Natural Language & Linguistic Theory

, Volume 35, Issue 4, pp 955–977 | Cite as

Non-adjacent reduplication requires spellout in parallel



Recent approaches to morphological spellout have been cyclic in nature, whereby category-defining heads trigger the spellout of phases in word formation. A prediction of these types of cyclic approach is that phonological conditioning of outer morphemes must be local, such that a conditioning morpheme must be linearly adjacent to the target. This paper presents evidence from Madurese reduplication that provides evidence to the contrary. Two major problems are isolated: (i) a long-distance relationship can exist between a reduplicant and a base, and (ii) the compositional semantics of reduplicants places them outside of a phase, even when the reduplicant must access properties of the root inside of the phase. Both of these problems provide prima facie evidence for a non-local configuration. In order to account for these non-locality effects, it is proposed that identity demands are placed on the base-reduplicant correspondence, and that reduplicative locality is a violable constraint in grammar.


Spellout Reduplication Locality Cyclicity Reduplicative correspondence 

1 Introduction

This paper investigates the question of whether morphology is spelled out cyclically or in parallel. At heart, this question is tied to locality requirements on the spelling out of morphemes. One approach views the morphology-phonology interface as cyclic, whereby morphemes are spelled out in phases, triggered by the merging of cyclic heads into word structure. This type of approach imposes a locality condition whereby contextual allomorphy is limited to structurally or linearly adjacent positions (Marantz 2001, 2013; Marvin 2002; Paster 2006; Embick 2010; Gribanova and Harizanov 2016; for an earlier version of such a constraint on linear adjacency, cf. Carstairs 1979). The cyclic nature of the mechanics of spellout in these theories prevents higher heads from having a phonological relationship with lower morphemes; the result is a locality condition on allomorph selection. The cyclic approach stands in contrast to parallel approaches, such as Optimality Theory, where morphological spellout takes place at PF in a single evaluation. The architecture of OT does not impose a locality requirement per se on contextual allomorphy or phonologically-dependent morphemes, as the correspondence relations between phonological objects and a triggering context can be independent of the linearization of those elements.

Data from Madurese (Austronesian) will be presented which defies locality requirements on phonologically-determined morpheme selection, where a type of non-adjacent reduplication is argued to be sensitive to the phonological content of inner morphology, but where the reduplicant can appear outside of intervening cyclic heads. This phenomenon is illustrated by comparing (1a), which involves a root and its corresponding reduplicated form, vs. (1b), where a derivational prefix attaches to a root, and where this morpheme intervenes between the root and reduplicant (data from Davies 2010:134, 523). For expository purposes, both reduplicants and roots will be underlined when there are intervening affixes.
  1. (1)








    ‘become afraid’


    ‘become afraid (pl)’

The existence of this phenomenon argues against cyclicity in the strictest form, and instead lends support for a global approach to the morphology-phonology interface, where phonological readjustments are implemented in parallel, and where the content of all morphemes in a given domain are spelled out simultaneously.

2 Background

Recent approaches to Vocabulary Insertion adopt a cyclic approach to the phonology-morphology interface, such that phases of morphological operations are followed by phonological spellout of those phases. These recent approaches advocate a type of syntax-within-words approach, whereby morphological heads define phase domains (for instance, Marantz 2001, 2013; Marvin 2002; Embick 2010). Since each cyclic domain is sent to PF separately, a prediction is that contextual allomorphy must be constrained by locality requirements. A well-known restriction on allomorphy in English, discussed by Embick (2010), can be observed in nominalized vs. gerund forms. Special nominals have multiple allomorphs (laugh-ter, marri-age, destruct-tion); gerunds have only a single one: -ing. Embick attributes this difference in allomorphy to the nature of cyclic heads and their (non-)adjacency, as illustrated in (2): Embick (2010:16) casts this distinction as a condition on cyclic heads, where the heads classified as cyclic include category-defining derivational morphemes such as v, n, a, etc. (cf. Williams 1981). As illustrated in (2), English nominalizations involve only a single n cyclic head, but gerunds involve two, both v and n.

Embick proposes a model of morphophonology based on principles of cyclic derivation and adjacency to account for the dynamics of the linear order of morphemes and their interaction with phonology. For the derivation of contextual allomorphy, there are two locality conditions. One is the domain of the phase, such that interacting morphemes must be co-located in the same phase; the other is linear adjacency, such that morphemes may interact if they are both linearly adjacent and concatenated with each other. Non-adjacent morphemes may interact only when an intervening head is phonologically null, and only if the outer morpheme is not a cyclic head.1 When a cyclic head is merged, the domains in the complement of the head are sent to PF and spelled out. The result is that cyclic heads cannot access root or other morphemes in the complement of lower cyclic heads; e.g. for the structure \([[[\sqrt{\mathit{marry}}] x] y]\), the visible head x effectively blocks contextual allomorphy in y. The corollary to this (Embick’s Activity Corollary) is that material in a lower head should not be visible to a higher head during spellout. In addition to this restriction, there is a condition on linear adjacency such that “contextual allomorphy, where one node X can see another node Y for the purposes of Vocabulary Insertion, is possible only when X and Y are concatenated” (Embick 2010:9). Under this general approach, allomorphy is “local” in the sense that each node must be local (cf. Marantz 2013), or may have an intervening node that has no phonological exponent.

It is important to note that this theory of locality is specifically designed to model contextual allomorphy. With respect to other types of phonological phenomena, Embick (2010:54) notes,

“In later stages when these elements are closed off by the Activity Corollary, these elements cannot be seen as Rootsor as particular functional heads. However, these elements possess a phonological matrix, and this representation may be visible to subsequent operations. For example, it is in principle possible for phonologically conditioned allomorphy at outer nodes to refer to a phonological matrix associated with a Root. A rule of this type could not, however, target certain Roots to the exclusion of others; it would have to apply to any phonological representation meeting its structural description.” [emphasis added]

It can be assumed that what is described above are phonological operations that are either iterative or long-distance, but which do not make reference to morphological categories that are rendered opaque by the Activity Corollary and instead, make reference to strictly phonological categories within those phases. The implication is that such processes could be triggered by phonological objects in a lower phase only if these objects were accidentally properties of the root.

This paper aims to widen the scope of this discussion around contextual allomorphy to include operations that will simply be referred to as morphophonological dependencies. The theory of locality sketched above requires these dependencies to hold over a local domain; any dependencies that extend beyond strict adjacency, such as long-distance dependencies, will be taken to be evidence against this locality restriction. The specific phenomenon under discussion here is reduplication, where there is a morphophonological dependency between a base and a reduplicant, where the reduplicant receives its segmental identity from the base.2 If there were to exist a language where the reduplicant were separated from the base by intervening cyclic heads, and it could be demonstrated that the form of the reduplicant is contingent on the morphological category Root, then this would pose a genuine problem for the locality approach. Madurese will be claimed to constitute such a language, and will be explored in more detail in the next section.

The discussion of derivational locality outlined above dovetails with ideas about phonological locality conditions on reduplication. Often an implicit, if not explicit condition that is assumed is that reduplicants must be in a local, i.e. adjacent relationship with the base. Locality constraints have been proposed by Marantz (1982) as a preference for reduplicants to be adjacent to their correspondent strings in the base. Locality in this sense is violated in cases of prefixing reduplicants copying from the end of a base, or suffixing reduplicants copying from the beginning, though inherent in this approach is the assumption that reduplicants will surface adjacent to the entire base in one way or another. This is also true for McCarthy and Prince (1993a, 1995), who encode locality into the formal definition of the base (as that string that is immediately adjacent to the reduplicant). In a similar fashion, Urbanczyk (1996) takes the position that adjacency is a hard constraint of grammar, and not subject to violation (her “Adjacent String Hypothesis”). Broselow (1983) has taken a position similar to the locality approach outlined above, claiming that subjacency is responsible for the locality constraints on reduplicants, whereby reduplication is bound by cyclicity (see also a recent similar approach by Idsardi and Raimy 2013).

If a pattern of non-adjacent reduplication were found to exist, and the non-adjacency was demonstrably not due to independent phonological pressures, then this could warrant viewing adjacency as a violable constraint of grammar (cf. Lunden 2004), and would also pose a challenge for theories of locality. Data related to that in (1) will be presented in the next section that poses precisely this challenge.

3 Non-adjacent reduplication

The evidence for non-local morphophonological dependencies in this work comes in the form of reduplication. However, before presenting the full range of data, it is worth explicitly stating the assumption that reduplicants are affixes or stems (or Vocabulary Items; cf. Haugen 2011; Cook 2013) that are devoid of underlying segmental content, and where the phonological exponence of a reduplicative morpheme is dependent on the properties of the base. That is, aside from independent prosodic structure requirements, the spelled out content of a reduplicant is subject to readjustment rules that modulate the relation between reduplicant and base.

The predictions of cyclic theories with respect to contextual allomorphs and morphophonological dependencies are clear: morphemes that are not adjacent (in the sense of being separated by a cyclic head) should not be phonologically available to each other. Thus, any long-distance identity relationship would constitute evidence for a more global approach to spellout.3 This importantly rules out intervening morphology whereby the linearization of which is not the result of phonological pressures. Embick (2010) illustrates how prosodic factors can conspire to yield the appearance of surface intervening morphology with the case of Palauan. In Palauan, there is a “verb marker” that surfaces as [mə-] except when immediately preceding a labial consonant, where it surfaces as [o-].
  1. (3)

    Palauan: mə-, o- verb markers; o- before labial-initial stems


    ‘walk, travel’







In past tense forms, the tense morpheme -il- appears between the verb marker and the root (examples here are middle verbs):
  1. (4)

    Palauan infixation




    o-balə ʔ

    o-il-balə ʔ


The result is an opaque ordering: in order to force the o- allomorph to surface, it must first be affixed to the root, then -il- must be infixed derivationally after o-affixation. The infixation analysis is consistent with the behavior of this affix elsewhere in the language (appearing after the first syllable), and accounts for the opacity created by the morphological ordering. This is an important observation, because it provides a litmus test for what type of morpheme should be able to intervene between a cyclic head and a root under a cyclic approach: only one where the placement is prosodically motivated (such as infixation).
One potential non-local phenomenon, and the one to be explored here, is non-local reduplication. Canonical reduplication imposes an adjacency requirement on the base and the reduplicant. There are, however, a handful of cases where the reduplicant is non-adjacent to the base. An example is the double reduplications found in Salish languages. Observe the following example from Thompson Salish (Broselow 1983:329; n.b. glottalization of resonants is a characteristic of stems marked as diminutive):
  1. (5)

    Thompson Salish reduplication




    calico (dim)


    calico (dist)


    calico (dist-dim)

The problem inherent in this paradigm is the double reduplication: the shape of the reduplicant marking the distributed form is dependent on the base for its phonological exponence (cf. the final consonant in [sil]), but in this case, it is not adjacent to the base—the diminutive reduplicant intervenes (and it crucially does not exhibit a final consonant). Broselow (1983) analyzes the intervening reduplicant as an infix for independent reasons, which allows the outer reduplicant to access the properties of the base. Shaw (2005) discusses similar cases of non-adjacent reduplication, and likewise claims that the intermediate reduplicant in all putative cases of non-adjacency is the result of infixation. This type of string adjacency is thought to be a part of UG, and not a violable constraint (cf. Urbanczyk 1996 for this specific claim relating to this set of data). This behavior in reduplication is parallel to the Palauan case, and so does not pose a challenge for the locality theory outlined in the previous section.

3.1 Madurese reduplication can be non-adjacent

A more problematic example involves reduplication in Madurese, where it can be demonstrated that (a) the relationship between the base and reduplicant is non-adjacent, and (b) the intervening morphemes are demonstrably not infixes, nor is their placement governed by phonological constraints. It is this type of reduplication that will be claimed to provide evidence for a parallel, rather than a cyclic derivational model.

Stevens (1965, 1994) and Davies (1999, 2010) note that reduplication in Madurese copies the final syllable of a root, and the reduplicant surfaces prefixed to the stem, as illustrated in (6). The result is a pattern whereby the reduplicant is seemingly discontiguous with the corresponding copied portion of the base, as it surfaces on the “wrong side.”4
  1. (6)









    ‘read (pl)’





    ‘return (pl)’





    ‘write (pl)’










    ‘play (pl)’





    ‘spray (pl)’

    (Davies 2010:129–130)

Davies (2010:129) notes that there are several meanings associated with reduplication in Madurese, though plural marking appears to be the most frequent (2010:137). This plural marking may include marking plurality of actions (either by a single or multiple individuals), or plurality of entities (2010:37). Davies (2000) discusses how verbal reduplication is used as a strategy in forming reflexives, and determines that the meaning it expresses involves multiple discrete events. It will be assumed that reduplication is a measure function that defines quantized predicates (Krifka 1998), and thus instantiates a number head (num) in the nominal domain (Ritter 1991), or an aspectual head (asp) that is merged with verbal predicates (Borer 2005).
It is important to note that the reduplicant consists of a copy of the final syllable of the base, whether this be an open syllable, a closed syllable, an onsetless syllable, or a syllable with a consonant cluster. Equally important to note is that the base for reduplication is limited to the morphological root; suffixes are not copied:
  1. (7)




    ‘introduce (pl)’


    ‘plant (n)’




    ‘send to’


    ‘send to (pl)’


    ‘the book’


    ‘the books’

    (Davies 2010:131–132)

While the base for reduplication is generalized as the morphological root in (7), this is a slight simplification. There is a set of phonological augments that appear with some roots, but which have no identifiable meaning, and which contribute toward the delimitation of the base. The augments in question are the set of root “extensions” discussed by Stevens (1965) and Davies (2010). These extensions are consonants that appear root-finally, and which can sometimes add meanings, but many times occur in free variation with the unextended root: kamma ‘where’ vs. kamma-n ‘where’ (Davies 2010:126). Stevens (1965) argues that the extension belongs to the phonological domain of the root, citing reduplication patterns whereby the extension is copied: man-kamma-n ‘everywhere’. It is this “extended root” that must be accessible to the grammar in order to derive the correct segmental content of the reduplicant. This notion of an extended root has a precedent in Bantu languages, which exhibit similar types of extended morphological structures (cf. Downing 2000), as well as in Kashaya, where in a similar manner, phonological changes introduced by suffixation form part of what Buckley (1999) terms the “extended root” in that language; cf. also Inkelas and Zoll’s (2005) notion “Proot”.
In a fashion similar to the root extensions, epenthetic consonants introduced through suffixation also count toward the extended root domain, even though they are not part of the underlying form of the root. The relevant phonological process is glide insertion, which is used in the language to avoid vowel hiatus. The palatal glide [j] is epenthesized after front vowels, and labio-velar [w] is inserted after back vowels. The glottal stop [ʔ] is inserted root-internally between identical vowels, and at boundaries, after low vowels. (8) illustrates this process root-internally (Stevens 1994:362–363, 368).
  1. (8)

    Root-internal glide insertion
















That this is a regular process induced by suffixation is illustrated below with the nominalizing suffix -an (Davies 2010:40–42). These examples also help to illustrate that the epenthetic glides are inserted between the boundaries of the underlying root and suffix.
  1. (9)

    Morphologically induced glide insertion

    [libɣli] + [an]


    ‘several times’

    [ka] + [ratɔ] + [an]



    [sakɔla] + [an]



    [buwɣ] + [an]



    (Stevens 1994:368)

These epenthetic glides can also surface in the reduplicant. As the environment for inducing epenthesis is not met independently in the reduplicant, this constitutes a case of overapplication (McCarthy and Prince 1995, 1999).
  1. (10)

    Copied epenthetic glides in reduplication





    [cf. wa-buwa ‘fruits’]


    ‘will ask often’







    (Stevens 1994:368)

While the glide [j] appears to be fairly free in its distribution, there are restrictions on [w] and [ʔ]. According to Davies (2010), the labio-velar glide [w] is banned in syllable codas, and the glottal stop [ʔ] is likewise banned in syllable onsets.5 As (11) illustrates, in reduplicants, the normal phonotactic restrictions apply to these segments, preventing [w] from being copied into a coda, and [ʔ] from being copied into an onset. While examples are sparse, the following two forms illustrate the blocking of overapplication with both the glottal stop and labiovelar glide:
  1. (11)



    ‘request (n)’

    (Stevens 1994:368)



    ‘yell at (pl)’

    (Davies 2010:131)

The fact that glide insertion occurring root-internally and glide insertion occurring at the juncture of root and suffix are both subject to overapplication in the reduplicant provides compelling evidence for the extended root; i.e. that copying is sensitive to everything within this domain. Likewise, epenthetic consonants at the root-suffix boundary and root extensions both appear to behave in a similar fashion, phonologically being affiliated with the extended root domain. Given this, for expository purposes, glides inserted at juncture boundaries will be segmented as part of the root and bolded (e.g. so-pesow-e).

Finally, gemination is also a process which can occur at root-suffix boundaries, but which does not overapply in reduplicative contexts. Gemination lengthens consonants in order to provide a closed syllable necessary for [ə] (orthographically represented by various vowels) (Stevens 1965; Davies 2010).6 Geminates do not transfer to the reduplicant, where only singleton counterparts are found. Gemination, and the lack of gemination in reduplicative environments (e.g. leng-celleng ‘black’; Davies 2010:222), can be accounted for with normal constraints on these structures; i.e. constraints prohibiting initial geminates, and constraints governing syllable structure, which would be violated by syllables with geminates in the coda (except when preceding [l] or [r]; Davies 2010:44). Derived portions of geminates at juncture boundaries will be graphically treated in the same way as epenthetic glides.

The mechanics of the overapplication of glide insertion, as well as the cases of normal application, will be expanded on later in Sect. 4.2; however, it can be noted up front that syllable structure constraints account for the selective blocking of overapplication. What is important is the fact that some processes can be overapplied, which does not imply that all processes must overapply (for discussion, see McCarthy and Prince 1995, 1999).

The unusual “wrong side” character of the pattern has been the topic of many works on reduplication (Marantz 1982; McCarthy and Prince 1986, 1999; Mester 1986; Weeda 1987; Steriade 1988; Stevens 1994; Inkelas and Zoll 2005; Nelson 2005, etc.). The placement of the reduplicant on the “wrong side” is commonly analyzed as a full copying of the root, with the reduplicant truncated to the final syllable (McCarthy and Prince 1986; Steriade 1988; Inkelas and Zoll 2005). The basic spirit of this “truncated-copy” approach will be assumed here (without the sequential flavor), as the prosodic shape and prefixing nature of the reduplicant will not be formally addressed. Despite this, the “wrong side” phenomenon will provide crucial morphological evidence against cyclic spellout. The pattern of reduplication in Madurese will be shown to involve two different but related problems for theories of locality, to be addressed in the next sections.

3.1.1 Problem 1: Non-adjacency of reduplicant and base

An important behavior with respect to reduplication in Madurese is the fact that the reduplicant can appear outside of other derivational affixes; i.e. the reduplicant can be non-adjacent to the root that serves as the base of reduplication. This morphological ordering is illustrated below with the abilitive prefix ka- (Davies 2010:134).
  1. (12)


    ‘become angry’


    ‘become angry (pl)’


    ‘become afraid’


    ‘become afraid (pl)’


    ‘can be read’


    ‘can be read (pl)’


    ‘get used as a belt’


    ‘get used as a belt (pl)’

The existence of these intervening affixes is a prima facie problem for the locality theory outlined above.
That some of these intervening affixes are category-defining heads, and by hypothesis trigger spellout (as cyclic heads), can be demonstrated with their attachment to various roots. This can be most clearly illustrated with the prefix ka-, which Davies (2010:103–104) notes can be attached to verbs to yield an abilitive or realized state (13a), noun stems to form instrumental verbs (13b), or adjective roots to yield resultant states (13c).
  1. (13)





    ‘can be read/has been read’




    ‘can be decided/has been decided’





    ‘get used as a belt/can be used as a belt’




    ‘get used as a hat/can be used as a hat’





    ‘become restless’




    ‘become angry’

Thus, the structure associated with ka- would be as in (14). (14) illustrates a root that is categorized by a null head (cf. Marantz 1997; Arad 2005; cf. Stevens 1965 for an early treatment of Madurese morphology that is similar in spirit), and subsequently merged with ka-. In addition to the abilitive prefix, there are other cases of category-defining heads that intervene between the root and the reduplicant. The nominalizing prefix pa- occurs as an intervening affix (Davies 2010:133–134):
  1. (15)























That this is a category-defining affix is illustrated in (16), where the output of pa- affixation is a noun, regardless of the category of root it attaches to:
  1. (16)




    ‘proficient swimmer’











    (Davies 2010:115)

Other intervening affixes that might be considered heads present similar problems. Among these is the involative prefix ta-, which attaches to verbs (Davies 2010:134):
  1. (17)


    ‘be hit accidentally’


    ‘be hit accidentally (pl)’


    ‘be pinched accidentally’


    ‘be pinched accidentally (pl)’


    ‘be sent accidentally’


    ‘be sent accidentally (pl)’


Importantly, these intervening morphemes are not the ‘linker morphs’ discussed by Inkelas and Zoll (2005); i.e. morphemes that surface between reduplicant and base and which help mark the construction as a whole. Linker morphs are typically construction-specific, and are limited to contexts involving reduplication (i.e. they don’t surface independent of reduplication); cf. an example from Khasi: nano-nano ‘from anyone’ vs. nano-re-nano ‘from someone or other’ (Henderson 1976:512). The intervening morphemes in Madurese are genuine and productive independent affixes that occur in contexts outside of reduplication, as shown above.

Intervening affixes are not limited to only one.7 Davies (2010:135) notes that the causative prefix pa-, as well as the negation ta’- (dialectally lo’-) can both appear between the reduplicant and the root, and presents the examples in (18a), while Stevens (1965:157) gives the underlying morphemic form for the example in (18b):
  1. (18)



    ‘not make sick’


    ‘not make sick (pl)’


    ‘not make tired’


    ‘not make tired (pl)’



    ‘to pretend not to know’ (cf. ta’-tau ‘not know’)

If there were prosodic pressures forcing intervening affixes to surface infixed after the first syllable, effectively placing them internal to the reduplicant and parallel to the Palauan case discussed above, this would be expected to apply in all contexts; however, this is not the case. The affix sa- ‘one/all’ provides a prime example. While sa- is an intervening affix (malem ‘night’, lem-sa-malem ‘each night’; Davies 2010:135), it does not exhibit these disrupting characteristics elsewhere. For instance, Madurese less commonly employs a full-copy type of reduplication; in constructions with sa-, this morpheme falls outside of the full copy (Stevens 1994:370):
  1. (19)



    ‘whatever one wants’



In addition, sa- in other non-reduplicative contexts surfaces consistently as a prefix, and never as an infix (data from Davies 2010:115):
  1. (20)




    ‘same house/all the houses’




    ‘same village/all the villages’




    ‘all the islands/same islands’

Likewise, any analysis predicated on affixes such as sa- being aligned to the immediate left edge of a foot (rather than infixed after the first syllable) would fail in cases such as the causative, which exhibits some variability in its ordering with reduplication (cf. Davies 2010:135; Stevens 1971:420; Stevens glosses the i- prefix as the passive):
  1. (21)


    ‘make fall’



    ‘make fall (pl)’


    ‘make sad’



    ‘made sad (pl)’




    ‘kept on being shown’

Supporting evidence for this position comes in the difference in meaning in the two affix orders, where Davies (2010:135) notes that the first variant of these forms has the additional meaning of ‘pretend to X.’

The converse possibility is that the placement of the reduplicant itself is prosodically motivated (Broselow and McCarthy 1983), such that it must be aligned with the left edge of the word. This would result in a type of pseudo-infixation of what is otherwise a prefix; i.e. the intervening prefix would be placed internal to the reduplicant by virtue of the pressure to align the reduplicant leftward. This analysis is likewise incorrect, as the reduplicant need not occur at the left edge of the word, and occurs following some prefixes, including a subset of the actor voice prefixes. Additional evidence against this approach comes from the compositional semantics of the word, to be discussed in detail in Sect. 3.1.2. In short, semantic scope requires the head which the reduplicant is an exponent of to be structurally higher than intervening affixes in order to derive the correct meaning (cf. Rice 2000). This being the case, the placement of the reduplicant does not appear to be prosodically motivated.

As demonstrated above, there are seemingly no phonological pressures that would force this particular morpheme to surface as an infix in any environment; thus, the head in question intervenes in a concatenative fashion, and not one governed by prosodic constraints. The overall result is an unambiguous case of non-adjacent reduplication, where the phonological exponence of the reduplicant is dependent on a root that is neither structurally, nor linearly adjacent to it. This is illustrated in (22). The crucial point is that the merger of this morpheme must be derivationally sequenced after the spellout of the lower phase.
  1. (22)

    gel-ka-peggel ‘become angry (pl)’

    Open image in new window


While the lower head can be ignored because it is null, the problem for cyclic spellout is that the higher intervening head has phonological exponence, a configuration predicted not to occur under Embick’s (2010) model.8 Thus, these are genuine cases of non-adjacency involving a morphological root, and a reduplicative affix that is dependent on the root for its phonological exponence. From this it is clear that the mechanism responsible for the phonological identity of the reduplicant must have access to the (extended) root, an issue that will be addressed in Sect. 4.

One potential solution to this problem is to separate out the issue of adjacency from the issue of cyclicity. For instance, Moskal (2015) and Moskal and Smith (2015) propose an accessibility domain that is distinct from a spellout domain, and which serves as an additional restrictor on allomorphy. This domain allows for spelled out structure to be accessible to other operations, and is defined as a root, a category-defining node, and a node above that. A less restrictive approach such as this could potentially prevent the intervening material from blocking the morphophonological relationship between base and reduplicant. The Madurese data, however, indicates that there is a null category-defining head, an additional intervening cyclic head, plus a reduplicant, a structure that extends beyond the accessibility domain; i.e. a root, an a head, a verbalizer, and reduplication: [numgel-[vka-[a[peggel]]]] ‘become angry (pl)’. Thus, even positing an additional wider domain as a restriction on morphophonological dependencies appears too restrictive in this case.

There are also other post-syntactic operations that can affect the surface linear ordering of morphemes and which should be entertained. This includes different varieties of morphological merger such as lowering and local dislocation. Following Embick and Noyer (2001), lowering is the merging of heads prior to linearization, which converts a syntactic string: [XPX°…[…Y°…]] → [XP…[YP…[Y°+X°]…]]. Given that lowering applies before linearization, adjacency can be violated, and intervening adjuncts can be ignored (cf. Embick and Noyer’s example Mary loudlyplay-edthe trumpet, where the past tense suffix -ed lowers from the position preceding loudly). Since the shape of the reduplicant in Madurese is dependent on the base, any operation resulting in a disruption of the adjacency relation would have to be post-Vocabulary Insertion (cf. Embick and Noyer 2001), as it is vocabulary-specific. This eliminates lowering as a solution for the non-adjacency problem. Local dislocation is a merger that applies after linearization and Vocabulary Insertion, and involves the inversion of string-adjacent elements: [X * [Z * Y]] → [[z° Z + X] * Y]. Under a local dislocation analysis, the reduplicant and any morpheme that is merged after it are merged into a complex head. This type of merger is, however, at present unmotivated. A complicating factor involves the local nature of the inversion, which is defied in cases of multiple intervening affixes. Finally, a larger problem involves adjuncts: Since local dislocation applies after linearization, it must be sensitive to adjuncts, and thus is predicted to be blocked by them; however, it is likely the case that intervening affixes in Madurese include not only heads, but adjuncts as well. The negation ta’/lo’ is a candidate, as it attaches to both verbs and adjectives, but does not change the category of the word (Davies 2010). If this analysis is correct, then morphological merger does not provide a compelling explanation for long-distance reduplication.

Stepping back, it is worth placing this phenomenon in a cross-linguistic and typological perspective. In their overview of contextual allomorphy, Bonet and Harbour (2012) note that while inwards-sensitive morphophonological dependencies are well established in adjacency contexts, the same type of long-distance phenomena do not seem to exist. They discuss the case of the Georgian adjectival suffix -uri, which undergoes dissimilation to [l] if there is a [r] in the root (cf. svan-uri ‘Svan’ vs. kart-uli ‘Georgian’). Bonet and Harbour note that the conditioning segment can be “an arbitrary distance away,” making this appear to be a long-distance phenomenon. They go on to note, however, that this process can be assigned to the phonology generally, as this dissimilation applies persistently in the phonology without reference to the morphology. Bonet and Harbour state that non-attestation of the phenomenon is difficult to claim, and they leave the possibility open that such a configuration could in fact exist. It is possible that Madurse long-distance reduplication fills out this slot in the typology. To add to this empirical base, and to make note of similarities, Mandara (Frajzyngier 1984) also exhibits a type of long-distance reduplication. Mandara employs reduplication for marking both the perfective and the plural. In circumstances where both types of reduplication are employed, it is possible for plural markers, as well as pronominals, to intervene between reduplicant and base:
  1. (23)

    Mandara reduplication (Frajzyngier 1984:37)



    ‘He got up and left.’






    ‘They got up and left.’






    ‘You (pl) got up and left.’



Thus, while comments on the Mandara patterns are at present speculative, it could very well be that this is an even more exuberant case of long-distance reduplication.9 The existence of this additional system implies that long-distance reduplication in Madurse is likely not an anomaly, but rather, simply a pattern that is relatively rare.

3.1.2 Problem 2: Constituencies problematic for locality

While the non-adjacent nature of reduplication in Madurese is a problem in itself, the morphological constituency of some reduplicated forms presents an even more severe problem. This is a problem associated with the “wrong-side” nature of Madurese reduplication. Some morphological heads in the language are category-defining suffixes, and by assumption, they trigger spellout; however, in these cases, the right-most syllable of the root inside of the cyclic domain must still be visible for reduplication. In other words, the right edge of the root must still be isolated for phonological copying, and where suffix material is not copied. Consider the following, where suffixes are not part of the base for reduplication (data from Davies 2010:131):
  1. (24)




    ‘introduce (pl)’


    ‘write for’


    ‘write for (pl)’


    ‘yell at’


    ‘yell at (pl)’

Davies (2010) argues that the suffixation must be derivationally ordered before reduplication, with the primary evidence being the composition of meanings. As an example, the root \(\sqrt{\mathit{tamen}}\) ‘plant’ must first be merged with the nominalizing n head -an in order to be pluralized, which is marked by reduplication: men-tamen-an ‘plants’. If the reduplicant were attached to the verbal root ‘plant’ first to form a plural, followed by the nominalization, the resulting meaning would presumably be something like ‘plantings’ (i.e. multiple planting actions). Thus, the structure for men-tamen-an must be: [red-[[\(\sqrt{\mathit{tamen}}\)]-an]]. In addition, as Stevens (1994) has argued, phonological effects induced by the suffix can affect the root (or the portion of the base to be copied). For instance, roots such as \(\sqrt{\mathit{buwa}}\) ‘fruit’ that are suffixed by -an create sequences of identical vowels which are not tolerated, and are broken up by an epenthetic glottal stop: [buwɣʔɣn]. This overapplication effect re-affirms the phonological dependence that the reduplicant has on the base, a state of affairs which remains problematic for cyclic approaches, but which is predicted under parallel approaches, such as Optimality Theory (cf. McCarthy and Prince 1995, 1999). The reason for this is that the insertion of the glottal stop in the reduplicant is not independently motivated, as the environment which triggers the process is not met. If reduplication of the root followed by nominalization were to obtain, this would not present any problem for the cyclic approach. The problem stems from the fact that reduplication appears to apply to the entire nominalization, and not to just the root.
Other examples that demonstrate this type of ordering are cases with the nominal circumfix ka-…-an. A root such as \(\sqrt{\mathit{raja}}\) ‘king’ can be circumfixed to form ka-raja’-an ‘kingdom’, and reduplication can apply to this form, yielding ja’-ka-raja’-an ‘kingdoms’. If reduplication derivationally preceded affixation, the predicted ordering under the cyclic approach, then the result would be *kaja’raja’an. Weeda (1987), Stevens (1994) and Davies (2010) make the convincing case that the ordering must be affixation preceding reduplication, as the form ja’karaja’an is the plural for ‘kingdom’, and not ‘king’. If reduplication derivationally preceded affixation, the compositional meaning would be ‘a place to find kings,’ not ‘places to find a king.’ Below are more examples (from Davies 2010:133, 324):
  1. (25)

    Suffixation precedes reduplication










    ‘district head’


















In the cases at hand, it is actually a n head which is a suffix, and not an intervening prefix, that should spell out a cyclic domain. Normally, this fact about linear morphological ordering would be immaterial, because in canonical “same side” reduplication, string adjacent material can blindly copy material to the right, in much the same way that infixation can blindly push an affix into structure that is already spelled out. However, in this case, since the portion of the base is non-string adjacent to the reduplicant (in fact, it’s on the “wrong side”), the internal structure of the spelled out complex head must be visible to operations at PF in order to identify the righthand root boundary for the purpose of copying the final syllable.10 Interestingly, it is not the problem normally associated with Madurese reduplication (i.e. the “wrong side” phenomenon) that plagues the analysis; instead, it is the fact that properties of the morphological root, which can be encapsulated by both prefix and suffix material, must still be available after cyclic spellout. Under adjacency-based theories, inner constituents that are already spelled out are predicted to be opaque to the further determination of morphophonological dependencies.

Cases with derived adjectives, including comparatives and superlatives, can be added to the morphophonological bracketing paradoxes above. According to Davies (2010), there are multiple strategies for forming comparatives and superlatives in Madurese, including analytic and synthetic options. The synthetic options involve deriving comparatives with a suffix -an, and superlatives with the addition of reduplication (from Davies 2010:117).11
  1. (26)



















Following Bobaljik (2012), it will be assumed that superlatives do not attach directly to adjectival roots, but rather, are formed from derived comparatives; i.e. [[[adj]cmpr]sprl]. Reduplication in these cases must apply after the comparative suffix is attached, again a case of a cyclicity paradox, where the structure must be [sprl wat- [cmpr [adj kowad] -an]]], but where the root must be accessible within the superlative structure in order to reduplicate the final syllable.

4 Morphology in parallel

The two problems presented above raise difficulties for the theory of locality presented in Sect. 2. Instead, these problems motivate an argument for a parallel approach to morphological spellout. A solution adopting OT will be sketched below, where it will be shown that a parallel approach allows for all morphemes to be spelled out simultaneously within a given domain, which facilitates the morphological ordering needed for semantic compositionality, as well as long-distance morphophonological dependencies.

4.1 Determining the base of reduplication

In order to develop an analysis, some assumptions must first be laid out with respect to the nature of the base. Following McCarthy and Prince (1993a, 1993b), the base will be assumed to be an output structure which can be defined in either prosodic or morphological terms. As McCarthy and Prince assert, the base could in principle be co-extensive with a foot, which is the minimal lexical word in many languages, including Madurese. Conceptualizing the base as a foot in the output would drive the establishment of a base, but not the attachment site (i.e. non-adjacent attachment). This would be consistent with the locality approach, as the output prosodic structure would be all that is required after the spellout of a cyclic head in order to establish an identity relation with the reduplicant, making all operations strictly phonological. The problem inherent in this approach is that it is contingent on there being only prosodic structure guiding the process in the output. As claimed by Weeda (1987; citing Kiliaan 1904/1905) and Davies (2010), there is no word-level stress in Madurese (or if there is, it is idiosyncratic), consistent with other closely related Indonesian/Malay substrate languages (van Zanten et al. 2003; Maskikit-Essed and Gussenhoven 2016). Since there is no (predictable) word stress, then there is no sense in which there are output cues to footing, which would not facilitate isolating the final syllable of the root for copying. Thus, it is more economical to invoke the morphological category “Root” as an output structure. There is also an empirical argument to support this view, tied to the observation in (27): in string-similar contexts consisting of different morphological boundaries such as […CV]-CV vs. […CVC]-V, reduplication targets the root boundary for copying, and not a prosodic unit; i.e. a prosodic approach predicts both reduplicants would be the same prosodic size (consistently either a CVC- or CV-reduplicant).
  1. (27)



    ‘the book’


    ‘the books’



    ‘send to’


    ‘send to (pl)’

    (Davies 2010:131–132)

In these cases, it is clear that copying holds only for morphological extended roots, and does not include any of the phonological material of the suffixes. Thus, the category of “Root” (or, more precisely, the “extended root”; see Sect. 3.1) is visible in the output as a base. It is not an unusual state of affairs for morphological categories to serve as the base of reduplication (cf. Mutaka and Hyman 1990; McCarthy and Prince, 1993a, 1993b; Downing 2000; Inkelas and Zoll 2005; Shaw 2005); however, demonstrating that it is in fact the extended root proves difficult for any approach that claims that the base is prosodic in nature, a solution that might be resorted to under the locality approach.

4.2 Base-reduplicant symmetry

The non-adjacent reduplication exhibited by Madurese is not a problem for theories where morphology and phonology are derived in parallel, such as Optimality Theory. Approaches that assume a correspondence relation between reduplicant and base (McCarthy and Prince 1995, 1999) are not necessarily bound by this relation being tied to the linear adjacency of the correspondent morphemes.12 Assuming (non-crucially) that there is a Vocabulary Item red that exists as one of the morphemes of the language (cf. Haugen 2011; Cook 2013), and that this morpheme receives its phonological features from the extended root (due to the relative ranking of a constraint such as Ident-BR), then given a red-base relationship, there is no difference between an adjacent and a non-adjacent correspondence: the constraints can demand identity between reduplicant and base regardless of their positioning in the string. In sum, there is nothing preventing long-distance correspondence in a theory of constraints.

There is also an empirical argument in support of the constraint-based approach. Overapplication effects fall out as a natural consequence of this framework, as argued in detail by McCarthy and Prince (1995, 1999). Such an overapplication effect in Madurese involves the appearance of a glide that is epenthetic in the base, triggered by a vowel-initial suffix, mentioned in Sect. 3.1.2. As an illustrative example, the overapplication of glottal stop epenthesis is highlighted in (28).
  1. (28)














    ‘will ask often’

    (Stevens 1994:368)

With respect to other overapplication effects, McCarthy and Prince (1993a:27) make the comment that reduplication “presupposes the outcome” of interactions between an affix and the root, which is an apt description of the Madurese facts. As discussed above, the epenthetic glides that form the boundary of the extended root are not always copied in the reduplicant. Recalling the conditions on glides, the labial glide is not allowed in syllable codas, which is precisely the position it would occupy in so-pesow-e if it were to surface in the reduplicant, a fact easily modeled by the ranking *w]σIdent-BR. The glottal stop is immune in this position simply because there are no constraints against this segment surfacing in codas normally. Conversely, there must be a ranking *σ[ʔ ≫ Ident-BR, which bans the glottal stop in onsets, regardless of morphological structure. The same mechanics account for the normal application of gemination, as well as for the normal application of laryngeal neutralization in syllable codas (cf. mat-ka-camad-an ‘districts’), the latter of which is specifically addressed by McCarthy and Prince (1995, Sect. 3.1). Thus, while some processes can be overapplied, this does not entail that all processes must be overapplied. In this case, the constraints on Madurese syllable structure will be ranked such that they trump B-R identity. In this way, Correspondence Theory allows for, and predicts, the flexibility in the application of processes when it comes to the base-reduplicant relationship, a point made clearly by McCarthy and Prince (1995, 1999).
As in other cases of overapplication, highly ranking markedness and Faith-BR constraints ensure that the base and reduplicant are identical. Thus, even if the base drifts from the input due to pressures from a high ranking markedness constraint, the reduplicant will follow suit. In this particular case, there is a markedness constraint which prohibits sequences of identical vowels (*Onset), and which must dominate Dep-IO. The effect is mirrored in the reduplicant due to the high ranking of Max-BR, preventing deletion.
  1. (29)

    Derivation of non-adjacent reduplication

    Open image in new window

While not formalized in the analysis in (29), an obvious component to the constraint ranking must be a constraint or set of constraints demanding (i) a fixed template order to the affixes which ensures non-adjacency in cases where there are intervening prefixes, and (ii) a constraint or set of constraints that ensures that the reduplicative template is a single syllable. Accounting for (i) is perhaps a trivial matter; accounting for (ii) is less trivial. Thus, the approach sketched above relies on morphological constraints (those regulating the templatic structure of affixes) to outrank prosodic ones, namely, any constraints demanding adjacency between reduplicant and base. The constraint antagonistic to adjacency would be whatever constraint demands the fixed affix order in the language. At present it is unclear what the nature or the precise content of that constraint would be. For simplicity’s sake, templatic constraints that demand precedence relations between morphemes (cf. Paster 2006) will be adopted here, though nothing crucial rides on this analysis; morpheme order could just as well be captured with a set of alignment constraints, or by constraints ensuring scope relations are maintained in a linear fashion.13
As Lunden (2004) notes, assuming that adjacency is a property of violable constraints predicts both discontiguous (“wrong side” reduplication) and non-adjacent reduplication. The objective of this paper was to present data from Madurese that confirms both of these predictions. Here it can be shown that adjacency is not simply a violable condition on a reduplicant and the portion of the base that is copied (such that there is intervening material between the two), but rather a violable condition on an entire base and a morphophonologically dependent morpheme such that intervening material can be tolerated. This is encoded in the definition of Adjacency:
  1. (30)

    Adjacency: Reduplicant and base must be adjacent

The fact that a templatic constraint like num > v, which demands that number marking precedes a verbalizer, must dominate Adjacency in Madurese is illustrated most effectively through a comparative tableau, where constraints favoring the winner are indicated with W and those favoring the loser with L:
  1. (31)

    gel-ka-peggel ‘become angry (pl)’

    /red, ka, peggel/ → gel-ka-peggel

    num > v


    gel-ka-peggel ∼ ka-gel-peggel



(31) clearly demonstrates that Adjacency is a violable constraint, as it is favored only by the losing candidate, and where num > v is favored by the winner.

The OT solution is actually a simple and elegant one: Given the morphological ordering, there are no other constraints that are necessary beyond what must be posited for “wrong side” reduplication in Madurese. So long as the internal morphological structures are visible to the constraints (as it is assumed they must be, in order to drive any kind of reduplication in morphologically complex forms), then base-reduplicant correspondence can derive the effects. Crucially, the OT analysis does not necessarily deny cyclicity at all levels; domains well-established in the framework of Lexical Phonology can still play a role in delimiting the effect of constraints (McCarthy and Prince 1993a).

4.3 Madurese reduplication is not root doubling

The non-adjacent reduplication problem outlined above is easily handled by approaches like Morphological Doubling Theory (MDT; Inkelas and Zoll 2005), where morphological entities are doubled. Under this approach, many of the overapplication effects found in Madurese (e.g. nasal harmony and glide formation that surface unexpectedly in the reduplicant; cf. Stevens 1994; McCarthy and Prince 1995, 1999) can be accounted for as the independent instantiations of two morphological objects with truncation of the first to a single syllable. In this way, MDT makes no use of an abstract red morpheme that receives its segmental interpretation from the base.

Such an approach would be consistent with the locality approach, and where morphological doubling would constitute the merger of a root twice: once in a lower position, and once higher in the structure. There is, however, a crucial problem with the analysis: While the approach is capable of accounting for overapplication effects14 such as cases of glide insertion which are triggered within the base (i.e. the base is simply copied wholesale, and then truncated), it cannot account for overapplication that is triggered by suffixes to the base, such as is illustrated for the specific case of glide insertion above. The reason for this is that according to Inkelas and Zoll (2005), doubling affects underlying objects, where the reduplicant and base have independent inputs. The problem is that the epenthetic consonant has no underlying correspondent, and so would be predicted to surface only in the base. This must be accounted for with a Base-Reduplicant correspondence, whereby any effects found in the base, whether through base-internal changes, or base-external changes, must be reflected in the reduplicant, given a highly ranked correspondence constraint.

5 Conclusion

This article has presented evidence of genuine non-adjacent reduplication, which was used to analyze components of the interaction between morphology and phonology. Embick (2010) presents multiple pieces of evidence to suggest that phonological spellout of morphemes is local and cyclic, including cases of opacity effects and other types of phonologically-controlled allomorphy. The phenomena presented above indicate that at least some morphological spellout must be global. This is evidenced by the morphological ordering facts above, and the long-distance phonological effects exemplified by Madurese. These cannot simply be cases of “breaking into” a cyclic domain by infixation, phonologically speaking, but stand as genuine cases of non-local morphophonological dependencies. What remains to be seen is what types of morphophonology are necessarily local, which are necessarily global, and how these types are defined and demarcated.

There exists a wealth of phenomena that appears to be cyclic in nature (cf. Embick 2010; Bobaljik 2012 etc.), and the present work acknowledges this, and does not intend to exorcise cyclicity from grammar entirely. Instead, it serves as a starting point for determining what phenomena count as phonological, and what count as ‘morphological’ (in Embick and Noyer’s (2001) sense of post-syntactic operations). It could also be the case that allomorphy is ‘morphological,’ and reduplication belongs to the realm of morphophonological dependencies that are predictable, given a ranking of prosodic constraints.

Like other recent approaches, this work has challenged adjacency as an absolute condition on spellout. Bobaljik (2000), Moskal (2015) and Moskal and Smith (2015) have moved away from adjacency as a restrictor on allomorphy (and by extension, reduplication). This work can be viewed as sympathetic to this general approach, though it constitutes a more radical move away from both adjacency, where the restricting factor is left entirely to the phonology, and to a certain extent, cyclicity. In this spirit, one possibility is that the cyclic approach presented in this article could be relaxed so as to allow for outer morphology to access the internal morphological and phonological structure of vocabulary items that have already been spelled out, a move which would mechanically amount to much the same as the parallel approach sketched above. This ultimately raises the question of exactly how much long-distance phonological interaction could be accommodated, and how much cyclicity is needed for the derivation of morphological structure.

Finally, locality conditions on reduplication have often been invoked, but the actual basis of these conditions has not been made explicit. Previous approaches have conceptualized adjacency as an inviolable constraint; however, there is no logical principle in the grammar that would rule out non-local reduplication. The existence of this phenomenon in Madurese is compatible with the status of locality as a soft, violable constraint in grammars.


  1. 1.
    The generalizations governing contextual allomorphy that Embick provides are as follows:
    1. a.


      Generalization: Noncyclic Z may show contextual allomorphy determined by α, as long as x is not overt.

    2. b.


      Generalization: Cyclic y may not show contextual allomorphy determined by α, even if x is not overt.

  2. 2.

    Stemberger and Lewis (1986) treat reduplication as a type of allomorphy, though one that is not lexically listed. If this position is adopted, then there is indeed little difference between contextual allomorphy and reduplication.

  3. 3.

    Recent work in the field has cited outward-looking morphology as a counterexample to cyclic spellout, with the idea that an inner morpheme should not be available for readjustment if it has already been spelled out. However, under versions of cyclic spellout more consistent with Chomsky’s (2001) Phase Impenetrability Condition, such as that endorsed by Marantz (2001), Marvin (2002), and Embick (2010), the merger of a phase head triggers spellout of the complement of that head, but the head remains visible for the spellout of a higher phase head. Thus, the approach here takes the conservative position that unambiguous evidence against cyclic spellout would include cases of non-adjacency with intervening heads.

  4. 4.

    Madurese data comes primarily from the extensive documentary work provided by Stevens (1965, 1994) and Davies (1999, 2010). Forms were confirmed by a Madurese speaker. Madurese data is presented in the orthography (cf. Davies 2010), where the glottal stop is represented by the apostrophe <’>. Phonetic forms are taken directly from sources and are indicated as such; in some cases, sources employ different levels of phonetic detail. Hyphenation has been provided in the current work in order to make the morphological boundaries transparent.

  5. 5.

    Both Stevens (1965) and Davies (2010) claim that VʔV sequences are syllabified [Vʔ.V]; i.e. with the glottal stop syllabified consistently as a syllable coda.

  6. 6.

    In addition, Davies (2010:49) notes there are two suffixes that consistently induce gemination of a preceding consonant.

  7. 7.

    Weeda (1987:408) also presents an example with final syllable reduplication falling outside of a prefix, the nasal stem modification marking the actor voice (marking active verbs with an actor subject), and a less commonly employed form of reduplication composed of a copy of the first syllable of the root with a fixed vowel (Weeda does not provide glosses): ne’-ma-ba-bine’ ‘act like a woman’ (from red-n-pa-red-bine-’).

  8. 8.

    This is also true for more relaxed versions of adjacency that involve ‘spans’ of heads within a maximal projection (Merchant 2015), as the allomorphy must be tied to each element in the span.

  9. 9.

    Many thanks to Daniel Harbour for bringing this case to my attention.

  10. 10.

    Haugen (2011) and Cook (2013) discuss scenarios where reduplicants are spelled out after Vocabulary Insertion. For instance, with respect to Bantu, Cook states that “When RED undergoes Vocabulary Insertion, it is realized as a bare template, and it is subsequently filled with segmental material from the constituent to its right” (18). While this operation is potentially a legal readjustment rule at PF, it still relies on locality conditions such as adjacency. The Madurese case thus remains problematic for cyclic approaches that entertain post-VI spellout.

  11. 11.

    Krifka’s (1998) definition of a measure function could provide a unified analysis of reduplication and the functional heads that merge with nominal, verbal, and adjectival structures, though this will be left for future research.

  12. 12.

    Recall from Sect. 2 that adjacency in McCarthy and Prince (1993a, 1995) is derived via the definition of a base, and not through constraint interaction.

  13. 13.

    For those morpheme orders that are optional, stochastic evaluation (Boersma and Hayes 2001) can be assumed.

  14. 14.

    Another case of overapplication in Madurese successfully modeled in Optimality Theory, but not discussed here, is nasal harmony (McCarthy and Prince 1995).



Thanks to Brian Agbayani for discussion of an earlier draft. Thanks also to three anonymous reviewers and to Daniel Harbour for valuable comments and guidance. All errors are my own.


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.University of AucklandAucklandNew Zealand

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