2. The peculiar placement of number in Murrinhpatha

Murrinhpatha is a morphologically highly complex language, which is spoken in the Northern Territory of Australia. The relative ordering of bound morphemes within the verbal complex in Murrinhpatha is sketched in Table 1.Footnote ² As shown in Table 1, the left edge of the verbal complex is occupied by a morpheme traditionally labeled as classifier stem or finite stem. Classifier stems are typically treated as portmanteau forms that encode classifying semantics, subject person and number, as well as tense and mood information (Mansfield Reference Mansfield2019, Nordlinger & Mansfield Reference Nordlinger and Mansfield2021). While information about subject person is realized as part of the classifier stem, object person is marked by affixes that attach right to the classifier stem in slot 2. Another crucial part of the verbal complex is the lexical stem, which is sometimes referred to as coverb (Seiss Reference Seiss2013, Mansfield Reference Mansfield2017, Reference Mansfield2019, among others). In contrast to the classifier stem, the lexical stem does not alternate for inflectional content and is realized in slot 5. In addition, a couple of morphemes may be concatenated in positions after the lexical stem; however, only two of these morphemes are relevant for the purpose of this paper. First, tam markers are realized after the lexical stem. Second, certain number markers may be realized in positions following the lexical stem. Note also that the relative order of the tam markers and the number markers is flexible to some extent, while the relative order of morphemes in the domain spanning from the classifier stem until the lexical stem is fixed (Mansfield Reference Mansfield2017). Table 1 further shows that subject number is realized in three different positions: first, it is part of the subject information encoded in the classifier stem. Second, additional morphemes realizing subject number are realized either in slot 2 and hence in direct adjacency to the classifier stem or in slot 8 at the right edge of the verb. In this paper, I will explain the distribution and positioning of the number markers in Murrinhpatha and how their position patterns with their phonological properties.

Table 1. Relative ordering of bound morphemes (Nordlinger & Mansfield Reference Nordlinger and Mansfield2021: 2)

Table 1 illustrates a crucial property of Murrinhpatha morphology: the verbal predicate is typically bipartite, comprising a classifier stem in slot 1 combined with a lexical stem in slot 5. Throughout this paper, classifier stems are boxed, while lexical stems are underlined. Classifier stems form a closed class, consisting of 38 distinct subparadigms (Nordlinger Reference Nordlinger and Baerman2015, Mansfield Reference Mansfield2019). The majority of predicates require both a classifier stem and an uninflected lexical stem. While a few classifier stems can function as standalone verbs without a lexical stem, lexical stems can never appear in the verb without a classifier stem (Nordlinger & Mansfield Reference Nordlinger and Mansfield2021). This is illustrated in (2). The predicate which roughly parallels the English predicate ‘to tear’ is formed by combining an uninflected lexical stem rartal with a specific form of the classifier stem subparadigm 24 ‘slash’ which matches the subject and tense information.

Nordlinger & Mansfield (Reference Nordlinger and Mansfield2021) discuss a remarkable alternation of the classifier stem in relation to the position of the dual marker ngintha. A relevant minimal example illustrating this alternation is given in (3). In (3a), the predicate roughly matching the English predicate ‘to see’ consists of the uninflected lexical stem ngkardu and the 1sg form of the classifier stem paradigm ‘see’, which is illustrated in Table 2. Since the subject of (3a) is 1du, there is an additional dual marker ngintha which is realized to the right of the classifier stem. The 3sg object is unmarked. In (3b), in contrast, there is an overt object affix encoding the 2sg object. In this context, the dual marker ngintha appears at the right edge of the word. In addition, the classifier stem does not appear in its 1sg form ba, but rather in its dual form nguba. Footnote ³

Table 2. Paradigm of classifier stem ba ‘to affect, see’ (Mansfield Reference Mansfield2019: 249)

In summary, the placement of the dual marker ngintha and the form of the classifier stem depend on whether an overt object marker is present. With a covert 3sg object, ngintha appears next to the classifier stem, which is in its singular form in this context. However, when an overt object marker is used, ngintha attaches to the right end of the word, while the classifier stem appears in its dual form. Thus, the pattern in (3b) looks like an instance of multiple exponence of dual and a discontinuous dependency between the classifier stem and the dual marker ngintha, two phenomena typically associated with templatic morphology (Nordlinger Reference Nordlinger2010). Nordlinger & Mansfield (Reference Nordlinger and Mansfield2021) use position classes to make empirical generalizations about these changes in form and position, where the dual marker and object affixes compete for the same position to the right of the classifier stem. In this paper, I will explain the relationship between the form of the classifier stem and the position of ngintha without relying on the concept of position classes as a fundamental component of morphological theory. Instead, I will examine the phonological features associated with the placement of ngintha in Section 3, arguing that the phonological properties uncover a cyclic structure of the word in Murrinhpatha.

3. Phonological properties of Murrinhpatha morphemes

In Murrinhpatha, the phonological behavior of a bound morpheme is determined by its position within the verbal complex. Put simply, we can predict the phonological processes that apply to a particular morpheme based on its position. Mansfield (Reference Mansfield2017) observes an interaction between the relative position of an affix to the lexical stem and the phonological processes in which this affix is involved. More precisely, affixes in positions following the lexical stem are not involved in the assignment of word stress, subminimal lengthening or obstruent lenition.Footnote ⁴

Prosodic words in Murrinhpatha must consist of at least two morae. In (4a), the word is assumed to have an underlying form of /me/. Since short vowels are typically assumed to be monomoraic, /me/ would violate the minimum quantity of having at least two morae. Therefore, the vowel of the syllable is lengthened to satisfy the bimoraicity condition. In (4b), however, the same root /me/ combines with another morph /ngala/. The resulting compound consists of three morae, thus fulfilling the minimum quantity of two morae. In this case, the vowel of the root is not lengthened, suggesting that the underlying form is in fact /me/. In (4c), the word consists of a monosyllabic classifier stem and an object suffix. Like the noun root in (4a), the classifier stem is a monomoraic CV syllable /na/. However, unlike (4a), the vowel of the classifier stem is not lengthened in (4c). This suggests that the presence of the object marker is taken into account for the bimoraicity requirement on prosodic words. Nevertheless, this generalization does not hold for all affixes. Example (4d) demonstrates that some affixes do not prevent subminimal lengthening. The vowel of the monosyllabic classifier stem /ti/ in (4d) is lengthened despite the presence of another moraic future affix. Mansfield (Reference Mansfield2017) concludes that the absence of subminimal lengthening indicates that a given affix belongs to the same phonological domain as the classifier stem, whereas subminimal lengthening of the root vowel in (4d) suggests that the future affix nu does not belong to the same phonological domain as the classifier stem.Footnote ⁵

Mansfield (Reference Mansfield2017) further notes that this domain coincides with the domain of stress assignment and obstruent lenition. In Murrinhpatha, morpheme-initial voiceless obstruents lenite after vowels. This is shown in (5a) where the initial consonant of /patha/ surfaces as [w] after the vowel-final prefix /ma-/. In similarity to stress assignment and the bimoraicity condition, obstruent lenition does not apply to morphemes appearing to the right of the lexical stem, as demonstrated in (5b). In (5b), the morpheme /paɖi/ would have the correct phonological shape and environment to surface as [waɖi], yet lenition does not apply because the morpheme attaches in a position outside of the relevant phonological domain. In this paper, I will not consider obstruent lenition further because the number affixes discussed lack the phonological shape for it. Therefore, obstruent lenition cannot determine the phonological domain of an affix.

Word stress is assigned to the penultimate syllable of the domain relevant to the bimoraicity condition and obstruent lenition. Thus, it follows that monosyllabic affixes that prevent subminimal lengthening interact with word stress, whereas monosyllabic affixes whose presence does not prevent subminimal lengthening are irrelevant for word stress assignment. This is exemplified in (6), where the phonological domain relevant for bimoraicity and word stress assignment is indicated by square brackets, and word stress is indicated by an acute accent.

In (6a), the first word pata fulfills the bimoraicity condition and assigns word stress to its penultimate syllable. The second prosodic word of the sentence consists of a classifier stem, an oblique object marker and a pst marker. As shown in the examples in (4), object and oblique object markers prevent subminimal lengthening (see (4c)), while tam markers do not, as in (4d). Example (6a) strikingly shows that word stress falls on the penultimate syllable of the domain including the oblique object marker ŋa, but excluding the tam marker đa. In (6b), the lexical stem pata receives word stress on its penultimate syllable, thus illustrating that the domain relevant for word stress spans from the classifier stem to the lexical stem and includes all affixes attaching between those two, while affixes attaching further right than the lexical stem are always outside the word stress domain. Table 3 integrates these insights and provides an overview of the morphemes within the verbal complex and their phonological domains.

Table 3. The verbal complex and phonological domains

This conclusion makes interesting predictions for the dual marker ngintha. As shown in the previous section, ngintha appears before the lexical stem in the absence of an overt object marker, but after the lexical stem whenever an overt object marker is present. The examples in (7a) and (7b) illustrate that the placement of ngintha correlates with its phonological behavior. In example (7a), there is no overt object marker, and ngintha receives word stress. In (7b), however, an overt oblique object marker is realized next to the classifier stem with the consequence that ngintha is realized after the lexical stem. In this case, word stress falls on the penultimate syllable of the lexical stem which clearly shows that ngintha is outside the word stress domain.

In summary, Mansfield (Reference Mansfield2017) shows that the behavior of affixes offers evidence for distinct phonological domains and that the placement of ngintha is closely related to its phonological properties. The presence of overt object markers does not simply cause a reordering of the dual marker ngintha but also affects its concatenation within a different phonological domain. This implies that the prosodic word in Murrinhpatha is layered and that its cyclic structure is significant in explaining the behavior of ngintha. However, morphological theories that assume a flat, templatic structure of words, such as Nordlinger (Reference Nordlinger2010), fail to account for this insight. In the following section, I will discuss how number information is scattered among different morphemes to find out more about the featural specifications of these affixes.

4. The distribution of number exponents

In the previous sections, we have seen that the presence of an overt object marker determines the form of the classifier stem as well as the position and the phonological status of the dual affix ngintha. To understand and explain this unique property of Murrinhpatha, it is crucial to delve deeper into how number information is distributed among multiple morphemes located in different positions within the verbal complex. Specifically, information on subject number is conveyed through three different positions: first, it is part of the portmanteau classifier stems. Second, additional number affixes can attach to the right of the classifier stem, thus belonging to the domain relevant for word stress assignment (slot 2 in Table 3). Third, number affixes can be found in positions after the lexical stem, and hence outside of the word stress domain (slot 8 in Table 3). I will refer to the former group of number markers as inner number affixes and to the latter group as outer number affixes. I follow Mansfield (Reference Mansfield2017, Reference Mansfield2019) in assuming the phonological behavior of an affix is a sufficient condition for this distinction, with inner number affixes affecting word stress assignment and outer number affixes being invisible to it. Crucially, the number value of an argument is conveyed through combinations of these three types of exponents. To capture this fact, I assume that number is morphologically represented by a set of privative features, which are organized in a feature geometry in the style of Harley & Ritter (Reference Harley and Ritter2002). Let me explain the general logic of a feature geometry using the toy feature geometry in (8). A value consists of a set of privative features, such as A, B, D, E or F. However, there are restrictions on how these features may be combined: sister nodes cannot be combined with each other, as they are assumed to be contradictory. Moreover, daughter nodes entail the presence of their mother (i.e. a feature F entails that D is present, which entails that B is present).

In Murrinhpatha, some number exponents can only occur in combinations with other number exponents (i.e. they entail the presence of other number exponents). Hence, we can make implications on the internal structure of the number geometry from the distribution of exponents. The attested combinations of number exponents are listed in Figure 1 for irr classifier stems and in Figure 2 for nfut classifier stems. As already mentioned in Section 2, the leftmost position is always occupied by the classifier stem. Hence, it is the only exponent of subject number present in all number contexts.

Figure 1. Distribution of subject number in irr classifiers stems (Mansfield Reference Mansfield2019: 143).

Figure 2. Distribution of subject number in nfut classifiers stems (Mansfield Reference Mansfield2019: 143).

In the case of irr classifier stems, there are three different forms: singular, daucal and plural, where daucal refers to a portmanteau of dual and paucal number (Blythe Reference Blythe2009).Footnote ⁶ The singular form of the classifier stem is interpreted as singular when it appears without any other number exponent, but it can also be combined with the dual marker ngintha in the inner position to refer to exactly two entities that are not siblings. The plural form of irr classifier stems does not occur with other number markers and is used to refer to plural entities. The daucal form of the classifier stem, which is used in both dual and paucal contexts, is combined with either the dual marker ngintha or the paucal marker ngime to refer to dual non-sibling entities and paucal non-sibling entities, respectively. If the daucal classifier stem appears without any additional number affixes, it is used to refer to dual sibling entities. Crucially, the paucal exponents refer to non-sibling contexts only. Paucal sibling entities are realized in the same way as plural entities: using a bare plural classifier stem. Blythe (Reference Blythe2009) and Mansfield (Reference Mansfield2019) note that the difference between paucal and plural is partially about the quantity of the entities referred to, but probably also about recognizable reference. Specifically, the paucal is typically used when the reference can be recognized, while the plural is used to refer to nonspecific referents. It should also be noted that the number system morphologically represents sibling relationships, which indicates the cultural significance of classificatory siblinghood.

The illustration in 1 shows that each number value is realized by exactly one combination of number exponents. However, the alternation of the placement of ngintha in the presence of overt object makers yields two possible realizations for dual non-sibling contexts. In the absence of overt object markers, the singular classifier stem is combined with ngintha in the inner position. When overt object markers are present, however, this number value is realized by the daucal classifier stem and ngintha in the outer position.

Figure 2 illustrates the distribution of number exponents in combinations with nfut classifier stems. Unlike irr classifier stems, nfut stems do not have morphologically distinct daucal forms. Instead, paucal and dual sibling contexts are expressed through the use of an inner number affix ka which combines with plural classifier stems. This suggests that the daucal is a specific form of a broader number category I will refer to as non-singular.

Drawing on our generalizations of the distribution of exponents, we can make inferences about the featural composition of morphological number and the specifications of the exponents. My conclusions about the complex number resolution patterns (illustrated in Figure 1 and Figure 2) suggest a feature geometry for morphological number as shown in (9). Specifically, the existence of only two distinct classifier forms in nfut paradigms implies a primary division of number into singular and non-singular entities. However, the non-singular classifier stem can also be combined with the daucal marker ka, suggesting that the non-singular category splits into plural and daucal. The daucal markers can be combined with dual non-sibling and paucal non-sibling exponents. An anonymous reviewer asked why the daucal feature is necessary for the analysis. The most compelling piece of evidence comes from the daucal object exponent ngku (see Figure 5 in Section 7.1), which combines both with dual and paucal exponents. Hence, dual and paucal form a natural class entailing the presence of another exponent, which I label daucal following the terminology by Blythe (Reference Blythe2009). Siblinghood is morphologically distinguished for dual participants: dual siblings are encoded with the daucal marker only, while dual non-siblings require an additional exponent. The presence of paucal exponents entails non-siblinghood, while paucal sibling entities always receive the same morphological marking as plurals. There is not a single context to distinguish them morphologically. The distribution of paucal is hard to capture in the feature geometry: we have already established that paucal is a subcategory of daucal, yet it occurs with the plural classifier stem when referring to siblings, rather than with the daucal classifier stem. Blythe (Reference Blythe2009) notes that the difference between paucal and plural is probably not primarily about quantity, but rather about referentiality, with paucals being referential and plurals being non-referentials. As a tentative solution to this problem, I assume that paucal sibling is not represented in the feature geometry in (9), given that there are no morphological contexts to distinguish it from plurals. Another solution would be to assume that paucal siblings receive the same features as plural entities plus an additional feature [specific].

Based on the morphological structure of number in (9) and the distribution of the number exponents in the different contexts, I further infer the following featural specifications of the different exponents. Crucially, I assume that the singular classifier stem does not carry any number features.

The plural classifier stem realizes only the feature [non-singular] since it can be combined with paucal markers in nfut contexts. Crucially, the most specific number context – dual non-sibling – is realized by a sg classifier stem and ngintha only. Since I have already established that the sg classifier stem does not realize any number features, it follows automatically that ngintha realizes [non-singular, daucal, dual, non-sibling]. The featural specifications of number exponents in irr contexts are shown in Figure 3, which also demonstrates that each combination of exponents corresponds to the minimal featural representation of each number context. For instance, the paucal context requires three features: [non-singular] and [plural] are represented in combination in the dc classifier stem, while [paucal] is represented by the distinct outer number affix ngime.

Figure 3. Featural specification of number exponents in irr classifiers stems.

Figure 3 further shows that combination of the dc classifier stem and ngintha as an outer number affix is exceptional, since the features [non-singular] and [daucal] are realized twice in this context. Hence, it is the only number context that is not minimally represented by morphological features. In the following two sections, I will connect the featural specifications of the number exponents to the observation that prosodic words in Murrinhpatha are cyclic in order to explain the exceptional phonological and morphological patterning of ngintha.

5. Background assumptions

In Section 3, I have demonstrated that the phonological correlates of morphemes serve as a window into the cyclic structure of the prosodic word in Murrinhpatha. Specifically, the prosodic domain relevant for word stress assignment spans from the classifier stem at the left edge of the word to the lexical stems, with all affixes following the lexical stem being invisible for stress assignment. In this paper, I implement the cyclic structure of the word by assuming that affixes are concatenated at different morphophonological strata, following the ideas of Stratal Optimality Theory (StratOT) (Kiparsky Reference Kiparsky2000, Bermúdez-Otero Reference Bermúdez-Otero and Trommer2012). StratOT is a derivational version of Standard Parallel Optimality Theory (SPOT) (Prince & Smolensky Reference Prince and Smolensky1993) and is based on assumptions similar to those posited by Lexical Phonology and Morphology (Kiparsky Reference Kiparsky1982). Just as SPOT, StratOT pursues the idea that the grammar of Human language consists of a set of violable, rankable and universal constraints. The grammar of each individual language results from an individual ranking of these constraints. A core difference of StratOT is the division of labor into several different cyclic domains. A concrete suggestion with respect to the number of domains comes from Bermúdez-Otero (Reference Bermúdez-Otero and Trommer2012), who assumes three different morpho–phonological domains:Footnote ⁷ the stemlevel, the word-level and the phrase-level.

An important assumption by StratOT is that morphological derivations are accompanied by cycles of phonological optimization such that the morphological component of the grammar and the phonological component of the grammar are interleaved. After each stratum, bracket erasure takes place, which renders morphological structure inaccessible to further cycles. Bracket erasure is a mechanism introduced by Pesetsky (Reference Pesetsky1979) (referring to Chomsky & Halle Reference Chomsky and Halle1968) and relates to the process of making morphological boundaries invisible to phonological or morphological rules at the end of a cyclic domain. Consequently, neither phonological nor morphological rules can make reference to these boundaries. The question of whether phonological rules have access to morphological structure is not trivial. Embick (Reference Embick2010) argues that allowing global access to morphological structures creates an excessively potent grammar. In cyclic approaches, morphological sensitivity is limited to smaller subdomains (i.e. morphological structure can only be accessed by phonological rules within a given cycle). Hence, cyclic approaches are conceptually less powerful than theories with global access to morphological structure and build on a strong empirical basis (see Orgun & Inkelas Reference Orgun, Inkelas, Booij and van Marle2002, among others). Bermúdez-Otero (Reference Bermúdez-Otero and Trommer2012) argues that bracket erasure arises most naturally from the assumption that the output of phonological optimization must be phonetically interpretable and must therefore not contain morphological representations, such as brackets. In this perspective, bracket erasure is not a mere stipulation but rather a logical consequence of modular assumptions. In the works by Pesetsky (Reference Pesetsky1979), Kiparsky (Reference Kiparsky1982), Mohanan (Reference Mohanan1982), Mohanan & Mohanan (Reference Mohanan and Mohanan1984), however, bracket erasure is an independent axiom of the theory that requires the existence of brackets as representational objects. This paper does not extensively contribute to this ongoing discussion, remaining compatible with both viewpoints. In the work at hand, I assume that only the morpheme boundaries are deleted, while the grammar still has access to the morphosyntactic information realized in a previous stratum. In other words, a morphologically complex word (e.g. a root plus its affixes) is treated as a morphologically simplex word after bracket erasure. It should also be emphasized that the analysis I forward in this paper does not require phonological access to morphological structure at all. Hence, it would also be compatible with cyclic approaches that are strictly modular.

The exact architecture of the cyclic model of the morphology–phonology interface I adopt is illustrated in Figure 4.

Figure 4. Assumed architecture of the morpho–phonology interface.

In this paper, I assume that two strata suffice to explain the phenomenon under discussion. Specifically, I assume that the word stress domain corresponds to the stem-level, while affixes attaching outside the stress domain belong to the word-level. Example (10) illustrates how these assumptions relate to the exceptional placement of ngintha. In the absence of overt object markers, ngintha is concatenated at the stem-level, as in (10a). However, when an overt object marker is present, as in (10b), ngintha attaches at the word-level.

Moreover, the dispersion of number information across different number exponents allows us to draw conclusions about the featural structure of morphological number, as well as the featural specifications of the exponents. Taking their phonological properties and their morphological position into account, we can now determine the featural specification as well as the stratum a morpheme belongs to. This information is summarized in Table 4 for each affix relevant for the discussion. Following Harley & Ritter (Reference Harley and Ritter2002), I assume that 1st and 2nd person are realized using privative person features, while the realization of 3rd person does not involve features and is inferred through default interpretation. The minimal pair in (10) involves two different classifier stem forms, both of which refer to 1st person subjects. As concluded above, singular classifier stems do not comprise any number feature, while the daucal stem carries the features [non-singular] and [daucal]. Hence, the featural specifications for the two classifier stems are [1, subject, irr] for ba and [1, subject, non-singular, daucal, irr] for nguba. I further assume that the 3rd person object in (10a) is realized by a covert object marker which has the feature [object, singular], while the 2nd person object marker nhi comes with the specification [2, object, singular].Footnote ⁸

Table 4. Murrinh-Patha affixes divided into strata

The final stem-level affix is the number affix ka, which combines with nfut classifier stems and carries the feature [daucal]. Two different types of affixes belong to the word-level in Murrinhpatha. First, all tam affixes attach at this level, like the [future] suffix nu. Second, some number affixes belong to this stratum, such as the [paucal] suffix ngime. Note that the illustration in Table 4 reveals that Murrinhpatha has no morphological possibility to realize the feature [paucal] at stem-level. Rather, its realization is delayed until the word-level. In the previous section, I argued that the dual marker ngintha has to be specified for the features [non-singular, daucal, dual, non-sibling], as it combines with the singular stem in the featurally most specific dual non-sibling context. In order to capture the observation that it occurs on both stem-level and word-level, I assume that ngintha is underspecified with respect to the stratum it belongs to, and may attach at any stratum, an analytical option previously made by Kiparsky (Reference Kiparsky, Hsiao and Wee2015). Note that this assumption is not problematic for the Cyclic Principle (see Chomsky Reference Chomsky1965, Perlmutter & Soames Reference Perlmutter and Soames1979), given here in (11), which states that an operation has to be carried out as early as possible.

In fact, I will show in Section 6 that ngintha has to be concatenated as early as possible, as long as the context for its realization is given. Hence, the realization of ngintha in a later cyclic domain does not pose a problem for the Cyclic Principle, since the context for the rule to apply is not given in the first domain. Without an overt object marker, it attaches at the inner level to fulfill a constraint that ensures the realization of all input features. With an overt object marker, this constraint will be outranked, hence blocking the realization of ngintha in the inner domain.

To illustrate how my analysis couched in StratOT derives the peculiar placement of ngintha, let me assume that the verb root comes with a list of contextual features that need to be realized by morphological exponents in an optimal way. This list is then checked against the available affixes at each stratum. To ensure that the morphological grammar on a given stratum concatenates only the affixes that are lexically affiliated with it, I assume that the Gen function accesses the lexical entries of the morphemes, in which the stratal specification is stored as a diacritic. Thus, Gen restricts possible output forms to those containing only morphemes with the correct stratal specification. In this paper, I remain agnostic about the origin of these features. Since the core of my analysis rests on the interaction of violable constraints, my analysis is compatible with presyntactic morphological theories based on Optimality Theory (Prince & Smolensky Reference Prince and Smolensky1993) – for example, Müller (Reference Müller2020) or postsyntactic theories combining OT and Distributed Morphology, like Trommer (Reference Trommer2001, Reference Trommer, Booij and van Marle2003) or Rolle (Reference Rolle2020). To derive the patterns in (10), let us assume that the verbal complex comes with the input features in (12), since it concatenates a classifier stem, a lexical stem, an object marker and a tam exponent. I follow the notation introduced by Müller (Reference Müller2020) in using the $ \bullet $ symbol to mark features that need to be expressed in a morphological word.

These input features are the same for both (10a) and (10b), yet the sentences differ with respect to the features of the arguments that need to be realized. Hence, there are also input feature sets belonging to the arguments of the sentence. The feature sets for (10a) are listed in (13a), while the feature sets of the arguments in (10b) are listed in (13b). An anonymous reviewer asked to specify how tam information is composed as both the classifier stem and external suffixes carry information about tense, aspect and modality. Similar to the argument features, I assume that tam information is given through the input features in (13c) where irr(ealis) will be provided by the classifier stem, whereas fut(ure) will be realized by the word-level suffix nu. I abstain from a more fine-grained decomposition of tam features, since tam morphology does not interact with the number exponents discussed in the paper. Hence, a deeper analysis of tam is far beyond the scope of this paper, and I refer the reader to Nordlinger & Caudal (Reference Nordlinger and Caudal2012) or Mansfield (Reference Mansfield2019: chapter 6.3.2).

Previous work by Trommer (Reference Trommer, Booij and van Marle2003, Reference Trommer2008), Crysmann & Bonami (Reference Crysmann and Bonami2016) and Müller (Reference Müller2020) has highlighted that the mapping between input features and output morphological forms is regulated by rules on morphological well-formedness. In this paper, I follow Trommer (Reference Trommer, Booij and van Marle2003, Reference Trommer2008) and Müller (Reference Müller2020) by implementing these morphological rules as violable constraints in Optimality Theory. An exhaustive list of constraints is given in (15). M(ax)(F) constraints are crucial since they ensure that each feature of the input F is realized by an exponent in the output. M(ax)(Arg) $ {}_{{\mathrm{S}}_{\mathrm{BJ}}} $ and M(ax)(Arg) $ {}_{{\mathrm{O}}_{\mathrm{BJ}}} $ are specific versions of M(ax) relating to the argument input feature sets. All M(ax) receive a violation mark for each feature in the input which is not realized by an exponent in the output.

In Section 4, we concluded that number is morphologically represented by a set of privative features and that arguments differ in the number of features in their specification. Concretely, a dual non-sibling argument creates four number features in the input [non-singular, daucal, dual, non-sibling], while a singular argument only requires [singular]. I have also stated that some number exponents such as the singular classifier stem ba are underspecified for number features. Let me now elaborate on how my analysis formalizes exponent selection. In other realizational models of morphology, like Distributed Morphology (Halle & Marantz Reference Halle, Marantz, Hale and Keyser1993), exponence is regulated by the Subset Principle, given here in (14). The Subset Principle states that an exponent needs to be matching and specific enough to be selected for exponence.

The Subset Principle prescribes two conditions on exponence: matching and specificity, both of which are relevant to my analysis, as well.Footnote ⁹ With respect to matching, I follow the definition in (14) in assuming that an exponent is matching if it contains a subset of features of the input but no features absent from the input. I further assume that matching is an inviolable condition and hence part of Gen.Footnote ¹⁰ Formalizing specificity is not that trivial. First, I suggest a stratal model of morphology, which means that exponence selection may target several morphemes at once. That is, an input feature set [A, B, C] is most specifically realized by an exponent [A, B, C] but also by two exponents [A, B] and [C], or even by three different exponents [A], [B] and [C]. Crucially, an exponendum (or a feature set) may also be underexponed (e.g. the input feature set [A, B, C] would only be realized by an exponent [A, B] if there is no way to realize [C] without violating higher ranked constraints). M(ax)(Arg) constraints are violated for each feature in the input that has no realization in the output, thus being the formal implementation of the concept of specificity. This will have the effect that some arguments are more likely to be expressed by underspecified exponents than others: if a [singular] argument is realized by an underspecified exponent, this will cause one violation of M(ax)(Arg). If, however, a [non-singular, daucal, dual, non-sibling] argument was realized by an underspecified exponent, the exponent would still be matching but causes four violations for each feature on the input set. Readers familiar with feature geometries like Rice & Avery (Reference Rice, Avery and Archibald1995), Brown (Reference Brown1997), Harley & Ritter (Reference Harley and Ritter2002) recall that their feature geometries include default nodes. In those systems, if a mother node has more than one daughter node, one daughter is marked as the default. If only the mother were present in an exponent, the default daughter would be inferred by an additional default rule. In my system, I get a similar effect without stipulating defaults: some nodes are more likely to be marked with underspecified exponents. It is, in contrast, not necessary to mark those nodes as special in the feature geometry or to specify an additional default rule. Following the ideas of the Subset Principle, an exponent is selected if it is the most specific and matching exponent of a given set. However, it could still be the case that an underspecified exponent is the most specific one. An anonymous reviewer commented that it is stipulative to assume that the ba classifier stem is underspecified, while other singular exponents like the object pronominals nhi and ngi are specified for [singular]. It is true that there is no independent evidence for these specifications; however, it is predicted that both specified and underspecified exponents exist in a language. In short, underspecified exponents do not inflate the system, they are part of it.

In addition, there are constraints regulating the relative position of certain categories within a morphological word. To this end, Trommer (Reference Trommer, Booij and van Marle2003, Reference Trommer2008) observes that person information is typically aligned to the left edge of the word, while number exponents tend to be realized at the right edge of the word. These cross-linguistic tendencies are captured by two constraints which are violated whenever another exponent intervenes between the left edge of a word and an exponent of [Person] (L $ \Leftarrow $ Pers(on)) or the right edge of the word and an exponent realizing [Number] (Num(ber) $ \Rightarrow $ R), respectively. In addition, the markedness constraint *M(ultiple) E(xponence) $ {}_{\mathrm{F}} $ is violated if a feature of the input is realized more than once, thus preventing multiple exponence. Finally, the constraint Coh(erence) ensures that features belonging to the same feature set (i.e. the argument feature sets) are realized in adjacency to each other. In this respect, it is irrelevant if the features of the shared feature set are expressed by one and the same exponent or by two different, adjacent exponents. It will only be violated if another exponent which is not part of the shared feature set intervenes.

In contrast to SPOT, the ranking of constraints is only fixed within a stratum. Between the strata, re-ranking may apply. This assumption is based on the observation that certain phonological rules apply only to certain subdomains, suggesting that the ranking of the constraints may differ from one stratum to the other. In the following, I will show how the anomalous positioning of ngintha follows from the constraint-driven interaction of the different exponents. Put shortly, my analysis is couched in StratOT and implements the following generalizations:

1. 1. Both objects markers and inner number markers are subject to morphological rules that require them to be a realized in adjacency to the classifier stem. First, L $ \Leftarrow $ Pers(on) ensures that object exponents carrying [Person] information are realized at the left edge of the word. Second, Coh(erence) requires exponents realizing features from the same feature set in adjacency to each other. Hence, both affixes are subject to constraints that force them to occupy the position to the direct right of the classifier stem, which always occupies the leftmost position in the word.

2. 2. In the presence of both overt object markers and inner number affixes, preference is given to the former.

3. 3. Since the number exponent ngintha cannot be concatenated next to the classifier stem, highly ranked placement constraints suppress its realization at the stem-level.

4. 4. To realize as many input features as possible, a featurally more specific form of the classifier stem is selected to minimize violations of M(ax)(Arg) $ {}_{{\mathrm{S}}_{\mathrm{BJ}}} $ , thus explaining the different form of the classifier stem.

5. 5. Since ngintha is not strictly bounded to the stem-level, its realization is delayed until the word-level.

6. A StratalOT analysis of Murrinhpatha

Having set the technical preliminaries in the previous section, let me now explain in detail how the peculiar placement of ngintha and its phonological correlates can be derived from the interaction of well-established morphological constraints. In this endeavor, let us first consider example (16), repeated from (10a), where ngintha attaches to the right of the classifier stem in its singular form.

The relevant tableau is given in (17). The input to this derivation is the root $ \sqrt{see} $ , a set of contextual features, as well as the feature sets for the subject and the object argument. As noted earlier in this paper, classifier stems are always portmanteau morphemes carrying subject features. To this end, I assume that the root is an abstract pointer $ \sqrt{see} $ to the respective classifier stem paradigm. That is, it refers to a set of inflected forms of one and the same classifier stem paradigm, but does not choose a specific form of that paradigm. Note that this assumption is unproblematic in StratOT since the root is not a cyclic domain and does not undergo phonological optimization.

The contextual features for (16) are [ $ \bullet $ cl.stem $ \bullet $ ], [ $ \bullet $ lx.stem $ \bullet $ ], [ $ \bullet $ tam $ \bullet $ ] and [ $ \bullet $ obj $ \bullet $ ], whose exponence is regulated by the constraints Max(cl.stem), Max(lx.stem), Max(obj) and Max(tam). Crucially, all candidates in (17) violate Max(tam) exactly once since there is no morphological way to realize fut at stem-level. Max(cl.stem), Max(lx.stem) and Max(obj) are high-ranked and ensure that a classifier stem, a lexical stem and an object marker are concatenated. As an example, candidate b. is ruled out since it does not comprise a lexical stem, thus fatally violating Max(lx.stem). The remaining constraints make sure that the argument feature sets are realized in an optimal way. Recall that the subject is a 1du non-sibling argument, thus requiring the features [subject, 1, non-singular, daucal, dual, non-sibling], while the 3^rd person object only requires [object, singular]. The output form of candidate a. splits the features of the subject onto two different morphemes: the 1^st person singular form classifier stem form ba realizes [1] and [subject], whereas ngintha spells out the remaining number features [non-singular, daucal, dual, non-sibling]. The candidates c. and d., both of which lack the dual marker ngintha, cannot become optimal, since they fatally violate Max(Arg) $ {}_{{\mathrm{S}}_{\mathrm{BJ}}} $ , which ensures that the subject feature set is exhaustively realized. In candidate a., each feature is realized exactly once, thus avoiding violations of *Multiple Exponence. Candidate e. with the 1^st daucal classifier stem, however, is ruled out since the two features [non-singular] and [daucal] are realized twice. Moreover, candidate a. does not violate Coherence, since the two exponents realizing features of the subject feature set are adjacent and not interrupted by different exponents. Most crucially, the object marker does not violate L $ \Leftarrow $ Pers although it is not at the left edge of the word, since it does not include any person features and is therefore not subject to this constraint. Note that candidate f., in which ngintha attaches as an outer affix, is ruled out as it violates Coherence due to two intervening morphemes.

The output of the morphological optimization at stem-level is ba-ngintha-ngkardu, which is then taken to the phonological component of the stem-level for further phonological optimization. Note that the output form contains exactly those affixes with are relevant for word stress assignment. Concretely, it contains the classifier stem, inner affixes and the lexical verb, but crucially, no external affixes. Within the phonological component of the stem-level, stress assignment and subminimal lengthening apply. After this computation, bracket erasure takes place and deletes morpheme boundaries. The next step of the derivation takes place in the morphological component at word-level. At this step of the derivation, the grammar has access to the output of the stem-level banginthangkardu, as well as word-level and underspecified affixes. The morphological derivation at word-level is illustrated in (18).

Most contextual features have already been satisfied at the previous stratum, except for [fut], which can only be satisfied at word-level. In order to anchor the input at the left edge of the word, I use the high-ranked Alignment constraint L $ \Leftarrow $ V which ensures that all affixes attached at word-level will end up in a suffixal position. The concrete definition of L $ \Leftarrow $ V is given in (19).

Since bracket erasure has taken place, the input banginthangkardu is treated as a morphologically simplex exponent of the features [subject, 1, non-singular, daucal, dual, non-sibling] and [object] as word-level. Hence, the constraint Num $ \Rightarrow $ R is violated once by candidate b. as the tam exponent nu intervenes between banginthangkardu and the right edge of the word. Nonetheless, candidate b. becomes optimal since candidate a. does not include any tam marker and violates the high-ranked Max(tam), while candidate c. violates the general suffixing constraint L $ \Leftarrow $ V. After this step of morphological optimization, the optimal candidate banginthangkardu-nu enters the phonological component of the word-level for further optimization.

Let us now turn to example (10b), which is repeated here in (20), where ngintha is concatenated as an external affix and the classifier stem appears in its daucal form.

Recall that Nordlinger & Mansfield (Reference Nordlinger and Mansfield2021) describe the pattern in (20) with position classes. Since ngintha is blocked in the position after the classifier stem in (20) in the presence of an overt object marker, Nordlinger & Mansfield (Reference Nordlinger and Mansfield2021) assume that both ngintha and the object markers compete for the same position class. Moreover, the different shape of the classifier stem in (20) is taken to be evidence for position-conditioned allomorphy where a different allomorph of the classifier stem is chosen in the presence of an object marker. Instead, I argue that the placement of ngintha follows from the interaction of well-established morphological constraints and the cyclic structure of the word. The tableau illustrating this derivation is provided in (21).

In contrast to example (16), there is an overt object marker nhi in (20), which comes with the featural specification [2, object, sing]. Thus, the constraint L $ \Leftarrow $ Pers becomes active, shifting the marker to the right of the finite stem.Footnote ¹¹ In the previous derivation in (17), the constraint remained inactive since the covert object marker does not spell out person features. In the context of nhi, however, L $ \Leftarrow $ Pers now causes a competition between the object marker and ngintha for the position to the right of the classifier, thus following the empirical intuition by Nordlinger & Mansfield (Reference Nordlinger and Mansfield2021). In my analysis, however, the competition arises from morphotactic constraints on positioning preferences rather than from position classes. Specifically, candidate b. replicates the order of affixes that became optimal in (17), yet fatally violates L $ \Leftarrow $ Pers since the overt object marker nhi carries person features. However, shifting the dual marker ngintha to the right of the object marker, as in candidates a. or d., causes fatal violations of Coherence. Not realizing an object marker at all in candidate g. or choosing a different object marker in candidate h. in order to avoid violations of L $ \Leftarrow $ Pers or Coherence is not possible either, due to the high-ranked constraint Max(Obj) and Max(Arg) $ {}_{{\mathrm{O}}_{\mathrm{BJ}}} $ . Since ngintha cannot be realized in the position preferred by Coherence, the grammar chooses to not concatenate the marker at stem-level. Since ngintha realized the input features [non-singular, daucal, dual, non-sibling], non-realization of the markers yields four violations of the constraint Max(Arg) $ {}_{{\mathrm{S}}_{\mathrm{BJ}}} $ , thus ruling out candidate c. However, the grammar still has the option to choose the more specific classifier stem nguba, which is specified for [1, subject, non-singular, daucal], in contrast to ba. In (17), the choice of nguba was blocked since simultaneous realization of nguba and ngintha creates a violation of *ME. In the derivation in (21), choosing nguba becomes now the preferred option since non-realization of ngintha prevents a violation of *ME and creates only two violations of Max(Arg) $ {}_{{\mathrm{S}}_{\mathrm{BJ}}} $ . Thus, candidate (e), which includes nguba, but excludes ngintha, becomes optimal. Note also that all possible candidates violate Max(tam) since there are no exponents of [fut] available at stem-level.

The optimal output form nguba-nhi-ngkardu is taken to the phonological component of stem-level, where the evaluation of the minimum quantity condition, stress assignment and subminimal lengthening apply. After this step, computation at stem-level is complete, bracket erasure takes place and the output is shifted to word-level, illustrated in (22).

In contrast to the derivation in (18), no exponent is realizing the input features [dual, non-sibling] yet, which caused two violations of M(Arg) $ {}_{{\mathrm{S}}_{\mathrm{BJ}}} $ at stem-level. As a consequence, the grammar will try to find a matching exponent and a tam exponent. Since ngintha is unbounded with respect to the stratum it attaches to, it is concatenated now at word-level and will therefore be realized outside the word stress domain. Since Murrinhpatha does not only have the underspecified ngintha number exponent but also a word-level only number marker ngime, I believe that the grammar at this level still requires access to the input feature structure to find the matching exponent. Thus, the constraints M(Arg) $ {}_{{\mathrm{S}}_{\mathrm{BJ}}} $ and *ME are still active; however, the relative ranking of these constraints has changed. At word-level, *ME is ranked below M(Arg) $ {}_{{\mathrm{S}}_{\mathrm{BJ}}}. $ As a consequence, the grammar will favor candidates in which all input features are realized. The high-ranked Max constraints require that both a number and a tam exponent are concatenated at this step, thus ruling out candidate a. in (22). Again, there is a constraint L $ \Leftarrow $ V ensuring that all affixes added at this level are suffixes, therefore excluding candidate d. At this point of the derivation, Num $ \Rightarrow $ R (Trommer Reference Trommer2001, Reference Trommer, Booij and van Marle2003, Reference Trommer2008) becomes active and regulates the relative ranking of tam and ngintha. Candidate b., which surfaces in (3b), is therefore successfully predicted to become the optimal candidate. It is worth mentioning that the relative order of the tam exponents and the number exponents are word-level is rather flexible. Thus, it remains unclear whether the relative order should be regulated by morphotactic constraints or whether the order is subject to free variation.

In the analysis suggested in this paper, the anomalous placement of ngintha is an instance of cyclic counterbleeding in grammar. On the surface, the pattern in (20) seems like overexponence of the features [non-singular] and [daucal]. However, the phonological properties of the word reveal that the apparent overexponence results from cyclicity. First, ngintha is suppressed in the presence of an overt object marker. Due to the non-realization of ngintha at stem-level, the grammar selects a featurally more specific classifier stem. Second, ngintha is underspecified with respect to the stratum at which it attaches and is therefore realized at word-level. Crucially, the grammar at stem-level cannot anticipate that ngintha will be realized in a later step. Hence, the stem-level grammar chooses the optimal option for its domain, although this results in overexponence at a later domain. It is worth mentioning that affixation itself is only limited by *Multiple Exponence and other constraints on morphological well-formedness. As long as these constraints are obeyed, affixation may in principle apply without any restriction on the maximum number of affixes. In this respect, this work differs from a position-class analysis in the style of Crysmann & Bonami (Reference Crysmann and Bonami2016), but also from other morphological analyses of affixation, such as Wunderlich & Fabri (Reference Wunderlich and Fabri1995), Wunderlich (Reference Wunderlich, Wilder, Bierwisch and Gärtner1997), Ortmann (Reference Ortmann1999), Aissen (Reference Aissen2003), Don & Blom (Reference Don and Blom2006), Müller (Reference Müller2020).

In this paper, I follow Nordlinger & Mansfield (Reference Nordlinger and Mansfield2021) in assuming that there is a competition between overt object markers and ngintha for the position to the right of the classifier stem. However, the theoretical devices triggering the competition are constraints that are based on crosslinguistic preferences of the realization of person and number markers rather than position classes. An anonymous reviewer notes that assuming a level specification for each morpheme is equally powerful as assuming a position class for each affix. While it is true that the level specification is stored in the lexicon, there are three major advantages in assuming stratification, rather than position classes: first, the level specification of a morpheme does not only explain the morphological irregularities but neatly derives the phonological asymmetries between the affixes involved. If the position of ngintha and the allomorphy of the classifier stem were derived with position classes or a similar morphotactic device, the phonological asymmetry would still lack an analysis – which would probably require cyclicity anyway (Mansfield Reference Mansfield2017). Second, Nordlinger & Mansfield (Reference Nordlinger and Mansfield2021) refer to position classes to describe the context of the classifier stem alternation to the daucal stem. That way, however, the context and the output of the alternation are not connected. In other words, it remains unclear why the classifier stem is daucal rather than plural in the context of an overt object marker. The analysis I put forth in this paper, in contrast, connects the context and the output. When an overt object marker is present, the interaction of morphological constraints causes the suppression of the dual marker ngintha and the choice of the daucal form. The third notable advantage of stratification to position classes, as emphasized by another anonymous reviewer, is that all theoretical tools employed rely on independent evidence, including phonological evidence for the strata and typological evidence for the constraints on linearity. Moreover, the morphological markedness constraints L $ \Leftarrow $ Pers and Coherence refer to specific morphosyntactic categories. Hence, they make clear predictions about the categories involved while position classes may in principle be associated with any morpheme.

In the remainder of this paper, I will first elaborate on how the interaction of morphological constraints can neatly explain the distribution of object number exponents in Section 7.1. Section 7.2 emphasizes that the anomalous placement of ngintha is an interplay of suppression, reranking and stratal underspecification, and hence a lexical property of ngintha. Moreover, the placement of ngintha and its phonological correlates are connected to cyclicity, universal morphological constraints and stratal underspecification. Since these properties can be assumed to exist in other languages as well, the analysis suggests that we should find more patterns of delayed realization in other languages than Murrinhpatha. To this end, I discuss Umlaut in Sinhala in Section 7.3.