2.1 Huozhou Chinese and its phonology

Houzhou is located in the Fenhe River valley, southern Shanxi Province. Huozhou Chinese is classified as a variety of Zhongyuan Mandarin (Shen 2008), and there are four sub-varieties: West Huozhou, East Huozhou, North Huozhou, and Wangzhuang (Feng & Zhao 2014: 10).

Huozhou Chinese shares the same syllable structure as Standard Chinese. The maximal syllable template is CGVX, in which G represents a pre-nuclear glide ([j], [w], or [ɥ]), and X can be either a post-nuclear glide ([j] or [w]) or a velar nasal ([ŋ]). Although there have been various proposals regarding the internal structure of Chinese syllables (e.g., Cheng 1966; Lin 1989; Bao 1990; 1996; Duanmu 1990; 2007; van de Weijer & Zhang 2008), it is the moraic representation of Chinese syllables that is relevant to the discussion in this paper, as illustrated in (2) (after Zhang 2023a: 4).

In Standard Chinese, syllables that carry a full lexical tone are treated as bimoraic (Duanmu 1990; 1993; 1994; 2007; Wu and Kenstowicz 2015). I assume that Huozhou Chinese shares the same property. Therefore, the nuclear vowel in an open syllable is represented as bimoraic on the surface to bear the lexical tone, as in (2a). Meanwhile, only elements in the rime domain (V or VX) can be moraic; namely, moraicity does not extend to the prenuclear glide (2b–d).

Since only syllables that end with [ŋ], [j], or [w] are closely related to the observed patterns, the possible (G)VX combinations in Huozhou are listed in (3), with their corresponding underlying forms in parentheses.

Regarding the underlying representations, both onglides and offglides are derived from their corresponding vowels (/i/ → [j], /y/ → [ɥ], and /u/ → [w]). The low vowel /a/ can be either front [a] or back [ɑ], depending on the influence of the postvocalic element, as in [jɑŋ] (*[jaŋ]) and [waj] (*[wɑj]). Similarly, /ə/ surfaces as [o], [e], and [ə] when followed by [w], [j], and [ŋ], respectively, which is a common phenomenon in Chinese syllables (Duanmu 2007; Lin 2015, among others).¹ The feature specifications of major surface vowels are given in (4) to facilitate the discussion.

Finally, there are five lexical tones in Huozhou Chinese: low-level, rising, mid-level, falling, and high-level. In this paper, I transcribe the tones with Chao’s (1968) digit system as “11”, “35”, “33”, “53”, and “55”, where “1” represents the lowest pitch while “5” represents the highest.

2.2 Diminutive formation in West Huozhou

Diminutives in Huozhou Chinese can be formed either through subtraction or reduplication. Subtraction in Huozhou is usually referred to as “rime change” in the literature, while reduplication is a common method for forming diminutives in Chinese dialects. Speakers also express smallness or cuteness in alternative ways, such as by adding the morpheme xiao [ɕjɑw³³] ‘small’ directly before a noun. The data presented in this paper are primarily from the author’s consultation with three native speakers (one male and two females, aged between 50 and 65) from the town of Bailong, a representative area of West Huozhou. Additional information can be found in the Appendix. This paper focuses on the subtracted forms.

The pattern of subtraction can be generalized as segment deletion with feature movement. Only syllables that end with [j], [w], or [ŋ] can undergo subtraction, specifically those with the combinations listed in (3).² These observations align with descriptions in previous literature, despite some notational and sub-dialectal variations, as well as some minor divergences, which will be discussed shortly.

The examples of diminutive subtraction are given in (5)–(7), and additional examples are provided in the Appendix. As mentioned earlier, the subtracted forms are represented with a length mark to indicate bimoraicity, since they still carry a full tone. This is a phonological assumption based on previous studies of Chinese languages (§2.1), and a comprehensive phonetic study is beyond the scope of this paper. In addition, most Chinese morphemes are monosyllabic, and some morphemes can stand alone as words (see Packard 2015 for relevant discussions on free and bound roots in Chinese). Thus, in the following examples, the subtracted form of certain nouns can be used independently (e.g., 5b), while for others, the subtracted form is more commonly seen in compounds (often disyllabic) that end with those nouns (e.g., 5a). The gloss of each compound is provided in a separate column when needed, along with the literal gloss in parentheses. Note that underlying /a/ surfaces as [ɑ] when followed by [ŋ] in a closed syllable or preceded by [w] in an open syllable, while it surfaces as [a] elsewhere; some tonal changes will also be discussed shortly.

In the examples above, the diminutive of a noun can be formed by deleting the last non-vocalic segment (post-nuclear glide or nasal), accompanied by featural changes of the nuclear vowel in some cases. This pattern is evident for nouns ending in [ŋ] and [j] in (5) and (6).³ When a noun ends with a labiovelar glide [w], the subtracted forms remain regular, involving segment deletion along with some featural changes, as shown in (7).

Regarding the featural changes, one highlighted pattern is mid-vowel raising; specifically, mid-vowels are always raised to [u] or [y], as in (5f), (6c–e), and (7e–g). Additionally, although high vowels retain their height after subtraction, the low vowel [ɑ] (/a/) can be raised to the mid [o] when it is followed by [w] in the same syllable, as in (7a–d). This differs from the examples in (5) and (6), where the low vowel remains low in the diminutive form (e.g., [saj¹¹] → [saː¹¹], [pʰɑŋ³⁵] → [pʰaː³⁵]).

Most subtracted forms still carry the same lexical tone as their non-diminutive counterparts and can be used independently. Therefore, the subtracted forms are viewed as bimoraic syllables on the surface, following the discussion in §2.1. However, in some cases, the tone of the subtracted form becomes a falling tone, as in (6a), (7b), and (7g). This tonal change was also reported in previous literature (e.g., Feng & Zhao 2014), but it does not seem to be systematic and requires further investigation. Further, the tones in compounds are subject to tone sandhi rules, as seen in (5a), (5d), and others.

As mentioned earlier, another way to form a diminutive in Huozhou Chinese is through reduplication, and in most cases, there are no significant semantic differences between the reduplicated forms and those formed through subtraction. Besides Huozhou Chinese, reduplication is a common way to express smallness or cuteness in many Chinese dialects, particularly those spoken in Shanxi Province (Shen 2003). Even verbal reduplication in Standard Chinese and many dialects serves a diminutive function, expressing actions of short duration or politeness (Li & Thompson 1981; Audring et al. 2021). Although the issue of reduplication will not be the focus of this paper, some examples are given in (8) for illustrative purposes.⁴ The reduplicant is always underlined. Relevant discussion can be found in §3.4.

Diminutive reduplication in Huozhou is partial reduplication (8a–f), except for nouns ending in [w] (8g–i). Additionally, since diminutive subtraction only occurs for nouns that end in [ŋ], [j], or [w], diminutive forms for nouns without endings can be expressed through full reduplication, as shown in (9). As a side note, the symbols [ɿ] and [ʅ] are not standard IPA symbols, but they are commonly used to represent “apical vowels” in various Chinese languages and dialects (see Lee & Zee 2017 for additional information).

Summing up, Huozhou Chinese uses subtraction to form diminutives, which is unique among Chinese dialects. Subtraction in Huozhou Chinese is a regular process where closed syllables are changed into open ones, as summarized in (10). The patterns in parentheses have been reported in other works but are less common in the author’s fieldwork. The alternation between [a] and [ɑ] is due to local assimilation.

Overall, the patterns of diminutive formation can be categorized into changes at the prosodic level and changes at the segmental level. At the prosodic level, if a noun ends with [ŋ], [j], or [w] (except for [-jaj]),⁵ the last non-vocalic element can be deleted to form a diminutive, as in (5), (6), and (7). At the segmental level, regular phonological processes accompany deletion, and two notable characteristics are observed. First, stepwise raising occurs in the diminutive form when the nuclear vowel is followed by [w] in a noun. The vowel is raised from low to mid ([ɑ] → [o]) or from mid to high ([o] →[u] or [y]). Second, although vowel quality alternations also occur in j-ending and ŋ-ending nouns, only mid vowels are raised in the diminutive form (e.g., [ə] → [u]) while the low vowel remains low. Both segment deletion and featural changes warrant analyses, and the underlying representations and grammar that lead to this unique phenomenon are the main puzzles. These will be addressed in the following sections.

2.3 Additional issues with the patterns

Before concluding the data description, several additional issues are addressed to provide a thorough understanding of the dataset.

The patterns described above generally align with the descriptions of Huozhou Chinese in previous literature. However, it is noteworthy that some discrepancies exist between the data presented in this paper and those described in earlier works, likely due to idiosyncratic variations. In previous studies, the featural changes of [ow] (/əu/) and [jow] (/iəu/) after subtraction have been described in various ways, such as [ɯ] and [iɯ] (Feng & Zhao 2014), [ɯ]/[ʉ] and [y] (X.Tian 1992), and [u] and [y] (J.Tian 2009). The data presented in this paper are consistent with the descriptions in J. Tian (2009). Nevertheless, despite the differences in featural changes, the general patterns of subtraction remain consistent across these descriptions. Moreover, although this paper mainly discusses the variety of West Huozhou, diminutives in other subvarieties of Huozhou Chinese can also be formed by dropping the final segment of a syllable (Feng & Zhao 2014).

Many aspects of Huozhou diminutive subtraction are consistent with the findings of previous studies on subtractive morphology. As Dressler (2000) and Manova (2011; 2020) point out, the deleted element in subtractive morphology is often the final segment of a morphological base, which aligns with the observations in Huozhou.⁶ In addition, diminutive formation is a common function of subtraction, as has also been observed in other language families, such as the Slavic languages (Manova 2011). Regarding the typology of subtraction, Manova (2011; 2020) concludes that root-based subtraction is rare, and this conclusion also applies to the patterns reported in this paper. Some cases of subtraction in Huozhou appear to act on monosyllabic noun roots, such as (5b), (6a), and (7a), but these are always free roots; namely, those that can stand alone as words. Therefore, the data of Huozhou do not contradict the insights of previous studies.

Regarding the relation between language types and subtraction, subtraction in Huozhou, an analytic language, supports Manova’s (2011: 173–174) insight that such a relation is questionable, despite Dressler’s (2000: 585) speculation that subtraction does not occur in non-agglutinating or non-fusional languages. Although subtraction has been observed in various language families, including Romance, Germanic, and Slavic languages (Manova 2020: 12, and references therein), Chinese dialectologists have well-documented the subtractive patterns of Huozhou Chinese. However, these patterns have not received much attention from theorists, likely because the descriptive works are written in Chinese, and the relevant discussions are not framed in contemporary linguistic terminology.

Finally, subtractive morphology should always be distinguished from templatic truncation. For instance, Bat-El (2002) distinguishes between “true truncation” and “fake truncation,” with subtractive morphology regarded as “true truncation.” In Bat-El (2002), “true truncation” is morphologically motivated and a-templatic. In other words, the remaining portion is not necessarily limited to a designated phonological unit, such as a foot or a syllable. In contrast, “fake truncation” results from the imposition of a prosodic template. In the case of Huozhou diminutive formation, the observed pattern should be treated as subtractive, or “true truncation”, since segment deletion clearly changes the meaning of the nouns. It is morphologically driven and occurs only when expressing diminutives.

3.1 Proposal

The item-and-arrangement approach builds on the standard view of morphemes inherited from structuralism, and a morpheme is defined as the smallest unit in a language that relates meaning and form (Anderson 1992: 48–51).⁷ The key proposal of the current analysis is that the underlying phonological form of the diminutive morpheme is a floating mora that has not been integrated into a prosodic structure, and subtraction is a way to repair the floating mora. Subtractive morphology is rare in general and challenges the item-and-arrangement approach where addition is the only way of morphological operation. Stonham (1994) argues that the cases of so-called subtractive morphology are all subject to reanalysis in support of the proposal of Combinatorial Morphology. For instance, the masculine form of French adjectives is not necessarily derived from the corresponding feminine form via segment deletion (e.g., [sɔt] ‘drunk.fem’ ~ [so] ‘drunk.masc’). In an alternative analysis, the underlying form of the base consists of a coda but it is only protected in the feminine form due to the addition of a schwa-like vowel. In contrast, the consonant is dropped to favor a coda-less syllable structure in the masculine form. To some extent, the proposal of floating mora affixation for Huozhou diminutive formation also aligns with this idea. Similar to the reanalysis of French adjectives, the diminutive form in Huozhou can also be viewed as a result of affixation involving a phonological element, which is a mora in this case. The mora affixation process would lead to segment deletion in order to meet the requirements of prosodic well-formedness.

In the framework of Optimality Theory (Prince & Smolensky 1993/2004), the idea that subtractive morphology can be reanalyzed as affixation is in line with the proposals of Trommer (2011), Bye & Svenonius (2012), Trommer & Zimmermann (2014), Zimmermann (2017), and Köhnlein (2018), among others. Although previous analyses involve different theoretical apparatuses (e.g., Colored Containment versus Correspondence Theory), the core insight is consistent; namely, subtractive morphology can emerge as a way of realizing affixal features or prosodic nodes to satisfy phonological well-formedness.⁸ Additionally, the treatment of various morphophonological patterns in Chinese dialects as the affixation of a floating mora and/or floating features has also been explored in Lin’s (1989; 1993; 2001; 2004; 2010; 2022) work.

With the underlying affixal mora being proposed, the representations of Huozhou diminutive formations are in (11). The subscript digits indicate input-output segment correspondence. Note that the alternation between [a] and [ɑ] is attributed to local assimilation in backness.

In (11), as well as in the analyses below, the phonological form of the diminutive morpheme is indicated by a mora in bold for the sake of readability. When the affixal mora is forced to be incorporated into the non-diminutive syllable, as in (11a), it triggers segment deletion (/ŋ^μ/) and vowel lengthening, as in (11b), in order to maximally preserve the floating mora and maintain a well-formed bimoraic syllable at the same time.

However, one concern regarding a synchronic analysis of diminutive subtraction pertains to its nonproductivity. Both Dressler (2000: 585) and Manova (2020: 14) mention that subtraction is cross-linguistically rare and nonproductive. Diminutive subtraction in Huozhou also seems nonproductive based on the number of subtracted forms reported in the Appendix. Nevertheless, nonproductive patterns do not necessarily indicate that subtraction is absent from synchronic grammar. In an artificial language learning experiment (Kapatsinski 2017), evidence showed that some participants can generalize and learn a subtraction rule, suggesting that the subtractive forms are computable rather than merely stored (see also Kurisu 2020). Furthermore, Jackendoff & Audring (2018: 399–400) argue that learners can learn nonproductive patterns. Learners cannot initially determine whether a given pattern is fully productive, and therefore, they may form hypotheses of rules based on all their observations. Even when the pattern is later determined to be nonproductive during the learning process, the hypotheses will not be completely removed from the brain (see also Köhnlein 2018: 623–624 for a discussion of subtractive patterns in the plural formation of German dialects). Therefore, although Huozhou diminutive subtraction may not be fully productive, it still warrants a synchronic analysis.

Before moving to the analyses, the illustration in (11) suggests that the prosodic structure of the root is established at the stage of mora affixation. Various strategies have been adopted to ensure that prosodification occurs at an earlier stage. In the current analysis, I use Stratal OT (Kiparsky 2000; 2003; 2010; 2015; Trommer 2011; Bermúdez-Otero 2018, among others) to model this layering effect. The core principle of Stratal OT is that word construction operates across multiple levels, which are organized in a feed-forward manner. Each level has its own phonological grammar, structured by a parallel ranking of constraints. Specifically, I assume the noun root has already undergone a phonological cycle for optimization and prosodification.⁹ To maintain focus and conciseness, I will not show the process of moraification in the following analyses. Instead, the input in the subsequent tableaux will contain a root with an established moraic structure, plus an affixal mora representing the diminutive morpheme, as in the structure of (11a).

3.2 Subtraction as floating mora affixation

As far as I am aware, the analysis of subtraction as mora affixation has not been explored in any non-Optimality-Theoretic ways. However, Lin’s (1993) pioneering work on Chinese morphophonology discusses a comparable case from Huojia Chinese, where segmental merger is driven by mora affixation. Lin (1993: 670–672) provides a rule-based analysis using the Affix Manifestation Principle (AMP), which states that “the effect of affixation of a phonologically expressed morpheme is always manifested” (Lin 1993: 656). Specifically, in this dialect, an affix is treated as a mora that can further be realized as a schwa ([ə^μ]). Following the requirements of the AMP and templatic constraints, the affixal mora (schwa) is incorporated into the stem and re-prosodified, resulting in the application of a segmental merger rule V₁X₂]_σ → V_1,2]_σ. An example of this derivation is as follows: /u₁n₂ + μ/ → [u₁n₂ + ə₃] → [w₁ɛ̃_2,3], where the segmental merger rule in the last step is driven by the templatic requirement of Chinese syllables (see also Lin 2022: 226–228; further discussion is in §4 of this paper).

Although mora affixation leads to segmental merger rather than subtraction in Lin’s (1993) rule-based analysis, the core insights can also be applied to the case of Huozhou diminutive subtraction. In this paper, I analyze the subtractive pattern in Huozhou as segment deletion, driven by the prosodification of the affixal mora, which is implemented in OT. Next, I will first address the analysis of segment deletion, leaving the discussion of featural changes for §3.3.

A floating prosodic unit in the input is considered marked, and the general driving force to repair such a marked structure is the constraint Headedness(μ), which is based on Headedness(X) (following Selkirk 1995).¹⁰ This constraint requires that every mora in the output be associated with segments. Additionally, MaxFloat enforces the presence of the affixal floating mora in the output (Wolf 2007). These constraints are defined in (12).

For an input such as /pʰjɑ^μŋ^μ + μ/, a straightforward way to satisfy Headedness(μ) is to dock the floating mora onto an existing segment, which would cause either vowel lengthening or gemination. Both scenarios will violate *σ_μμμ, which penalizes a super-heavy trimoraic syllable, as defined in (13a). If the floating mora is deleted to satisfy Headedness(μ), a violation of MaxFloat will be incurred. Note that MaxFloat is not equivalent to Max-μ (13b). One violation of MaxFloat entails one violation of Max-μ, but not vice versa. These constraints can drive coda deletion at the expense of Max-S (13c). A tableau is provided in (14). Tones are not marked in the analysis.

The winner (14a) realizes the floating mora by docking it onto the nucleus vowel, and the deletion of the coda in (14a) avoids a super-heavy syllable at the expense of Max-S and Max-μ, compared to (14b). The floating mora in (14c) does not dominate any segments, thus violating Headedness(μ). Finally, the candidate in (14d) fails to preserve the floating mora and is ruled out by MaxFloat. In summary, MaxFloat and Headedness(μ) drive the realization of the floating mora, while *σ_μμμ motivates coda deletion in the output. Note that the unfaithful mapping between /ɑ/ and [a] in (14a) arises from the markedness restriction that a low back vowel cooccurs only with a velar nasal or a labiovelar glide.

However, a challenge is posed by two additional candidates, [pʰjɑ^μŋ^μ] and [pʰjɑ^μŋ^μ], where the affixal mora replaces an existing mora in the input. These two candidates harmonically bound the expected winner [pʰjaː^μμ], since neither candidate violates Max-S. I propose that the candidates with mora replacement are ruled out by NoVacuousDocking(μ). This constraint is an extension of NoVacuousDocking(F) proposed by Wolf (2007), which requires that “floating features cannot dock onto segments that already bore the same feature value in the input” (Wolf 2007: 21). In terms of moras, when a floating mora replaces an existing mora in the output, it is considered vacuous. In other words, the docking of the floating mora is expected to manifest in the output structure and cause phonological consequences, which is comparable to Lin’s (1993) Affix Manifestation Principle. The proposed NoVacuousDocking(μ) is defined as follows:¹¹

With the constraint NoVacuousDocking(μ), the candidates [pʰjɑ^μŋ^μ] and [pʰjɑ^μŋ^μ] can be ruled out, as shown in (16).

The ranking established in (16) is NoVacDoc(μ) >> Max-S. The constraint NoVacDoc(μ) is violated by (16b) and (16c), where the floating mora replaces an existing mora in the input.

The constraints introduced so far can generate subtraction, and their interactions are summarized in (17). The affixal mora is forced to be realized on the surface, and the pressure of *σ_μμμ and NoVacDoc(μ) triggers segment deletion. Although there are other ways to repair a floating mora, those repair strategies can be suppressed by ranking relevant faithfulness constraints higher than Max-S and Max-μ. For example, the floating mora can also be docked on an epenthetic segment, but this will violate the higher-ranked Dep-S. The position of various faithfulness constraints determines the specific phonological instantiation of mora affixation (see §4 for additional discussion).

Although the ŋ-ending noun [pʰjɑŋ⁵³] ‘braid’ is used for demonstration above, this same analysis applies to j- and w-ending nouns as well. It is noteworthy that featural changes, such as mid-vowel raising, are regulated by a separate set of constraints, which is the focus of the following section. The current analysis centers on how mora affixation leads to segment deletion in the diminutive form.

One reviewer asks whether it is reasonable for a mora in the root (e.g., /ŋ^μ/) to delink and give way to a floating one. Additionally, deleting a mora in the root also incurs violations of Max-Link, which evaluates association lines (Morén 2001), thus suggesting the ranking MaxFloat >> Max-Link. Although the current analysis might seem counterintuitive, particularly given the ranking schema Faith_Root >> Faith_Affix (McCarthy & Prince 1994), it is not uncommon to protect and realize a floating mora by deleting others in the root. A relevant example can be found in the weight polarity of Diegueño. For instance, /saːw/ becomes [saw] to form the plural (Topintzi 2008: 512). Topintzi (2008: 512–513) treats the plural marker in Diegueño as a floating mora that is realized by the force of MaxFloat. A tableau is given in (18) to illustrate the evaluation (adapted from Topintzi 2008: 513; μ₃ is the floating mora).

Among the losing candidates, the superheavy syllable *[sa^μ1μ2μ3w] (18b) is banned by *σ_μμμ. The candidate [sa^μ1μ2w] (18c) is ruled out by MaxFloat since it does not preserve the floating mora μ₃. As for *[sa^μ1μ3w] (18d), it is ruled out by P-Dep-μ, which penalizes any non-positional μ-licensed mora in the output that does not have a correspondent in the input (Topintzi 2008: 513). Specifically, a non-positional μ-licensed mora refers to a mora that dominates a segment along with other moras, and its input correspondent must also be associated with the same segment in the output (Topintzi 2006: 85). Thus, μ₃ in *[sa^μ1μ3w] violates this requirement because it is a non-positional μ-licensed mora and does not link to /a/ in the input. However, the winner [sa^μ3w] is exempt from the evaluation of P-Dep-μ because it is a positional μ-licensed mora, i.e., the only mora that dominates the segment.¹² The core insight of the analysis is that MaxFloat provides extra protection to the floating elements, allowing them to take precedence over root faithfulness.

Furthermore, prioritizing and manifesting an affix in the output aligns with Samek-Lodovici’s (1993) Affix Realization constraint and Lin’s (1993) Affix Manifestation Principle (AMP). A well-established example of the AMP is -er suffixation in Beijing Mandarin (Lin 1989: 97–98; Lin 1993: 677, cf. Duanmu 2007: 218–221), where the -er suffix /ɹ/ leads to coda deletion (e.g., /pan + ɹ/ → [paɹ]). Thus, the example of -er suffixation in Beijing also suggests that extra faithfulness protection can be afforded to the affix, even at the cost of coda deletion in the root. The idea also applies to the Huojia case discussed in §4.

3.3 Vowel raising in subtraction

This section addresses the featural changes that occur during subtraction, in order to provide a more comprehensive analysis of the diminutive patterns and resolve the related phonological issues. The most prominent process is the change in vowel height. Some examples are repeated in (19).

There are several remarkable patterns in (19). First, the low vowel is raised only when followed by [w] (19a), compared to [aj] (19c) and [ɑŋ] (19e). Second, the low vowel followed by [w] is raised only to mid (19a), which is an instance of stepwise raising. Third, mid vowels are raised to high regardless of the following segment, as in (19b, d, f).

To account for these patterns, I propose that the raising of the nuclear vowel is attributed to the preservation of the [+high, +round] features of the deleted segment. The constraint Max(feature) governs featural correspondence and preservation (McCarthy & Prince 1995; Causley 1997; Zhang 2000). Although there have been some debates over whether Max(feature) can replace Ident-IO(feature), some studies show the utility of both types of featural faithfulness in the grammar (e.g., Walker 2001; Wolf 2007; cf. Zhang 2000).

The idea that vowel change is due to the preservation of features in [w] can be further illustrated in (21). When [w] is deleted, the [+round] and/or [+high] features are retained by Max(+round) and Max(+high), resulting in the rounding and raising of the input low vowel.

In (21a), the main motivation for vowel raising is attributed to Max(feature). However, one potential concern is that the preservation of the [+round] feature in /w/ of /tʰo^μw^μ + μ/ may seem vacuous because the main vowel already has a [+round] feature. Given feature correspondence, we may assume that the [+round] feature in /w/ (labeled as [+round]₂ in the tableau) is deleted instead of merging with the [+round] feature in /o/ (labeled as [+round]₁ in the tableau),¹³ while the output is still generated correctly. See (22) for illustration.

In (22), the pressure of Max(+round) and Max(+high) forces the output to preserve the relevant features in the input, ruling out (22b) and (22c), respectively. Subtraction is motivated by the constraints introduced in §3.1, and (22d) is ruled out by MaxFloat.

However, the issue of stepwise raising in (21b) requires additional treatment. To block raising from low to high, I employ local conjunction (e.g., Smolensky 1993; Itô & Mester 1998; Łubowicz 2002; Smolensky 2006), which has been used in the analysis of stepwise raising (e.g., Kirchner 1996; Walker 2005; 2011). Local constraint conjunction forms complex constraints from simple ones. I follow the theoretical assumptions of Itô & Mester (1998), and the conjoined constraint relevant for Huozhou is Ident-IO(high)&Ident-IO(low), as shown in (23).

If a segment in the output violates both Ident-IO(high) and Ident-IO(low), the conjoined constraint Id(high)&Id(low) (a shorthand version) will be violated. This constraint penalizes the change from a low vowel to a high vowel, which skips one intermediate height level and changes from [+low, –high] to [–low, +high]. A tableau is provided in (24).

The winner (24a) raises the input low vowel to [o], violating Max(+high) but satisfying Max(+round). Since only Ident-IO(low) is violated, the winner avoids violating the conjoined constraint. When the low vowel becomes high, as in (24b), it satisfies both Max(+high) and Max(+round) at the expense of Ident-IO(high) and Ident-IO(low), thereby triggering Id-IO(high)&Id-IO(low). Candidate (24c) fails to retain the [+round] feature in the output, fatally violating Max(+round). Finally, (24d) violates the set of constraints driving subtraction.

The evaluation indicates that low vowel raising is epiphenomenal. Max(+high) is expected to promote vowel raising, but the higher-ranked Id(high)&Id(low) blocks two-step raising of the low vowel to [u], which involves a simultaneous change of [high] and [low]. Further, Max(+round) drives the low vowel to [o] rather than [ɒ], since the low back rounded vowel [ɒ] is not permitted in Standard Chinese (Duanmu 2007, cf. Zhang 2023b), and this restriction also holds in Huozhou Chinese.

This analysis accounts for the asymmetrical pattern of vowel raising. For j-ending and ŋ-ending nouns, vowel raising from low to high is also blocked by the conjoined constraint, while Max(+round) does not motivate any epiphenomenal raising, as in (24). I assume the velar nasal is [+high, –low] (e.g., Hall 2007: 332).

With the same ranking, the grammar predicts no raising of ŋ-ending nouns (the same applies to j-ending nouns). The constraint Id-IO(high)&Id-IO(low) rules out (25c), while the winner (25a) is favored over (25b) by Ident-IO(low). As a side note, a back low vowel is penalized in an open syllable (*ɑ]_σ) as a basic phonotactic rule in Huozhou Chinese unless it is preceded by a prenuclear glide [w]. Thus, the candidate in (25a) ends with [a].

The last issue concerning the featural changes is the raising of mid vowels in j-ending and ŋ-ending nouns, including [əŋ] (/əŋ/), [wej] (/uəi/), and [ej] (/əi/), all of which become [uː] after subtraction. In brief, the case of [əŋ] aligns with the analysis above, and the change from [əŋ] to [uː] can be attributed to the preservation of [+high] in [ŋ] after subtraction (recall that in (4), [ə] is specified [+back]), as illustrated in (26). The backness of the nuclear vowel is preserved by Ident-IO(back).

For [wej], I propose that [wej] → [uː] is conditioned by both Max(+high) and local agreement. First, mid-vowel raising is motivated by Max(+high) during subtraction; then, the onglide [w] can influence the nuclear vowel through local agreement. I posit that [kʰwuː] is phonetically realized as [kʰuː]. Finally, for [ej] (/əi/), the only syllable that has diminutive forms is [pej] (/pəi/), and the output [puː] is also possibly due to consonant-vowel interactions.

3.4 Reduplication in Huozhou diminutive formation

Although this paper focuses on subtraction in Huozhou diminutive formation, reduplication is another method for forming diminutives and deserves attention. This section briefly discusses the reduplicative patterns and addresses several essential issues. A comprehensive investigation of Huozhou diminutive reduplication, especially the patterns of w-ending nouns, will be undertaken in separate work.

It has been observed that, in most cases, there are no significant semantic differences between subtraction and reduplication. However, one speaker mentioned a pair that differs in meaning. The subtracted form [muː³⁵], derived from [məŋ³⁵] ‘door’, often refers to doors of houses or rooms, whereas the reduplicated form, [məŋ³⁵.mu⁵⁵], specifically indicates the door of animal stalls (e.g., pigpen). However, this semantic difference is not prevalent in the data collected, nor has it been reported in previous literature (e.g., X.Tian 1992; Feng & Zhao 2014). Additionally, the examples in the Appendix show that some nouns have both subtracted and reduplicated forms, while others have only one form commonly used by the consultants. Although the nature of these gaps requires further investigation, the grammar should at least be able to generate both forms.

If we view subtraction and reduplication as two ways to express the same meaning, the question becomes what the underlying form would be in order to generate both forms. Reduplication is also a common method for realizing an affixal prosodic template, where the input’s empty prosodic template is populated by copying the existing segments. This idea is in line with Marantz (1982) and McCarthy & Prince (1986/1996), which is developed in Saba Kirchner’s (2010; 2013) Minimal Reduplication with a constraint-based implementation (cf. McCarthy et al. 2012). Given the current proposal that subtraction is attributed to mora affixation, I tentatively assume that reduplication and subtraction are surface variants of a single underlying form. As presented earlier, subtraction can be attributed to mora affixation, as in (27b); reduplication can serve as an alternative way to incorporate the floating mora into a prosodic structure; namely, by populating the empty template with existing segments, as in (27c).¹⁴ In other words, two nonconcatenative effects can arise from the affixal mora.

Similar to the analysis of subtraction, the constraints MaxFloat and Headedness(μ) enforce the presence and realization of the input floating mora in the output. The faithfulness constraint that penalizes reduplication is Integrity-S. Since copying segments is considered segment fission, Integrity-S is violated by multiple correspondence relations between input and output segments. The constraint is defined in (28) (after McCarthy & Prince 1995: 124), and a tableau is provided in (29).

The tableau demonstrates that reduplication can also be predicted using the same underlying form and the same set of constraints as in (14), along with Integrity. In (29a), the floating mora is populated by copying the existing segments in /pjɑ^μŋ^μ/, violating Integrity.¹⁵ By comparing the rankings in (29) and (14), it is evident that a reduplicated output can be generated by adjusting the ranking between Max (including both Max-μ and Max-S) and Integrity. Thus, the subtracted form (29b) will no longer be optimal if the Max constraints are ranked higher. In other words, with the same underlying representation, the surface form can vary depending on the ranking of specific faithfulness constraints.¹⁶ In (29), with a lower ranking of Integrity, reduplication takes precedence over segment deletion.¹⁷

Nevertheless, a critical issue is how the grammar determines whether the output is a subtracted form (29b) or a reduplicated form (29a) if a single underlying representation is assumed. I speculate that the choice between these forms could be influenced by prosodic and/or syntactic factors.¹⁸ Therefore, additional higher-ranked constraints might evaluate the prosodic context and favor one form over the other, but further investigation is needed to explore this hypothesis. It is not uncommon, however, for prosodic or syntactic factors to play a role in determining surface morphophonological patterns. A relevant example is zi affixation in the Linyi dialect of Zhongyuan Mandarin, also spoken in south Shanxi Province.¹⁹ The phonetic form of the zi affix in Linyi can be either the monosyllable [təw⁰] (“0” indicates a neutral tone) or realized as vowel lengthening, the latter of which can also be viewed as mora affixation. Based on the descriptive data in Wang (1993), the selection between these two forms is influenced by the syntactic structure, as exemplified in (30) (adapted from Wang 1993: 98). The [təw⁰] form is used when the noun serves as the object of a VP (30a), while vowel lengthening is adopted when the noun is part of a compound (30b).

For Huozhou diminutive formation, whether syntactic or prosodic factors determine the choice between subtraction and reduplication requires further investigation.²⁰ If relevant, additional markedness constraints would intervene in the current ranking and select between (29a) and (29b).

To some extent, the brief discussion on reduplication also supports an item-and-arrangement analysis for subtraction. Since both subtraction and reduplication are variations of a single morphological construction, a unified treatment of both patterns is desirable. Specifically, since various studies have successfully analyzed reduplication as the affixation of prosodic nodes (e.g., Saba Kirchner 2010; McCarthy et al. 2012), it is better to treat subtraction with the item-and-arrangement approach as well.

3.5 Summary

In sum, §3.2 demonstrates how the affixal mora is realized as subtraction under the pressure of a set of markedness constraints, including MaxFloat, Headedness(μ), *σ_μμμ and NoVacDoc(μ). Further, the patterns of vowel raising are discussed in §3.3 to provide a more comprehensive analysis. The constraint interactions from both sections are integrated and summarized in (31) (the phonotactic constraint *ɑ]_σ is omitted for conciseness). Since this paper focuses on subtraction, the issues related to reduplication in §3.4 are not included in the summary below. The ranking arguments for the constraints in §3.2 are presented in (17).