, the presupposition of this operator is not satisfied and the question is again undefined.

4.2 PolQPs are focus-sensitive

Another characteristic property of PolQPs discussed in detail in Section 2.4 is their focus-sensitivity. In particular, they can combine with any constituent in the structure as long as this constituent is F-marked or contains an F-marked expression. In particular, in a polar question like (57), Turkish mI can either follow the subject or the object, or it can appear in final position. The position of this particle affects the interpretation of the question, and in particular the presuppositions it comes with.

In Section 3.2, I have shown how the proposed account captures the interpretation of a question where mI associates with the subject. In the following examples, I turn to the other positions of mI. In particular, I derive the interpretations of questions where mI follows the object and where mI occurs in final position. When mI follows the object, it can either associate with the object, the VP (not illustrated here for sake of space) or the whole proposition out of which the question is formed (Kamali 2011). This is illustrated in examples (58)-(60).

The fact that mI can associate with the object, the VP and the whole proposition when it attaches to the object on the surface is not a property specific to this particle. As shown by Kamali (2015a), other focus-sensitive particles like also/even show the same behavior in Turkish.

Let us now consider polar questions where mI appears in final position. In this case, this particle can for instance associate with the predicate (63) or the polarity head (65) (Kamali & Krifka 2020, a.o.). See Kamali (2011) and Kamali (2015b) for more detailed discussions of the interpretation of questions involving mI in final position.

Kamali (2015b) shows that questions with final mI, in contrast to questions where mI follows the object, cannot be used out of the blue, as illustrated in (67)-(68). The analysis presented above helps us better understand this contrast. Questions involving final mI share the same presuppositions as the alternative questions Did someone break the window or not? and Did the baby roll down the bed or not?. These alternative questions, just like questions with final mI, are unfelicitous in such contexts, suggesting that this infelicitousness should be derived from the presuppositions.

4.3 PolQPs can be embedded

Not only can PolQPs occur in matrix interrogatives but also in embedded ones. In that case, they can be embedded under both rogative and responsive predicates, as illustrated again in (69) for Turkish mI.

When questions are embedded under rogative predicates like wonder, their presupposition is filtered to the attitude holder’s beliefs, as is the case with any attitude predicates (Karttunen 1974; Heim 1992: a.o.). Similarly, the sentence in (69a) comes with the presupposition that Ali believes that someone bought Sessizev. In contrast, when questions are embedded under responsive and factive predicates like know, their presupposition projects all the way to the matrix level. Unlike English know, Turkish bil- shows a factivity alternation (Özyildiz 2017a). For the sake of simplicity, we will focus on its factive use in this paper. In that case, the embedded question in (69b) comes with the presupposition that someone bought Sessizev.

We start with the analysis of the embedded question in (69a). The question-embedding predicate wonder is defined in (75). Just like other attitude predicates (Heim 1992), wonder_w(Q)(x) presupposes that x believes π(Q).

Proponents of the singleton analysis of polar questions claim that the singleton-set denotation of a polar question must sometimes be mapped to the corresponding bipolar denotation (Biezma & Rawlins 2012; Uegaki 2018: a.o.) to avoid some type mismatch or other composition issues. In particular, this extra operation is necessary in accounting for question-embedding. One way to retrieve this bipolar denotation is to combine the singleton denotation of the question with the operator defined in (71).

To illustrate how the composition works, let us consider again the embedded question (69a) repeated in (72). The semantic value of the embedded CP is given in (73b). Composing (73b) with the operator in (71), we obtain the semantic value in (73c). This resulting semantic value then combines with the predicate wonder defined in (70) and the matrix subject. As a result, we obtain in (73d) the desired interpretation for the embedded question in (72).

Now that we have seen how the proposed account captures the interpretation of PolQPs-questions embedded under rogative predicates like wonder, we turn to PolQPs-questions embedded under responsive predicates like know. The meaning of know can be paraphrased as ‘to know the answer of’. To retrieve the answer of a question, I adopt Dayal’s (1996) answerhood operator ANS defined in (74). ANS is a partial function from questions to propositions which presupposes the existence of a unique most informative true member of the question denotation. When defined, it returns the most informative true answer.

Recall that we focus here on the factive use of Turkish bil- ‘know’. In that case, it presupposes the truth of its complement.

To see how these pieces combine together, consider again the embedded PolQPs-question in (76). The step-by-step composition of this question is provided in (77). First, the operator OP_Y/N composes with the embedded CP in (77b). The resulting denotation given in (77c) then combines with ANS, as illustrated in (77d). Finally, (77d) combines with know and the matrix subject. As a result, we derive for the sentence in (76) the expected reading in (77e) which is only defined in case someone bought Sessizev in w.

This section has shown how the proposed account derives the fact that POlQPs-questions can be embedded under rogative and responsive predicates, capturing at the same time the presuppositions these questions come with. In the next section, we turn to the last characteristic property of PolQPs, i.e., their restriction to polar and alternative questions.

4.4 PolQPs are restricted to polar and alternative questions

In section 3.2, I have provided an account of polar questions involving PolQPs. Let us now show how the proposed account extends to alternative questions. Following Gračanin-Yuksek (2016), I assume that alternative questions in Turkish are disjunctions of polar questions. Similar analyses of alternative questions have been put forth by Uegaki (2014) for Japanese alternative questions, and Mayr (to appear) for Polish alternative questions, among others. The step-by-step composition of a question like (78) is provided in (79). In each disjunct, mI satisfies the non-singleton requirement of the ~-operator that co-occurs with C_[+Q]. The disjunction is interpreted as a generalized disjunction (Partee & Rooth 1983), as defined in (79d). Composing the semantic values of the two CPs with the semantic value of the disjunction, we derive in (79e) the desired interpretation of the alternative question in (78).

The astute reader may have noticed that the uniqueness requirement that comes with alternative questions (i.e., that not more than one alternative is true) is not captured in the derivation in (79). The source of this inference has been subject to debate in the literature; some have claimed that it is a presupposition, a conventional implicature, or some other non-assertive component (Karttunen & Peters 1976; Romero & Han 2003; Biezma & Rawlins 2012; Pruitt & Roelofsen 2013; Mayr to appear: a.o.). To know exactly what the source of this inference is is outside the scope of this paper. One can choose their favorite analysis to derive this uniqueness requirement as long as it is compatible with the proposed account for PolQPs and PolQPs-questions.

The final signature property of PolQPs is that they cannot participate in the formation of wh-questions, as illustrated again in (80).

Intuitively, these data suggest that there exists a competition between what the wh-word and the mI-phrase contribute in a question. In particular, both contribute a set of alternatives. In a question like (80a), these sets of alternatives are redundant, whereas in a question like (80b), they are incompatible.

However, deriving the incompatibility of these two interrogative elements is not an easy task. The main reason is that in standard analyses of wh-questions, the wh-word is interpreted as an indefinite and overtly or covertly moves to be interpreted above the interrogative C_[+Q] head. However, given that PolQPs are interpreted below C_[+Q], these two elements cannot easily combine with each other in a question like (80a). In the literature, we find analyses of wh-questions according to which wh-words are interpreted within the proposition out of which the question is formed. Versions of such analyses have been proposed by Beck (2006), Kotek (2014), and Mayr (2014), among others. However, none of these analyses are compatible with polar questions, and more specifically with polar questions involving PolQPs. As a result, one cannot adopt analyses of wh-in-situ questions to derive the incompatibility of the wh-word and PolQPs in questions like (80).

Another possible line of inquiry is to postulate that interrogative C_[+Q] heads in wh-questions and in polar questions differ from each other. Specifically, the interrogative C_[+Q] head found in wh-questions selects a TP and denotes a total function, as in (81a), whereas the interrogative C_[+Q] head found in PolQPs-question selects a FocP and denotes a partial function, as in (81b). In that case, we could maintain a standard analysis of wh-questions according to which wh-words are interpreted above the interrogative C_[+Q],

If one assumes that the existential presupposition of wh-questions is contributed by the wh-words (e.g., Chierchia & Liao 2015), the incompatibility of the wh-words and mI in questions like (80) would come from a redundancy of the existential presupposition (80a) or an incompatibility of these existential presuppositions (80b). Further work is required to detail the implementation of such an analysis. More generally, the impossibility of PolQPs to participate in the formation of wh-questions raises core questions regarding what varies across different types of questions (e.g, the interrogative C_[+Q] head, the way interrogative elements combine with the interrogative C_[+Q] head) which will be addressed in future research.

5.1 Interaction with quantifiers

Because the position of Turkish mI is flexible in a question, we can investigate how it interacts with other logical operators like quantifiers. Özyıldız (2015) shows that when a universal quantifier co-occurs with negation in a declarative, the narrow scope interpretation of the universal quantifier is the preferred interpretation for all speakers, as shown in example (82). Even though Özyıldız’s (2015) example involves a subject quantifier, example (83) shows that the same is true of sentences involving object quantifiers.

When we turn these declaratives into polar questions by combining PolQP mI with the universal quantifier, that quantifier must now take wide scope with respect to negation, as illustrated in (84). The reading where the universal quantifier takes narrow scope with respect to negation (i.e., ‘Is it not the case that everybody is going to Ankara?’) is not available. Again, questions involving universal quantifiers in object position pattern the same way, as shown in (85).

The above examples show that combining PolQP mI with a universal quantifier changes the scope of that quantifier. In particular, the quantifier takes a wider scope than the one it takes in declaratives. Now, when mI combines with constituents other than the quantifier, a contrast is observed depending on the position of mI with respect to the quantifier. Specifically, when the quantifier precedes mI on the surface, it must take wide scope with respect to negation. Example (86) shows that this is true of both subject and object quantifiers. In contrast, example (87) shows that when herkes follows mI, it must scope under negation just like in declaratives. Again, both subject and object quantifiers pattern the same.

These examples show that the surface position of mI with respect to a universal quantifier matters and affects the interpretation of the question. Table 3 summarizes the generalizations I just established.¹⁰

Let us see how the account put forth in Section 3 can capture these scope facts. In Turkish, negation occurs above vP and below TP, as suggested by the order of the morphemes on the verb (see e.g. Jeretič 2022). The fact that the universal quantifier herkes must take narrow scope with respect to negation in a declarative for most speakers (88) suggests that for them the quantifier must reconstruct under negation at LF, as shown in (89a). With this structure, we derive for the sentence in (88) the interpretation in (89b).

To derive the interpretation of PolQPs-questions involving both herkes and negation (schematized in the second and third column of the above table), I adopt Kratzer’s (1991) implementation of Rooth’s (1992) theory (cf. discussion by Beck 2006). In this system, the ordinary value of a (non-complex) constituent α is its usual denotation, which is derived by applying the interpretation function. For the secondary value, a designated assignment function h is invoked. The F feature of a focused expression carries an index which serves as a distinguished variable subject to interpretation by h. h maps the variable on α onto an object of the same semantic type as ⟦α⟧^g.

The secondary value of a complex constituent is then derived recursively by applying the usual semantic rules to its subconstituents. The rules of functional application and predicate abstraction are defined in this system as follows.

To illustrate how this system works, let us consider again a polar question which involves neither negation nor a quantifier like (93). The step-by-step composition is given in (94). We derive for this question the denotation in (94g), as expected. That is, the question denotes a partial function from worlds to sets of propositions, which is only defined in worlds in which one proposition in the alternative set g(Γ) is true – namely, in worlds in which someone left.

Consider now a polar question where the interrogative particle mI co-occurs with a universal quantifier, as (95). This question has the underlying structure in (96a). Combining the negative proposition in (96b) with the phrase made of mI and the constituent it associates with in (96b), and then with the ~-operator and the interrogative C_[+Q] head, we obtain the denotation in (96e) for the polar question in (95), as expected. That is, we derive the interpretation according to which the universal takes wide scope with respect to negation.

Just like other quantifiers in the language (Kelepir 2001; Özyıldız 2017b; Demirok 2019), I propose that mI can freeze the scope of another quantifier it co-occurs with. The phenomenon of scope rigidity between two quantifiers in Turkish declaratives is illustrated in example (97).

As a result, when the mI-phrase precedes the universal quantifier on the surface, it takes wide scope over it at LF. In that case, the universal can reconstruct under negation just like in declaratives, and we derive for the question the reading ¬ > ∀, as shown in (99).

In contrast, when the mI-phrase follows the universal quantifier on the surface, it scopes under it at LF. In that case, the universal quantifier cannot reconstruct to its base position, as illustrated in the structure in (101a), and we derive for the question in (100) the reading ∀ > ¬ given in (101b).

To summarize, this section builds on Özyıldız (2015) and establishes a new empirical generalization regarding the interaction between PolQP mI and quantifiers. On the theoretical side, I show how the account of PolQPs and PolQPs-questions provided in Section 3 combined with Kratzer’s (1991) implementation of Rooth’s (1992) theory captures this generalization. As pointed out by an anonymous reviewer, one prediction this account makes is that the universal quantifier herkes should take narrow scope with respect to negation in broad focus contexts, that is, when mI associates with the whole proposition. This prediction will be carefully investigated in future work.

5.2 Intervention effects

In the proposed account of PolQPs-questions, the focus alternatives triggered by the constituent PolQPs combine with must project all the way to the interrogative C_[+Q] head. Therefore, we expect the following: if an operator which can use these focus alternatives intervenes between C_[+Q] and the mI-phrase, the corresponding polar question would not be well-formed. This final section shows that this prediction is indeed borne out. Before turning to the discussion of PolQPs-questions, I first introduce the phenomenon of intervention effects with wh-questions as it has – to my knowledge – never been discussed in the domain of polar questions before.

In wh-in-situ languages, when some logical operator like the focus particle only precedes the wh-word, the resulting wh-question is ill-formed (Beck 2006; Beck & Kim 2006; Mayr 2014; and references therein). This is illustrated in (102a) for Korean. When the wh-word moves accross the focus particle, the question becomes fully acceptable, as illustrated in (102b).