2.1. Basic patterns of Korean vowel harmony

In Korean verbal inflection, certain vowel-initial suffixes have two allomorphs, one of which has [a] as its first vowel and the other [ʌ]. The suffix-initial vowel is determined by the last vowel of the verb or adjective stem (henceforth, verbal stem).Footnote ² The initial suffix vowel is [a] if the last stem vowel is /a/ or /o/, as in (2a); otherwise, it is [ʌ], as in (2b). (The uppercase A represents the underlying form of the suffix vowel.)

The Korean vowel inventory presented in Table 2 assumes seven contrasting vowel phonemes. The vowels /a, o/, traditionally termed ‘light’ vowels, do not form a natural class, nor do the ‘dark’ vowels /i, ɨ, u, e, ʌ/.Footnote ³ Some studies propose backness as the harmonic feature (Kim Reference Kim, Kenstowicz and Kisseberth1973), while others suggest lowness (McCarthy Reference McCarthy, Richardson, Mitchell and Chukerman1983; Ahn Reference Ahn1985; Kim Reference Kim2007). However, neither [back] nor [low] distinguishes /a, o/ from other vowels (see Table 2). A number of studies adopt [±ATR] or [±RTR] (Kim Reference Kim1984; Lee Reference Lee1992; Cho Reference Cho1994; Chung Reference Chung2000; Hong Reference Hong2008; Kang Reference Kang2012). For concreteness, I will follow the latter set of studies and use [ATR] (for /i, ɨ, u, e, ʌ/) and [RTR] (for /a, o/), rather descriptively, noting that this choice remains controversial on phonetic grounds. It is beyond the scope of this article to figure out which feature best divides the two harmonic groups, and the main claim of the article about the link between alternation and phonotactics will be unaffected even if some other feature than [ATR]/[RTR] is used.

One class of verbal stems, the so-called p-irregular stems, systematically resist harmony when the last stem vowel is [RTR]. P-irregular stems are stems whose stem-final /p/ surfaces as [w] when followed by a vowel-initial suffix, as illustrated in (3) and (4). The forms with the consonant-initial suffix /-ciman/ ‘but’ show that these are stems with underlying /p/. It is shown in (3a) and (3b) that when the last stem vowel is [ATR], the suffix vowel is [ʌ], as expected. However, as (3c) and (3d) show, p-irregular stems whose last vowel is /a/ or /o/ typically take the disharmonic [ʌ] suffix forms, although the harmonic variant does arise (Hong Reference Hong2008; Kang Reference Kang2012). Exceptions to this disharmonic behaviour of p-irregular /a/- and /o/-stems are monosyllabic /o/-stems, illustrated in (4), which still take harmonic suffix allomorphs. (Monosyllabic p-irregular /a/-stems do not exist.)

In Korean verbal paradigms, /o/ and /u/ may surface as [w] when followed by vowel-initial suffixes. For instance, /po-A/ ‘to see-declarative’ can be realised as either [poa] or [pwa], and /cu-A/ ‘to give-declarative’ as either [cuʌ] or [cwʌ]. As far as p-irregular stems are concerned, it is plausible to think that [w] behaves more like the [ATR] vowel [u] at least in multisyllabic /a/- or /o/-stems, such that it is frequently followed by [ʌ]-initial suffix forms.

As mentioned in §1, vowel harmony in Contemporary Korean is arguably a case of DEE, once we set aside the special case of p-irregular stems. The harmony rule of suffix alternation has been studied extensively in the literature (Kim Reference Kim, Kenstowicz and Kisseberth1973; Kim-Renaud Reference Kim-Renaud1976; Ahn Reference Ahn1985; Cho Reference Cho1994, Reference Cho2001; Kim Reference Kim2007; Hong Reference Hong2008; Kang Reference Kang2012, among others), and harmony applies fairly regularly in alternation (although variations and exceptions exist, as will be discussed in §2.3). In stems, by contrast, disharmonic patterns are common, as illustrated by (5). An [ATR] vowel can be followed by an [RTR] vowel as in (5a)–(5c), and an [RTR] vowel may be followed by an [ATR] vowel as in (5d)–(5f).

Phonotactic generalisations in the lexicon that might reflect the harmony pattern of verbal inflection have not been studied extensively. A few studies suggest that the Korean lexicon has gradient phonotactic restrictions that reflect the harmony pattern of ideophones, another class of words in Korean in which harmony is observed (Hong Reference Hong2010; Park Reference Park2020). However, the grouping of harmonic vowels in ideophones is different from that of verbal inflections (see Hong Reference Hong2010 and Jun Reference Jun and Aronoff2018 for details; see also Nuckolls et al. Reference Nuckolls, Nielsen, Stanley and Hopper2016 and the references therein for studies on many other languages whose ideophonic stratum shows distinct phonology from other strata in the lexicon). The present study aims to investigate the vowel co-occurrence restrictions in the lexicon that directly reflect the harmony pattern of verbal inflection, following the research program of Chong (Reference Chong2019) (see §4).

2.2. Productive harmony in Middle Korean

For purposes of documenting gradual retreat of the harmony, it is useful to review vowel harmony in Middle Korean. The discussion of this section follows Kim (Reference Kim1978), Ko (Reference Ko2018), Lee (Reference Lee1947) and Lee (Reference Lee1998) among others. In Middle Korean, the ancestor of the present-day Korean spoken from the 10th century to the 16th century, the vowel system was symmetrical with regard to the number of vowels in each harmony group; the alternating vowel pairs were [a]\textasciitilde[ʌ], [ə]\textasciitilde[ɨ] and [o]\textasciitilde[u], while [i] was neutral. The vowels [a], [ə] and [o] were the ‘light’ vowels, and [ʌ], [ɨ] and [u] were the ‘dark’ vowels. Vowel harmony in Middle Korean was far more productive than Contemporary Korean and applied in broader morphological and phonological environments, although it was not without exceptions (see Han Reference Han1996 and Park Reference Park2016 for a quantitative analysis of the decline of harmony). First, whereas vowel harmony in Contemporary Korean applies only across a verbal stem and a suffix, it was obeyed even within (native) roots in Middle Korean, as shown in (6). A root consisted of vowels from the same harmonic group, with the possible addition of the neutral [i]. Note that the Contemporary Korean forms of each root in (6) contain vowels from the different harmonic groups.

Moreover, while [a]/[ʌ]-initial suffixes are the only ones eligible for harmony in Contemporary Korean, suffixes that began with other vowels also participated in harmony in Middle Korean, as illustrated in (7). For example, [o]-initial suffixes alternated with [u]-initial ones, as shown in (7a). The accusative marker (which has the invariant form [-ɨl] in Contemporary Korean) alternated between [-əl] and [-ɨl], as in (7c).

Even the p-irregular /a/- and /o/-stems, which frequently take disharmonic [ʌ]-initial forms in Contemporary Korean, were followed by the [a]-initial suffix forms in Middle Korean, as illustrated in (8).

However, a number of diachronic changes led to the disruption of the vowel harmony system, including vowel loss and the adoption of Sino-Korean words. Breakdown of the harmony system is most attributed to loss of [ə] (resulting from a vowel-shift-like process, not detailed here), which was replaced with [ɨ] in non-initial syllables and with [a] in initial syllables. Let us take [kaɨl] ‘autumn’ in (6e) as an example. The 16th century form of this word was [kəəl]. In the 17th century, the second [ə] was replaced with [ɨ], giving rise to [kəɨl]. In the 18th century, [ə] in the initial syllable was transformed into [a], hence the present form [kaɨl]. Crucially, the change from [ə] to [ɨ] disrupted the harmony, since the two vowels belonged to different harmony groups. In addition, a significant amount of Sino-Korean vocabulary, which did not conform to the harmony, was brought into Korean over the period of Middle Korean. This is illustrated by the Sino-Korean words like [sonjʌ] ‘girl’ which contains two disharmonic vowels. As a result, Korean became abundant with forms that did not follow the harmony.

For these reasons, the vowel harmony that was once productive in Middle Korean now applies in limited contexts in Contemporary Korean. Harmony is not fully active within morphemes, and the only affixes that harmonise are those that begin with [a]/[ʌ], which all happen to be verb suffixes. From the viewpoint of Chong (Reference Chong2019), we could also say that the harmony in alternation was productive in Middle Korean because it had phonotactic support in the lexicon. After a number of changes, the phonotactic harmony was disrupted while still leaving some of the alternation behind.

2.3. Limited productivity of harmony in Contemporary Korean

Several characteristics of Korean vowel harmony of the present day converge to demonstrate its limited productivity. First, it is limited to [a]/[ʌ]-initial affixes. Strikingly, the process is not iterative – it fails to self-feed – so that the harmony does not apply to the second vowel of the suffix in [pat-asʌ] ‘receive-because’ (2a-i) and [mantɨl-ʌla] ‘make-imper’ (2b-iv); if it applied iteratively, we would expect *[pat-asa] and *[mantɨl-ʌlʌ], respectively. The latter of these examples also shows that only the last stem vowel can be the trigger; other vowels in the stem do not affect harmony.

Moreover, there is indication that the harmony is receding. When the last stem vowel is [RTR], variation is shown in the selection of the suffix vowel; that is, the disharmonic [ʌ] suffix allomorph is often observed, as shown in (9). Considering that [ʌ] shows a wider distribution than [a], and that suffixes surface with [ʌ] when not eligible for harmony (e.g., the second suffix in /pat-As*-A/ ‘receive-past-decl’, which is not subject to harmony, surfaces as [ʌ], as in [pat-as*-ʌ], cf. *[pat-as*-a]), it is plausible to think of the default as [ʌ], so that the variation represents regularisation to the default.Footnote ⁴

When the stem vowel is [ATR], only the expected [ʌ]-initial forms are observed (i.e., a perfect harmony).

In judgement surveys in which younger and older speakers’ well-formedness ratings were compared (Kang Reference Kang2012, Reference Kang2016), it was found that younger speakers were more flexible in allowing variation compared to older speakers, also suggesting a loss of productivity over time. In addition, Jo (Reference Jo2020) reports that the disharmonic forms are more frequently observed in the spoken corpus than the newspaper corpus; given that innovative forms arise first in more casual and vernacular styles of speech (Labov Reference Labov1966, Reference Labov1972), the finding suggests that Korean vowel harmony is following the typical stages of rule loss.

Furthermore, the harmony pattern is not fully reproduced in wug tests reported in previous studies (discussed in detail in §6). Kang (Reference Kang2012) conducted a production experiment using real and nonce stems to test the speakers’ intuition on the harmony pattern. When the last stem vowel was /a/ or /o/, the proportion of harmonic suffix forms was only 32.0% for nonce stems, as compared to 76.7% for real stems. The result is striking in that the dominant pattern in the speakers’ response for wug words was the disharmonic one.

One reason for the loss of productivity would be, as discussed in §2.1, that there is no single phonetically transparent feature that governs the harmony.Footnote ⁵ The present study suggests yet another cause of the decreasing productivity: stem phonotactics matches the alternation pattern only weakly. Looking ahead, the corpus study presented in §3 also provides evidence that the harmony rule has begun to break down in specific phonological and morphological contexts, and an examination of gradient vowel co-occurrence restrictions in the lexicon in §4 suggests that the rule breakdown tends to be more pronounced in contexts for which there is weak phonotactic support.

3.1. The factors influencing variation

The variable harmony of /a/-stems and /o/-stems is conditioned by various phonological and morphological factors. This section focuses on four factors, namely the effect of suffix type, stem vowel quality, the number of intervening consonants between the two vowels and stem type. A subset of these factors were already investigated using the spoken data of the Sejong text corpus in Hong (Reference Hong2008). He reported that p-irregular stems generally prefer disharmonic suffix forms and that regular stems show variation when (i) the last stem vowel is /a/ and (ii) the stem ends in a consonant. In this section, I additionally show that those two effects that emerged in regular stems are strongest for the /-A/ ‘decl’ suffix. I eventually aim to test, in §4, whether these effects are phonotactically motivated.

I first calculated harmony rate for each word by dividing the number of tokens in which the stem took a harmonic suffix by the total number of tokens employing either of the suffix allomorphs. For instance, if the word /pat-A/ ‘receive-decl’ appears 51 times as [pat-a] and 152 times as [pat-ʌ], its harmony rate was calculated as $51/(51+152) = 25.1\%$ . Then I calculated the average harmony rate of words that belong to each category of interest. To illustrate, if there were three words in the corpus that have /a/ as the last stem vowel and /-A/ ‘decl’ as the suffix (e.g., /pat-A/), whose harmony rate is 25%, 50% and 100%, respectively, the mean harmony rate for words that have /a/ stem vowel and /-A/ ‘decl’ would be $(25+50+100)/3 = 58.3\%$ .

A logistic regression analysis was conducted to statistically test the effects of the four factors mentioned above. The results are provided in §3.2.

3.1.1. The /-A/ ‘decl’ suffix discourages harmony

It has been noted in Kang (Reference Kang2012) that the proportion of the [ʌ]-initial forms is the highest for the /-A/ ‘decl’ suffix. The representative data are in (11). While /-A/ ‘decl’ frequently surfaces with the disharmonic vowel (11a–11c), other suffixes show little variation, as shown in (11d–11f). Interestingly, we can see in (11c) and (11f) that although /-A/ ‘decl’ and the connective suffix are phonologically the same, only the former is subject to variation, suggesting that it is the morphological identity of /-A/ ‘decl’ that lowers the harmony rate, rather than its phonological characteristics.

• 

The effect of suffix type on the harmony in the current data is shown in Figure 1. The numbers at the top of each bar indicate the number of words that belong to each category. Confirming the finding of Kang (Reference Kang2012), the average harmony rate of words with the /-A/ ‘decl’ suffix is substantially lower (43.9%) compared to that of other suffixes aggregated (93.2%). Considering that /-A/ ‘decl’ represents casual and vernacular styles of speech, as mentioned earlier, we can say that the innovative disharmonic forms are more frequently observed in informal speech. The finding suggests another piece of evidence showing that Korean vowel harmony is retreating, beginning from the more informal register, as is typical of a receding rule (Labov Reference Labov1966, Reference Labov1972).

Figure 1 The effect of suffix type. Numbers at the top of each bar indicate the number of words in that category.

I further show below that /-A/ ‘decl’ and the other suffixes behave differently with respect to some phonological factors that modulate the harmony. I present the results by dividing the data into two parts – declarative and non-declarative – based on the suffix type.

3.1.2. /o/ is a stronger trigger than /a/

The quality of the last stem vowel conditions the harmonic pattern (Kim-Renaud Reference Kim-Renaud1976; Cho Reference Cho1994; Hong Reference Hong2008; Kang Reference Kang2012), illustrated in (12). If the last vowel of the stem is /a/, and the stem ends in a consonant, as in (12a–12c), both the harmonic [a]-initial forms and the disharmonic [ʌ]-initial forms can surface. In comparison, /o/ stem vowel is more likely than /a/ to take the harmonic suffix forms, as illustrated in (12d–12f).Footnote ⁷

• 

This trigger vowel effect is confirmed in the current data, but in a way that interacts with the suffix type (declarative, non-declarative) and the stem type (regular, p-irregular). As shown in Figure 2, /o/-stems, represented by the right-hand bar in each pair, exhibit categorical harmony unless they are p-irregular (in both the declarative and the non-declarative). In the declarative, /o/-stems showed a higher rate of harmony than /a/-stems regardless of the stem type. In the non-declarative, this trigger vowel effect is observed in the p-irregular stems, and the regular stems exhibited a ceiling effect in which both /a/-stems and /o/-stems had a 100% harmony rate. Regarding the stem type effect, which will be discussed further in §3.1.3, p-irregular stems had a lower harmony rate than regular stems (e.g., Hong Reference Hong2008; Kang Reference Kang2012).

Figure 2 The effect of stem vowel. Numbers at the top of each bar indicate the number of words in that category.

In sum, /o/-stems show a higher rate of harmony than /a/-stems in the suffix alternation, confirming the findings of previous studies, but the difference between /a/ and /o/ was only observed in the declarative data and in the p-irregulars of the non-declarative data. In §4, I examine the possibility that this trigger vowel effect is motivated by phonotactic patterns in the lexicon.

3.1.3. Hiatus encourages harmony, p-irregular stems discourage it

It has been reported that the variation arises only when the /a/-stems end in a consonant (Cho Reference Cho1994; Kang Reference Kang2012). As (13) shows, if there is no intervening consonant between the last stem vowel and the suffix-initial vowel in the surface form (i.e., hiatus context), only the harmonic [a]-initial form is possible. (13b) and (13c) show that whether there is an intervening consonant or not should be evaluated at the surface level. When the stem-final /h/ deletes (due to an independent deletion process) to create a hiatus context in the surface form, only the harmonic form is possible.

• 

If this hiatus effect is present in the current data, we expect to see variation only in the non-hiatus context, or at least observe that the harmony rate is higher in the hiatus context. Crucially, it is necessary to test if the apparent hiatus effect is an artefact of the stem type effect, since all the p-irregular stems, which are reported to resist harmony, are in the non-hiatus due to the [w] (i.e., /p/) that intervenes between the two vowels. Figure 3 shows that the hiatus effect emerged in the declarative data, even in regular stems, suggesting that the hiatus effect is observed independent of the stem type effect.Footnote ⁸ As we already saw in §3.1.2, the regular stems in the non-declarative data show a categorical harmony. Based on the findings of §3.1.2 and this section, we can say that the difference in the harmony rate between the declarative and the non-declarative (see Figure 1) is largely driven by regular /a/-stems with at least one intervening consonant between the stem vowel and the suffix vowel.Footnote ⁹

Figure 3 The effect of number of intervening consonants and the stem type. Numbers at the top of each bar indicate the number of words in that category.

The effect of p-irregular stems and its interaction with the stem length confirmed findings of previous studies, summarised in (3) and (4). Figure 3 shows that the p-irregular stems were more disharmonic than regular stems, in both the declarative and the non-declarative data. Although not separately presented in Figure 3, it was confirmed that monosyllabic /o/-stems showed categorical harmony.

To sum up, the findings are in line with those of previous studies in that harmony was encouraged when the stem vowel and the suffix vowel are adjacent to each other, and that p-irregular stems discouraged harmony. The hiatus effect was only observed in the declarative data, while the stem type effect was observed in both the declarative and the non-declarative data. In §4, I test the hypothesis that the hiatus effect and the stem type effect have phonotactic grounds in the lexicon.

3.2. Statistical testing of conditioning factors in alternation

In order to test whether the generalisations described so far are statistically valid, I ran a Bayesian logistic regression model. The dependent variable was the suffix form, which was binary-coded with harmonic [a] or disharmonic [ʌ] (baseline). Independent variables are presented in (14). All the predictor variables were sum-coded, which means that the reference level (underlined) is coded as $-1$ and the other value is coded as $+1$ . In addition to these predictors, random intercepts for word and speaker were also included.

The model was fit using the brms package (Bürkner Reference Bürkner2017, Reference Bürkner2018, Reference Bürkner2021) in R (R Core Team 2018). A total of 10,000 samples were drawn in each of four chains from the posterior distribution over parameter values. The first 1,000 samples were discarded for warm-up. A weakly informative Student-t prior with 5 degrees of freedom was used for the intercept and all coefficients, following recommendations of Ghosh et al. (Reference Ghosh, Li and Mitra2018) for Bayesian logistic regression. There were no divergent transitions. The R-hat value was 1 for all parameters presented in Table 3, indicating that the model has converged. More details about the model, including a sensitivity analysis, are available on the following OSF page: https://osf.io/tjcqr/?view_only=9e6077702ee44344b449459c9a415f14. The sensitivity analysis suggested that the choice of priors does not substantially affect the posterior estimates.

Table 3 presents coefficient estimates along with their 95% Credible Interval (CrI) for each independent variable. In Bayesian analyses, 95% CrI is the range within which we can be 95% certain that the true value of a parameter lies (see Nicenboim & Vasishth Reference Nicenboim and Vasishth2016; Vasishth et al. Reference Vasishth, Nicenboim, Beckman, Li and Kong2018 for interpretation of CrI and a general introduction to the Bayesian framework). When the CrI included zero, I also report the probability of an effect in the direction of the sign of the coefficient (p-direction; the proportion of the posterior distribution of the coefficient values that is of the median’s sign). This value typically ranges between 50%, that is, the posterior distribution is centred around zero (indicating no evidence for an effect of either direction), and 100%, that is, the whole posterior distribution lies to either positive or negative side (indicating strong evidence for an effect in that direction).

Table 3 Results for the logistic regression analysis: harmony in suffix alternation.

First, the negative coefficient for suffix type suggests that the declarative portion of the data had a lower harmony rate than the non-declarative data. The 95% CrI included zero, and the p-direction was 87.4%, indicating that the declarative suffix is probably associated with less harmony. The coefficient for stem vowel was positive with 95% CrI not including zero, so we can be confident that harmony was encouraged for /o/-stems. The positive coefficient for num C indicates that the hiatus context is associated with increased harmony. The 95% CrI did not include zero, so we can be confident about the effect of the number of intervening consonants. The analysis also confirmed that the trigger vowel effect was stronger in the declarative data, compared to the non-declarative data, represented by the positive coefficient of the suffix type (Declarative) : stem vowel (/o/), whose 95% CrI did not include zero. For the positive coefficient for suffix type (Declarative) : num C (0), 95% CrI included zero and the p-direction was 89.5%, suggesting that the hiatus effect is likely to be stronger in the declarative data. The negative coefficient for stem type suggests that p-irregular stems resisted harmony; the 95% CrI included zero, but the p-direction of 96.6% indicates that p-irregular stems are likely to be associated with less harmony. The positive coefficient for stem length, whose 95% CrI did not include zero, indicates that monosyllabic stems are more harmonic than multisyllabic stems. Last, consistent with previous studies (see (4)), the interaction between stem type and stem length had a positive coefficient and the 95% CrI did not include zero, confirming that despite the tendency of p-irregular stems to discourage harmony, monosyllabic p-irregular stems still had a high harmony rate.

To sum up the results of the corpus study for suffix alternation, harmony is retreating in particular phonological and morphological contexts, while others are more resistant to rule breakdown. The non-declarative portion of the corpus exhibited a higher harmony rate than the declarative data, suggesting that the vowel harmony is observed less strictly for the /-A/ ‘decl’ suffix. Further, the trigger vowel effect whereby the suffix vowel was more likely to be harmonic for /o/-stems was stronger in the declarative data. The hiatus effect was observed, with moderate statistical evidence suggesting that the effect was stronger in the declarative data. It thus seems that the /-A/ ‘decl’ suffix is leading the breakdown of the harmony process, first in the /a/-stems and in non-hiatus contexts. The stem type effect (i.e., p-irregular stems discourage harmony) is robust, confirming findings of the previous studies.

In the next section, I first investigate whether vowels in the lexicon show a tendency to harmonise at all, in order to explore the possibility that the loss of productivity in alternation may be attributed to lack of matching phonotactic generalisations. Then I assess whether the phonotactic harmony, if any, is modulated by three factors, that is, the trigger vowel, the number of intervening consonants and the type of intervening consonant ([w] vs. non-[w]) that is analogous to the effect of stem type in suffix alternation. By testing whether the alternation and the phonotactic harmony are regulated by the same factors, I aim to investigate the link between alternation and phonotactics at a more detailed level. If the two types of generalisations are closely related, the conditioning effects that are observed robustly in alternation are expected to have a strong phonotactic support; conversely, the relatively weak effects are expected to have feeble phonotactic support.

4.1. Gradient harmony in phonotactics

As a first step towards comparing phonotactic patterns against alternation patterns, I examined how V₂ is realised depending on the [ATR]/[RTR] specification of V₁. For phonotactic data, I first consider all seven vowels as candidates for V₂. If the tendency for harmony is present in the lexicon, it is expected that the proportion of [RTR] in V₂ will be higher after [RTR] V₁ than after [ATR] V₁. Figure 4 compares the proportion of [RTR] in V₂ in the two sets of alternation data (declarative and non-declarative) with the two sets of phonotactic data (all stems and verb stems). For the alternation data, V₁ corresponds to the last stem vowel and V₂ to the suffix-initial vowel, and the [RTR] V₂ is [a]. As mentioned in §3, when the last stem vowel is [ATR], the suffix vowel shows categorical harmony; for both the declarative and the non-declarative portion of the alternation data, the proportion of [RTR]/[a] in V₂ is shown to be near zero, meaning that the proportion of [ATR]/[ʌ] is near 100%. The grey bars for these two datasets, for which the stem vowel was either /a/ or /o/, were already presented in Figure 1. The alternation data, then, show a huge discrepancy in the proportion of [a] in V₂ between [ATR] and [RTR] V₁, confirming the harmony in suffix vowels.

Figure 4 The percentage of [RTR] in V₂ in alternation and phonotactics. Numbers at the top of each bar indicate the number of V₁C₀V₂ sequences in that category.

In the phonotactic data, the tendency towards harmony is at best moderate. In the all-stems data, it can be seen that the proportion of [RTR] in V₂ is only slightly higher when preceded by [RTR] vowels, compared to when preceded by [ATR] vowels. In other words, [ATR] V₁ and [RTR] V₁ do not differ in their probability of being followed by [RTR] V₂. In the verb-stems data, we see that [RTR] V₁ is more likely than [ATR] V₁ to be followed by an [RTR] V₂, suggesting phonotactic harmony. This confirms the hypothesis laid out earlier that phonotactic harmony, if any, may be stronger in the verb stems than other parts of the lexicon. However, the harmony shown in the verb-stems data is still weaker than that of the alternation data. Whereas the suffix vowel is rarely realised as [RTR]/[a] when the stem vowel is [ATR], V₂ is realised as [RTR] to a fair degree after [ATR] V₁ in verbal stems. In short, when all the seven vowels are considered for the V₂, the harmony is nearly absent in the all-stems data, and is observed in the verb-stems data to some degree.

Could it be that the harmony in the lexicon looks feeble because the alternation data and the phonotactic data are not perfectly parallel, that is, all seven vowels are considered as candidates for V₂ in the phonotactic data, whereas [a] and [ʌ] are the only vowels that participate in the alternation harmony? In what follows, I only included [a] and [ʌ] as V₂ in the phonotactic data, trying to allow maximum room for phonotactics to match the alternation.

For phonotactic data that have only [a] and [ʌ] as V₂, simply speaking, if there is no harmony at all, we would expect to see 50% [a] in V₂ (i.e., chance level) both after [ATR] V₁ and [RTR] V₁. It can be seen in Figure 5 that for both sets of phonotactic data, the proportion of [a] in V₂ is higher when preceded by [RTR] vowels, suggesting a tendency towards harmony. However, it is not as strong as what is found in alternation. In the all-stems data, the proportion of [a] in V₂ is around 50% when V₁ is [ATR], contrasting with the near 0% in the same context in the two sets of alternation data. The proportion of [a] in V₂ after [RTR] V₁ (which can be said to be intermediate, in the sense that it is higher than the declarative data but lower than the non-declarative data) is slightly higher compared to [ATR] V₁, suggesting that there is a weak tendency for V₂ to harmonise with V₁. Overall, the strength of harmony, as may be indicated by the difference in the proportion of [a] in V₂ between [ATR] V₁ and [RTR] V₁, is much weaker in the all-stems data than in the alternation data. Such difference between alternation and phonotactics is statistically supported (see the regression analysis in §4.2.)

Figure 5 The percentage of [a] forms in V₂ in alternation and phonotactics. Numbers at the top of each bar indicate the number of V₁C₀V₂ sequences in that category.

In the verb-stems data, we again find a stronger harmony than the all-stems data, indicated by the larger gap between [ATR] V₁ and [RTR] V₁. However, the harmony shown in the verb-stems data is still weaker than that seen in the alternation data. Whereas the proportion of [a] in V₂ after [ATR] V₁ is (near-)zero in the alternation data, V₂ following [ATR] V₁ is realised as [a] 34.9% of the time in verbal stems. Similar to the all-stems data, the proportion of [a] in V₂ after [RTR] V₁ was intermediate between the declarative data and the non-declarative data. The harmony in the verb-stems data, then, is stronger than the all-stems data, but still not as robust as in the alternation data, even when the phonotactic data was given its best possible chance to match the alternation data.

In sum, an investigation of phonotactic data revealed that the Korean lexicon shows at least a tendency towards harmony. Comparing alternation and stem phonotactics, however, the harmony is stronger in alternation. Within phonotactics, verbal stems show a stronger harmony than the entire lexicon. We can thus say that the harmony has varying strengths in different parts of the language. In the broader context of the link between phonotactics and alternation, we can infer that the harmony in suffix alternation is losing its productivity because it is only weakly supported by the lexicon.

4.2. Statistical testing of harmony in alternation vs. phonotactics

To assess the amount of credence we should give to the data patterns observed above, a Bayesian logistic regression analysis was implemented, with the alternation data and the smaller version of the phonotactic data (only [a] and [ʌ] considered for V₂). The dependent variable was binary-coded V₂, [a] vs. [ʌ] (baseline). The model included two independent variables, both of which were dummy-coded. The first was data with four levels, declarative (baseline), non-declarative, all stems and verb stems. The other independent variable was V₁ feature with two levels, ATR (baseline) and RTR. Crucially, interaction terms between data and V₁ feature were included to test whether the effect of V₁ feature on the realisation of V₂ is stronger in the declarative compared to the phonotactic data. Specifics of the model implementation are the same as those of §3.2 such as the number of samples and the priors. There were no divergent transitions. All parameters had an R-hat value of 1, suggesting model convergence. A sensitivity analysis showed that the posterior distribution of the parameters is not substantially aff ected by the prior specification. More details of the model can be found on the following OSF page, inc luding the sensitivity analysis: https://osf.io/tjcqr/?view_only=9e6077702ee44344b449459c9a415f14.

The results of the analysis are provided in Table 4. As expected, the coefficient of V₁ feature was positive and the 95% CrI did not include zero, indicating that V₂ is more likely to be [a] in V₁=[RTR] context compared to V₁=[ATR], when the data are declarative (i.e., the baseline level of data). Importantly, the interaction between data (All Stems) and V₁ feature (RTR) had a negative coefficient, with the 95% CrI below zero, indicating that an [RTR] V₁ enhanced the proportion of [a] in V₂ to a greater degree in the declarative data relative to the all-stems data. Similarly, the interaction between data (Verb stems) and V₁ feature (RTR) also had a negative coefficient and the 95% CrI below zero, suggesting that the effect of V₁ feature was stronger in the declarative data compared to the verb-stems data. Finally, the interaction between data (Non-declarative) and V₁ feature (RTR) had a positive coefficient and 95% CrI above zero, confirming that the effect of V₁ feature is stronger in the non-declarative compared to the declarative.

Table 4 Results for the logistic regression analysis: harmony in alternation vs. phonotactics.

In sum, a comparison between alternation and stem phonotactics revealed that although tendency to harmonise is observed in both, it is more robust in alternation, specifically in suffixes other than the /-A/ ‘decl’. Therefore, we can conclude that the harmony shown in alternation is partly supported by phonotactics in the lexicon. In the following section, I investigate whether the trigger vowel effect, the hiatus effect and the effect of intervening consonant (analogous to the stem type effect in alternation; see below) are present in the lexicon by comparing the two sets of phonotactic data against the alternation data.

4.3. Trigger vowel effect in the lexicon

Recall from §3.1.2 that /o/ is a stronger trigger than /a/ in the suffix alternation (also presented in Figure 6, with all categories aggregated). Such a trigger vowel effect was rarely observed in the two sets of phonotactic data; Figure 6 demonstrates that the proportion of [a] in V₂ was very similar whether V₁ was [a] or [o]. Therefore, the effect of trigger vowel in alternation is not supported by generalisations in the lexicon, indicating a mismatch between alternation and phonotactics. In §5, I statistically test whether there is really no difference between V₁=[a] and V₁=[o] as a harmony trigger in the lexicon, because it is possible that [a] and [o] are skewed with respect to some other factors that affect the harmony.

Figure 6 The trigger vowel effect in alternation and phonotactics, in which V₁ (or stem vowel) = [a, o], V₂ (or suffix vowel) = [a, ʌ]. Numbers at the top of each bar indicate the number of V₁C₀V₂ sequences in that category.

4.4. The effect of intervening consonants in the lexicon

I then examined whether the hiatus effect and the stem type effect observed in the alternation have phonotactic support. For the latter, once we set aside the special case of the monosyllabic /o/-stems that always conform to harmony (see (4)),Footnote ¹⁰ a matching phonotactic pattern for the general tendency of p-irregular stems to take the disharmonic [ʌ]-initial suffix forms (e.g., [komaw-ʌ] ’to be thankful-decl’) rather than [a]-initial forms (e.g., [komaw-a]) would be that [wa] is dispreferred in the lexicon; that is, [w] would be followed by [a] less frequently than non-[w] consonants are.

It is necessary to tease apart the effect of an intervening [w] from the effect of the number of intervening consonants, because it is possible that the lower harmony rate in the non-hiatus context in the lexicon, if any, might be solely driven by the (potential) effect of [w] in lowering the proportion of [a] in V₂. Figure 7 thus compares three categories, namely [w], other C(s) and hiatus, in which ‘other C(s)’ represents one or more non-[w] consonants between the vowels. The three-way contrast made here is analogous to that of Figure 3 (recall that words with a p-irregular stem are always in the non-hiatus category, due to the intervening [w] between the stem vowel and the suffix vowel that is derived from the stem-final /p/.) The [w] category in the alternation data in Figure 7 represents p-irregular verbs.

Figure 7 The effect of intervening consonants in alternation and phonotactics, in which V₁ (or stem vowel) = [a, o], V₂ (or suffix vowel) = [a, ʌ]. Numbers at the top of each bar indicate the number of V₁C₀V₂ sequences in that category.

A comparison between ‘other C(s)’ and ‘hiatus’ reveals that the hiatus effect is weakly observed in the all-stems data, and a bit more clearly in the verb-stems data. This finding indicates that there is a hiatus effect that is independent of the [w] effect. In a more rigorous test of the conditioning effects in the lexicon using a Maximum Entropy grammar learner (see §5), it was found that the hiatus effect is present in both the all-stems and the verb-stems data when all other irrelevant factors are controlled for, despite the small difference between ‘other C(s)’ and ‘hiatus’ in the all-stems data shown in Figure 7. Thus, one can say that the hiatus effect in the suffix alternation, presented earlier in Figure 3 and again in Figure 7 with all categories aggregated, has a matching phonotactic generalisation.

Comparing ‘[w]’ and ‘other C(s)’, we see that the effect of intervening [w] in discouraging harmony is clear in the alternation data (as we already saw in Figure 3) and in the two sets of phonotactic data. Then, regardless of the type of data, [a] is disfavoured after [w], compared to after non-[w] consonants. Therefore, the behaviour of p-irregular stems dispreferring [a]-initial suffix forms align with the gradient phonotactic constraint that disprefers [wa] in the lexicon. One caveat is that only a small number of stems in the phonotactic data had [w] as the intervening consonant, especially in the verb-stems data, where only seven stems were found for the category [w]. This might explain why the observed tendency of [w] to discourage harmony is not reliably supported by the statistical testing, as will be reported shortly.

5.1. Maximum Entropy grammar

The variable harmony of the suffix alternation and of the lexicon was analyzed within the framework of Maximum Entropy (MaxEnt) grammar (Smolensky Reference Smolensky, Rumelhart and McClelland1986; Goldwater & Johnson Reference Goldwater and Johnson2003) in order to formalize the harmony and to statistically test whether the same factors that condition the alternation harmony also modulate the phonotactic harmony. In phonological variation, a MaxEnt grammar can model statistical tendencies observed in a variable pattern by assigning numerical weights to Optimality-Theoretic (OT) constraints, each of which encodes some factor that regulates the variation. The weights are calculated to maximise the probability of the observed frequencies in the data. For phonotactic data, specifically, I adopted a MaxEnt theory of phonotactics proposed in Hayes & Wilson (Reference Hayes and Wilson2008).

A conditioning factor of the variable harmony was regarded as having a significant effect when the relevant constraint was assigned a non-zero (positive) weight and determined to significantly improve the model fit to the data. To find the constraints that significantly improve the model fit, I first constructed models with all possible combinations of constraints. For instance, there are four test constraints in the alternation learning (see (15)), and each constraint can either be included in the model or excluded, resulting in 16 ( $= 2^4$ ) models that differ in the set of test constraints they include. Then I selected the model with the lowest Akaike Information Criterion (AIC), a measure that takes into account both the goodness of the fit to the data and the simplicity of the model (i.e., the number of free parameters). Constraints included in this minimal adequate model were considered to significantly improve the model performance.

All the learning simulations were conducted in maxent.ot package in R (Mayer et al. Reference Mayer, Tan and Zuraw2022). For all constraints, the default or expected weight μ was set at 0, meaning that no prior bias was given to the weights, and σ was assigned a large value of 100,000, meaning that the constraint weights are allowed to deviate from the default weight with little penalty. The upper bound of each weight was set at 50. The materials for the learning simulation can be obtained from the OSF page https://osf.io/tjcqr/?view_only=9e6077702ee44344b449459c9a415f14.

5.2. Learning data

The corpus frequencies reported above in §§3 and 4 were used as learning data. For the alternation learning, there were a total of 12 types of input forms for [RTR] stem vowels, resulting from all possible combinations of the conditioning factors, that is, suffix type (/-A/ ‘decl’ vs. other suffixes), stem vowel (/a/ vs. /o/), the number of intervening consonants (0 vs. 1 or more) and the stem type (regular vs. p-irregular). The observed frequencies of a single input type fed to the model was split based on the ratio between the harmonic and disharmonic forms. Let us take as an example the input type with the /-A/ ‘decl’ suffix, stem vowel /a/, one or more consonants and a regular stem. There were 38 such words in the corpus, and the average harmony rate of these words was 0.29; thus, the frequency for the harmonic form was entered as $38 \times 0.29=11.02$ , and that of the disharmonic form as $38 \times 0.71=26.98$ . For [ATR] stem vowels, which exhibited a categorical harmony regardless of the phonological (e.g., stem vowel type) or morphological (e.g., suffix type) environments, there was only one input type with two outcomes [a] and [ʌ], that is, the input type was not divided into subtypes according to the properties of the word.

The phonotactic learning data included stems that have V₁ as any of the seven vowels, and V₂ as either [a] or [ʌ]. I performed two separate sets of learning simulations: one for the all-stems data and the other for the verb-stems data. The learning data consisted of 42 types of V₁C₀V₂ sequences, that is, all possible combinations of V₁, V₂, the number of intervening consonants (0 vs. 1 or more) and the type of consonant ([w] vs. others).

5.3. Constraint set

The constraints included in the alternation modelling are presented in (15). There were two types of constraints: baseline constraints and test constraints. The test constraints were those listed in (15b), each of which accounts for some factor that affects the harmony, and the primary goal of the modelling was to test whether each can explain a significant amount of variance in the harmony. The baseline constraints, shown in (15a), explain the general tendency to harmonise. When these baseline constraints are included in the model, we are able to assess the explanatory power of the test constraints above and beyond the general harmony, and test whether the harmony is especially encouraged in specific contexts. The baseline constraints were included in every model that was compared against each other (following the model comparison method explained in §5.1); it is only the test constraints that were tested for their significance in improving the model.

Two things should be noted about the constraints in (15). First, they are in large part segment-based. That is, rather than defining Agree as ‘An [RTR] vowel is followed by an [RTR] vowel, and an [ATR] vowel is followed by an [ATR] vowel’, I defined it as ‘An [RTR] vowel is followed by [a], and an [ATR] vowel is followed by [ʌ]’. These more specific, segmental constraints align better with the unique properties of the Korean vowel harmony, in which only two vowels participate, although their definitions may seem somewhat ad hoc. The same constraints are used in the phonotactic learning as well (see (16)). Given the analytic choice made in §4 that the phonotactic data including only [a] and [ʌ] in V₂ should be used to be compared against the alternation, employing the segment-based constraints makes more sense in this regard, too.

Second, the constraints are rather descriptive. Notably, the constraint in (15b-iv) explains the effect of stem type by militating against [RTR][wa] sequence, with an additional note that this constraint penalises only those cases in which [w] is derived from /p/ (of a p-irregular stem). Previous studies have employed different mechanisms within the framework of OT to account for the effect of p-irregular stems (e.g., cophonology in Kang Reference Kang2012; lexically indexed constraints in Hong Reference Hong2008). In the current discussion, I abstract away from choosing the exact formalisation of the phenomenon and introduce a rather ad hoc constraint *[RTR][wa]. One advantage of employing this constraint is that the same constraint can be used in explaining the harmony in the lexicon with a minimal change in its definition (see (16b-v)), as one of the claims the current study tests is that some trends in the alternation are aligned with those of phonotactics.

The constraints used to model the phonotactic data are presented in (16). As was the case in alternation learning, the phonotactic model also includes baseline constraints. First, the unigram constraints in (16a-i–16a-ix) penalise each vowel in each position.Footnote ¹³ The constraints in (16a-x–16a-xiii) and (16a-xx) and (16a-xxi) militate against the contexts in which the strength of (dis-)harmony is tested, and (16a-xiv) accounts for the potential preference for two identical vowel sequences. These constraints, along with the more general Agree constraints in (16a-xv–16a-xix) are included to test whether the observed harmony in specific environments is simply a phonotactic pattern; for instance, in testing whether the harmony is significantly encouraged in hiatus context when V₁ is [RTR] (i.e., Agree(RTR)-VV in (16b-iii)), we want to make sure that the preference for V_RTRV_RTR, if any, is not merely a preference for VV sequences in the lexicon, prevalence of [a] in V₁ or in V₂, and so on.

Note that for an effect of interest (e.g., trigger vowel effect), there is only one test constraint in the alternation analysis (e.g., Agree(RTR)-/o/; see (15b-ii)) but two relevant test constraints in the phonotactic analysis (e.g., Agree(RTR)-/a/ and Agree(RTR)-/o/; see (16b-i) and (16b-ii)). This is because in alternation learning, Agree(RTR)-/a/ and Agree(RTR)-/o/ interact with all other constraints in exactly the same way; two forms that differ only in their trigger vowel will be penalised by the same set of constraints except Agree(RTR)-/a/ and Agree(RTR)-/o/.Footnote ¹⁴ This is not true in the phonotactic model. For instance, the forms that are penalised by Agree(RTR)-/a/ will also be penalised by *[a] in V₁, while those that are penalised by Agree(RTR)-/o/ will also be penalised by *[o] in V₁. It is therefore necessary to include both Agree(RTR)-/a/ and Agree(RTR)-/o/ in the constraint set to test which of them gets a positive weight.

5.4. Learning results

The results of the learning simulations are presented in Table 5, which shows the learned weights for constraints that were retained in the model with the lowest AIC value. For the alternation data, it was found that the best model was the one that includes all of the four test constraints. Thus, the modelling results suggest that all four factors – that is, suffix type, stem vowel, number of intervening consonants and the stem type – significantly improve the model fit.

Table 5 Results of the learning simulation: the models with the lowest AIC values (an empty cell indicates that the constraint is not included in the learning data).

For the all-stems data, Agree(RTR)-/a/ and Agree(RTR)-/o/ were not included in the best model identified, suggesting that the lexicon does not show a preference for [aa] or [oa] sequences. This result confirms what was observed in Figure 6, that is, no difference between [a] and [o] in triggering the harmony. This result does not support the hypothesis that the trigger vowel effect that was shown to significantly improve the alternation model has a matching phonotactic pattern (but see §§6 and 7 for an alternative view). Regarding the hiatus effect, Agree(RTR)-VV was assigned a positive weight, while Agree(RTR)-VC(C)(C)V was omitted in the model, suggesting that there is a trend in the lexicon to prefer harmony in the hiatus context. This was not obvious in Figure 7; it seems that the preference for harmony in the hiatus context in the lexicon was masked by some other confounding factors. Because the constraint that enforces harmony in the hiatus context significantly improved both the alternation model and the phonotactic model, we can conclude that the alternation and phonotactic patterns match in terms of the hiatus effect. Finally, comparing *[RTR][wa] and *[RTR]C_non-[w][a], only the former was judged to significantly improve the model. This is in line with the observation in Figure 7 that [a] is disprefered only after [w] when V₁ is [a] or [o].

The learning results for the verb-stems data were similar to those of the all-stems data. The only difference was that the *[RTR][wa] was dropped in the verb-stems model. This seems to be because the number of stems in the verb-stems data that had [w] between the two vowels was very small ( $N=7$ ; see Figure 7). Otherwise, we can draw similar conclusions as we did for the all-stems data.

5.5. Summary

In sum, the learning simulation results generally support the claim that alternation is productive to the extent that it is supported by phonotactic patterns. We first observed that the harmony in suffix alternations is supported by a feeble tendency of harmony in the lexicon (§4), which might explain why the harmony is losing productivity. Further, we found a fair degree of, although not perfect, correlation between factors that modulate the harmony in alternation and those of the lexicon. The hiatus effect improved the model performance in both the alternation learning and the two sets of phonotactic learning. Similarly, the effect of [w] was significant in both the alternation model and the all-stems model. The trigger vowel effect, however, improved the model fit to the alternation data but did not significantly improve any of the phonotactic models. (The lack of phonotactic support for the trigger vowel effect is further discussed in §§6 and 7.) Thus, the findings suggest that (i) there is a link between alternation and phonotactics at the level of the general harmony, and (ii) for some factors that regulate the variable harmony in alternation, matching phonotactic generalisations emerge in the lexicon.