Unveiling Multiple wh- Free Relative Clauses and their functional wh-words

We provide the first description and compositional semantic analysis of a construction that we label a “multiple whfree relative clause”⎯an embedded non-interrogative whclause with more than one wh-word. We show that multiple whfree relative clauses are closely related to the more familiar free relative clauses with one whword⎯single whfree relative clauses. We argue that a fully satisfactory semantic analysis for multiple whfree relative clauses can be grounded in the semantic analyses that have been proposed for single whfree relative clauses, but crucially requires non-trivial broadening of the meaning of wh-words. Focusing on Romanian, we propose a compositional account of multiple whFRs building on two main components: (i) the assumption that wh-words can license complex traces/variables with a functional component⎯an option that has been independently suggested for several other whconstructions, and (ii) a new functional meaning for wh-words⎯a close variant of the functional meaning of whwords that has been independently proposed to account for functional whinterrogative clauses.

early access 2 languages: wh-interrogative clauses, headed relative clauses, correlative clauses, and free relative clauses⎯just to mention a few. Wh-clauses with more than one wh-phrase raise at least a couple of broad issues. Which kinds of wh-clauses allow for more than one wh-phrase and which don't? Can the semantic analyses that have been proposed for single wh-clauses (i.e., wh-clauses with one wh-phrase) be straightforwardly extended to multiple wh-clauses (i.e., wh-clauses with more than one wh-phrase) and, in particular, can the meaning that has been assumed for wh-words in single wh-clauses be retained and applied to wh-words in multiple wh-clauses as well? To the best of our knowledge, these two broad issues have not yet been systematically investigated within languages, let alone across languages. They are relevant issues not just for a more complete description of wh-clauses but also, and crucially, for a better understanding of the semantic behavior of wh-words⎯one of the most powerful and least understood building blocks of the logic behind human language. In this paper, we focus on a construction that exemplifies both issues: (i) it is a multiple wh-clause whose existence has not yet been recognized, unlike its single wh-variant, and (ii) its semantic analysis cannot be a simple extension of its single wh-variant but requires non-trivial broadening of the meaning of its wh-words. We label this construction a multiple wh-free relative clause or, in short, a multiple wh-FR. We focus our investigation on Romanian, a language that displays an articulated system of multiple wh-FRs. 2 Examples are given in brackets in (1)−(4).
(1) Bunica a împachetat [ ce cui dă de Crăciun]. Grandma has wrapped what who.DAT gives for Christmas 'Grandma wrapped the things she'll give to the appropriate people for Christmas.' (2) Muncitorii au montat [ce cum fusese instalat înainte de incendiu]. workers-the have.3PL assembled what how had.been.3SG installed before of fire 'The workers assembled the things that had been installed in the appropriate ways before the fire.' (3) Bunica a pregătit [ce când va lua în următoarele săptămâni]. Grandma has prepared what when will.3SG take in next-the weeks 'Grandma prepared the things that she'll take at their appropriate time in the next weeks.' (4) Proprietarul a aranjat [ ce unde a trebuit instalat]. owner-the has arranged what where has needed installed 'The owner arranged the things that needed to be installed in the appropriate place.' 2 Our ten consultants are all from Transylvania, a region from North-Western and Central Romania. Two anonymous conference-abstract reviewers reported that in their (unspecified) variety of Romanian multiple wh-FRs are not allowed. Subsequent feedback from colleagues who are native speakers of other varieties suggests a split between northern varieties (which allow multiple wh-FRs) and southern ones (which disallow them), but further investigation is necessary to determine the extent and nature of the observed variation. From now on, whenever we use the label Romanian in discussing multiple wh-FRs, we are specifically referring to the variety of Romanian spoken in Transylvania, unless mentioned otherwise. early access 3 The multiple wh-FRs in (1)−(4) are full clauses containing two wh-phrases, all in clause-initial position in a fixed order, as in multiple wh-interrogative clauses in Romanian. Still, the multiple wh-FRs in (1)−(4) occur as the complements of matrix predicates that usually select for a DP in their complement position, rather than a clause. The multiple wh-FRs in (1)−(4) are not interpreted as conveying a question, but as referring to a maximal (plural) individual, as (plural) definite DPs do. In all these multiple wh-FRs, the first wh-phrase affects the interpretation of the other one in a way that we tried to partially render with the adjective "appropriate" or "corresponding" in most translations. The precise nature of this "functional" connection is at the center of the paper and will be discussed at length.
In brief, we argue that multiple wh-FRs are free relative clauses, rather than any other new or already attested kind of wh-clause in Romanian. At the same time, we show that a satisfactory compositional account of the semantic behavior of multiple wh-FRs requires a revision of the semantic contribution of wh-words that is usually assumed for single wh-FRs. This revision will introduce a "functional" component in the lexical entry of wh-words and their traces that will be very close to what has been argued for in the case of the so-called functional interpretations of single wh-interrogative clauses and headed relative clauses with universally quantified subjects across languages (Engdahl 1980(Engdahl , 1986Groenendijk & Stokhof 1984;Chierchia 1991Chierchia , 1993Jacobson 1994;Dayal 1996Dayal , 2016Sharvit 1999a,b, a.o.). Therefore, our investigation of Romanian and its multiple wh-FRs broadens the meaning space of wh-words in free relative clauses and in general. In doing so, it also highlights how this meaning space is constrained and holds across different kinds of wh-clauses.
We also provide further evidence that free relative clauses in general cannot be reduced to headed relative clauses without an overt nominal head. If this were the case, then languages like Romanian would be expected to have multiple wh-headed relative clauses. Although Romanian does make use of a subset of wh-words to introduce headed relative clauses, they are not exactly the same subset that single wh-FRs make use of (see Grosu 2013;Caponigro & Fălăuș 2017). More crucially, it is not possible to have a headed relative clause with more than one wh-word. The bracketed string in (5) shows an attempt to build a headed relative clause with the wh-words for 'what' and 'where', which can introduce headed relative clauses separately (and a multiple wh-FR together, as in (4)). The result is completely unacceptable, regardless of the presence of either both the DP head ('the furniture') and PP head ('in places'), or only the former.
(5) * Proprietarul a aranjat mobila (în locurile) [ ce unde a trebuit owner-the has arranged furniture-the in places-the what where has needed instalată]. installed ('The owner arranged the furniture that needed to be installed (in the places) where it needed to be installed.') Lastly, we aim to promote the crosslinguistic investigation of multiple wh-FRs. There are strong reasons to believe that multiple wh-FRs are not confined to Romanian. Below we provide some preliminary crosslinguistic evidence from speakers of varieties of American English, Franconian German, Czech, and Serbian. We hope that the methodology and the series early access 4 of tests that we have developed will encourage further investigation within those languages and help unveil multiple wh-FRs across more languages. 3 (6) I gave you [what you had to put where].
[American English] 'I gave you the things you had to put in the appropriate places.' (7) Ich bereite vor,[ was wir wem geben müssen].
[German] I prepare what we whom give must 'I'll prepare the things we should give to the appropriate people.' We proceed as follows. In the next section, we describe multiple wh-FRs in Romanian in more detail and introduce their main properties. In Section 3, we show that they cannot be reduced to any other wh-clause that is attested in Romanian but free relative clauses. Section 4 offers a compositional account of multiple wh-FRs building on two main components: (i) the assumption that wh-phrases can license complex traces/variables with a functional component, an option that has been independently argued for several other wh-constructions, and (ii) a new functional meaning for wh-phrases, a variant of the functional meaning of wh-phrases that has been independently proposed to account for functional wh-interrogative clauses. Section 5 concludes and discusses some open issues for future research.

Main properties of multiple wh-FRs
In this section, we highlight four core properties that characterize multiple wh-FRs in Romanian. We start with two distributional properties: one having to do with where multiple wh-FRs occur within their matrix clause (Section 2.1) and the other dealing with which wh-phrases can or cannot introduce multiple wh-FRs (Section 2.2). We then turn to properties pertaining to the interpretation of multiple wh-FRs: their referentiality and maximality (Section 2.3) and the "functional" component that is associated with their interpretation (Section 2.4). Finally, we consider a potential fifth property, agentivity, which has been suggested by an anonymous Reviewer on the basis of data from Czech multiple wh-FRs, and conclude that our data do not support this property for Romanian (Section 2.5).
3 The judgments about American English come from one speaker from Maryland and one from Georgia. The Franconian German judgments come from a speaker from Baden-Württemberg. We are grateful to Daniel B. Kane, Harold Torrence, Eva Wittenberg, Radek Šimík, and Boban Arsenijevic for the data and the judgments. early access 5 Each of the attested four properties in Romanian multiple wh-FRs will give rise to one or more tests that we use in the next section (Section 3) to compare multiple wh-FRs with other kinds of wh-clauses, of which Romanian has several. A formal and compositional semantic account for the semantic properties of multiple wh-FRs in Romanian and their distribution is provided in Section 4.

Distribution
Multiple wh-FRs can occur as arguments of an embedding clause and can be replaced by a DP, despite being clausal and looking more like CPs. For instance, the multiple wh-FR we saw in (2), repeated in (10)a below, occurs as the object of the matrix clause and can be replaced (and roughly paraphrased) with the (complex) definite DP in brackets in (10) installed before of fire 'The workers assembled the furniture in the way in which it had been installed before the fire.' Multiple wh-FRs can also occur as complements of prepositions. The multiple wh-FR in brackets in (11)a acts as the complement of the preposition la 'at' and can be replaced by the DP in (11) Finally, multiple wh-FRs can also occur as subjects of the clause embedding them, although not without restrictions. The multiple wh-FRs in brackets in in (12)a behave as the subjects of their matrix clauses and can be replaced by the DPs in (12) The matrix predicate taking a multiple wh-FR as its subject can be intransitive, as e ascuns 'is hidden' in (12)a, or transitive, as sperie 'frightens' in (12)a. These predicates allow for either a preverbal or postverbal subject when the subject is a DP, while they prefer a postverbal subject when the subject is a single or multiple wh-FR, as we discuss further in Section 3.1. Overall, what seems to emerge is some (poorly understood) restriction on free relative clauses in preverbal subject position in Romanian, regardless of whether they have one or more whphrases. Further research on this is needed.
What matters the most for our current investigation is to have established that multiple wh-FRs can unambiguously occur in argument positions (subject, object, complement of a preposition), since this distributional property will be used in Section 3 to distinguish multiple wh-FRs from other multiple wh-constructions.

Restrictions on wh-phrases
Multiple wh-FRs cannot be introduced by the complex wh-phrase [care NP] ('which' NP). The bracketed string in (13) is almost identical to the multiple wh-FR in (1), except that the simple wh-phrase ce 'what' in (1) has been replaced with the complex [care cadou(ri)] ('which gift(s)') or [ce cadou(ri)] ('what gift(s)'). The resulting sentence is unacceptable with care cadou(ri), while it is fully acceptable with ce cadou(ri). This contrast shows that there is no independent incompatibility between multiple wh-FRs and complex wh-phrases.

Referentiality and maximality
In this section, we show that multiple wh-FRs are always interpreted as referential and maximal. These are the same properties that definite DPs exhibit, following Sharvy 1980, Link 1983, and subsequent work. Referentiality is the semantic property of referring to an individual (or a portion of matter, or a kind). A referential expression is, therefore, non-quantificational. Maximality is the property that some referential expressions have to refer to the maximal individual of a given set. For instance, the definite DP the dogs is referential and maximal because it refers to the maximal plural individual made of the sum of all the single dogs in the given context. The deictic DP those dogs is referential, but not maximal: it can refer to a plural individual resulting from the sum of some, but not necessarily all, the single dogs in the given context. Finally, quantificational DPs like some dogs and every dog are neither maximal nor referential. 4 One piece of evidence that multiple wh-FRs are referential and maximal comes from the fact that speakers agree with paraphrasing them by means of referential and maximal expressions like definite DPs. For instance, the multiple wh-FR we started with in (1) can be roughly paraphrased using the complex definite DP in (15). Other examples of multiple wh-FRs with their DP paraphrases were provided in Section 2.1.
(15) Bunica a împachetat [DP lucrurile pe care le va oferi oamenilor Grandma has wrapped things-the ACC REL CL will.3SG offer people-the.DAT de Crăciun]. for Christmas 'Grandma wrapped the things that she'll give to the people they are for at Christmas.' There is also another way to test maximality: by building a scenario that would force a multiple wh-FR to violate it. For instance, imagine a situation in which Grandma started wrapping Christmas gifts, and managed to wrap 3 out of 10 before she got interrupted. In this scenario, it is not felicitous for the speaker to utter the sentence in (16)a with the bracketed multiple wh-FR, nor the sentence in (16)b with the bracketed definite DP instead of the multiple wh-FR. In both cases, the two-place relation of wrapping is claimed to hold between Grandma and the maximal plural individual made of those 10 gifts, which would be false, since 7 of them early access 8 are still unwrapped. Notice that in this scenario a DP can occur as the complement of the matrix predicate, as long as it is not definite, as shown by the bracketed indefinite DP in (16) In conclusion, multiple wh-FRs share the same semantic properties as definite DPs: they are referential and maximal.

Wh-phrases and functional dependencies
The next property of multiple wh-FRs that we discuss is semantic as well. Unlike maximality, it does not have to do with the overall meaning of a multiple wh-FR, but rather the way the wh-phrases are interpreted. In particular, in all multiple wh-FRs, the interpretation of the first/higher wh-phrase⎯the wh-phrase preceding and c-commanding the other⎯affects the interpretation of the other wh-phrase. In other words, the interpretation of the lower wh-phrase depends on the interpretation of the higher. To see this, let us consider the example in (18), a slight variant of the example in (3).
(18) Azi mama a pregătit [ ce când va lua bunica în următoarele today Mom has prepared what when will.3SG take Grandma in next-the săptămâni]. weeks 'Today Mom prepared what Grandma will take at its appropriate time in the next weeks.' This sentence would be used in a context like the following. Imagine Grandma is getting worried about having a lot of medication to take, at different times of the day, and having it all mixed up. To put her mind at ease, Mom prepared Grandma's morning and evening medication for the next few weeks, putting it in separate boxes so that Grandma doesn't get confused. In this context, it is clear that for each medicine Mom prepared, there is an appropriate/unique time for it to be taken. Crucially, (18) cannot mean that today Mom prepared what Grandma will take at some random/non-unique time in the next weeks, with the wh-phrase când 'when' acting as an existentially quantified expression. Nor can it mean that today Mom prepared what Grandma will take at that one specific time in the next weeks, with când acting as a free pronoun over instances whose reference is contextually determined. Both these meanings are logically possible and natural. In fact, they can be conveyed by a single wh-FR with an indefinite ('sometime next week') or a referential ('on Sunday') temporal expression in place of 'when', as shown in (19) It is a specific property of the multiple wh-FR in (18) that the time at which each medication has to be taken is functionally dependent on the specific medication: each medication is associated with a unique specific time.
Speakers share this "functional" intuition across all multiple wh-FRs we have discussed: their interpretation of the lower wh-phrase (or, more precisely, of the argument that the whphrase plays the role of) depends on the interpretation of the higher wh-phrase (or, more precisely, of the argument that the wh-phrase plays the role of). This kind of functional early access 10 dependency is from one individual to another⎯a Skolem function, as we discuss in detail in Section 4.

An agentivity constraint?
An anonymous Reviewer confirmed our preliminary findings about the existence of multiple wh-FRs in Czech (see our example in (8)), but pointed out that a further semantic constraint may hold, together with referentiality, maximality, and functionality⎯the core properties of multiple wh-FRs that we have argued for so far. This further constraint requires a multiple wh-FR to occur as the non-agent argument of an agentive predicate, as shown in (20) and (21) (data and judgements from the Reviewer). (20)a is the Czech equivalent of our example in (1). The multiple wh-FR (20)a occurs as the object of the agentive matrix predicate 'pack' with Grandma as the agent. The sentence is judged fully acceptable. If the very same multiple wh-FR occurs as the subject of an intransitive locative predicate like 'to lie' as in (20)b, the resulting sentence is unacceptable. If a closely related single wh-FR replaces the multiple wh-FR in (20)b, the resulting sentence is fully acceptable, as in (20) . daughter spotted what.ACC REFL next week put on self 'The daughter spotted/saw the clothes that she will wear next week.' early access 11 The Reviewer suggests that these contrasts show that the "functionality" of multiple wh-FRs has to be relativized to a syntactically expressed agent. In other words, multiple wh-FRs are licensed only if the functional mapping triggered by the interaction between the two wh-phrases is determined by the agent of the matrix predicate. Whenever no overt agent is present, as in (20)b and (21)b, a sentence is predicted to be unacceptable.
Our findings do not support an agentivity constraint in multiple wh-FRs in Romanian. First, the examples in (12)a already showed that Romanian allows multiple wh-FRs as subjects of non-agentive predicates. Second, even with agentive predicates, there is no need for an overt agent in sentences with multiple wh-FRs nor does the overt matrix agent need to be the one determining the functional mapping, as shown in (22). Both matrix options in (22) make the sentence acceptable, although they both violate the agentivity constraint. The option with the matrix predicate at the impersonal form doesn't have an overt agent anywhere in the sentence. The option with an overt matrix agent (Grandma) is acceptable even when the agent is not the one determining the functional mapping between gifts and people who receive them. The continuations in (22)a-c are fully compatible with the sentence(s) with the multiple wh-FR in (22), despite depicting scenarios in which neither Grandma nor the speaker are familiar with the functional mapping, let alone being responsible for it. The scenarios in (22) So if the functional construal of the multiple wh-FR is not relativized with respect to an agent, why is an example like (23)a (the Romanian version of (21)b in Czech) degraded with respect to its single wh-FR counterpart in (23) We do not have a conclusive answer, but we would like to at least offer some observations that may help future investigation on multiple wh-FRs in Romanian, Czech, and across languages in general. Drawing on our consultants' comments, the action of seeing clothes doesn't seem to justify the relevance of the functional mapping in (23)a from clothes to the time at which those clothes will be worn. On the other hand, organizing medicines that will have to be taken at the appropriate moments, as in (3), may be affected by those chosen moments (e.g., medicines would be put in different places according to when they have to be taken). Overall, this could be the manifestation of a pragmatic restriction penalizing semantic complexity (e.g., Skolem functions) unless it is informationally relevant.
If this observation is on the right track, why are the sentences in (12)a acceptable then? How does the status of being hidden or frightening gifts relate to the people who will receive those gifts? Unlike (23)a, the multiple wh-FR in (12)a is a subject, which is notoriously a much better topic than the object⎯in Romanian and across languages (on the complex relation between subjects and topics in Romanian, see Giurgea 2019 and references therein). It could be that being a topic (at least with certain intransitive predicates) facilitates the licensing of a multiple wh-FR by assuming that it has already been introduced in the discourse, or, equivalently, it was part of the question under discussion.
To sum up, the data from Romanian do not support a ban on multiple wh-FRs lacking an overt (or covert) matrix agent. There are however a variety of factors affecting the acceptability of multiple wh-FRs, some of which we discussed in the previous sections. One extra factor that has emerged in this section is the need for a justification for the introduction of a functional mapping via a multiple wh-FR⎯a justification that could be pragmatic in nature. Agentive predicates like 'arrange/organize' or 'wrap' seem to facilitate the satisfaction of this requirement in a way that non-agentive predicates like 'spot' do not. Being in a topic vs. nontopic position could be another way to satisfy that pragmatic requirement. A related open issue is whether Czech and other languages with multiple wh-FRs may not all be sensitive to exactly the same factors in the same way.
In the rest of the paper, we set these issues aside and focus on examples of fully acceptable multiple wh-FRs in object position with mainly agentive predicates. We hope that future crosslinguistic work will shed light on this and other potential constraints on the distribution and interpretation of multiple wh-FRs. At the same time, we think the analysis of multiple wh-FRs we propose in Section 4 is not incompatible with possible further restrictions and could be modified to incorporate those as well.

Interim summary
The discussion in this section has revealed the properties summarized in (24) as the ones characterizing multiple wh-FRs in Romanian: (24) Main properties of multiple wh-FRs in Romanian: (i) they are embedded wh-clauses that can occur as arguments of their embedding predicates; (ii) they cannot be introduced by the wh-phrases care NP 'which NP' nor cine 'who'; early access 13 (iii) they are referential and maximal, like definite DPs; (iv) they are associated to a functional mapping that is triggered by the lower whphrase and its interaction with the higher wh-phrase.

Multiple wh-FRs are free relative clauses rather than any other wh-clauses
In this section, we compare multiple wh-FRs with other wh-clauses in Romanian using the properties of multiple wh-FRs we presented in Section 2 and summarized in (24). We conclude that multiple wh-FRs are free relative clauses, while they exhibit crucial differences with all the other wh-clauses that are found in Romanian, in particular Rudin's multiple wh-clauses, wh-interrogative clauses, correlative clauses, and modal existential constructions.

Multiple wh-FRs are free relative clauses
Single wh-FRs are clauses with one wh-phrase, like the bracketed string in (25). 5 (25) Muncitorii au montat [ce fusese instalat înainte de incendiu]. workers-the have.3PL assembled what had.been installed before of fire 'The workers assembled the things that had been installed before the fire.' They share the first three properties in (24) with multiple wh-FRs (they cannot share the last property since they only have one wh-phrase by definition). First, single wh-FRs can occur as arguments, as shown by the bracketed single wh-FR acting as the object of the matrix predicate in (25). Second, they can be introduced by all wh-phrases but care NP 'which NP' (26)  In fact, cine could easily be replaced with the morphologically related free choice item oricine 'anyone'/'whoever' without any change in meaning. When cine FRs are episodic (27) (25) can be replaced and paraphrased by the definite DP in (28)⎯a prototypical referential expression.
(28) Muncitorii au montat [DP lucrurile care fuseseră instalate înainte de workers-the have.3PL assembled things-the REL had.been installed before of incendiu]. fire 'The workers assembled the things that had been installed before the fire.' (29) with a bracketed single wh-FR is infelicitous in the given context in which Grandma hasn't wrapped all Christmas gifts: the single wh-FR has to refer to the maximal gift, the plural gift resulting from the sum of all the individual gifts that Grandma will give for Christmas. But Grandma hasn't yet wrapped the maximal gift, i.e., all the individual gifts the maximal gift is the sum of.
(29) CONTEXT: Grandma started wrapping her Christmas gifts, but got interrupted.
# Bunica a împachetat [ ce va oferi de Crăciun]. Grandma has wrapped what will.3SG offer for Christmas 'Grandma wrapped the things she'll give for Christmas.' Single and multiple wh-FRs also share the poorly understood ban on being used as subjects in preverbal position (although the ban seems weaker for single wh-FRs). In Section 2.1, we showed that multiple wh-FRs (12)a and complex definite DPs (12) In view of all these similarities, we conclude that multiple wh-FRs are free relative clauses. To further support this conclusion, we now provide evidence that they differ in significant ways from other multiple wh-constructions that are attested in Romanian.

Multiple wh-FRs are not Rudin's multiple wh-relative clauses
To our knowledge, the literature has so far only mentioned multiple wh-relative constructions in a few languages, mostly spoken in the Balkans (Bulgarian, Macedonian, Romanian). Rudin 1986Rudin , 2007Rudin , 2008  Rudin analyzes each of the bracketed multiple wh-clauses in (32)−(33) as a "headless relative clause in a non-left-peripheral, argument position", i.e., a free relative clause with more than one wh-word (Rudin 2008). However, despite the common label of 'multiple wh-free relative clause', we think that these examples are different from the multiple wh-FRs we investigate in this paper and, more generally, the two kinds of multiple wh-clauses exhibit several properties that set them apart.
The first property is the relation between the wh-phrases and the predicates in the matrix and relative clause. In the examples in (32)−(33) above, each wh-phrase is related to an argument of both the matrix and the embedded predicate: the people blabbing/eating are the ones that want to blab/eat and the things they blab/eat are the things they want to blab/eat. An even clearer example is the one in (34), where the agent(s) and the patient(s) of the attacking and the finding are the same. (35) shows that it is also possible to have adjunct wh-phrases in these constructions, once again modifying both the matrix and the embedded predicate.
has attacked who ACC who has found 'Everyone attacked whoever they found.' In contrast, our multiple wh-FRs satisfy only one argument of the matrix predicate (typically the object) and the lower wh-phrase is in no way related to the matrix predicate. In (36)a, for instance, repeated from (1), the wh-clause refers to a set of objects wrapped by Grandma; the receiver of the gifts is an argument of the embedded predicate 'give' and not an argument of the predicate 'wrap'. Similarly for the example in (18), repeated in (36) Second, the interpretation of the wh-phrases in (32)−(35) is akin to a universal quantifier or a free choice item, like 'anyone' or 'whoever'. These elements can also replace the wh-phrases without any detectable change in meaning, as shown in (37), where the higher wh-phrase is replaced by the universal quantifier fiecare 'every' and (38) These substitutions are not possible in multiple wh-FRs. (39)a shows a variant of the multiple wh-FR in (36)a in which the higher wh-phrase has been replaced by a universal quantifier. In (39)b, instead, both wh-phrases in (36)  A further difference between the two kinds of multiple wh-clauses concerns the use of cine 'who'. It is extremely productive in the multiple wh-constructions discussed by Rudin (32)−(35). In contrast to this, as already pointed out in Section 2.2, all the examples of our multiple wh-FR introduced by cine 'who' are judged degraded, as illustrated in (40)  Finally, it should be mentioned that the acceptability of the construction in (32)−(35) is not subject to any kind of speaker or dialectal variation-examples such as these are extremely productive and systematically accepted by all native speakers we have consulted, independently from the varieties of Romanian they speak. In contrast, our multiple wh-FRs are more restricted and are only accepted by a subset of native speakers (see footnote 2). This, we think, provides further support for the claim that we are dealing with two different multiple wh-constructions. In this paper, whenever we use the label multiple wh-FRs, we are referring to examples such as (1)−(4), and not to the kind of construction analyzed by Rudin, which deserves an independent investigation. early access 18

Multiple wh-FRs are not interrogative clauses
Multiple wh-interrogative clauses are widespread across languages. 8 They are very productive in Romanian as well (Comorovski 1996, Rațiu 2011, both as matrix and embedded clauses, as shown in (41) and (42) There are at least three properties indicating that multiple wh-FRs are not interrogative clauses. First, like single wh-FRs, multiple wh-FRs can occur as arguments of non-interrogative predicates like 'assemble', 'prepare', or 'wrap', as shown above in (1)−(4). None of these predicates can take a polar or wh-interrogative clause as its complement.
Second, recall from Section 2.2 above that multiple wh-FRs disallow the use of the wh-phrase [care NP] 'which NP' as the first wh-phrase, as in (43)a, as well as that of cine 'who', as in (43) Third, the interpretation of multiple wh-FRs does not resemble the interpretation of (single or multiple) wh-interrogative clauses. We discuss the semantic contribution of multiple wh-FRs in more detail in Section 4. Here it suffices to observe that multiple wh-FRs denote (singular or plural) individuals, as highlighted by the definite descriptions paraphrasing them and the early access 19 semantic properties discussed in Section 2. Wh-interrogative clauses, instead, denote a question, i.e., a set of propositions or some other semantic object different from individuals.
Lastly, a few words of caution. Examples like (45) provide evidence that the matrix predicate 'show' allows for an analysis of the bracketed multiple wh-clause that is ambiguous between an embedded interrogative reading, where the children showed both where and when the puzzle pieces must be put, and a multiple wh-FR reading, where the second wh-phrase has a functional interpretation, i.e., the children showed the places where the pieces had to be put and for each piece there is an appropriate time to put that piece in its place. In the remainder of the paper, we will refrain from using predicates that can select for both multiple wh-FRs and interrogative clauses, or for more than one multiple wh-construction in general.

Multiple wh-FRs are not correlative clauses
In addition to multiple wh-interrogative clauses, some languages-including Romanian-also allow for multiple wh-correlative clauses like the bracketed strings in (46) Correlative clauses can be clearly distinguished from multiple wh-FRs. A well-known feature of correlative clauses⎯also illustrated in (46)a−b above⎯is that they occur at the periphery of their matrix clause (e.g., Dayal 1996;Lipták 2009). In contrast, as discussed in Section 2, multiple wh-FRs occur in argument positions within their matrix clauses (similarly to single wh-FRs), rather than dislocated. Furthermore, the wh-phrases used in a correlative clause have corresponding anaphoric (pronominal/demonstrative) markers in the matrix clause⎯typically one for each wh-phrase. FRs on the other hand (be they single or multiple wh-ones) do not have this property⎯their matrix clause does not contain anaphoric elements linked to their whphrase(s). early access 20 Finally, correlative clauses in Romanian can be introduced by the wh-phrases [care NP] 'which NP' and cine 'who'⎯unlike multiple wh-FRs (see Section 2.2 above). This is illustrated in the sentences in (47)  (48) [Pe cine ți-a fost alături la greu], pe acela să-l ții aproape și la bine. ACC who you-has been close at hard ACC DEM.3MSG SUBJ-him keep close at good 'Who(ever) has been there for you in hard times, you should keep them close in good times.' Given that neither defining property of correlative clauses (peripheral position, anaphoric marker) holds in multiple wh-FRs and taking into consideration the different distributions of [care NP] and cine in multiple wh-clauses, we conclude that multiple wh-FRs and correlative clauses are different constructions.

Multiple wh-FRs are not modal existential constructions
Multiple wh-"Modal Existential Constructions" (MECs) like the bracketed strings (49) Grosu 2004Grosu , 2013Grosu and Šimík 2011 provide crosslinguistic evidence that multiple wh-MECs are introduced by a limited class of matrix predicates, i.e., existential 'be' and 'have', as illustrated in (49) with the Romanian existential predicate a avea 'to have'. In contrast, predicates like 'wrap', 'prepare', 'assemble', and 'arrange' are not existential and do not embed MECs. 9 Since these are exactly the matrix predicates introducing the multiple wh-clauses in (1)-(4), we take it that the embedded multiple wh-clauses cannot be MECs.
Another, possibly stronger argument against a MEC analysis for the multiple wh-clauses we are investigating comes from mood. Grosu 2004Grosu , 2013Grosu and Šimík 2011 There are other predicates that can introduce single wh-MECs crosslinguistically, like 'give', 'send', 'find', 'choose', 'get'. However, to our knowledge no multiple wh-MECs have been discussed in the literature with predicates other than 'be' and 'have' (see Šimík 2011 for more details); see (51) for a possible example. early access 21 that MECs require the subjunctive or the infinitive, as also exemplified in the Romanian sentences in (49). In contrast, multiple wh-FRs do not impose any mood restrictions: all our examples of multiple wh-FRs allow the indicative, behaving like single wh-FRs in this respect as well. 10 Lastly, MECs and multiple wh-FRs differ in their interpretation. MECs have been argued to have the meaning of existentially quantified expressions. As already suggested by the paraphrases above and discussed in the previous sections, this is unlike the semantic behavior of multiple wh-FRs, which semantically behave like definite descriptions. To see this more clearly, compare the sentences in (50)a−b below with those we already saw in (1) and (16) (50)a, with a MEC in brackets, asserts the existence of an unspecified non-empty set of things that Grandma will offer to some unspecified non-empty set of children for Christmas without any (functional) relation between the members of those two sets. When we try to replace and paraphrase the MEC with a DP, we need to use an indefinite DP or a bare plural, as in (50)b. In contrast, the bracketed multiple wh-FR in (1) refers to the maximal individual of the set of things that Grandma wrapped in order to give them to the appropriate people. As we saw in (16)b, a definite DP needs to be used to replace and roughly paraphrase the multiple wh-FRs in (1) (see discussion in Sections 2.3 and 2.4).
The properties mentioned above therefore provide both syntactic and semantic arguments against an analysis of multiple wh-FRs as MECs.
Together with the clear cases we just discussed, there are cases of multiple wh-constructions that are truly ambiguous and could be analyzed as multiple wh-FRs or MECs, depending on the interpretation. For instance, the sentence in (51)⎯which contains a bracketed multiple wh-clause in the subjunctive in the complement position of the MECembedding predicate da 'give' (Šimík 2011)⎯is ambiguous, as highlighted by the two different readings. 10 This does not mean that FRs disallow the use of subjunctive. As (i) shows, subjunctive mood is also possible in FRs, both single and multiple wh-ones (on subjunctive mood in Romanian, see Farkas 1985Farkas , 1992 Reading 1 results from parsing the multiple wh-clause as a MEC: the wh-word 'what' introduces a set of things, while the wh-word 'where' introduces a set of places and both sets are asserted to be non-empty, i.e., they are existentially quantified over. Crucially, this reading does not require the existence of a specific connection between things and places. On the other hand, the sentence in (51) can also be interpreted along the lines of Reading 2, resulting from analyzing the multiple wh-clause as a multiple wh-FR: the whole embedded clause now refers to the maximal individual of the set of things that had to be installed, each at its own specific place, according to a mapping that the speaker and the hearer share. The predicates 'find' or 'choose' exhibit similar ambiguous selectional properties (see Šimík 2011). Speakers rely on the context to determine the appropriate interpretation.

Interim summary
The discussion above has highlighted the many commonalities between multiple wh-FRs and single wh-FRs and the substantial differences between multiple wh-FRs and other constructions involving multiple wh-phrases. We summarize the main ones in (52) There is convincing syntactic and semantic evidence to distinguish the construction that we are investigating⎯multiple wh-FRs⎯from other kinds of multiple wh-clauses attested crosslinguistically, be they correlatives, interrogatives, MECs or the kind of multiple whclauses discussed by Rudin. The next section will provide a compositional account of the semantic properties of multiple wh-FRs and most of their features above (we won't have much to say about the restriction on wh-phrases). Before concluding, though, we would like to add some further remarks.
In this section, we have provided a series of tests and contexts that could help set apart various multiple wh-constructions. The attentive reader may have noticed that we used a fairly limited number of predicates (e.g., 'wrap', 'assemble', 'prepare', 'arrange') and most of our multiple wh-FRs examples have ce 'what' as their first wh-phrase. In the remainder of the paper, we will continue with this restrictive strategy and focus exclusively on multiple wh-FRs that occur as arguments of non-interrogative and non-existential predicates, are only in the indicative mood, and are headed by ce 'what'. This is motivated by the desire to avoid any possible ambiguity in order to facilitate our consultants' judgments and make the data we report in the paper as clear and solid as possible. However, it is important to keep in mind that multiple wh-FRs are not necessarily restricted to these predicates and these wh-phrase combinations.
Taking stock, we have seen that multiple wh-FRs behave in all relevant respects like single wh-FRs: they have a very similar distribution and, as we will discuss in detail in the following section, they have the same overall meaning. The question then becomes what the interpretation of multiple wh-FRs is and how it is derived by a compositional procedure resembling the one used by single wh-FRs.

Semantic analysis of multiple wh-FRs
In this section, we develop a compositional semantic analysis for multiple wh-FRs by building on a well-established semantic analysis of single wh-FRs. First, we show the limits this analysis faces when it is extended to multiple wh-FRs. Then, we propose an analysis that overcomes those limits by broadening the semantic contribution of wh-phrases in FRs.
Before going into the formal details and its supporting arguments, let's sketch the main ideas behind our proposal. Let's return to the multiple wh-FR we started with in (1), which is repeated in (53)  Our proposal treats the bracketed multiple wh-FR in (53) as a construction that semantically behaves like a referential expression and denotes an object of the gift kind, similarly to the plural definite DP the gifts. Like the gifts, the multiple wh-FR in (53) denotes the largest ('maximal') object out of a certain set of gifts⎯the plural gift resulting from the sum of all the individual gifts inside the given set of gifts.
What is peculiar about multiple wh-FRs and makes them different from simple definite DPs like the gifts is the way the set of gifts is construed. It is not associated to a lexical item like the noun gift with or without further restrictions (cheap gifts, gifts from Italy, etc.). The gifts in the set that is associated to the multiple wh-FR in (53) are all and only those gifts that Grandma will give to the people those gifts are mapped onto according to a certain mapping.
There are many ways to map gifts to people. A multiple wh-FR imposes one specific kind of mapping⎯a function⎯rather than a relation of any kind, and a specific kind of function⎯a Skolem function⎯rather than any function. It also imposes that this Skolem function must exist and must be unique in the given context. early access 24 This "functional" construction of the relevant set is triggered by the semantic properties of the lower wh-phrase and its interplay with the higher wh-phrase, as we'll discuss in detail soon. None of the other multiple wh-constructions we have discussed so far exhibit the same semantic properties as multiple wh-FRs. Simple definite DPs and single wh-FRs are similar to multiple wh-FRs in both being referential. This explains why they can all occur as arguments. On the other hand, only multiple wh-FRs exhibit the "functional" dimension we sketched above.
It's now time to formulate our proposal more precisely. We will start by summarizing a well-established semantic analysis for single wh-FRs (Section 4.1) to then show that it cannot be extended to multiple wh-FRs straightforwardly (Section 4.2). We present our analysis of multiple wh-FRs in detail (Section 4.3) and then discuss various aspects of it and provide various argument in its support (Section 4.4).

Semantics of single wh-FRs
The main idea behind a well-established semantic analysis of single wh-FRs⎯details aside⎯is that their wh-phrase licenses a trace/variable over individuals over which lambda-abstraction applies, producing a set of individuals. A silent maximality operator or a type-shifting operation applies to this set returning the unique maximal member of the set (Jacobson 1995;Dayal 1996;Caponigro 2003Caponigro , 2004. This analysis for FRs is based on what has been argued for definite descriptions (e.g., Link 1983). Let us look at the details of this approach by considering a specific example.
The sentence in (54) a cumpărat t1 has bought early access 25 In (55), the wh-phrase leaves a trace t1 in its base-generated position, which translates into a variable over individuals x1 (type e). CP1 ends up denoting a set of individuals (type ⟨et⟩) by lambda-abstraction over x1: the set of all the singular and plural individuals that Grandma (gm) bought up to its unique maximal individual (i.e., the individual resulting from the sum of all the atomic individuals in the set). The wh-phrase syntactically combines with CP1, while semantically acts as a set restrictor (type ⟨et,et⟩): it applies to the set that CP1 denotes and returns the subset of all the inanimate (in) singular or plural individuals that Grandma bought as the denotation of CP2 (type ⟨et⟩). Finally, a default type-shifting operation applies, where the set that CP2 denotes is converted into its maximal individual (type e) via the maximality operator , which has been argued to be the semantic contribution of the definite determiner the in English and similar languages (Link 1983). Notice that such an operation from a set to its maximal individual is information-preserving: it is always possible to construct the unique maximal individual of a finite set of atomic individuals (and all the plural individuals that can be formed out of the atomic ones) and it is always possible to reconstruct a set of atomic individuals (and all the plural individuals that can be formed out of the atomic ones) from its maximal individual.
Summarizing, this analysis of single wh-FRs accounts for their behavior as definite descriptions by assuming that a silent version of the definite operator applies by default⎯an assumption that crucially relies on a set of individuals resulting from abstracting over a variable over individuals. This is the same variable that wh-phrases in wh-interrogative clauses license. The meaning that is assumed for wh-phrases in single wh-FRs (56) is close, but not identical, to the meaning that is assigned to wh-phrases in common analyses of wh-interrogative clauses (57) (e.g., Karttunen 1977).
According to (57), a wh-phrase in an interrogative clause (WHINT) behaves exactly like an existential generalized quantifier: for instance, who means exactly the same thing as someone. As we just saw, the existential quantification over the variable licensed by the wh-phrase in a wh-interrogative clause is replaced by lambda-abstraction over the variable translating the wh-trace in a FR (56). The one-place predicate wh in (56) and (57) stands for whatever semantic restriction the wh-phrase carries (human for 'who', inanimate for 'what', location for 'where', etc.).

Problems with extending the semantics of single wh-FRs to multiple wh-FRs
The approach in Section 4.1 cannot be straightforwardly extended to multiple wh-FRs. Let us briefly see why with an example, such as (58), which contains a multiple wh-FR in brackets. (59) attempts to provide a semantic derivation for the bracketed FR in (58) by assuming that all wh-phrases license traces translating into variables over individuals.
The translation of CP2 in (59), i.e., the CP containing only the lowest wh-phrase and the remainder of the FR, is the usual set of individuals, in particular, the set of individuals Grandma gives a certain object x1 to. 12 Problems arise with the next step. As usual, before a wh-phrase can combine with the remainder of its clause, lambda-abstraction over the variable that is coindexed with the wh-word must apply. Abstracting over x1 produces the denotation of CP3: a function from an inanimate individual x1 to a set of human individuals x2 such that Grandma gives x1 to x2⎯a semantic object of type ⟨e,et⟩. On the other hand, the sister of CP3 is a wh-word that semantically behaves like a set restrictor (type ⟨et,et⟩). No function application can apply, nor any other independently motivated semantic rule. Therefore, CP4 ends up without a denotation and the semantic derivation crashes. Even if we assumed an ad hoc semantic rule to combine the two meanings, it would not return the correct meaning for CP3 and the whole FR. The semantic analysis we just tried to pursue treats each wh-phrase as semantically independent from any other wh-phrase in the same clause. This clashes with speakers' intuitions, according to which the meaning of the lowest wh-phrase "depends" on the meaning of the highest wh-phrase, as we showed in Section 2.4. In conclusion, a simple extension of existing analyses of single wh-FRs to multiple wh-FRs is both formally and empirically problematic. 13

Proposal: the semantics of multiple wh-FRs by means of complex traces and functional wh-phrases
To overcome the problems in the analysis we just discussed, we propose two changes that broaden the available meaning inventory for wh-phrases in FRs. First, we assume that the first/higher wh-phrase in a FR, i.e., the wh-phrase that c-commands the other in a multiple wh-FR, licenses a standard wh-trace, which translates into a familiar variable over individuals. This is the same translation for wh-phrases we assumed in a single wh-FR. It is repeated in (60)a. The other wh-phrase, instead, licenses a complex trace translating into the complex functional variable in (60)b, which is made of a variable over Skolem functions (f2, type ⟨e,e⟩) taking a variable over individuals (x1, type e) as its argument and returning an individual (type e) as its value.
(60) a. Simple wh-trace: t1  x1 b. Complex wh-trace: t2 1  f2 (x1) In the end, both traces/variables in (60) denote individuals, but, while the simple wh-trace does so through a direct assignment of an individual by the assignment function, the complex wh-trace denotes an individual through the interplay of a variable over Skolem functions and a variable over individuals acting as the argument of the function. The individual variable that occurs as the argument of the Skolem function is coindexed with the higher wh-phrase⎯a feature that plays a crucial role in the semantic composition, as we discuss below. Our second change is strictly related to the first one and has to do with the denotation of wh-phrases. We summarize it in (61)a−b. 14 Comments follow. The denotation in (61)a is the one that has been proposed for wh-phrases in single wh-FRs like those we discussed in Section 4.1. A wh-phrase licensing the trace over individuals in (60)a semantically behaves like a set restrictor: it applies to a set of individuals to return a subset. This is why we labeled it Individual WHFR. The denotation in (61)b, instead, is new and we are proposing it for a Functional WHFR⎯a wh-phrase licensing the complex wh-trace in (60)b. The denotation in (61)b can be unpacked in prose as in (62): (62) Denotation of the Functional WHFR in (61)b in prose A Functional WHFR denotes a function that takes a set F of Skolem functions as its argument (type of F: ⟨ee,t⟩) and returns the value true iff there is a Skolem function f (type of f: ⟨ee⟩) in the context C satisfying the following restrictions: I. Wh-restriction: WH(f) f outputs individuals that satisfies the semantic restriction that is carried by the Functional WHFR (human, inanimate, place, etc.).

II. FR restriction: F(f)
f is a Skolem function satisfying the restriction provided by the remainder of the FR, i.e., f is a member of the set F. F is the argument fed to the Functional WHFR and results from lambda-abstracting over the Skolem function variable introduced by the trace of the Functional WHFR (see semantic derivation in (64) below).

III. Uniqueness restriction: U(f)
f is the only Skolem function in C satisfying Restrictions I and II above⎯literally, every Skolem function f* in C satisfying Restrictions I and II above must be identical to f.
The uniqueness restriction in (62)III is not a logical/mathematical one, like the uniqueness of a maximal individual for a set of individuals (Section 4.1). It is rather a context-dependent kind of uniqueness, as we highlighted with the restriction to the given context C ("C") in the denotation in (61)b. Logically, there will always be more than one Skolem function satisfying the WH and F restrictions, as long as the domain of individuals is not a singleton. This restriction may be seen as another instantiation of the more general phenomenon of quantifier domain restrictions in natural language (see von Fintel 1994, Stanley & Szabó 2000, and references therein). Before we further discuss and motivate our assumptions about complex traces and Functional WHFR (Section 4.4), we first show how, with these two assumptions in hand, we can overcome the issues that led to the failed derivation in (59). Going back to the example with a multiple wh-FR in (58), repeated and simplified in (63) below, let us examine the new semantic derivation in (64) Starting from the bottom in (64), IP contains the two wh-traces: a simple one from the higher wh-word (t1), which translates into x1, and a complex one (t2 1 ), from the lower wh-word, which translates into f2(x1). CP1 denotes the function resulting from lambda-abstracting over the variable f2, or, equivalently, the set of all Skolem functions such that Grandma gives the individual x1 to the individual that f2 associates to x1. The lower wh-word cui2 no longer denotes a set restrictor, as in (59), but an existential quantifier that applies to a set F of Skolem functions and returns true if there is a unique function in F that outputs people, i.e., human individuals. Therefore, the combination of cui2 and its sister CP1 results in CP2 denoting true iff there is one and only Skolem function f that outputs people such that Grandma gives an individual x1 to the person that f associates to x1. The next step is the lambda-abstraction that is necessary before the higher wh-word ce1 can combine. The abstraction applies to all the instances of x1⎯the variable that is coindexed with ce1 in CP2. The result is that CP3 denotes a set of individuals x1 that Grandma gives to the people that are associated to the individuals x1 according to a unique Skolem function f. This is the set the higher wh-phrase ce1 applies to and restricts to the subset of objects (inanimate individuals), returning the denotation of CP4. Finally, the familiar type-shifting operation from single wh-FRs (see (55) and related discussion) can apply here as well, returning the maximal individual the multiple wh-FR refers to.
In this way, the multiple wh-FR in (64) ends up denoting the unique maximal individual of the set of objects x1 that Grandma gives to the people associated with x1 according to the 17 We are crucially assuming that x 1 ranges over singular and plural individuals (see x 1 and the final denotation in (64) and the discussion in Section 4.4.5). Therefore, we also assume the shortcut in (i) below, in order to ensure the relevant distribution with distributive predicates like give when they take plural individuals as their arguments and, at the same time, to keep the length of the expressions in our semantic derivation manageable.
A welcome prediction of our proposal is the one schematized in (65): wh2, the wh-phrase that is c-commanded by the other (wh1), must receive a functional interpretation and, therefore, has to license a complex wh-trace. Any other meaning combination of wh-phrases would make the semantic derivation crash (essentially for the same reasons discussed in Section 4.2).

Further support for the two core assumptions and related remarks
The analysis of multiple wh-FRs we just presented crucially relies on two core assumptions about the semantic nature of wh-traces/variables and wh-phrases, at least in FRs in Romanian. We elaborated on and made use of those assumptions in the previous section. In this section, we provide further support for both and discuss possible objections.

Further support for complex wh-traces
We assumed that a wh-phrase can license a familiar simple mono-indexed trace translating into a variable over individuals, as shown in (60)a, or, crucially, a complex trace carrying two indices that are associated to two different antecedents⎯one of which is the wh-phrase itself⎯and translating into a variable over Skolem functions taking a variable over individuals, as shown in (60)b. The latter kind of trace/variable has been argued to be licensed in other constructions as well. Complex traces/variables were initially suggested to account for functional readings of single wh-interrogative clauses with universal quantifiers (Engdahl 1980(Engdahl , 1986Chierchia 1991Chierchia , 1993Dayal 1996). For instance, the single wh-interrogative clause in (66)a allows for an answer like His mother (66)b, which doesn't refer to any individual in particular but rather to the function mapping every Italian male to a specific and unique female.
This approach was subsequently extended to account for headed relative clauses with a universal quantifier like (67) by assuming that their possibly null wh-operator (Op2) licenses a functional trace (Sharvit 1999a Furthermore, Sharvit (1999b) argues that single wh-FRs with universal quantifiers in the subject position of predicational copular sentences like (68) also contain a functional trace licensed by the wh-phrase introducing the FR.
(68) [What2 [every student]1 got t 2 1 ] was a nuisance to him. 20 To this, we can add the fact that multiple wh-clauses, such as correlative clauses (Dayal 1996: 200−202;Brașoveanu 2012: 41) and multiple wh-interrogative clauses have also been argued to license functional traces (e.g., Comorovski 1996;Dayal 1996Dayal : 117−118, 2016. For instance, a multiple wh-interrogative clause like the one in (69)a receiving a functional answer like (69) In conclusion, our core assumption that wh-phrases can license complex traces/variables is independently supported by proposals that have been made for several different constructions in different languages.

Functional wh-phrases in free relative clauses and interrogative clauses
The second assumption at the center of our proposal is that a wh-phrase in a FR in Romanian exhibits a dual semantic behavior: as Individual WHFR, they denote a set restrictor over sets of individuals (61)a, while, as Functional WHFR, they denote an existential quantifier over a set of Skolem functions (61)b. In (70), we repeat the denotation of Functional WHFR in order to more easily compare them with the denotation in (71), which has been proposed for Functional WHINT⎯wh-phrases in interrogative clauses that receive a functional interpretation, like the one we discussed in (66) (Engdahl 1986;Chierchia 1991;Dayal 1996). The only difference between the two denotations is that the denotation for the Functional WHFR includes an extra restriction: the uniqueness of the relevant Skolem function. In Section 2.4, we already showed why our consultants' semantic intuitions justify a functional component associated to the interpretation of the lower wh-phrase. In the next sections, we further discuss and support the need for the Skolem function f in multiple wh-FRs to be existentially quantified and unique.

Further evidence for the existential requirement in the denotation of Functional WHFR
Let us return to the example in (63) we have discussed so far, which is repeated in (72)  According to our semantic analysis in (64), the bracketed multiple wh-FR in (72) denotes the maximal plural entity of a set of things, each of which is associated with a corresponding person, who will be given one of those things for Christmas. This closely matches speakers' intuitions, as we discussed in Section 2.4. The denotation for the Functional WHFR in (70) requires the existence of at least one appropriate Skolem function. In fact, when the context makes it hard or impossible to find one, the sentence containing the multiple wh-FR sounds infelicitous, as shown in (73) The example in (73) is minimally but crucially different from the fully felicitous example in (72). What makes (73) odd is the fact that typically for a given birthday, there aren't multiple gift-receivers. So, there's no appropriate Skolem function mapping gifts to gift-receivers. Notice that we are excluding the extreme case of a Skolem function whose domain contains just one individual (i.e., Andrei) and whose range is a singleton as well (i.e., Andrei's gift). The ban on such Skolem functions may receive a pragmatic explanation: why would the speaker use a functional dependency in (73) when she could just utter the bracketed single wh-FR in (74) or the even simpler bracketed DP in (75) (73) would be acceptable only in a context where, for some reason, Grandma decided to give things to people on a particular day, which happens to be Andrei's birthday, and had some way to establish which gift goes to which person.
Multiple wh-FRs with negation illustrate a similar point, as shown in (76).
(76) # Bunica a împachetat [ce cui nu dă de Crăciun. ] Grandma has wrapped what who.DAT not gives for Christmas 'Grandma wrapped the things she will not give to the appropriate people for Christmas.' The reason why (76) is infelicitous is that there is no natural Skolem function that associates wrapped objects to people to whom the objects are not given. The presence of negation makes a natural mapping from objects to individuals unavailable. Note, however, that it is perfectly natural to refer to the set of things Grandma will not give for Christmas, which is why the single wh-FR in (77) is felicitous and can be used, for example, in a context where Grandma wrapped things she bought for Christmas but decided not to give them as gifts anymore. It is therefore the presence of the second wh-phrase (and the need for an appropriate functional dependency) that makes (76) infelicitous.
(77) Bunica a împachetat [ce nu dă de Crăciun]. Grandma has wrapped what not gives for Christmas 'Grandma wrapped the things she will not give for Christmas.' The evidence we just presented argues in favor of existential quantification over Skolem functions as part of the denotation for wh-phrases. We now turn to the evidence supporting the uniqueness requirement.

Further evidence for the uniqueness requirement in the denotation of Functional WHFR
The denotation for a Functional WHFR in (61)b not only requires that there is a Skolem function in the context C satisfying WH and F restrictions, but it must be unique in C (see also (62)III). Let us imagine a context C that makes it clear that there may be more than one Skolem function satisfying the WH and F restrictions in it, due, for instance, to the agent's epistemic uncertainty. Grandma bought Christmas presents for the family. She knows her two children and their wishes well, so she bought a book for Donka and a coffee machine for Adrian. She also has a couple of toys (a board game and a science set) for her two grandchildren, but she wants to check with the parents before deciding who receives which toy. This means that Grandma has two different mappings or Skolem functions from gifts to gift-receivers in mind⎯those represented in (78): fa and fb. The shading highlights what is identical/permanent between the two functions, while the clear areas cover the variation/uncertainty.
(78) Uncertainty context C: the two Skolem functions that Grandma has in mind In the context C described in (78), there is no maximal individual that can act as the denotation of the multiple wh-FR in (63)/(72), which was given in (64) and is now repeated in (79) below for convenience.
According to (79), the multiple wh-FR refers to the maximal individual x1 of the set of objects x1 that Grandma gave to those individuals f(x1) that are associated to the objects x1 in a unique way, i.e., by a unique Skolem function f in C. But, in the given context C, there are two different Skolem functions that satisfy the relevant restrictions. It follows that no object x1 satisfies the relevant requirements, the resulting set of objects is empty, and, as a consequence, the set has no maximal individual x1. Since the multiple wh-FR ends up with no denotation, the semantic derivation for the whole sentence crashes and the sentence receives no semantic interpretation in the scenario in (78). We take this output as a welcome formal correlate to our consultants' rejection of the sentence in the scenario in (78).
Notice that it wouldn't be justified to restrict the set of objects to just the book and coffee machine, i.e., the objects that are always assigned to the same people in the mappings in (78) in the shaded areas. Although this restriction would assign a denotation to the maximal wh-FR, it wouldn't correctly represent the scenario we are in. This restriction would be equivalent to claiming that Grandma has in mind only the Skolem function fc in (80). (80) implies that Grandma has no idea about who she will give the remaining two objects to⎯in other words, those two objects don't even count as gifts in Grandma's mind, which is not the case.
To sum up, multiple wh-FRs are infelicitous in scenarios that make more than one relevant Skolem function available. The uniqueness constraint on the Skolem function in our proposal captures this fact.

Further remarks on the denotation of Functional WHFR
In this last section before concluding, we touch on a few other issues concerning the denotation of Functional WHFR: the nature of the Skolem function, the projective behavior of the uniqueness requirement, and plural individuals as arguments or values of the Skolem function.
In Caponigro & Fălăuș 2018, we proposed a slightly different denotation for a Functional WHFR⎯the one in (81).
Like our current proposal, it is a function from sets of Skolem functions to true values and imposes the WH and F restrictions on a Skolem function. The crucial difference is on how this Skolem function is introduced. In our current proposal, it is via existentially binding a variable f over contextually given Skolem functions together with a uniqueness requirement, while in (81) the Skolem function is introduced as contextually salient via a free variable f over Skolem functions. In other words, our current proposal only requires the speaker to know that there is such a function and is unique in the context. Our former proposal presupposed that the speaker had some knowledge of the Skolem function. Our consultants' intuitions show that speakers don't need to be familiar with the relevant Skolem function, at least not its extension. They can utter (63)/(72) felicitously even if they don't know what appropriate mapping Grandma has in mind, as long as they know she has one, and only one (see the related discussion in Section 2.5 and the possible continuations in (22)). 21 Our Editor observed that the speaker could be familiar with just the intension of the Skolem function⎯for instance, she would be familiar with the function mapping objects to people Grandma is giving those objects to, without knowing the actual mapping in the world of evaluation. Still our consultants can accept a sentence with a multiple wh-FR like (63) without knowing anything about Grandma and her plans ahead and become familiar with the intension of the relevant Skolem function only after hearing the sentence and the multiple wh-FR in particular. One possibility (suggested by our Editor) is that a parameterized version of the free variable over Skolem functions could allow some other cognitive agent to be the one familiar with the Skolem function, along the lines of the parameterized choice functions argued for by Kratzer 1998 in her treatment of indefinites and their scopal behavior. We leave the exploration of this intriguing option for future research.
Another concern that was raised by our Editor and one of our Reviewers is whether the existence and uniqueness restrictions that are introduced by a Functional WHFR would be more appropriate as presuppositional content rather than asserted content. In particular, one may wonder whether clausal negation in the matrix clause wouldn't be predicted to interact with the existential quantifier over Skolem function or the universal quantifier in the uniqueness requirement within the multiple WHFR. For instance, wouldn't our proposal predict that a sentence like (82) be acceptable in contexts in which either there is no mapping between gifts early access 37 Lastly, we observe that a multiple wh-FR like (72) is fine in the scenario in which Grandma gives each grandchild a gift and, if a grandchild has a significant other, then the grandchild's gift is actually a gift to the couple as a whole. In other words, we are dealing with a mapping from atomic gifts to atomic or plural human individuals. Our proposal can handle this fact by allowing the range of the Skolem function to include plural individuals as well. It is also possible to utter (72) felicitously in a scenario in which more than one object is given as a gift to one or more individuals. For instance, if Grandma gives two gifts to each grandchild that has received all A's in school. Once again, we can accommodate this scenario by allowing the domain of the relevant Skolem function to include plural individuals as well. 24 The move to allow for plural individuals in the domain and range of Skolem functions is not unconstrained. It is only justified when the plural individuals form a natural unit in the given context. In the scenarios above, one of Grandma's children and their partner do form a natural unit, which is even lexicalized by nominals like couple. Similarly, it is easy to imagine a gift as made of more than one component. On the other hand, there are cases where a plural object is not granted and the sentence with a multiple wh-FR sounds infelicitous. For instance, let us consider a scenario in which a stage manager is in charge of carefully arranging, in boxes that are backstage, the objects that will be put by the actors in different places on the stage during the performance. Crucially, for several objects it will be the case that each of them will be put in different places at different times during the performance. For instance, suppose a special precious book will be put on the coffee table in Act 1 and then back in the bookcase in Act 2. Similarly, a plate will be on the main table in Act 2 and then on the floor in Act 3. The coffee table and the bookcase are two independent places, the same for the main table and the floor. So we are in a situation in which there are at least two objects, each of which is mapped to two independent and unrelated places. In this situation, (85) is infelicitous and speakers comment that this is the case because there is no singular or plural place each object can be mapped to, since at least two objects are associated with two places.
(85) # În culise, directorul de scenă a aranjat [ ce unde trebuia pus în timpul in backstage manager-the of stage has arranged what where needed put in time-the spectacolului]. show-the.GEN 'Backstage, the stage manager arranged the things that needed to be put in their appropriate places during the performance.' The discussion in this section offered further support in favor of our proposal about the existence of a Functional WHFR in (70). This new denotation for wh-phrases is what is crucially needed⎯we have argued⎯to both capture speakers' intuitions about how the meaning of the two wh-phrases interacts and to provide a fully compositional semantic analysis of multiple wh-FRs that is faithful to those intuitions. 24 Thanks to Adrian Brașoveanu for making us think about these kinds of examples and contexts. early access 38

Conclusions
We have started unveiling a previously ignored multiple wh-construction: multiple wh-FRs. We have shown that they exist and are productive⎯at least in the variety of Romanian spoken in Transylvania. We have compared them to and distinguished them from the other kinds of multiple wh-clauses that are attested in the language⎯interrogative clauses, correlative clauses, Rudin's sentences, and MECs. We have argued that multiple wh-FRs are FRs and their basic semantics is the same as that of single wh-FRs: both FRs are referential and maximal. We have proposed a compositional semantic analysis for multiple wh-FRs that builds on two main components: (i) the assumption that wh-phrases can license complex functional traces/variables, which has been independently argued for several other wh-constructions, and (ii) a new functional meaning for wh-phrases, which is essentially a variant of the functional meaning of wh-phrases that has been independently proposed to account for functional wh-interrogative clauses.
Finally, we have provided some preliminary evidence in (6)−(9) that multiple wh-FRs are attested in at least four more languages (or varieties thereof). These findings do not stem from a systematic crosslinguistic investigation, but simply from feedback we received by presenting our work to different audiences. We hope that our work will foster research on multiple wh-FRs by providing a clear case from Romanian, analytical tools and tests to identify them and distinguish them from other wh-constructions, as well as an analysis to account for their main properties. We are confident that other languages will turn out to have multiple wh-FRs. On the other hand, it is incontrovertible that multiple wh-FRs are less common across languages, which is probably a reason why they have been almost completely neglected so far. Even within our limited investigation, it is clear that languages that have both single wh-FRs and multiple wh-interrogative clauses do not necessarily have multiple wh-FRs. Most varieties of American and Canadian English we are aware of do not allow for multiple wh-FRs, nor do most varieties of German we have checked. Also, we have not found any variety of Spanish or French that allows for multiple wh-FRs. Although we do not have an explanation for this restriction, we would like to offer some speculations.
Functional WHFR as defined in (70) require two major changes from their most likely lexical source⎯Functional WHINT as defined in (71). First, the uniqueness requirement needs to be added to the denotation of Functional WHFR. This is a semantic change that imposes further restrictions on the use of this kind of wh-word: the existence of one, and only one, relevant Skolem function in the given context. Second, Functional WHFR have to be licensed in a non-interrogative clause⎯a syntactic change. Notice that the semantic change is different and independent from the semantic change from the denotation of Individual WHINT as generalized quantifiers, as defined in (57), to the denotation of Individual WHFR as set restrictors, as defined in (56). This semantic change does not impose further restrictions on the wh-words, but it actually "weakens" their meaning, by eliminating the assertion of existence. As a result of all this, we predict the existence of languages that allow for the semantic change from Individual WHINT to Individual WHFR without necessarily allowing the semantic change from Functional WHINT to Functional WHFR. In other words, we predict the existence of languages with single wh-FRs but no multiple wh-FRs. On the other hand, we do not predict the reverse pattern⎯languages with multiple wh-FRs but no single wh-FRs⎯since the first/highest early access 39 wh-phrase in a multiple wh-FR cannot be functional in multiple wh-FRs like the one in (58), as made it clear by its semantic derivation in (64). These predictions seem to be borne out, although our crosslinguistic evidence is still very limited and tentative. We hope that our work will help to fill in this gap by encouraging further investigation on multiple wh-FRs in Romanian and across languages.