Reduplication and the structure of nouns in Xining Chinese

Reduplication and the structure of nouns in Xining Chinese Qi Wang Anders Holmberg University of Wuhan Newcastle University Abstract In Xining Chinese, especially as used by older people, free nouns are always reduplicated, as a purely formal condition without any semantic effects. We argue that the reduplication takes place when an acategorial root is merged with a null nominal categorizer which copies the phonological matrix of the root, as an effect of a condition ruling out free monosyllabic nouns. When the condition is not independently satisfied, as in a compound or derived noun, reduplication is how the condition is met. Reduplication also occurs optionally in compounds or derived nouns. In conjunction with a minimalist theory of word formation, this will be shown to predict the distribution of reduplication in various contexts. For instance, the head of a compound can be reduplicated, but not the modifier, some affixes but not others permit reduplication of the base, non-compositional compounds do not allow reduplication, and so called ‘bound roots’ (really, bound words) are not reduplicated. The phenomenon provides very strong evidence that simple content words are made up of an acategorial root and a categorizer which is often null, but can be overt in some languages, including Xining Chinese, where it is overt in nouns by virtue of reduplication.


Introduction
A morphological peculiarity of the variety of Chinese traditionally spoken in and around Xining in the North West of China is that common nouns are always reduplicated, as exemplified in (1) The reduplication has no semantic effect whatsoever, but is a purely formal requirement. In particular in the variety of Xining Chinese spoken by the older generation, which we will refer to as Traditional Xining Chinese, the reduplication is compulsory. Similar reduplication is common also in other dialects spoken in North West China. Our data are exclusively from Traditional Xining Chinese, though, abbreviated TXC (called Old Xining Chinese in Wang 2018). 1 The reduplication, we claim, is required to satisfy a language-particular condition that a free noun must consist of at least two syllables. There is a well-known tendency in Chinese to favour disyllabic words over monosyllabic ones (Duanmu 1999). An effect of this is a strong preference for compounds of various kinds. Another effect, characteristic of TXC, is reduplication of nouns, compulsory with monosyllabic nouns, optional in certain disyllabic nouns in ways to be discussed in the paper.
The analysis we propose here is that the reduplication of nouns in TXC is the result of copying of the phonological features of the root by a nominal categorizer. It is based on the premise that lexical categories are made up of a root devoid of a syntactic category feature, merged with a categorizer, that is a functional head encoding syntactic category (Marantz 1997, Josefsson 1997, 1998, Harley & Noyer 1999, Lieber 2006, Embick and Noyer 2007, Harley 2011, Embick 2015, Hu and Perry 2018. The categorizer is often a null morpheme. That is the case with lexical categories generally in for example Standard Mandarin (henceforth called Mandarin), except in some cases where the category is provided by an overt affix. It is also the case in TXC with categories other than the noun. But for nouns in TXC, the nominal categorizer is mostly overt. If it is not realized as an affix, it is realized by copying the phonological features of its sister root. We will refer to this as noun reduplication, as a convenient descriptive term, but with the understanding that this is not reduplication of a noun, but reduplication of a root, by copying its phonological features onto a null nominalizer.
This hypothesis makes a number of predictions about contexts where reduplication will be found, predictions that are all met. This means that we can always tell a root from a noun in Xining Chinese: a root not accompanied by a nominal categorizer will not be reduplicated, while a root merged with a nominal categorizer will be. In this way the reduplication serves as a probe into the structure of words, 2 particularly nouns, in TXC. This will be shown to shed new light on controversial categories in Chinese morphology, including various kinds of compounds and the category called 1 One of the authors is a native speaker of TXC. The data are checked with other speakers of TXC, including speakers that are older than 70. 2 The point that reduplication can serve as a probe into the structure of words and phrases is also made by Travis (2001). The reduplication that we describe does not fall into any of the classes of reduplication that Travis identifies, but we will return to Travis (2001) in the conclusions.
bound roots in the literature (Packard 2000). On a more general level, reduplication in TXC provides strong evidence for the hypothesis that content words are made up of an acategorial root merged with a designated categorizer. This hypothesis is widely but not universally assumed within generative morphosyntax (see Borer 2014 for a partial rebuttal), and is even more controversial in more traditional morphological theory.
The rule which derives the reduplicated form is phonological in that it operates on a phonological unit, the phonological matrix of a root, with effects only at PF (the Articulatory-Perceptual interface), none at LF (the Conceptual-Intentional interface). It is a morpho-syntactic rule in the sense that the conditions on the reduplication are syntactically defined. First, it concerns specifically nouns. It is thus not, for example, motivated by a general condition on the size of minimal words in TXC (McCarthy and Prince 1990;Hall 1999). Verbs and adjectives are not usually reduplicated in TXC, and if they are, it has a semantic effect, denoting repetition or intensification, among other things. Second, the reduplication is a matter of copying of features by a syntactically derived head, the categorizer n, which furthermore can take place if and only if the root and n are sisters; adjacency is not sufficient. The upshot is that the reduplication of nouns in TXC is a postsyntactic rule but dependent on a specific syntactic input, categorial and structural.
The paper has the following structure: Section 2 provides some background information on the language. Section 3 outlines the basic theoretical assumptions. This will include a review of a certain kind of nominal compound in Swedish, because it provides a particularly clear case of overt root-noun distinction, to be compared with the overt root-noun distinction in TXC. In section 4 we go through a set of correct predictions made by our theory concerning the distribution of noun reduplication in compounds and affixed words in TXC. In section 5 we discuss a class of items characteristic of Chinese, called bound roots or stems in the literature, but that we will refer to as bound words. These cannot be reduplicated in TXC, a finding with interesting theoretical consequences discussed in this section. Section 6 will be about non-compositional compounds. Our theory, conforming with Zhang's (2007) and Hu and Perry's (2018) theory in relevant respects, correctly predicts absence of reduplication in such compounds. Section 7 discusses recursive compounding, which presents a challenge to the theory assumed. Section 8 is the conclusions.

Background: Morphology of Traditional Xining Chinese
The city of Xining is situated in the north-western part of China and is the capital city of Qinghai province. What we call Traditional Xining Chinese (TXC) is what is called 'old Xining dialect' in Dede (2006). It is a language which is spoken by the Han and the Hui people, especially the elderly, who live in the city of Xining and nearby villages, that is, Huangyuan, Huangzhong, Pingan, Menyuan, older speakers of other ethnic groups in the area also use TXC as their second language. This paper will concern TXC as spoken by the Han.
TXC belongs to the group of Central Plains Mandarin (Dede 2003:330-331;Wang & Dede 2016:407) and is incomprehensible to (Standard) Mandarin, which is a variety of Northern Mandarin (Huang and Shi 2016:2;Po-Ching and Rimmington 2016:3). TXC has its own distinctive character, which is due to the prolonged contact with non-Sinitic languages used by other ethnic groups in the region (Dede 2006:320-321, 327). In terms of syntax, SOV is the dominant word order. There is a wider range of functional categories than in Mandarin: a case marker, for instance -ha, is often needed for the preverbal object (Dede 1993:72;Dede 2006:327;Bell 2017; see examples under (1)), and there is a clause-final complementizer and a VP-final tense-marker (Dede 1999:51;Bell 2017, to appear). In terms of morphology, TXC is not so different from Mandarin, though, except for the obligatory reduplication of free nouns which is characteristic of TXC (Wang 2018). Affixation and compounding are used as ways of forming nouns in both Mandarin and TXC, but for TXC, there is another way of forming nouns in a regular fashion, which is reduplication.

Merge and the structure of Swedish nouns
In this section we will first outline our basic theoretical assumptions. As mentioned, a crucial assumption is that content words are made up of an acategorial (categoryless) root merged with a designated categorizer, which may be null, and often is, which is one reason why the assumption is controversial (Lieber 2006, Lehmann 2008. We will argue that the categorizer in the case of nouns is usually overt in TXC, being realized as reduplication. As a preliminary we will discuss another, already investigated case of overt nominal categorizer, in a class of Swedish nouns. The point of this comparison is to establish what we expect to see if the reduplication in TXC is another case of overt nominal categorizer. We assume that words are composed by the same rule as phrases, that is Merge in the sense of Chomsky (1995: 243) and subsequent work within the Minimalist program, following much work within Distributive Morphology: Harley and Noyer 1999, Borer 2005, di Sciullo 2005, Embick and Noyer 2007, Harley 2011, Embick 2015 (2) Merge α and β to form a set {α, β} with a label γ, where γ is = either α or β, depending on which one is the head.
Following standard practice we represent the set as a tree. The two trees formed by α and β are That α and β make up a set, rather than a pair means that they are not linearly ordered by Merge.
That is to say, order is not a matter of phrase-syntax or word-syntax, but is a morpho-phonological matter, part of the externalization of the structure built by Merge (in Chomsky's 2013 sense). We also assume that labelling of the set formed by Merge is crucial for the set to function as a morphological or syntactic unit (Hornstein 2009, Chomsky 2013 Traditionally, following early work in generative morphology (Lieber 1980, Williams 1981, the head in English words is determined by the Righthand-Head Rule (Williams 1981): the rightmost constituent of a word is the head. In the case of (4) this entails that paper is the head of wallpaper and design is he head of wallpaper design. However, if Merge builds sets without linear order, then the linear order cannot determine whether α or β in {α, β} is the head. Instead, something else determines whether α or β in {α, β} is the head, and this, in turn, determines the linear order of α and β. The 'something else' is the syntactic features of α and β and the relation between them, which must be asymmetric in such a way that one of them is the head, i.e. one of them provides the label for the set {α, β} constructed by Merge. We are familiar with asymmetry in syntax: phrases are made up of a word-level category merged with a maximal phrase-level category, and the word-level category is the head. Merging two phrases presents a problem for labelling, though, which has to be resolved; this is the basis for Chomsky's (2013) 'labeling algorithm', building on Moro (2000). If words are constructed by the same operation Merge as phrases, we expect to see analogous asymmetry in words, including compounds (cf. di Sciullo 2005). While English nominal compounds do not show any obvious visible signs of asymmetry, there are languages where they do. One such language is Swedish.
Swedish has a large class of nouns (the so called first and second declensions) which are made up of a root plus a vowel -a or -e (Kiefer 1970, Holmberg 1992, Josefsson 1997, 1998: The vowel can be analysed as encoding singular number, as it alternates with plural suffixes: skol-or 'schools', flick-or 'girls', pojk-ar 'boys'. For nouns denoting people and gendered animals it also encodes semantic gender: -a for females, -e for males. The analysis of the vowel is controversial. According to Kiefer (1970) it has no features except a declension class feature, while according to Ejerhed and Bromley (1986) and Holmberg (1992) it has the number feature [-PL]. Inspired by Harris's (1991) theory of Spanish word formation, where Harris argues that the Spanish nominal vowels -a and -o (as in muchacha, muchacho) are not gender markers but 'word markers' that serve to make a word out of a root, Holmberg (1992) assumes that the Swedish vowels -a and -e in (5) are word markers, whose "essential grammatical function is to combine with a Root, and thereby permit the Root to take part in phrase-and word-syntactic processes". According to Holmberg (1992) the root is a 'maximal category' not projecting any features onto a dominating node, which allows the vowel to project its features. The question is taken up again in Josefsson (1997Josefsson ( , 1998, who argues that the reason why the root does not project any categorial feature is that it does not have a categorial feature, and therefore always has to combine with an item that has one. The noun class exemplified in (5) is a special case, where a nominal feature is realized as a vowel.
The idea that roots are acategorial has since become standard within the Distributed Morphology model of morphology (Halle and Marantz 1993, Marantz 1997, 2007, Harley and Noyer 1999, Borer 2005, di Sciullo 2005, Embick and Noyer 2007, Harley 2011, Belder 2011, Embick 2015, Hu and Perry 2018. In this model there is no single list of words as in the traditional Lexicon (Chomsky 1965(Chomsky , 1970. Instead, words are constructed as part of the syntactic derivation by combining items from different lists: One is the list of formatives, including the roots and the functional morphemes. Another is the list of exponents, that is vocabulary items, including those of functional categories (even particularly listing functional vocabulary, depending on the theory; see Embick 2015). Yet another is the Encyclopedia, containing the non-compositional meanings of words and idiomatic phrases. The derivation of words and phrases proceeds by merge of roots and functional categories, as described above, until the point where the derivations splits; the derived syntactic structure is 'transferred to PF and LF' separately; call it the point of Transfer (Chomsky 2001(Chomsky , 2008. On the PF-branch, the structure undergoes Vocabulary Insertion, Linearization, and other rules affecting the phonologically realized form but not the meaning. A controversial issue, within this theory, is the nature of roots. One question is whether roots are identified in the syntax by their phonological features, semantic features, or neither. Harley (2014) articulates a radical version of the model, where the roots in the list of formatives are purely abstract objects, identified only by an index which ensures that the root receives a particular phonological form at Vocabulary Insertion in the derivation of PF, and a particular semantic interpretation in the derivation of LF, after Transfer. According to a more conservative version of the theory, following Borer (2014a,b) and Embick (2015), roots are identified phonologically in the syntax already. The facts we discuss and the generalizations we formulate can be modelled in either version of the theory. We will, however, represent the roots and functional categories by their phonological, written form, for ease of exposition. What is crucial is that the reduplication takes place postsyntactically, in connection with Vocabulary Insertion, consistent with the observation that the reduplication has no semantic effect.
Another controversial issue concerning roots is when they merge with their categorizer.
According to Marantz (1997Marantz ( , 2001 roots are inert until they are merged with a categorizer or other item with syntactic category, thus forming part of a syntactic object with a categorial label. Harley (2014), on the other hand, articulates a version of the theory where roots behave like other syntactic heads, in that they can take a complement, project a phrase (a Root Phrase), and undergo head movement to a categorizer head. We assume a 'conservative' theory of word formation, in line with Marantz (1997Marantz ( , 2001Marantz ( , 2015, Borer (2014a,b), Embick (2015), where roots do not directly take part in syntactic operations, but do so only by way of merging with a categorizer or other category-bearing item. That is to say, we do not adopt the idea that roots take complements, project phrases, and undergo head movement. 3 Getting back to the Swedish compounds, the structure of Swedish skola 'school' is (6); 'R' does not represent a feature or categorial label but is just a marker of the index that minimally identifies a root, along with its phonological features. 4 The root has no syntactic features except a declension class feature, which we represent by a number.
The root merges with a functional head made up of a nominal feature, a number feature, and a feature selecting declension class (represented as u1, in this case), which deletes once merged (represented as strikeout). Vocabulary insertion will substitute the feature complex by the vowel -a, deriving the spelled-out form skola. 5 The root form shows up in derived words: skol-ning, *skola-ning, flick-aktig, *flicka-aktig (Swedish) school-ing girl -ish The structure of for example flickaktig 'girlish' is (8), the acategorial root flick merging with the adjectival suffix -aktig, projecting an adjective.
The form flicka-aktig in (8), merging a noun flicka with an adjectival suffix, is ill-formed on account of merging two items each projecting a categorial feature, meaning, we assume, that neither projects, so that the resulting construct does not have a category (Josefsson 1997(Josefsson , 1998. Another place where the root form shows up is as modifier of attributive compounds: 6 4 The square root symbol √ is often used as a symbol of 'root' in current linguistic theory. We use R, primarily for ease of presentation. 5 A slightly more complex analysis may be considered, where the root first merges with [n, u1], deriving a noun, which subsequently merges with the number feature. The so derived structure [N [N R [n u1]] −PL ] would be spelled out as skola (in the case at hand). 6 Here and throughout the article we use the term attributive compound for endocentric compounds consisting of a head and a modifying/restricting non-head, including compounds where there is, arguably, a thematic relation between the head and the non-head, as in toothbrush, snow shovel, etc.
(9) skol -flicka, flick-skola, *skola-flicka, *flicka-skola, *skol-flick, *flick-skol (Swedish) school girl, girl school The structure of for example skolflicka 'schoolgirl' would be (10) (representing the nominalizer feature complex as 'n') Here, the root flick merges with the nominalizer spelled out as -a, projecting a noun. 7 This noun merges with the root skol. Since the root has no categorial feature, the noun labels the dominating node, deriving a compound noun denoting a kind of girl. The ungrammatical form *skolaflicka is ruled out as being 'too symmetrical': It would be composed of two merged nouns, with the grammar unable to determine the head. The form *skolflick is ruled out as well, being composed of two merged roots, which yields a construct without categorial or other syntactic features.
By hypothesis, the derived noun has no linear order until it is sent to PF. In this process the linearization rule corresponding to Williams's (1981) Righthand Head Rule applies to (6), (8), and (10), deriving the strings skola, flickaktig, and skolflicka. The rule for Swedish can be stated as: (11) A set {α, β} where α is the head projecting a word is linearized as β>α.
As discussed, following the trend in Distributed Morphology, we assume that common nouns generally have the structure [N R, n], not just in Swedish but universally (although we shall also claim that exceptions exist, which have particular, identifiable properties). In many cases, perhaps most cases across languages, the categorizer is realized as null.
The condition that the non-head of a compound must be a root cannot hold universally, in view of left-recursive compounding, as in football pitch, high-street fashion, etc. We will return to this issue in section 7. The issue is avoided in TXC, though, as this variety of Chinese does not allow recursive compounding.

The structure of common nouns in Traditional Xining Chinese
Free common nouns in TXC are always reduplicated; see examples in (1). As in other languages, a common noun in TXC is minimally made up of a root and a nominalizer n, merged in the syntax. The nominalizer n, like its verbal and adjectival counterpart, can only merge with an acategorial unit, that is typically with a root, as dictated by the morphological implementation of Chomsky's (2013) labeling algorithm: a set consisting of a categorized item, say a verb, and a categorizer n could not be labelled, being 'too symmetrical'. 8 As other functional categories, and following the Distributed Morphology model, the nominalizer is provided with phonological form at Vocabulary Insertion, in the derivation of PF after the Transfer point. In many languages, including Mandarin, the nominalizer n is mostly realized as phonologically null. However, as discussed above, with many Swedish nouns, n is realized as -a or -e. And in the case of TXC, n is mostly realized as a phonological copy of its sister root. At Transfer, the structure of, for example, the noun sū sǔ 'lock' is (12) (assuming that roots have their phonological matrix in the syntax already). At Vocabulary Insertion the phonological matrix of the root, [sū], is copied by n, and the word is spelled out sū sǔ. 9 (12) N (TXC) R n  sū sǔ sū This is a phonological feature copying operation, but operating under a syntactically defined condition: The root and n have to be sisters. 10 As for the formal trigger of the reduplication, it is not the case that n triggers the operation, say, by virtue of an unvalued feature (Chomsky 2001 et seq.) or because it is somehow 'defective' (Harley 2004). 11 The nominalizer n does not 'need' phonological features. This will be seen in section 6, where we discuss cases where reduplication does not take place because the sisterhood condition is not met, but where the so derived nouns are nevertheless well-formed. We propose, instead, that the reduplication is an optional phonological feature copying operation allowed by n, but forced in a case like (12) by a language-particular output condition or 'filter', applying after Vocabulary Insertion in TXC.
(13) *N if N is a free word and has less than two syllables.
If the free noun is a compound, reduplication need not apply, as (13) is satisfied anyway. But if the structural condition is met, that is if the compound contains a root with a sister nominalizer, reduplication may take place. In section 4 the optionality of noun reduplication will be exemplified by various complex nouns which independently have two syllables, and where reduplication can take place or not.
The formulation (13) also implies that nouns with a polysyllabic root need not undergo reduplication. Now, Chinese is notorious for its close correspondence between syllable and morpheme, and, in addition, grapheme; Norman (1988) A reviewer for NLLT suggests that the copying can be regarded as a variety of Conflation, a mechanism suggested but ultimately rejected by Hale and Keyser (2002) but revived by Harley (2004). Simplifying somewhat, Conflation is movement of the phonological features of a complement to a head, triggered when the head is somehow phonologically defective. Phonological feature copying, the reviewer suggests, would be a variety of Conflation where the original copy is not deleted. However, as will be discussed in section 6, n in TXC can be spelled out as null when copying is ruled out. That is to say, it is not defective.
steamed.bun n PRT eat Q 'Do you want steamed buns? ' The fact that reduplication in (14) is not just unnecessary but ill-formed is an indication of another condition on the reduplication: Only a single syllable can be reduplicated. 12 We will see other effects of this condition in section 6. 13 Our formulation of noun reduplication in TXC entails that it applies to 'lexical nouns' only, that is nouns made up of a root and a nominalizer. Pronouns do not undergo reduplication, nor do nominal quantifiers. 14 (16) nāo (*nāo) 'I ', nī (*nī) 'you', jiá (*jiá) 'he/she', fěi (*fěi) 'who' Proper names are an interesting case. They can be reduplicated, and often are, as pet names. This is true not just in TXC but in Mandarin as well (and other varieties of Chinese). This seems to be a different kind of reduplication, though, than in (12), indicated by the fact that it can have a semantic effect, namely endearment. This is true of TXC as well as Mandarin. We will, however, leave proper names aside in the present paper.
Like other varieties of Chinese, TXC also has reduplication of verbs and adjectives (cf. Ren 2006, Wang 2009). This is clearly a different phenomenon, though, from the nominal reduplication we are investigating here. It is always associated with a semantic effect, with verbs repetition or continuation, and with adjectives intensification. It is thus not obligatory. We take this to mean that the reduplication does not apply to roots, but to words, that is roots with either a verbal or an adjectival categorizer, affecting their interpretation as verbs and adjectives. We are sympathetic to 12 While this appears to be common as a feature of reduplication, there are many cases of disyllabic reduplication reported in the literature; see e.g. Frampton (2009: 117-128). 13 Reduplication also cannot apply to a part of the polysyllabic root hǎdá: *hǎhǎdá, *hǎdádá. This follows from the condition that noun reduplication applies only to a root merged with a null categorizer. 14 A widely assumed analysis of pronouns is the one pioneered by Postal (1969) according to which the spelledout pronoun is the head of a DP with a complement NP which is mostly null. As a functional head, the pronominal D is predicted not to reduplicate in TXC. Arguably the most convincing argument in favour of Postal's analysis is the fact that pronouns, in particular plural pronouns, can occur with an overt NP complement, as in we teachers, you children (see Höhn 2018). This construction is found in TXC as well: (i) nī -men xiǔ séng, nāo-men jiǒu yuān 2 -PL school student 1 -PL education member 'you students' 'we teachers' As predicted, if the noun is monosyllabic (is not a compound), it will be reduplicated: (ii) nāo-men mǒ mó 1 PL cat cat 'we cats'. the idea, articulated by Travis (2001), that the reduplication is a matter of phonological feature copying in this case, too, but by a head encoding, for instance, intensity, merged with an adjective, or perhaps an AP. We will not deal with this kind of reduplication in this paper, though.

Predictions
We have proposed that reduplicated nouns in TXC consist of a root and a categorizer, and that the reduplication is a procedure where the categorizer copies the phonological features of its single sister root. Based on this, a set of predictions are made concerning reduplication in TXC affixed nouns and attributive compound nouns, which will all be seen to be true.

Head Affixes
There are suffixes in TXC which are used to form nouns, as demonstrated here.
The suffixes -bóng and -dán have the meaning 'person who is associated with X', where X is the entity that is denoted by the item the suffix is merged with, similar to that of the English suffixer in teenager, foreigner or -y in fatty. Both suffixes have pejorative connotation. (17a) denotes a kind of person, so the suffix -bóng is the head: its categorial and semantic features label the word xiǒng-bóng 'country bumpkin'. Similarly in (17b), the word denotes a kind of person, so the categorial and semantic features of the suffix -dán label the word róu-dán 'blockhead'. The suffixes, we claim, are nominalizers, coming from a list of nominalizers which also includes the semantically vacuous nominalizer which attracts reduplication or has a null exponent (to be discussed in section 6).
This means that the object-denoting items xiǒng 'countryside' and róu 'meat' that the suffixes in (17a) and (17b) are merged with are the non-head elements. Their status as non-heads is ensured if they are roots, not words, comparable to the roots in the Swedish derived nouns in (7). As roots they have no categorial feature to project, and are hence by necessity non-heads. The structure of, for example (17b) would be (18).
If xiǒng 'countryside' and róu 'meat' in (16a,b) were nouns, the head of the construct would not be determinable, and they would be predicted to be ill-formed, comparable to the ungrammatical Swedish word forms in (8).
In the previous section we proposed that the reduplication in TXC nouns is a process where the semantically and phonologically null nominalizer copies the phonological matrix of its sister root.
In other words, the presence of this nominalizer is crucial for the reduplication to take place in TXC nouns. Based on this and the classification of the object-denoting item xiǒng 'countryside' and róu 'meat', it is predicted that items such as xiǒng 'countryside' and róu 'meat' which are merged with the suffixes -bóng and -dán, as in (16) As independent nouns, xiōng 'countryside' and róu 'meat' can be, and have to be reduplicated.
In this case they are merged with the semantically and phonologically null nominalizer, which will copy their phonological features in order to comply with the two-syllable condition (13). We will from now on gloss the reduplicant as 'n', reflecting the analysis that it is the categorizer spelled out as a copy of the sister root.  (19a,b) are not ruled out by a condition which excludes reduplication in derived words, or excludes reduplication in words which already have two syllables. As we shall see directly, reduplication does occur in derived words, resulting in words with at least three syllables.
The suffixes -bóng and -dán themselves cannot be reduplicated, either, neither on their own, nor when merged with a root.
(21) * bǒng-bōng, * dǎn-dān, *xiōng-bǒng-bōng, *róu -dǎn-dān (TXC) This follows if they are pure functional heads, not made up of a root and a categorizer. They are the spell-out of a small bundle of syntactico-semantic features and a nominal feature. They are members of a list of nominalizers which also includes the semantically vacuous nominalizer.
This analysis of -bóng and -dán may be called into question. Josefsson (1997Josefsson ( , 1998 argued that certain derivational affixes in Swedish are, in fact, roots. More recently the analysis of derivational affixes has been debated again; see de Belder (2011), Lowenstamm (2015), Creemers, Don, and Fenger (2018). Lowenstamm (2015), for example, argues that the derived noun librarian has basically the following structure, using our notation. In section 6 we will argue that there are words in Mandarin and TXC that have this structure, including various kinds of non-compositional compounds. However, we do not adopt this analysis for words formed by the suffixes -bóng and -dán. Classifying them as roots would require assuming that there is a special subcategory of roots which have a selection feature, selecting to merge with a root, and a linearization feature: they are always spelled out following their sister. We maintain that roots have no syntactic features. But the derivational suffixes -bóng and -dán have syntactic features: they are nominal and select a root. Being heads, they follow their sister: they are suffixes.

Non-head affixes
Consider the suffixes in (24): The suffix appears to have no effect on either the semantics or the category of the word: mǒ-é is a noun which means 'cat' and zā-zī a noun which means 'powder'. Alternative forms are the reduplicated forms mǒ mó 'cat' and zā zā 'powder' (reduplication needed to satisfy the filter (14)). A possible analysis is that -é and zī are exponents of n, alternatives to reduplication. However, the suffix -é can occur with adjectives as well, as an optional addition, so it is not an exponent of n: As in (24), the addition of -é has no effect on the semantics of the adjective. It is optional since adjectives can have a null categorizer. We take it to be an item devoid of any features other than an index linking it to a phonological matrix, and a selection feature selecting merge with a noun or adjective. We take this to be true of zī as well, except it can only merge with a noun. If so, the other constituent in (24a,b), mǒ and zā, must be a noun, and the other constituent in (25a,b) must be an adjective, providing a head for the word. It cannot be a bare root, or the word would have no category. By hypothesis, in (24a,b) this means that it is made up of a root and a nominalizer. The structure of for example (24a), after Vocabulary Insertion, inserting the null exponent of n, would be (26): Comparison of (24) and (27) shows that the reduplication is optional. This, we contend, is because filter (13) is satisfied in (24)  16 A reviewer points out, correctly, that the notion of a syntactic category, such as -e and -zi, with only phonological features seems paradoxical. However, the fact that they select certain syntactic, not phonologically defined categories implies that they are syntactic categories. Furthermore, the fact that they can be found in reduplicated words shows that they are not triggered in order to satisfy a phonological condition, in the manner of epenthetic vowels. They are items which are available, apparently, in the list of morphemes, and which can be employed to satisfy phonological conditions, if need be, but can also occur redundantly. 17 Consideration of the options mǒ mó, mǒ é, and mǒ mó é indicates that the filter (13) steps in only once the whole word has gone through Vocabulary Insertion. Assuming the conventional from-root-outwards application of Vocabulary Insertion (Bobaljik 2000), if (13) would apply at every step of Vocabulary Insertion, the word mǒ é would not be derivable, as it would always be bled by mǒ mó. Thanks to a reviewer for NLLT for pointing this out.
The addition of the prefix is optional. An alternative to (28a,b) is the reduplicated forms yǐ yí and chēi chēi (reduplication needed to satisfy (13)). The affix makes no contribution to the interpretation of the words. We take this to mean that the category that the prefixes merge with is a noun, which is the head of the affixed word, exhaustively determining its syntactic and semantic features. If the item the prefix is merged with is a noun, it is made up of a root and a nominalizer. This predicts, given that reduplication is optional, that it can be reduplicated, a correct prediction.  (1999), only 27% of the 3000 most commonly used words in Standard Chinese, were monosyllables.
According to a more recent study of new words in Chinese (Li & Bai 1987, cited in Duanmu 1999, not a single new word is monosyllabic. Given the close correspondence in Chinese between syllable and morpheme (Norman 1988: 154, Basciano & Ceccagno 2009, Chung et al. 2014) most of the disyllabic words, by far, are compounds (as will be discussed more in section 6), but employing purely phonological suffixes is another way to avoid monosyllables. In this light, the reduplication in TXC is yet another, particularly radical way to avoid monosyllables.
In addition to derivational affixes, there are also some inflectional affixes in TXC. One of them is the pluralizing suffix -men: The suffix is a syntactic category which will only merge with another syntactic category, that is, with a noun (Li 1999;Ueda and Haraguchi 2008). A root cannot merge with an inflectional suffix. If the sister of the plural suffix is a noun, it will consist of a root and a null nominalizer, which predicts that it may undergo reduplication. This prediction is right as the following example shows: (32) duěng duěng -men (TXC) hole n -PLURAL 'holes' The structure of (31) is (33)

Attributive compound nouns in TXC
Above, based on how reduplication operates in TXC and the analysis of components of affixed nouns, predictions are made which are confirmed. Furthermore, based on the same principles, a prediction can be made concerning attributive compounds which is also accurate. The following are examples of attributive compounds in TXC: 18 According to Li (1999) and Huang, Li and Li (2009: 311-315), N+men is the result of head-movement in the syntax. This is consistent with what we have argued, namely that the filter (13)  On the other hand, the non-heads cěi 'vegetable' in (34a) and mēi 'ink' in (34b) cannot be nouns made up of a root and a null nominalizer, but, following the theory in section 3, are bare roots.
Since reduplication in TXC nouns requires a nominalizer, it is predicted that the non-head in the attributive compound in TXC cannot be reduplicated. This prediction is confirmed by the following ungrammatical examples:  (13): In an attributive compound with two pronounced components this condition is satisfied already without reduplication, hence reduplication is allowed but not required.
In this section, we have looked at affixed nouns and attributive compound nouns in TXC.
The affix may or may not be the head of the resultant word. Where the affix is the head, the item it is merged with, the non-head, is shown not to be able to reduplicate, as predicted. Where the item the affix is merged with is the head, this item is predicted to be able to reduplicate, another correct prediction. In attributive compounds, we predict that the head can be reduplicated, while the nonhead cannot, another correct prediction. In short, the distribution of the reduplication in TXC nouns is predicted on the basis of morphosyntactic properties of the components of the nouns: If the item is lexical (root-based) and is the head of the noun, it can reduplicate, if it is not the head or is not lexical, it cannot reduplicate. Whether a word component is head or not is not phonologically marked in TXC. Thus a purely phonological approach which does not take word-syntactic structure and category into account cannot explain the distribution of reduplication in TXC nouns 19 .

Bound words
Chinese has a very large class of content words distinguished by the property that they have to be morphologically bound. In this section we will consider the observation that these items cannot undergo reduplication in TXC, as noted in Wang (2018), and discuss the theoretical consequences that this observation has. In the literature these items are called bound stems (Dai 1992:40,75-76) or bound roots (Sproat and Shih 1996, Packard 2000, Pirani 2008); see Wang (2018) (37). We maintain, therefore that they are based on roots, but like light verbs they are monomorphemic: a root with inherent category. Now if noun reduplication in TXC is copying of the phonological matrix of a root by a sister nominalizer, it follows that bound nouns do not undergo reduplication.
Why can they not form free words? Note first how the absence of reduplication of bound nouns in TXC provides an argument that the boundness condition is not phonological by nature, as claimed in some of the literature; see Chung & al. (2014: 613). It is not for instance the case that the items are subject to a phonological condition that they must be part of a disyllabic word. If that were the case, reduplication would seem to be the perfect mechanism to satisfy it in TXC, but reduplication is not even possible.
Following Wang (2018: 68), we propose that there is a condition (41) in Chinese, which may even be universal.
(41) A free content word (= root-based word) must contain at least two morphemes.
'Content word' is meant to exclude light verbs and comparable functional heads. In the common case of an acategorial root merged with a categorizer the result is of course a bimorphemic word. The hypothesis put forward by Wang (2018) is that the Chinese bound word is monomorphemic, a root with a categorial feature forming a single item. The principle (41) is, then, the reason why it cannot function as a free word. But once a bound word is merged with another morpheme (an affix, a free word or another bound word) the result is a licit free word, satisfying (41). The one functional category they cannot merge with, though, is a categorizer, since they already have syntactic category.
As mentioned at the start of section 3.2, a categorizer can only merge with an acategorial item. We proposed that this is an effect of Chomsky's (2013)  Yǐ 'clothing' in (42a,b) and miǎn 'cotton' in (42b) are bound words, shown by the fact that they cannot reduplicate (*yī yī, *miǎn mián ), jiá 'shelf is a regular noun, shown by the fact that it can reduplicate (jiǎ jiā). (42a) shows that a bound word can be modifier of a compound headed by a regular noun, (42b) shows that a bound word can be modifier of a compound headed by another bound word. In both cases it looks like a noun, a bound word, is merged with a noun, a regular noun in (42a) and a bound noun in (42b). This is predicted to be ungrammatical, not allowing either of the constituents to label the compound. This suggests that bound words can alternatively occur without a categorial feature. That would be the case with the non-head bound words in (42a,b). Bound words would thus occur in two guises, either as roots with inherent category or as acategorial roots.
However, that raises the question why bound words cannot in the latter case merge with a categorizer after all, allowing reduplication. We are led to the conclusion that bound words, even when occurring in acategorial shape, as when they are non-heads of compounds or derived words, are distinct from roots in that they fail to merge with a categorizer.
We leave the problem in this unresolved state. Note, however, that we now have a handle on this enigmatic class that we did not previously have, thanks to TXC. All previous formal descriptions of bound words have been based on one observation: they have to be bound. We can now add another observation: They cannot be reduplicated. This restricts the hypothesis space in interesting ways, which we hope will eventually lead to a fuller understanding of the phenomenon. 22

The syntax of non-compositional compounds: root merger
In a non-compositional compound (abbreviated NCC) the meaning of the compound is not the sum of the meaning of its components. Hu and Perry (2018) (Hu and Perry 2018:711) Following Marantz (2007), Embick and Noyer (2007) and Borer (2013), Hu and Perry (2018:718) propose that the NCCs in Yixing Chinese are the result of merging two bare roots which are devoid of syntactic features, followed by merge of a categorizer. Since the bare roots have no syntactic features, the object which is the result of merging two roots has no label. Hu and Perry use the zero symbol Ø for this unlabelled phrase (Hu and Perry 2018:724). The categorization comes after the merge of two roots (Hu and Perry 2018:719), by merging a categorizer with the unlabelled phrase. 22 A reviewer asks whether a non-nominal bound word, say an adjective, can be merged with n, triggering reduplication. This does not occur; bound words do not reduplicate. As pointed out in the beginning of section 3.2, there is a straightforward reason, in the present model, why this does not occur: the grammar cannot label such a construct.
So for example the NCC ʃɑo ʃy 'small book: comic' which is a noun, will have the following structure where two roots make a unit which is merged with a null nominalizer: According to Zhang (2007), the above abnormality concerning verb-object compounds can be explained if the components of such compounds are roots without syntactic features, while the category of the compound is determined by a third element, which is a category-defining functional head. In this way there will be no discrepancy between the category of the root components (as they have no category) and the category of the compound. So for example (46), which is a noun, will have the following structure where two roots are merged first, then the resultant complex Root+Root will merge with the category-defining functional head f. In (46) f is nominal, in (47)  By standard assumptions, which we have adopted, labelling of syntactic units is needed for linearization: The linear order of a phrase as well as a complex word depends on which constituent is the head, with variation across languages and also within a language depending on the category of the phrase or word. This also determines the semantic interpretation of the phrase or complex word. Also by standard assumptions, widely although not universally accepted, labelling is needed to make a word or phrase visible for further (morpho-) syntactic operations. 23 Another, less well established hypothesis is that labelling is needed in order to link a syntactic unit to an encyclopedic entry (Zhang 2007, Bauke 2014: 65-70, Hu and Perry 2018. This would be why a compound consisting of two roots is not interpreted compositionally. The bare roots cannot be linked with any encyclopedic entry, but the compound can be, as it has a label, provided by the categorizer. The meaning of the compound thereby need not have any direct, systematic relation to the meaning that the roots would have if they were labelled. This is an idea which we cannot accept. Recall from section 3 that compositional compounds are typically made up of a root merged with a word, as seen very clearly in the case of nouns of the 1 st and 2 nd declension in Swedish, and corroborated by the distribution of reduplication in nominal compounds in TXC, This means that bare roots have access to their full interpretation. Assume, for the sake of argument, a model where roots are not identified by semantic features prior to Transfer, but only by an index by which they will be linked to an entry in the Encyclopedia following Transfer (Harley 2014). This link, we contend, is independent of prior merge with a categorizer. Our take on NCCs is therefore the following: The two roots of an NCC are each linked with an entry in the Encyclopedia, but in the absence of a label, hence of a head, the compound does not yield a compositional reading. Merging a categorizer with the root-root compound makes possible linking it to an Encyclopedic entry, providing it with an interpretation which is in principle independent of the interpretation of the two roots. 24 The Encyclopedic entry also provides it with a linear order. Being labelless, the root-root compound cannot be seen by the Righthand Head rule which determines the linear order of regular, headed compounds in Chinese.
At the outset of section 3 we stated that the categorizer n can only merge with a labelless (= acategorial) construct, typically with a root. Two merged roots is still a labelless construct, hence can be merged with n. We will represent the root-root compound as labelless. 25 Recall that the presence of the categorizer n is a precondition for reduplication to occur in TXC. So apparently the object-referring items fóng 'room ' and tuēi 'leg' in (49) are not words which contain a categorizer. But as free words they can be, and need to be, reduplicated: fǒng fóng 'room', tuēi tuěi 'leg'. And as we would also predict, as heads of compositional compounds, they can be reduplicated:  ' and tuēi 'leg' in (49) are roots. Jiěng 'quiet' and chǒng 'long' are roots which may merge with a categorizer to form words, but in (49) they can only be roots. We know this, because as words they would be heads in (49), which they are not.

Non-compositional compounds in TXC
(49a) and (49b) are nouns, so they will have the following structure: If an object-referring item is the head in a compound in TXC and is not a bound word, then it can undergo reduplication. If it is not the head, it is a root and cannot undergo reduplication, as we showed in section 4.2. The absence of reduplication seen in (49) is therefore predicted if the structure of the NCCs is (52): The categorizer cannot copy the phonological matrix of either of the roots, as they are not sisters. As for why it cannot copy the phonological matrix of the unit made up of the two roots, we proposed in section 3.2 a condition on reduplication prohibiting reduplication of more than one syllable. This rules out reduplicating the root-root unit in (52) to derive (50c,d).
The structure which is proposed here for NCCs is in line with what Hu and Perry (2018) and Zhang (2007) have proposed. In TXC there is now additional direct empirical evidence, that is absence of reduplication, to support the analysis.

Non-compositional coordinative compounds
Synonymy-compound nouns and parallel compound nouns, which are two subtypes of coordinative compounds in Mandarin and TXC, are introduced and analysed in this section (see Wang 2018 for discussion of other types of non-attributive compounds in Mandarin and TXC).
Synonymy-compounds are compounds in which the components are synonyms (Chao 1968:374-375, Ceccagno andBasciano 2011:481 Parallel compounds are a type of coordinative compounds where the components are semantically associated, but are neither antonyms nor synonyms (Chao 1968:377 We have argued that reduplication applies where a root is merged with a nominalizer. This implies that a constituent in a compound which cannot be reduplicated will not have that structure. As a matter of fact, the constituents of synonymy and parallel compounds cannot be reduplicated. We take this to be evidence that the constituents of these compounds, when they are not bound words, are roots, not nouns. This also tallies with the fact that the compounds are non-compositional. This is clearer in the case of parallel compounds, and we therefore begin with a discussion of parallel compound nouns. The following is a list of parallel compound nouns in TXC. The meaning of these compounds is clearly not the sum of their parts, and there is no systematic semantic relation between the two parts. For instance, niān 'eye' in (55a) does not modify wù 'pit' , or bear any other definable semantic relation to it, the same is for bān 'board' and jiěng 'neck' in (55b). The meaning and linear order of the compounds is idiosyncratic, represented as such in the Encyclopedia. Following Zhang (2007), Hu and Perry (2018), and Wang (2018) The components of (55a) cannot be reduplicated, nor can the entire compound be reduplicated: (57) a. *niān nián wū (TXC) eye n pit b. *niān wū wū As independent words, niān 'eye' and wū 'pit' can, and must, undergo reduplication, so in this case they are roots merged with a null nominalizer: niān niǎn 'eye', wū wū 'pit' . We conclude from this that the components of the parallel compound (55a) are bare roots. Bān 'board' in (55b) is a root, as well, as it cannot be reduplicated, while it can be and must be reduplicated as a free word. As for jiěng 'neck' in (55b), it is a bound word. As such it cannot be reduplicated in any context, including (55b), and cannot occur alone as a free word in phrases. As discussed in section 5, bound words occur in two guises, either as roots with inherent category or as bare roots. In the parallel compounds it must be the bare root version or they would label the compound, which would thus be compositional, contrary to fact. Thus (55b) will have the following structures respectively: 26 Tǔ 'saliva' cannot occur alone as a free word in a phrase, nor can it ever be reduplicated alone, so it is a bound word. Given the fixed word order of (61), it must be the root version of the bound word, or it would be head, but in that case it would be the rightmost item. We assume the same is true of géng 'neck' in (62), although in this case it is not as easy to show that it is not the head of the compound. As for mō 'saliva' and bó 'neck', they are roots, based on the fact that they cannot be reduplicated in (61) and (62) respectively, but can be reduplicated alone. So the structure of the synonymy compounds (61) and (62) would be the same as for parallel compounds and other NCCs, that is (60).
We assume that synonymy-compound nouns and parallel compound nouns are formed by merge of roots or bound words in Mandarin, as well, even though we do not have the direct evidence of it that we see in TXC. For instance, hào 'number' and mǎ 'number' in (53a), shuǐ 'water' and guǒ 'fruit' in (54a) can each occur as a free word, which is to say, they are roots that can merge with a null nominalizer to form a free word. However, we propose, by analogy with the corresponding compounds in TXC, that the compounds in (53a) and (54a) are formed by merge of two bare roots, followed by merge of a null nominal categorizer.
The order of the constituents of the parallel and synonymy compounds is fixed. The opposite order of the constituents in (53a,b) and (54a,b), for example, yields ungrammatical compounds. In compositional compounds the order is determined by headedness (see section 3.1); in Chinese, the head is spelled out rightmost. In NCCs, being headless, the order as well as the interpretation is not derived but encoded in the Encyclopedia.

Recursion in word formation
In section 3 we argued that an attributive compound with two members could not consist of two merged words, for instance two merged nouns, as the grammar could not then determine which one is the head, i.e. which one will label the set. A solution is to form a compound by merging a root with a noun, in which case only the noun can be head. This is evident in a class of nouns in Swedish which overtly consist of a root plus a vowel serving as nominalizer. We have shown that it is also evident in the case of attributive compounds generally in TXC, as in this language nouns, as opposed to roots, are always reduplicated, by virtue of the nominalizer copying the phonological matrix of the root. However, compounds can be more complex. In compounds such as wallpaper design and football pitch the modifier is itself a compositional compound, hence not a root but a noun. So these compounds do consist of two nouns, one of which is itself a compound. They exemplify recursion, more precisely left-recursion, in compounds. How can the grammar determine which noun is the head?
As discussed in Holmberg (1992) and Josefsson (1997Josefsson ( , 1998 According to Holmberg (1992), the effect of the Case is to close the nominal projection, preventing projection of the features of the Case-marked noun onto the dominating node, thus allowing the other noun to project its features, and label the set made up of the compound and the simple noun.
The generalization in Swedish is that the modifier of an attributive compound is either a root or it is Case-marked.
TXC has a different way of solving the problem: It has no recursive compounding. The compounds in (65) There are languages that have endocentric attributive compounds but where recursion is either rare or non-existent. Greek is one example (Ralli 2013: 95), Polish is another (Stekauer 2009). 27 We can add TXC to the list. We conclude that TXC, along with at least some of the other languages which lack recursion, only allows roots as non-heads of compounds.
Mandarin, along with many other languages including English, allows recursion and shows no overt evidence of any special marking of non-heads of compounds. How to accommodate this with the present theory is something we leave for future research (see Mukai 2008 for a proposal).
One possibility, suggested in Holmberg (1992), is that there are two different ways allowed by UG to form compounds. One is by means of set merge in Chomsky's (2001) sense, as outlined in section 3.1. The other is by 'pair merge' (Chomsky 2001), that is adjunction, an inherently asymmetric process, where labelling is therefore not a problem: adjunction of α to β does not create a new category, only expands β. Holmberg (1992) suggests that Swedish is of the former type, English of the latter type, supported by the fact that English allows inflection of the non-head, as in arms race and parks attendant, which is never allowed in Swedish. Mandarin would be of the pair merge type, allowing recursive compounding without any special marking of complex non-heads, while TXC would be of the set merge type along with Swedish, but as it lacks means to case-mark complex nonheads, the effect in TXC would be absence of recursive compounding.

Conclusions
In Xining Chinese, particularly as spoken by the elderly, what we have called Traditional Xining Chinese (TXC), free nouns are always reduplicated, as a purely formal requirement with no effect on interpretation. The relevant descriptive generalization can be stated as follows: (66) a. Reduplicate a free, simple noun. b.
Optionally reduplicate the head of a complex noun, except if it is functional or a bound word.
27 Anders Holmberg and Samuel Andersson have collected data on compounding from 208 languages on the basis of descriptive grammars. Typically there is no mention of whether compounding is recursive or not. In fact, only in one grammar was absence of recursive (nominal) compounds explicitly mentioned: Hellenthal (2010: 180) on Sheko, an Omotic language spoken in Ethiopia.
There are languages that have compound words, but only exocentric ones, including the Romance languages and Arabic; cf. French essui-glace lit. 'wipe-glass', i.e. 'windscreen wiper'. These are not composed of a root and a head, in the manner of nominal compounds in Chinese, English, and other languages discussed in the present article. They may be constructed as NCCs in Chinese and other languages. The compounds in Sheko appear to be of the endocentric type. phonological features of a monosyllabic root onto a sister categorizer n. We have referred to it as noun reduplication. The reduplication is optional, but forced in the case of free monosyllabic nouns by an output condition or filter: (67) *N if N is a free word and has less than two syllables There is a condition restricting the reduplication which is likewise sensitive to syllable structure: It can only apply to a syllable. This rules out reduplication of root-root compounds (which are by definition non-compositional, in the present theory) and polysyllabic roots.
Given this, every part of the generalization in (66) is explained by the theory we articulate, building on Chomsky (1995Chomsky ( , 2013, much work in the Distributive Morphology tradition, and recent work on the morphology of Mandarin and TXC in Wang (2018). An important theoretical premise is that roots are acategorial. Content words are derived by merging a root with a categorizer, which may be, and often is, spelled out as null (Marantz 1997, Josefsson 1997, 1998, Harley & Noyer 1999, Lieber 2006, Embick and Noyer 2007, Harley 2011, de Belder 2011, Hu and Perry 2018.
The reduplication in TXC is the result when a nominal categorizer copies the phonological matrix of its sister root, thus meeting the condition that a noun must have two syllables/two pronounced morphemes.
The reason why the non-head of a compound or derived word cannot be reduplicated is that it is a root, merged with a word (compounds) or with an affix other than a categorizer (derived words). A root without a categorizer as sister cannot reduplicate. Functional heads cannot reduplicate, as they are single items with inherent category. As we show, there are also acategorial affixes, though, which merge with nouns (not roots). These nouns therefore can undergo reduplication in TXC but need not be, as they satisfy (67) even without reduplication.
Bound words is a class of words typical of Chinese including TXC. Like function words they do not consist of a root with a categorizer, but are single items with inherent category (Wang 2018). As such they cannot undergo reduplication. Due to the output condition (41), they have to be morphologically bound, though, either by affixation or by compounding.
In NCCs there is no reduplication. Following work by Zhang (2007). Bauke (2014), and Hu & Perry (2018) we assume that NCCs are made up of two merged roots, forming an unlabelled unit which is merged with a categorizer. This configuration does not meet the structural conditions for reduplication in TXC, as the null categorizer is not a sister of either root, and the unit consisting of two roots cannot be reduplicated, as reduplication can only apply to a single syllable.
compound nouns typically consist of a root and a noun, the latter the head. This conforms to the principle that units built by merge must be asymmetric for labelling to be possible (Chomsky 2013), and explains why the non-head of a simple compound cannot be reduplicated in TXC. This raises the question how complex, recursive compounds are derived, where the non-head is itself a compound.
The issue is avoided in TXC, as the language does not allow recursive compounding.
A question we have not touched upon yet is why only nouns undergo semantically vacuous reduplication in TXC. Nothing in the theory we have articulated predicts this. It is suggestive, though, that, as discussed by Duanmu (1999), most nouns in the common vocabulary of Mandarin are disyllabic or more; only 16% are monosyllabic. The percentage of monosyllables is clearly higher for verbs (41%), and for adjectives (31%). Whatever the explanation is of this distribution, the restriction of reduplication to nouns in TXC is an extreme version of the same pattern: In TXC no nouns are monosyllabic.
As mentioned, the obligatory noun reduplication we have investigated is characteristic of the variety of Xining Chinese spoken by the older generation, Traditional Xining Chinese (TXC). For younger speakers, presumably as an effect of the increasing influence of Standard Mandarin, reduplication is common but not compulsory. Just what the factors are which govern the variation between reduplicated and non-reduplicated forms, grammatical, lexical, and social factors, is an interesting topic for future research, which may itself shed more light on the formal nature of the reduplication.
Considering the place of the reduplication discussed here in the architecture of the grammar, it is interesting to compare with Travis's (2001) findings. She describes three cases of reduplication. None of them is a close relative of the reduplication we have described here. In particular, they all have semantic effects (on quantity, one way or other), and they all apply in the phrasal domain, across a maximal category boundary. Her conclusion is still interesting and relevant for the reduplication described here: "…all cases of reduplication [discussed in her paper] are filling (by creating copies) positions that are independently available in the syntax." (Travis 2001: 11) This makes them different from the cases of reduplication described and discussed in the (morpho-) phonological literature (see Frampton 2009), which may be triggered by a null functional head, but which perform a phonological operation typically on an adjacent vocabulary item realizing a root, expanding that item by reduplicating it, or more often, a part of it (see Frampton 2009). In this perspective, noun reduplication in Xining Chinese is more like Travis's (2001) cases of reduplication, more 'syntactic' in the way it employs copying of the phonological matrix of a vocabulary item onto an independently generated head.