4 Verifying the hypothesis

Under the proposed analysis, instances with a sentence-final particle are interpreted as providing a ‘catalytic’ environment facilitating the overgeneralization — because (80) is assumed as an intermediate step prior to (83). If so, it is predicted that there should be a stage where des- (high) is only permitted when there is a sentence-final particle. Even though we cannot access the I-language of speakers in the past, we can alternatively examine E-languages of the given period to see if there is any indication that the new use truly started out from such environments.

In fact, this prediction is partially verified by previous quantitative studies (Tanomura 1994; Noda 2004; Ozaki 2004; Kawaguchi 2014), which all show that the presence of a sentence-final particle facilitates people’s producing of the new form. Yet the findings of the previous literature have some room for improvement.

First, the data examined in the literature are samples produced in the late twentieth and twenty-first centuries. The change from Grammar 1 to Grammar 2 is, however, estimated to take place in the early twentieth century (Kawaguchi 2014). To assess and verify our analysis in Section 3, we need to observe the data from much earlier days.

Second, the methods used in the literature do not utilize appropriate methods in the inferential statistics, preventing us from making an inference of the population beyond the samples accidentally at our disposal.

Third, without an elaborate statistical model, it is quite hard to tease an effect of one factor from the other. The use of a new form is quite likely to be simultaneously affected by multiple factors. For example, genres may affect the use as well as the use of -ne. We, thus, need to separate the influence of such extralinguistic factors from intralinguistic factors, so we can avoid making the wrong inference about the extent to which each factor contributes to the change in language.

For these reasons, we cannot conclude that our prediction is fully supported by the literature. However, by closely examining data from the first half of the twentieth century with elaborate statistical reasoning, this section now shows that our prediction is borne out.

4.1 Data

To look at examples from the first half of the twentieth century, the current paper examines the tokens in the CHJ (Corpus of Historical Japanese), one of the largest corpora covering the early twentieth century (National Institute for Japanese Language and Linguistics, version 2021.3; Last accessed Nov 24, 2021) — and investigates the alternation between the gozai-mas-form and the des-form, as shown below.

1. (86)
1. a.

1. [_cP[_TP
2.  
1. Alex-ga
2. Alex-nom
1. utukusyuu
2. beautifully
1. gozai-masi-ta]
2. exist.ahu-ah-pst
1. (ne)].
2. sfp

1.  
1. b.

1. [_cP[_TP
2.  
1. Alex-ga
2. Alex-nom
1. utukusi
2. beautiful
1. k-at-ta]
2. pred-cop-pst
1. des-u(-ne)].
2. ah-u-sfp
1. ‘Alex was beautiful.’

Accessed through Chunagon 2.5.2, the instances of (86) are obtained with the following query formulae:

1. (87)

1. Prescriptive form: pos like “Canonical Adjective%” and following words: lexeme gozar- on 1 words from key and following words: lexeme -mas on 2 words from key

1. (88)

1. New form:

1.  
1. a.

1. pos like “Canonical Adjective%” and following words: lexeme des- on 1 words from key

1.  
1. b.

1. pos like “Canonical Adjective%” and following words: lexeme -ta on 1 words from key and following words: lexeme des- on 2 words from key

The results, however, contain unwanted examples, so we restrict our results to a subset. First, to avoid unintended homophonous instances from the earlier period, the current study only focuses on the observations from the Meiji era and onward (1868–1947). Second, since the annotation scheme of the CHJ classifies some negation markers as a canonical adjective, we exclude such spurious cases.³⁷ Finally, to accurately make an inference on the random-effects, adjectives whose raw frequency is less than five are excluded; the remaining 1,031 instances (32 canonical adjectives) are used to estimate the parameters of the statistical models (see also Appendix A).

4.2 Statistical modeling

The diachronic development of the new form against the old prescriptive variant is reasonably modeled as a type of (i) logistic regression, one having (ii) a mixed-effects component combined with (iii) a time series structure.

In the linguistic literature and other fields, logistic regressions are used in modeling the choice of binary variants (Cedergren & Sankoff 1974; Levshina 2018; Yamada 2019b); in the current study, the following variables are used as fixed-effects independent variables:³⁸

1. (89)
1. a.

1. Textbook x₁: Dummy variable taking the value of 1 iff the sample is taken from a textbook, and 0 otherwise.

1.  
1. b.

1. Literature x₂: Dummy variable taking the value of 1 iff the sample is taken from the literature, and 0 otherwise.

1.  
1. c.

1. Sentence-final particle x₃: Dummy variable taking the value of 1 iff the ah is used with a sentence-final particle, and 0 otherwise.

1.  
1. d.

1. Epistemic model suffix x₄: Dummy variable taking the value of 1 iff the ah is used with an epistemic modal suffix -oo, and 0 otherwise.

1.  
1. e.

1. Tense x₅: Dummy variable taking the value of 1 iff the ah is used in a past tense, and 0 otherwise.

The CHJ provides information about the genre from which each sentence is sampled: whether it is from a textbook, the literature (e.g., novels and essays), or the non-literature (the remaining genres).³⁹ We create two dummy variables that indicate whether it is from a textbook and the literature (x₁ and x₂), making the remaining miscellaneous non-literature genre as the reference category. The variables in (89)c through (89)e are designed to capture the linguistic factors. To test the predictions from the previous section, we use dummy variables for a sentence-final particle and epistemic marker. For example, if ne is pronounced in (86)a or (86)b, x₃ is coded 1, and 0 otherwise. Since the variants can take both present tense and past tense sentences, the tense variable is created to see the difference (x₅).

Furthermore, the following random-effects variable is taken into consideration to scrutinize the idiosyncrasies among canonical adjectives (Levshina 2018; Yamada 2019b).

1. (90)

1. Idiosyncrasies among canonical adjectives u₀₁, u₀₂, …, u₀₃₂: The idosyncrasy of the j-th adjective, which is assumed to follow N(0, τ²).

In addition, to incorporate chronological information, the intercept is assigned a time-series structure (the State-Space Model; Shumway & Stoffer 2017; Durbin & Koopman 2001; Hagiwara 2021, a.m.o). Here each intercept (the state) at time t is designed to depend only on the state at the previous time point (i.e., a random walk).

These structural components are combined to yield to the model provided in (91); $y_{\mathit{\text{ij}}}^{(t)}$ and ${\pi }_{ij}^{(t)}$ , respectively, denote the dependent variable and parameter of the Bernoulli distribution of the i-th observation of the j-th adjective at time $t;y_{\mathit{\text{ij}}}^{(t)}=1$ iff it takes the new variant, and 0 otherwise. $x_{1i}^{(t)},x_{2i}^{(t)},\dots ,x_{5i}^{(t)}$ are the values of the aforementioned independent variables at time t, and β₁, β₂, …, β₅ are the corresponding effect sizes; ${\beta }_0^{(t)}$ is the intercept at t. u_0j (j ∈ {1, 2, …, 32}) are the random effects representing the idiosyncrasies attributed to the j-th adjective.

1. (91)

1. 

The parameters are estimated using a Hamiltonian Monte Carlo algorithm with Stan (Stan Development Team 2020) on R (Gelman et al. 2013; R Core Team 2020). The model comparison is conducted by the R package loo, which provides us with an efficient approximate leave-one-out cross-validation information criterion (LOOIC), approximate standard errors for the estimated predictive errors, and the Watanabe-Akaike/widely applicable information criterion (WAIC). As a result, among the 2⁵ (five fixed- and random-effects variables) =32 constructed models, the model in which x₅ is unselected turns out the best model (see Appendix B). The subsequent discussion proceeds based on the results of the posterior distribution of the parameters of this model.

4.3 Results

Figure 1 summarizes the results of the estimated random-effect of each adjective (i.e., u_0j’s). Each bar represents the 95% and the 66% credible intervals of the random-effects u_0j (the white circles are the posterior medians and the number in the square brackets shows how many times the adjective is used with an ah form in the CHJ). Arigata ‘rare’ has the largest negative value, showing its strong preference for the prescriptive. However, the results are not surprising, because arigatoo gozai-mas is entrenched as a fixed expression meaning thank you, which should reasonably increase the relative ratio of the old variant. On the other hand, there are no adjectives with an extremely large positive value (a candidate leading to a change). The largest is atu ‘hot,’ but the posterior median is not as high as +2; although the upper limit of the 95% credible interval slightly goes beyond the commonly-assumed +3 threshold, the sample size for this adjective is as many as twelve instances, and with few more examples, it is expected that the posterior range becomes smaller. It is, thus, reasonable to conclude that other than arigata, the adjectives are almost randomly distributed with no significant idiosyncratic tendency in the change in language.

Figure 1

Posterior Distributions for the Random-Effects.

Figure 2 shows the posterior distribution of π^(t) from 1873 to 1947. For each year, the posterior median (the solid line) and its 95% credible intervals (the shaded gray area) are drawn. The clear trend of increasing values corroborates the findings of previous studies that the new variant is gradually becoming popular in the first half of the twentieth century (Kawaguchi 2014).⁴⁰

Figure 2

Posterior Inference on $\{{\pi }_0^{(t)}:t\in \{\text{1873, 1874,}\dots \text{,1947}\left\}\right\}$

Figure 3 represents the results of the posterior distributions of the fixed-effects. β₁ and β₂ are text genres, which are associated with formality and other sociolinguistic factors. The textbook (β₁) takes a large negative value, suggesting that examples in this genre are resistant to a change; given that textbooks are written maximally respecting the prescriptive grammar, its preference for the old variant seems reasonable. In contrast, the literature (β₂) (novels and essays) has a positive value, suggesting examples in this genre prefer taking the new form. Since novels and essays reasonably reflect everyday conversations to a greater degree, this tendency is also understandable.⁴¹

Figure 3

Posterior Distributions for the Fixed-Effects.

Finally, let us turn to intralinguistic factors. First, tense (x₅) is excluded from the best model in (91), suggesting that when other factors are controlled, it is not useful in predicting the use of new variants: the spread of the new form is not sensitive to the present/past tense distinction.⁴² Second, the extreme large value for β₄ (an epistemic marker) stems from the fact that -oo is used with des- (high), not with -mas, as discussed in Section 2.3.3. Lastly, what is most relevant for our discussion is β₃ (a sentence-final particle). As clearly seen, it has a positive effect size, whose 95% credible intervals are far from 0, strongly supporting our prediction that a new form is facilitated in the structure of [X_[ah:+] sfp (c)].⁴³

Appendix B: Statistical Modeling

Priors

This study uses the flat uniform prior, which is the default setting in Stan; for standard deviations, the lower limit is set to 0 so that they do not take negative values.

Convergence

By taking into account all combination of the variables, the present paper builds 2⁵ = 32 models. Under the condition of THIN = 15, ITER = 25000, and WARMUP = 18000, most models are converged under the commonly-used threshold (Vehtari et al. 2021).

Model Comparison

The performance of their models are assessed using Leave-One-Out Cross-Validation (LO-OIC) and the Watanabe–Akaike/Widely Applicable Information Criterion (WAIC), which are methods used in estimating pointwise out-of-sample prediction accuracy from a fitted Bayesian model (Watanabe 2010; Vehtari et al. 2017), which are computed by loo package in R (Vehtari et al. 2016). The results are summarized in Figures 4 and 5; the models are ordered in increasing order. The barcode plots in the lower panel represent the variables included in the given model. For example, the leftmost models contain the variables from x₁ to x₄ lacking x₅. The model with the lowest LOOIC/WAIC is the best model, so this leftmost model is identified as the best model.

Figure 4

The LOOIC of each model.

Figure 5

The WAIC of each model.

Notes

1. ah markings are found in genealogically unrelated languages; see e.g., (Souletin) Basque (Isolate, Oyharçabal 1993; Haddican 2018), Thai (Tai-Kadai, McCready 2014), Tamil (Dravidian, McFadden 2017), Punjabi (Indo-European, Kaur 2017), Magahi (Indo-European, Alok 2021), Korean (Koreanic, Pak 2008; Portner et al. 2019) and Japanese (Japonic, Harada 1976; Miyagawa 2017; Yamada 2019c). [^{^}]
2. More accurately, they analyze c and SentMood as being fused and supnita as the spellout of the complex head. [^{^}]
3. To be more precise, -mas is pronounced in a position between an aspectual marker and negation marker:
   1. (i)

   1. Mitome-rare-te
   2. recognize-pass-cv
   1. i-mas-en
   2. prg-ah-neg
   1. desi-ta
   2. cop.ah-pst
   1. ka
   2. q
   1. nee?
   2. sfp
   1. ‘Was (it) not being recognized?’
   [^{^}]
4. Two comments are in order. First, some may wish to propose a new functional projection in place of Σ, but the subsequent discussion does not hinge on the choice of a functional projection, as long as it is located somewhere between V and T. Second, in (6)b, an interpretable feature is in a higher c-commanding probe, and the uninterpretable feature is located in a lower projection in ΣP, which is an assumption different from that in Chomsky (2000; 2001). However, in later studies, the valuation and interpretability are considered two independent properties (Pesetsky & Torrego 2007). Under this view, the honorific feature in Σ is unvalued when externally-merged. Alternatively, one can assume that an Agr-node with a feature is post-syntactically introduced when c-commanded by a triggering feature (Kramer 2009; 2010; Norris 2014; Baier 2015). The analysis of Yamada (2019c) in (6)b adopts the latter strategy. [^{^}]
5. Although non-contracted examples of ku are rarer (when compared with de) — this is why I put a question mark in (10)b — there are few cases where the contraction is unaccepted. First, with beki ‘should,’ the non-contracted form is obligatory:
   1. (i)

   1. Hana-ga
   2. flower-nom
   1. utukusi
   2. beautiful
   1. {ku
   2. pred
   1. ar/*kar}-u
   2. cop/pred.cop-u
   1. beki
   2. should
   1. da.
   2. cop
   1. ‘Flowers should be beautiful.’
   As in (ii), the -u preceded by a non-contracted form does not alternate with -ta. Thus, it is likely that the contraction is sensitive to the position where the ar-support takes place (i.e., whether it is in T or not).
   1. (ii)

   1. *Hana-ga
   2.   flower-nom
   1. utukusi
   2. beautiful
   1. {ku
   2. pred
   1. at/kat}-ta
   2. cop/pred.cop-u
   1. beki
   2. should
   1. da.
   2. cop
   1.   ‘Flowers should have been beautiful (intended).’
   Second, the contraction is prohibited with -mas-en:
   1. (iii)

   1. Hana-ga
   2. flower-nom
   1. utukusi
   2. beautiful
   1. {ku
   2. pred
   1. ari/*kari}-mas-en.
   2. cop/pred.cop.ah-neg
   1. ‘Flowers are not beautiful.’
   [^{^}]
6. For gozar-, see Section 2.3.1. [^{^}]
7. As for nouns and nominal adjectives, gozai-mas can also be used to encode the highest level of politeness; hence, three honorific levels are clearly identified. Based on this observation, Mikami (1959 [2002]: 157) convincingly argues that the canonical adjective lacks the intermediate polite meaning. [^{^}]
8. When the negation marker is adjacent to -mas, -nak (-nai is its allomorph) changes its from to -en (Yamada 2019c). [^{^}]
9. In contrast, such an ar-support is not obtained with a present tense marker. The so-called present tense marker -u does not seem to be a genuine tense suffix, but it is more reasonable to see it as a postsyntactically inserted vowel (Yamada 2019a; 2020). By seeing that the stranded affix filter is only applicable to the suffix present in the narrow syntax, we can explain the absence of the ar-support in (18). [^{^}]
10. Technical analysis of how it concords with -mas does not affect the subsequent discussions (for an attempt at a detailed analysis, see Yamada 2019c; 2020); for our purposes, it suffices to state that there is a concord between the two positions. [^{^}]
11. In most cases, a focus particle -wa in inserted to mark the scope of the negation. [^{^}]
12. Nowadays, some (young) people use Grammar 2 even in a formal context, and the boundary is quite complex. [^{^}]
13. This also applies to des- (concord):
    1. (i)

    1. *Alex-wa
    2.   Alex-top
    1. utukusi
    2. beautiful
    1. ku-wa
    2. pred-foc
    1. ar-mas-en
    2. cop-ah-neg
    1. {de at/dat}-ta.
    2. pred cop/cop-pst
    1.   ‘Alex was not beautiful (intended).’
    [^{^}]
14. The sentences sound more natural when the nominative marker -ga is replaced by -wa, the focus particle. However, for expository purposes, the current paper uses a sentence with a nominative subject. [^{^}]
15. Some native speakers (especially people in older generations) may not like the examples in (27) through (31), because they sound too casual. But in younger generations, some speakers who do use (27), (28), (29), and (31) find (30) too colloquial to use, with a nuance of the speaker’s being jokey or deliberately cutesy/childish. A possible reason for this may have to do with the fact that a verb is the only part-of-speech that requires -mas, but not des-, in Grammar 1. The strong connection with -mas may have a negative ‘carry-over’ effect in Grammar 2, to the extent that people are less comfortable using a verb with des- particularly in formal situations, so they are limited in very casual registers. Marked as they are, it remains true that they are produced in a daily conversation, so following the literature (Ogawa et al. 2020), this paper takes the widest scope treating examples found in casual registers as also reflecting the mental grammar of contemporary Japanese native speakers. [^{^}]
16. Source: https://twitter.com/mmm_drama/status/872447904169943041?lang=fr. [^{^}]
17. Source: https://www.hotpepper.jp/strJ001194986/report/detail_om0001452178_rn20180611A00066/. [^{^}]
18. Source: https://www.city.yonago.lg.jp/item/45473.htm. [^{^}]
19. This is because of the ambiguous status of -u. In Grammar 1 (e.g., the sentence in (i)), the -u is analyzed as a non-past (present tense) marker, because it triggers an ar-support. In contrast, in Grammar 2 sentence like (ii), -u is considered a vowel inserted only for phonological purposes.
    1. (i)

    1. Alex-ga
    2. Alex-nom
    1. gakusya
    2. scholar
    1. de
    2. pred
    1. ar-u.
    2. cop-prs
    1. ‘Alex is a scholar.’
    1. (ii)

    1. [[Ii
    2. good
    1. mise
    2. restaurant
    1. dat-ta]
    2. pred.cop-pst
    1. des-u].
    2. ah-u
    1. ‘(It) was a good restaurant.’ (noun)
    On the one hand, if -u is analyzed as a tense marker, the sentence in (32) is seen as an instance of des- (low). On the other hand, if it is seen as an epenthetic vowel, the same sentence can be seen as an instance of des- (high). [^{^}]
20. Looking at the CHJ, we can find some examples of the gozar-, even in the government-designed textbook published in 1947. This paper, however, maintains that the ‘gap’ did exist in Grammar 1, as has been proposed in the literature. First, the apparent counter-examples in CHJ turn out to be examples from sections designed to familiarize students with old Japanese cultures (e.g., to learn Kyoogen texts, which were written in early Edo period Japanese); hence, such examples are not representative of twentieth-century Japanese. Second, if gozar- had been used in the twentieth century, linguists should have mentioned as such, which is convincingly denied by the survey of Kawaguchi (2014). Finally, previous studies examining the history of gozar- have revealed that after it had obtained the use of an AH marking, it underwent several morphosyntactic/semantic changes in the Edo period, before eventually being only observed in the fossilized grammatical context (namely, the gozai-mas- construction). Of course, why the gozar-based system became obsolete is another important question. However, I leave this issue to future research, because the change took place during a different historical period. [^{^}]
21. A reviewer asks how the sentence in (35)b is generated in Grammar 1. One possible analysis is that the no is a nominalizer/complementizer making a nominal clause:
    1. (i)

    1. (Zyookyoo-wa)
    2. situation-top
    1. [Alex-ga
    2. Alex-nom
    1. utukusi
    2. beautiful
    1. i
    2. pred.prs
    1. no]
    2. comp
    1. des-u.
    2. pred.cop.ah-prs
    1. ‘It (= the situation) is that Alex is beautiful.’
    This is consistent with several observations. First, no clauses can receive a case marker, just like a noun:
    1. (ii)

    1. Watasi-wa
    2. I-top
    1. [Alex-ga
    2. Alex-nom
    1. utukusi
    2. beautiful
    1. i
    2. pred.prs
    1. no]-o
    2. comp-acc
    1. sit-ter-u.
    2. know-prf-prs
    1. ‘I know that Alex is beautiful.’
    Second, the preceding element takes the adnominal form (the form for a relative clause):
    1. (iii)

    1. (Zyookyoo-wa)
    2. situation-top
    1. [Alex-ga
    2. Alex-nom
    1. gakusya
    2. beautiful
    1. {na/*da}
    2. pred.cop.adn/pred.cop
    1. no]
    2. comp
    1. des-u.
    2. pred.cop.ah-prs
    1. ‘It (= the situation) is that Alex is beautiful.’
    Third, notice that the English translation is given ‘it is [ that … ].’ Since the subordinate marker that introduces a clause appearing in an argument position, it is no wonder why the corresponding no introduces as a noun clause. [^{^}]
22. In contemporary Japanese, the form in (37)a can no longer encode an epistemic meaning, but nonetheless, the form hasir-oo has continued to be used to encode the volitionality of the subject; to put it another way, in the old days, the form in (37)a was ambiguous between the volitional reading and epistemic reading, just like the English work will. [^{^}]
23. The y in yoo is not an inserted consonant. I use the Cabinet-ordered romanization system, in which [∫] is expressed as a combination of s and y as in des-yoo. Under the IPA system, however, it is expressed as [des-o:] > [de∫o:]. So what looks like an allomorph of oo is in fact a phonological change in des. [^{^}]
24. For representational purposes, I use Epi(stemic)P à la Cinque (1999) for presentational purposes, but the choice of this label does not affect the analysis of this paper. [^{^}]
25. To be more precise, Nishiyama (1997; 1999) assumes that the dummy element is the head of VP (cf., Miyama 2011; Watanabe 2013), whereas in (45), the ar- is analyzed as a post-syntactically inserted supporting element. However, this difference does not make any significant differences to the subsequent discussions. [^{^}]
26. Given that the pattern in the plain form is well-organized, we do not have motivation for analyzing dar and kar as a single fused form, and I assume that the fusion is applied when there is an honorific feature in Pred. [^{^}]
27. A reviewer asks what would happen if we dispensed with the morphological merger, proposing (i)a or (i)b.
    1. (i)
    1. a.

    1. 
    1.  
    1. b.

    1. 
    Unfortunately, these analyses run into an empirical problem: a focus particle can be introduced between de and ar for the de ar-sentence, as in (ii)a, indicating that a focus particle can select a PredP. The structures in (i) predict (ii)b and (ii)c, contrary to the fact.
    1. (ii)
    1. a.

    1.   Alex-ga
    2.   Alex-nom
    1. gakusya-de-wa
    2. scholar-pred-foc
    1. ari-masi-ta.
    2. be-ah-pst
    1.  
    1. b.

    1. *Alex-ga
    2.   Alex-nom
    1. gakusya-d-wa
    2. scholar-pred-foc
    1. esi-ta.
    2. cop-pst
    1.  
    1. c.

    1. *Alex-ga
    2.   Alex-nom
    1. gakusya-∅-wa
    2. scholar-pred-foc
    1. desi-ta.
    2. cop-pst
    1.   ‘It is true that Alex was a scholar.’
    [^{^}]
28. In Adger (2003), the c-selection is done via checking. However, the choice between checking and agreement is rather conceptual, and does not result in a significant change in the subsequent discussion. [^{^}]
29. For the ease of illustration, I adopt the bracket notation in place of the set notation. The number used in the value slot is intended to capture the scopal hierarchies (i.e., the Hierarchies of Projection, HoPs), and constrains the distribution of the features. For instance, ⟨ca, 1⟩ and ⟨Pred, 2⟩ ensure that Pred appears in a position higher than the CA in the structure (Adger 2010: 198). [^{^}]
30. For limited space, the current paper only presents examples of past-tense sentences. However, our analysis can explain the data in the present tense (e.g., de ar-u and des-u), if the following rule is added to the list in (62): T_[pst:–] ↔ u. A potential problem that has been acknowledged by the previous literature is the treatment of i that appears in the non-polite, present-tense canonical adjective, as shown below (Nishiyama 1997; 1999). Note that this is not a vowel harmony: even if the root does not end with i (e.g., omosiro ‘funny’), it is pronounced i.
    1. (i)

    1. Alex-ga
    2. Alex-nom
    1. utukusi i.
    2. beautiful i
    1. ‘Alex is beautiful.’
    The status of this i can be analyzed in different ways. One can see it as an allomorph of u ‘prs.’ Under this view, it remains unclear why it does not trigger an ar-support, as in ku ar-u. Nishiyama (1999) tries to answer this question by proposing that that “present tense does not require an overt form of the (dummy) copula (ibid.: 191–192).” This explanation raises a deeper question of why a dummy copula tends to disappear cross-linguistically, and why there is a split in Japanese between u and i. An alternative is to see it as an allomorph of k(u) ‘pred.’ By seeing k as the real morpheme and u as an epenthetic vowel, this line of thinking seems plausible with an additional rule such that k → i. Under this view, we assume a silent tense morpheme at T, and the absence of a dummy copula is easily derived; since ∅ is silent, it does not need substance to which it attaches. This analysis, too, is not without problems. For example, the choice of T (u and ∅) must be sensitive to the phrase to which Pred is merged with. However, T and CA/NA are not in a sister node relation, so we need to devise a mechanism as to how this works. The current paper does not have a good solution to the problem of this morpheme, either, leaving this issue to future research, but it is not likely that a treatment of this morpheme will substantially change our main analysis. [^{^}]
31. The sequence de ar-u can be contracted to da, as shown below. So, one may wish to propose an additional fusion rule $([[\text{Pr e}{d}_i^{[\text{AH}:–]}\mathit{\text{dummy}}]T_{[\text{PST}:–]}]\to \#\mathrm{Pr}e{d}_i^{[\text{AH}:+]}\mathit{\text{dummy}}]T_{[\text{PST}:–]}\#)$ and a vocabulary insertion rule $(\text{Pr} \text{e}{d}_i^{[\text{AH}:+]}+\mathit{\text{dummy}}+T_{[\text{PST}:–]}\leftrightarrow \mathit{\text{da}})$ .
    1. (i)

    1. Alex-ga
    2. Alex-nom
    1. gakusya
    2. scholar
    1. {de
    2. pred
    1. ar-u/da}.
    2. cop-prs/pred.cop.prs
    1. ‘Alex is a scholar.’
    But this analysis is empirically challenged; this morpheme cannot be embedded in a relative clause, as in (ii) although it can be embedded in a quotative and an interrogative clause (= (iii) and (iv)).
    1. (ii)

    1. [Alex-ga
    2. Alex-nom
    1. gakusya
    2. scholar
    1. {de
    2. pred
    1. ar-u/*da}]
    2. cop-prs/pred.cop.prs
    1. zizitu-o
    2. fact-acc
    1. sitteir-u.
    2. know-prs
    1. ‘I know the fact that Alex is a scholar.’
    1. (iii)

    1. [Alex-ga
    2. Alex-nom
    1. gakusya
    2. scholar
    1. {de
    2. pred
    1. ar-u/da}]-to
    2. cop-prs/pred.cop.prs-comp
    1. sitteir-u.
    2. know-prs
    1. ‘I know that Alex is a scholar.’
    1. (iv)

    1. [Alex-ga
    2. Alex-nom
    1. gakusya
    2. scholar
    1. {de
    2. pred
    1. ar-u/da}
    2. cop-prs/pred.cop.prs
    1. ka]-o
    2. q-acc
    1. sitteir-u.
    2. know-prs
    1. ‘I know whether Alex is a scholar.’
    Therefore, we must make the vocabulary insertion rule sensitive to the status of it being in a relative clause. Two analyses seem plausible. The first is to assume an agreement between C_[Rel:+] and T (or Pred), and use the rule in (vi). Another is to assume a further morphological merger, making the c and Pred, dummy, and T within the same terminal node when there is C_[Rel:+]: with the rule in (vi), this analysis works, as desired.
    1. (v)
    1. a.

    1. 
    1.  
    1. b.

    1. 
    1. (vi)
    1. a.

    1. 
    1.  
    1. b.

    1. 
    Admittedly, the current paper does not have any further data to show which is better, leaving this problem to future research. However, in either way, the rules in (62) remain intact and the analysis of da does not affect analysis of the historical development of des-. [^{^}]
32. In addition to a verb, some auxiliaries are followed by -mas, but not by des-. For example, consider the example in (i)b, where the passive auxiliary is attached to the verb.
    1. (i)
    1. a.

    1. Bernie-ga
    2. Bernie-nom
    1. Alex-o
    2. Alex-acc
    1. home-{masi/*desi}-ta.
    2. praise-ah-pst
    1. ‘Bernie praised Alex.’
    1.  
    1. b.

    1. Alex-ga
    2. Alex-nom
    1. home-rare-{masi/*desi}-ta.
    2. praise-pass-ah-pst
    1. ‘Alex was praised.’
    However, Japanese auxiliaries are, in fact, constituted by miscellaneous elements, and there are ‘auxiliaries’ that are used with des-, such as hazu ‘should’ and yoo ‘seems’:
    1. (ii)

    1. Alex-ga
    2. Alex-nom
    1. siawase
    2. happy
    1. na
    2. cop.adn
    1. {hazu/yoo}
    2. should/seem
    1. {desi/*masi}-ta.
    2. pred.cop.ah/ah-pst
    1. ‘Alex {should/seems to be} be happy.’
    These expressions differ from (r)are-type auxiliaries in three important ways. First, unlike -(r)are in (i)b, they can be preceded not only by verbs, but also by adjectives and nouns; n.b., *siawase-rare ‘happy-pass.’ Second, etymologically, these expressions used to be nouns referring to a specific part of an arrow, and to a manner, respectively. Third, the copula preceding them takes the adnominal form na (the form for a relative clause), not da, (see also Footnote 21). With all these considerations into account, hazu and yoo are morphosyntactically ‘nouns’ (or ‘nounish auxiliaries’) being modified by a relative clause, despite their semantics which would be expressed by auxiliaries in English. In other words, only ‘verbish’ auxiliaries are used with -mas. The rule in (70) has room for capturing this selectional restriction. Notice that the idea that categorical information can be further decomposed into more primitive features has been advocated since old days (e.g., Chomsky 1974; Stowell 1981: 21). If a primitive feature is shared by a verb and a verbal auxiliary, we can replace the “V” in (70) with that feature, and correctly capturing the distributional property of -mas. Although a full resolution awaits further work, it should be noted that at least as far as the rules for -mas restricted to verbs and auxiliaries (i.e., something ‘verbish’), the subsequent discussion is unaffected. [^{^}]
33. This chain reduction could be a side-effect of pursuing an economical grammatical architecture (Chomsky 2005), and the diachronic loss of Agree has been discussed in the literature (Roberts 2007: 123, 193). However, the detailed mechanism needs further elaboration in future research: since agreement applies before vocabulary insertion, one cannot tell (in advance) how the AH-feature is pronounced at the time when Agree is ready to apply, which appears to cause an ordering paradox. [^{^}]
34. (80) predicts that when des- can also be distributed in positions other than T/c. This prediction is borne out by a phrase-final particle construction. Japanese can put a particle in every phrase-boundary. When politely used, des is used with each phrase-final particle:
    1. (i)

    1. [Watasi-wa
    2. Alex-top
    1. desu-ne]
    2. ah-pfp
    1. [totemo
    2. very
    1. desu-ne]
    2. ah-pfp
    1. tukare-ta
    2. get tired-pst
    1. desu-yo.
    2. ah-sfp
    1. ‘I got so tired. ’
    [^{^}]
35. Considering the phrase-final particle (see Footnote 34), X_[ah:+] is more reasonable than c_[ah:+]. [^{^}]
36. One could ask what other morphological rules are responsible for multiple grammars. Although this paper does not have a decisive answer, proposals for synchronic variations — such as probabilistic impoverishment rules (Nevins 2008; Nevins & Parrott 2010; Havenhill 2016) — are also other candidates that deserves our attention. [^{^}]
37. Apparently nai and utukusi i look similar regarding the conjugation (they both result in a sequence of k-at-ta), so one might wish to treat the sentence in (i)a as an instance of a canonical adjective in Grammar 2. But there is good reason to believe that this is not the case.
    1. (i)
    1. a.

    1. [_cP[_TP[_ΣP[_PredP
    2.  
    1. Alex-ga
    2. Alex-nom
    1. gakusya
    2. scholar
    1. de]-wa
    2. pred-foc
    1. nak]
    2. neg
    1. at-ta]
    2. cop-pst
    1. des-u].
    2. ah-u
    1. ‘Alex was not a scholar.’
    1.  
    1. b.

    1. [_cP[_TP[_ΣP[_PredP
    2.  
    1. Alex-ga
    2. Alex-nom
    1. gakusya
    2. scholar
    1. de]-wa
    2. pred-foc
    1. ari-mas-en]
    2. cop-ah-neg
    1. desi-ta]].
    2. ah-pst
    1. ‘Alex was not a scholar.’
    First, the corresponding sentence in Grammar 1 is given in (i)b, which is predicated by a noun. If one treated (i)a as a canonical adjective construction, it would follow that the sentence changes the sentence type depending on whether it is in Grammar 1 or not. Second, a canonical adjective takes the adverbial form when used in Grammar 1, as in (17), but nak in (i) does not. Note, however, that this does not mean that nai completely lacks the use of a canonical adjective. When used alone, that is, not being preceded by a PredP, it can be used as an adjective that means ‘absent.’ The nai in (i) is, thus, seen as a negation marker, and the one in (ii) as a canonical adjective. In the present study, I manually distinguished all the instances of nai, and exclude the former cases only; however, the frequency of such examples is less than five, and as a result, the remaining examples are ruled out based on an independent criterion.
    1. (ii)
    1. a.

    1. [_cP[_TP[_PredP
    2.  
    1. Sato-ga
    2. sugar-nom
    1. na
    2. absent
    1. ]
    2.  
    1. k-at-ta]
    2. pred-cop-pst
    1. des-u].
    2. ah-u
    1. ‘There was no sugar (lit., sugar was absent).’
    1.  
    1. b.

    1. [_cP[_TP[_PredP
    2.  
    1. Sato-ga
    2. sugar-nom
    1. noo
    2. absently
    1. ]
    2.  
    1. gozai-masi-ta]
    2. ahu.exist-ah-pst
    1. ].
    2.  
    1. ‘There was no sugar (lit., sugar existed absently).’
    [^{^}]
38. Each sentence of this corpus is provided with an annotation about the genre (textbooks, literature, and nonliterature) and the neighboring morphemes; based on this annotation scheme, the variables x1, x2, x4, and x5 are created. As for x3, the researcher manually annotated the information for all instances. [^{^}]
39. The textbook in this data set consists of government-designed textbooks on Japanese published from 1904 to 1947. Rather than explicitly teaching grammar rules, they comprise essays and writings for elementary school (the 1st to the sixth year) and the first year middle school students. Such censored writings are reasonably considered representing the prescriptive grammar at that time. The literature includes novels and essays written not for the purpose of promoting the prescriptive grammar, but for general purposes, reasonably seen as being sensitive to the use of day-to-day conversation. The non-literature genre consists of miscellaneous remaining categories (e.g., magazines). [^{^}]
40. One unexpected move is the ‘spike’ between 1897 and 1907, which may be attributed to the idiosyncrasies of the sampled texts. It could, however, be caused by a social movement: in those days, some novelists started writing novels in a colloquial register (aka the Genbun-Icchi movement, that is, the movement to unify the written and spoken forms of a language; Yamamoto 1971, Kamei et al. 1965: 184, Nomura 2013: 269). However, to convincingly prove the influence, finer-grained analysis would be necessary, which I would like to leave open to future research. [^{^}]
41. Although it does give us a natural interpretation, we need to be aware that the effect size of this variable is not as strong as the others. Furthermore, in terms of LOOIC and WAIC, the second best model in the model selection lacks this variable (see Figures 4 and 5). Thus too much emphasis on the difference would not be helpful; it is the least important among the four fixed-effects factors. [^{^}]
42. Even when we include x₅ and refit the model, the posterior median of the past tense shows a slightly negative value but the 95% credible interval includes 0. [^{^}]
43. Due to the limitation of the corpus used for this study which does not annotate the speaker of each instance, intraspeaker variations cannot be detected. With a fully annotated-corpus, future research is expected to improve the model by including the variable to such variations. [^{^}]

Acknowledgements

References