Phonology and orthography : The orthographic characterization of rendaku and Lyman ’ s Law

This paper argues that phonology and orthography go in tandem with each other to shape our phonological behavior. More concretely, phonological operations are non-trivially affected by orthography, and phonological constraints can refer to them. The specific case study comes from a morphophonological alternation in Japanese, rendaku. Rendaku is a process by which the first consonant of the second member of a compound becomes voiced (e.g., /oo/ + /tako/ → [oo+dako] ‘big octopus’). Lyman’s Law blocks rendaku when the second member already contains a voiced obstruent (/oo/ + /tokage/ → *[oo+dokage], [oo+tokage] ‘big lizard’). Lyman’s Law, as a constraint which prohibits a morpheme with two voiced obstruents, is also known to trigger devoicing of geminates in loanwords (e.g. /beddo/ → [betto] ‘bed’). Rendaku and Lyman’s Law have been extensively studied in the past phonological literature. Inspired by recent work that shows the interplay between orthographic factors and grammatical factors in shaping our phonological behaviors, this paper proposes that rendaku and Lyman’s Law actually operate on Japanese orthography. Rendaku is a process that assigns dakuten diacritics, and Lyman’s Law prohibits morphemes with two diacritics. The paper shows that a set of properties of rendaku and Lyman’s Law follows from this proposal. However, since some aspects of rendaku and Lyman’s Law are undoubtedly phonological, the ultimate conclusion is that it is most fruitful to recognize a model of phonology in which it has access to orthographic information. Several consequences of the current proposal are discussed.


Theoretical context
In the traditional view, phonology is strictly about sounds, and orthography has been considered to have nothing to do with phonological theory or phonological knowledge.This has been the case since linguistics distinguished itself from philology under the influence of landmark studies like Saussure (1916Saussure ( /1972)).However, there are a few recent proposals and observations in the phonological literature that cast doubts on traditional, strictly orthographic-free versions of phonological theory.Ito et al. (1996) offer an illustrative example.In a Japanese argot language game, known as zuuja-go, reversing occurs based on bimoraic feet: e.g./(batsu)+(guɴ)/ → [(gum)+(batsu)] 'exquisite'.When the first syllable contains a geminate, the reversed segment, which corresponds to a geminate marker in the original word, appears as [tsu]; e.g./(bik)+(kuri)/ → [(kuri)+(bitsu)] 'surprised'.Why does [tsu] appear in place of coda /k/ in /bik/?The most reasonable conjecture about this conversion of a coda /k/ to [tsu], according to Ito et al. (1996: 224-225), is because the gemination is marked with a smaller version of the letter for /tsu/ (っ) in Japanese orthography.Thus, in terms of orthography, this argot can be expressed as びっくり → くりびつ, in which the gemination marker っ is realized as the full-size version of the letter つ after the reversal (っ cannot stay small after the reversal, because っ needs a following segment to express its gemination).This is an example in which orthography offers a straightforward explanation for the sound pattern under question.This conclusion does not mean, however, that the Japanese argot pattern is entirely dictated by orthography.Ito et al. (1996) show that various prosodic factors affect the formation of the argot-after all, the pattern is based on a bimoraic foot (see Poser 1990 et seq.), which is very phonological.It therefore seems that both phonological and orthographic factors together shape the Japanese argot pattern.
More recently, Nagano & Shimada (2014) proposed that Japanese kanji-Chinese characters used in the current Japanese orthography system-should be used as a representation of lexemes in the Japanese lexicon.More often than not, one kanji in Japanese has two readings: for example, 繁 can be read as /ɕige/ or /haɴ/, both meaning 'prosperous' (see Nagano & Shimada 2014 for extended exemplification).This dual reading creates apparently extremely complex suppletive morphological patterns, which can be modeled very simply if kanji for Japanese speakers is a part of linguistic knowledge over which morphological representations can operate.
Relatedly, Poser (1990) points out one hypocoristic formation pattern in Japanese which makes sense only in terms of orthography.For example, a person named 丘 (/takaɕi/) can be called /kjuu/, because /takaɕi/ and /kjuu/ are two readings of the same kanji 丘.Likewise, a girl with the name 恵 (/megumi/) can be called /kei/, because 恵 has these two readings.It is unlikely that phonology alone converts /takaɕi/ to [kjuu] or /megumi/ to [kei].This hypocoristic formation is instead mediated by the kanji characters.At the same time though, this hypocoristic formation pattern is based on a bimoraic foot in that the outcome of the conversion is bimoraic (Poser 1990), as is the case with the argot pattern discussed by Ito et al. (1996).Shaw et al. (2014) found something essentially similar in Chinese: in order to account for compound truncation patterns in Chinese, it is crucial to consider Chinese characters as part of lexical representations.Shaw et al. (2014) demonstrate that what survives in truncation is affected by the predictability of each compound member, and that "predictability" is arguably a crucial part of our linguistic knowledge (Hall et al. 2016 for a recent overview).Shaw et al. (2014), moreover, showed that the frequencies of Chinese characters are a good measure for quantifying their predictability, again suggesting that Chinese characters are an important part of the linguistic knowledge of Chinese speakers.Overall, this example too illustrates the importance of considering the interplay between orthographic knowledge and lexical/phonological knowledge.
Importantly, none of these proposals reviewed here undermine the importance of phonology or morphology as an explanation of our linguistic behavior.To the extent that orthography offers a simple explanation of our linguistic behavior, and to the extent that that behavior is also dictated by phonological and other grammatical considerations, it seems that the most natural conclusion is that phonological and morphological grammar has access to orthographic knowledge.More concretely, in current theoretical frameworks using (violable) constraints (e.g.Optimality Theory: Prince & Smolensky 2004), constraints should be able to refer to orthographic information.This paper further explores this sort of grammar-orthography interaction, by studying in detail rendaku and Lyman's Law from this fresh perspective.

The current case study: rendaku
The interaction of rendaku and Lyman's Law is probably one of the most well-studied phenomena in the phonological studies of Japanese (Irwin 2016a;Vance & Irwin 2016).A traditional phonological description of rendaku is that "the first consonant of the second member of a compound becomes voiced"; e.g., /oo/ 'big' + /tako/ 'octopus' → [oo+dako] 'big octopus'.Lyman's Law (Lyman 1894;Vance 2007) blocks rendaku when there is already another voiced obstruent in the second member of the compound; for example, /oo/ 'big' +/tokaɡe/ 'lizard' → *[oo+dokaɡe], [oo+tokaɡe] 'big lizard'.Rendaku and Lyman's Law were studied extensively by the traditional grammarians (see Irwin 2016a), and were brought to the attention of theoretical linguists by Otsu (1980), who presented the first analysis of rendaku in the SPE-style (Chomsky & Halle 1968). 1 Ito & Mester  (1986) made rendaku and Lyman's Law famous in the field of theoretical phonology, as they provided an elegant analysis of rendaku and Lyman's Law using theoretical devices that were being developed at that time: autosegmental spreading, underspecification, and Obligatory Contour Principle (henceforth, OCP).Later, Ito & Mester (2003a) in their monograph developed a comprehensive reanalysis of rendaku and Lyman's Law within the framework of Optimality Theory (OT: Prince & Smolensky 2004).Reflecting the fact that they are now well-known in the field of theoretical phonology, rendaku and Lyman's Law appear in a number of introductory phonology textbooks (Kenstowicz 1994: 493, 511-512;Roca 1994: 75-76;Spencer 1996: 60-61;Roca & Johnson 1999: 663;Gussenhoven & Jacobs 2011: 58).Most generative studies on rendaku and Lyman's Law consider them to be purely phonological or morphophonological (however, see Vance 2014 and Kawahara 2015a for critical assessment of this common assumption in theoretical linguistics).
Building on some previous work (Vance 2007;2015;2016;Kawahara 2015a), this paper presents an alternative interpretation of rendaku and Lyman's Law, which explains their properties arguably better than the purely phonological view.In essence, this paper proposes the following: (1) Orthographic interpretations of rendaku and Lyman's Law.a. Rendaku is a process that adds a dakuten mark, an orthographic diacritic to represent obstruent voicing.b.Lyman's Law prohibits two occurrences of diacritics within a single morpheme.
For this theory to work out, one needs to assume that Japanese speakers' phonological mental representations contain kana representations (following Ito et al. 1996;Nagano & Shimada 2014;Shaw et al. 2014), and that the phonetic component of Japanese knows how to phonetically implement kana letters, the system which is summarized in Table 1 below.In particular, the phonetic component of Japanese implements those elements with a dakuten mark as voiced obstruents.It is important to note here, however, that knowledge about how to pronounce each kana letter is something that all literate Japanese speakers have.Therefore, the only novel assumption that this paper adds to phonological theory is that Japanese speakers' phonological representations also contain kana representations.Even this assumption is, as reviewed in the introduction, not in and of itself an entirely new proposal.Now consider Table 1, which illustrates the basic Japanese kana-orthographic system, in which one letter generally corresponds to a (C)V mora.As shown in rows (a1-3), Japanese orthography marks voiced obstruents by putting two dots (called dakuten) on the upper right corner of the letter for the corresponding voiceless obstruents.As shown in (b), /ba/ is written with dakuten on the letter for /ha/./pa/ is represented by putting a little circle-known as han-dakuten 'half dakuten'-on the upper right corner of the letter for /ha/, as in (c).Sonorant consonants and vowels, despite being phonetically voiced, are not written with dakuten, as in (d1-3).This paper proposes that (i) rendaku is a process that assigns dakuten, and that (ii) Lyman's Law prohibits two diacritics (dakuten or han-dakuten) within a morpheme.In this view, Lyman's Law can be considered as orthotactics, restrictions on letter configurations (Bailey & Hahn 2001), rather than pure phonotactics, restrictions on sound configurations.Although this proposal may seem rather radical, it did not come out of the blue- Vance (2007;2015;2016) repeatedly drew attention to the relevance of Japanese orthography in the patterning of rendaku, as we will see below in section 3.1.This proposal is also inspired by other work showing the interplay between orthographic and linguistic knowledge in shaping our phonological behaviors, which was reviewed in the introduction of this paper (Poser 1990;Ito et al. 1996;Nagano & Shimada 2014;Shaw et al. 2014; see also Taft 2006).
Under the current proposal, formally speaking, rendaku can be understood as follows.The compound juncture morpheme postulated by Ito & Mester (2003a) is actually a dakuten diacritic, instead of a floating [+voice] feature, and the morpheme realization constraint requires this dakuten diacritic to realize on the surface.Lyman's Law can be understood as OCP(diacritic), which prohibits two diacritics within a morpheme, where "diacritic" can be either dakuten or han-dakuten.Once rendaku assigns dakuten to a target consonant, the phonetic implementation component of Japanese produces it as a voiced obstruent.

Some properties of rendaku and Lyman's Law
Before developing this orthographic theory of rendaku and Lyman's Law, let us first review some crucial properties of rendaku (Kawahara & Zamma 2016).As stated in the introduction, rendaku was first formalized in the SPE format by Otsu (1980), and later analyzed by a series of work by Ito and Mester (1986;1996;1997b;2003a;2003b).There are a number of theoretical contributions that they have made over the years, but this section focuses on those aspects that will become relevant later.First, rendaku has been treated as a manifestation of several grammatical operations, including a featurechanging SPE-style rule (Otsu 1980), an autosegmental spreading rule (Ito & Mester 1986), morphophonologized intervocalic voicing (Ito & Mester 1996), and a morpheme realization requirement of a compound juncture morpheme (Ito & Mester 2003a).
Second, rendaku has been discussed in the context of the internal organization of the Japanese lexicon (Ito & Mester 1995;1999;2008) in that rendaku mainly occurs in native words, and only somewhat regularly in some Sino-Japanese words (Irwin Table1: The basic Japanese kana-orthography systems.

Letters Sounds Letters
2005; Takayama 2005), but very rarely in recent loanwords.Third, Ito & Mester (1986) proposed that Lyman's Law is an instantiation of a universal constraint schema, the OCP on the [+voice] feature (Leben 1973;Goldsmith 1976;McCarthy 1986).They further argued that OCP(+voice) acts as a morpheme structure condition on the Japanese lexicon as well, in that there are only a few native morphemes that contain two voiced obstruents.
Fourth, Lyman's Law is not triggered by [+voice] on sonorants, and hence Ito & Mester (1986) argue that the [+voice] feature is underspecified for sonorants.Mester & Ito (1989) argue instead that [voice] is a privative feature and sonorants do not bear that feature at all throughout the phonological derivation.Rice (1993;2005) instead argues that sonorant voicing and obstruent voicing are represented by different features ([SV] for "Sonorant Voicing" and [LV] for "Laryngeal Voicing"), and that Lyman's Law targets only the [LV] feature.Alderete (1997) and Ito & Mester (2003b) formulated Lyman's Law as the result of the self-conjunction of an OT constraint *VoiObs (=*D 2 ), which allows one not to commit themselves to a particular representation of [voice] for sonorants.This short review shows that rendaku and Lyman's Law have been extensively discussed in multiple theoretical frameworks (see Kawahara & Zamma 2016 for more details).

Arguments for the orthographic characterizations of rendaku and Lyman's Law
This section develops the orthography-based theory of rendaku and Lyman's Law in (1), presenting four pieces of evidence.It is probably worth pointing out at this point that some arguments are stronger than others.However, I would like to emphasize here that this orthography-based theory explains a constellation of properties about rendaku and Lyman's Law, which is the reason that I put forward this analysis in this paper.Taken in isolation, the arguments presented in each of the following subsections may not be entirely convincing-or rather theory-dependent-but we should evaluate the orthographic theory of rendaku and Lyman's Law in light of all of the arguments.

Phonetic diversity, orthographic unity
The first argument to treat rendaku as a matter of orthography comes from the fact that when viewed from the phonetic point of view, rendaku is not simply a matter of "voicing of initial consonants", but instead involves more complicated pairings of sounds.This observation was reiterated in a series of work by Timothy Vance (Vance 2007;2015;2016), but did not seem to receive serious attention from formal phonologists.The surface phonetic pairs that are related by rendaku are shown in Table 2.In the left column, for each pair, the original sound is shown on the left, and the one that appears after the application of rendaku is shown on the right.The middle column shows examples.The right column shows how these sounds are written in Japanese orthography before and after rendaku.
Table 2 highlights the fact that rendaku is not simply a matter of "voicing the target consonant."Among those in Table 1, (d, g, h, i) are straightforward minimal pairs that differ in voicing, but the others are not; for example, in (b), [ç] is a voiceless palatal fricative, but [b] is a voiced labial stop; in (c), [h] is a glottal fricative, but [b] is a labial stop; in (e) and (f), the original sounds are affricates, but the resulting sounds are fricatives.
I am not arguing that this complexity is impossible to solve with a phonological analysis; for example, for (a-c), it is possible to posit an underlying labial stop /p/ (McCawley 1968), which is realized as [h] in non-voicing contexts and as /b/ in voicing contexts; /h/ further undergoes allophonic changes before /i/ and /u/, realizing as [çi] and [ɸu] and as [h] before non-high vowels.The deaffrication in (e, f) can be attributed to independently motivated intervocalic deaffrication (see Maekawa 2010 for details and complications of this deaffrication process), because rendaku usually occurs in intervocalic contexts. 2 It is not impossible to construct a phonological analysis of the complicated patterns in Table 2 in this way.However, it does face some problems.Concretely, positing underlying /p/ for surface [h] can be problematic, because /p/ realizes faithfully in native words as well, as in tanpopo 'dandelion' and paipan 'shaved genitalia' (Fukazawa & Kitahara 2002). 3The stronger evidence against positing the /p/ → [h] alternation in the native phonology of Japanese comes from a reversing argot pattern (Ito et al. 1996): the purported process that turns underlying /p/ to [h] is not active even for native items; e.g./(kap)(pa)/ → [(pak)(ka)], *[(hak)(ka)] 'river imp' and /(op)(pai)/ → [(pai)(otsu)], *[(hai)(otsu)] 'breast'.These considerations show that the purported rule that turns underlying /p/ to [h] is not active in the native phonology of Japanese.
It is also possible to posit underlying /ɸ/, instead of /p/ to explain the alternations in (a-c) in Table 2.When voiced by rendaku, since Japanese does not allow a voiced bilabial fricative /β/, it becomes a bilabial stop [b]./ɸ/ is palatalized before /i/, becoming [ç].One problem of this approach is that one has to further postulate a delabialization rule before /a/, /e/, /o/, but this delabialization rule seems unmotivated phonetically, especially before [o], because [o] involves lip rounding.Note that Japanese /o/ is more protruded than /u/ (Vance 2008), which can be observed in MRI data (Isomura 2009).Why would /ɸ/ be delabialized before /o/ but not before /u/, when the former is more rounded?The point of this discussion is that although it is not impossible to construct a phonological analysis of Table 2, it will always face some complications.
More crucially, it is important to note that from the viewpoint of orthography, all the pairings in Table 2 can be treated very simply as a unitary rule-the addition of the same diacritic mark (dakuten) (Vance 2007;2015;2016).All the letters for the sounds that appear on the right are identical to those letters that represent the sounds on the left, with addition of the dakuten diacritic mark.Rendaku therefore can simply be understood as 2 When rendaku occurs after a coda nasal, this deaffrication does not occur.Therefore, this intervocalic deaffrication process can explain the complexity presented by the examples (e, f). 3 Whatever the actual etymological origins of these words may be, what is important is that native speakers of Japanese do not consider these words to be recent loanwords; nevertheless the /p/ → [h] alternation does not apply to these words.

Phonetic pair Example
"the addition of a dakuten mark".As Vance (2016: 4) states, "the Japanese writing system represents all the [rendaku] alternations in a uniform way".In short, the orthographybased analysis is undoubtedly simpler than the purely phonology-based analyses. 4n the discussion of the Japanese argot in which /tsu/ (つ) appears as the argot correspondent of a gemination marker (っ), Ito et al. (1996: 224) entertain some possible phonological analyses, but conclude that "such proposals have a ring of artificiality in comparison with the perfectly straightforward kana account" The same argument can be made against the possible phonological analyses of rendaku in Table 2, given that the orthographic characterization is so simple.
Since this /p/-driven devoicing of geminates seems counterintuitive, Kawahara & Sano (2016) ran a judgment experiment to investigate whether this devoicing is real.In one of their experiments, they presented native speakers of Japanese with a list of existing words that contain particular sorts of structures: (i) geminates that appear with /p/ (e.g./paddo/ 'pad'), (ii) geminates that appear with another voiced obstruent (e.g./baddo/ 'bad'), (iii) geminates that occur neither with /p/ nor a voiced obstruent (e.g./heddo/ 'head'), (iv) two voiced singletons (e.g./baado/ 'bird'), and (v) one voiced singleton (e.g./haado/ 'hard').For each word, they presented participants with two forms, one "faithful form" (e.g./beddo/) and one "devoiced form" (e.g./betto/), and asked them which pronunciation they would use.The stimuli were presented in Japanese katakana orthography, which is conventionally used for loanwords.Although the test was based on orthography, the participants were asked to read each stimulus in their heads, and make judgments based on their auditory impression rather than on the orthography.
The results of Kawahara & Sano (2016) are reproduced in Figure 1, which shows that geminates are indeed judged to be pronounced as devoiced 40% or 30% of the time when they co-occur with /p/ or another voiced obstruent (the first two bars); the results also show, on the other hand, that the other conditions show very few devoiced responsesmost importantly, context-free devoicing of geminates rarely occurs (the third bar).Kawahara & Sano (2016) also examined corpus data, and found some instances of /p/-driven geminate devoicing as well as devoicing of geminates that co-occur with a voiced obstruent.On the other hand, context-free devoicing of geminates was barely found.Given these results, the question that arises is why /p/ would cause devoicing of geminates, or in other words, why /p/, in addition to voiced obstruents, triggers Lyman's Law.OCP(+voice) (Ito & Mester 1986) or *D 2 (Ito & Mester 2003a) cannot be the explanation, because /p/ is not a voiced obstruent-it would turn into [b] if it were [+voice].
If Lyman's Law prohibits two diacritics within a morpheme, this /p/-driven devoicing makes sense, because /p/ also has a diacritic mark (han-dakuten: see Table 1).In summary, the triggers of geminate devoicing in Japanese loanwords include /p, b, d, ɡ/.There does not seem to be a purely phonological natural class to characterize this group of sounds.However, all of these sounds have an orthographic diacritic in Japanese: ぱ (pa), ば (ba), だ (da), が (ɡa).In essence, then, it is natural to consider Lyman's Law as OCP(diacritic).It may be that OCP is a general cognitive schema to avoid adjacent similar entities (Pierrehumbert 1993;Frisch 2004), which can take both phonological features and orthographic characteristics as its arguments.Alternatively, one could say that ぱ, ば, だ, が (=/p, b, d, ɡ/) form a phonological natural class in Japanese as [+dakuten] sounds, as long as we admit that phonology can have orthographic features like [+dakuten].
Mark Irwin (p.c., December 2014) pointed out that the orthography-based theory of Lyman's Law makes a certain prediction about geminate devoicing.Since devoicing /bb/ would result in /pp/, which would still have a diacritic mark, /bb/ should not devoice.Loanwords containing /bb/ are rare in the first place (Katayama 1998;Shirai 2002;Ito et al. 2017), but there is one word that contains both /bb/ and a voiced stop, /ɡebberusu/ 'Göbbels,' and the prediction seems to be borne out.In the naturalness judgment using a 5-point scale reported by Kawahara (2011), the devoicing of this word was rated much less natural than the devoicing of geminates in other Lyman's-Law-violating words: 3.16 vs. 3.86.This score for the devoicing of /ɡebberusu/ (3.16) is in fact lower than the average naturalness of devoicing of non-Lyman's-Law-violating words (3.26) in Kawahara (2011), whose devoicing was deemed almost impossible in Kawahara & Sano (2016)  Figure 1, the third bar).This result further supports the formulation of Lyman's Law as an orthotactic constraint which prohibits two diacritics. 5n anonymous reviewer asked whether /p/-driven geminate devoicing (the first bar in Figure 1) and geminate devoicing caused by a voiced obstruent (the second bar in Figure 1) are the same phenomenon.In Kawahara & Sano's (2016) corpus data, the latter showed higher devoicing probabilities, and the difference was statistically significant; on the other hand, in the judgment experiment, the former showed higher devoicing probabilities (Figure 1), although the difference did not reach significance.The current analysis, which relies on OCP(diacritic), treats the two devoicing patterns as one and the same phenomenon, which may at first sight seem to predict that they should occur with equal probability; however, it is not easy to tell from the observed probabilities alone whether they are caused by the same constraint-hence the same devoicing pattern-because the probability of devoicing is influenced by several other factors such as the number of triggers and the lexical frequencies of each item under question (Kawahara 2011;Coetzee & Kawahara 2013;Kawahara & Sano 2013;Sano & Kawahara 2013).Thus, in order to falsify the orthographic theory of Lyman's Law from this perspective, one has to show that devoicing caused by /p/ and devoicing caused by a voiced obstruent are quantitatively different, with all other relevant factors controlled.A follow-up experiment is warranted to address this issue.

Explaining why sonorants do not cause Lyman's Law
Treating rendaku and Lyman's Law as a matter of orthography comes with additional virtues.Recall that Lyman's Law ignores voicing in sonorant consonants and vowels, and that several theoretical apparatuses were proposed to account for that observation: underspecification (Ito & Mester 1986), a privative feature (Mester & Ito 1989), and obstruent-specific voicing feature (Rice 1993;2005).However, there is a very simple explanation in terms of orthography: as shown in Table 1, Japanese orthography marks voicing on obstruents with a diacritic mark, but not on sonorants.Therefore, if Lyman's Law were to be understood as a prohibition against two diacritics-or OCP(diacritic)-then the inactivity of sonorant voicing directly follows.No additional theoretical machinery is necessary. 6his argument is admittedly theory-dependent, and is possibly weak to the extent that mechanisms such as underspecification or obstruent-specific voicing features are independently motivated.And indeed there is currently a heated debate about whether phonological and lexical representations are underspecified or richly detailed (or both) (see e.g.Steriade 1995;Johnson 1997;Lahiri & Reetz 2002;Archangeli 2011;Pierrehumbert 2016).Therefore, the argument in this subsection largely depends on the choice of whether one embraces underspecification or not.However, as emphasized at the beginning of this section, it is the constellation of these pieces of evidence that makes the orthographic-based theory of rendaku and Lyman's Law plausible and attractive.Put differently, if Lyman's Law operates on orthography, it predicts that voicing on sonorants should be ignored; the actual data supports this prediction.
This interaction is opaque because the surface [ŋ] acts as if it is a voiced obstruent: it triggers Lyman's Law, although its surface realization is a sonorant.In other words, the blockage of rendaku due to Lyman's Law overapplies and rendaku underapplies, despite the application of velar nasalization.In a derivational sense, velar nasalization needs to occur after rendaku applies; when rendaku occurs, /ɡ/ is still /ɡ/ (Table 3).Ito & Mester (2003b) developed this derivational ordering analysis in OT (Prince & Smolensky 2004).Ito & Mester (1997b) and Honma (2001) instead proposed analyses based on Sympathy Theory (McCarthy 1999).
One particular challenge that this opaque pattern presents is as follows.To the extent that [ɡ] and [ŋ] are in an allophonic relationship (a la Ito & Mester 1997a;1997b;Honma 2001), the Richness of the Base hypothesis (Smolensky 1996;Prince & Smolensky 2004) makes us consider a case in which /ŋ/ appears in the input; e.g./toŋe/.In order for this form to block rendaku, the underlying /ŋ/ has to be changed to /ɡ/ at the level in which rendaku applies, and then has to turn back to [ŋ] at the surface.This pattern would thus instantiate a "Duke-of-York" derivation (Pullum 1976) (schematically, /A/ → /B/ → [A]; in this case, /ŋ/ → /ɡ/ → [ŋ]).However, the existence of such derivation is debatable (Wilson 2000;McCarthy 2003b;Rubach 2003); granting phonological theory enough power to allow this type of derivation may overgenerate.
The orthographic formulation of Lyman's Law explains why /ɡ/, after becoming [ŋ], would still block rendaku, because [ŋ] is still written with a dakuten mark and velar nasalization is not reflected in the Japanese orthography-[ŋ] is written using the same letter as [ɡ].No theoretical machinery to deal with derivational opacity is necessary, and in fact, there is no opacity in this analysis at all.See arguments by Hooper (1976), Sanders (2003), Green (2004) and Padgett (2010) that there are perhaps no productive synchronic cases of opacity. 77 Bruce Hayes also mentions some statement to this effect in his lecture at "50 Years of Linguistics at MIT", which succinctly summarizes the problem: "We don't understand the opaque languages well enough.In particular, I don't think we fully understand the degree to which the opaque pattern is internalized by language learners, and it is time to do more checking" (viewable on Youtube: https://www.youtube.com/watch?v=IRRyxW6xPeg).Rubach 2003;McCarthy 2007), in which case the argument presented in this subsection does not hold.Hence the argument in this section, like the one presented in section 3.3, is theory-dependent.With that said, again, the orthographic theory of rendaku and Lyman's Law, independently motivated for other reasons, actually predicts that velar nasalization should not affect rendaku application, and this prediction is supported by actual data.

Summary of arguments and further considerations
In summary, many properties of rendaku and Lyman's Law make sense, once we consider them from the viewpoint of Japanese orthography.When viewed at the surface phonetic level, rendaku is not a simple matter of "voicing the target consonant", but involves different sets of more complicated pairings.However, in terms of orthography, rendaku is simply an addition of dakuten; it allows us to characterize rendaku much more simply than a purely phonology-based analysis.Treating Lyman's Law as orthotactics comes with three additional virtues: (i) it explains why /p/ can cause devoicing of geminates; (ii) it explains why Lyman's Law ignores [+voice] of sonorants; and (iii) it explains why /ɡ/ blocks rendaku, even after it turns into [ŋ].Admittedly, some arguments may not be as strong as one wishes, especially when considered in isolation.For example, the fact that Lyman's Law ignores [+voice] in sonorants (section 3.3) may follow if sonorants are indeed underspecified for [+voice] or if there is an obstruent-specific [+voice] feature.The argument in section 3.4 holds only insofar as phonological systems should not allow (Duke-of-York) opacity patterns.
The orthographic theory of rendaku and Lyman's Law makes one specific prediction about rendaku, which is unfortunately not easy to test-/p/ should block rendaku, because it should trigger Lyman's Law. 8Unfortunately, rendaku applies mainly to native items, and native items rarely contain non-geminate /p/, because Japanese lost this phoneme at some point in its history (Ueda 1898;Ito & Mester 1995;1999;2008;Frellesvig 2010;Takayama 2015).In the rendaku database (Irwin 2016b;Irwin & Miyashita 2016), there is one monomorphemic native stem that contains /p/ or /pp/, suppa-i 'sour', which undergoes rendaku (e.g.ama-zuppa-i 'sweet and sour').This word would have to be treated as an exception.There are two more relevant native words happa 'leaves' and sippo 'tail', neither of which undergoes rendaku (Vance 2007).Another relevant word kappa 'coat' undergoes rendaku (e.g.ama-gappa 'rain coat'), contra the prediction of the orthographic theory of Lyman's Law.This word, however, is doubly exceptional, because it is a loanword from Portuguese capa (Labrune 2012) (recall that rendaku is usually limited to native words).Overall, there are exceptions for the original formulation of Lyman's Law based on [+voice] as well (e.g.hasigo 'ladder' and saburoo (personal name), which undergo rendaku)-I thus contend that these exceptions are not detrimental to the orthographic theory of Lyman's Law.
Table 4 provides a summary of what has been discussed in the paper.The leftmost column shows whether each segment triggers devoicing of geminates.Whether [ŋ] triggers devoicing of geminates is unclear, because there are no words with a voiced geminate and a word-medial /ɡ/ (and no other potential trigger). 9The second column shows whether each segment blocks rendaku.The third column shows whether they are phonetically voiced.The fourth column shows voicing in obstruents.The last column shows whether each sound is written with a diacritic mark in Japanese orthography.It seems that the last column matches the first two columns best. 10inally, there are a few ways to explicitly falsify the current proposal.One is that if some time in the future, a new sound starts to be expressed with a diacritic mark in the Japanese orthography system, then the current proposal predicts that that soundwhatever its phonetic property may be-will trigger Lyman's Law.On the other hand, as long as that new sound is not a voiced obstruent, it is not predicted to trigger Lyman's Law, if Lyman's Law is to be characterized as OCP(+voice).Such a situation will provide a potential opportunity to tease apart the orthographic-based theory of Lyman's Law and the more traditional voicing-based theory of Lyman's Law.Another prediction is that pre-literate children would not show /p/-driven geminate devoicing, until they learn that /p/ in Japanese is written with a diacritic.These predictions, especially the latter, can be tested in future research.

Do we need the [voice] feature in Japanese?
The current proposal, according to which Japanese phonology has a class of dakuten sounds, raises the question of whether we need a phonological [+voice] feature in Japanese phonology.At the descriptive level, there are cases which require reference to "[+voice]" in Japanese phonology; for example, native words do not have voiced geminates, but they allow voiceless geminates (Ito & Mester 1995; 1999; 2008). 11To capture this characteristic of Japanese phonology, we may need to posit a constraint like *[+voice, -son, +gem] (Ito & Mester 1999;2008;Kawahara 2006).However, it is not impossible to reformulate these cases using dakuten diacritics instead-the constraint can potentially be reformulated as Since voicing in sonorants is not marked by dakuten, if sonorant voicing is active in Japanese phonology, we would need a feature for sonorant voicing, in addition to dakuten.Rice (1993;2005) in fact argues that such a feature is necessary because nasals cause post-nasal voicing in Japanese.However, this post-nasal voicing has been reanalyzed as an effect of a *NT constraint (Pater 1999), which has independent motivations (Hayashi & Iverson 1998) (see footnote 6).Based on these considerations, it does not seem impossible to eliminate the [+voice] feature from Japanese phonology entirely in favor of dakuten (though see also footnote 12).The advantage of dakuten over [+voice], to reiterate the argument from section 3.2, is that it can form a natural class with han-dakuten, which is necessary to model the geminate devoicing pattern.
It is more difficult to eliminate the [-voice] feature.For example, Japanese high vowels devoice between two voiceless obstruents, and after a voiceless obstruent before a pause (see e.g.Tsuchida 1997;2001;Fujimoto 2015 and many references cited therein).Crucially, Japanese orthography does not distinguish voiceless obstruents from sonorants in terms of diacritics, and therefore, there is no way in which we can describe the environment for high vowel devoicing in terms of Japanese orthography.
Neither is it possible to describe the high vowel devoicing itself with Japanese orthography.In this sense, we would need the [-voice] feature to describe the high vowel devoicing pattern.It is possible, however, that voicelessness should be represented as [+spread glottis] in Japanese (Tsuchida 1997;2001), in which case, Japanese phonology may lack the [voice] feature entirely in its system.Kawahara & Sano (2016) entertained possibilities other than the orthographic-based explanation for /p/-driven geminate devoicing, discussed in section 3.2.This subsection compares the current proposal with these alternatives to model /p/-driven geminate devoicing.For example, one alternative possibility is to posit OCP(Infrequent) (Fukazawa et al. 2015), which prohibits two segments that are infrequent within the same word; indeed, singleton /p/s and voiced geminates are both infrequent in the entire Japanese lexicon, as they in principle appear only in loanwords.Another possibility that Kawahara & Sano (2016) entertained is OCP(LaryngeallyMarked) to the extent that both singleton /p/ and voiced geminates are laryngeally marked (Hayes 1999;Hayes & Steriade 2004).

Comparison with other theories
One general argument against these alternatives is that they do not explain the other aspects of rendaku that are discussed in this paper (i.e., phonetic diversity of pairs related by rendaku, inertness of [voice] in Lyman's Law, and opacity of rendaku with respect to velar nasalization).To reiterate, the orthographic explanation accounts for a constellation of properties of rendaku and Lyman's Law.These alternatives do not have this general explanatory power.
Another major difference between the current proposal and the alternatives is that the current proposal predicts that /p/-driven devoicing of geminates occurs only if a language uses the same or similar diacritic marks for /p/ and voiced obstruents, as in Japanese.
12 There is a non-trivial drawback of this proposal, however.The constraint *[+voice, -son, +gem] has a clear phonetic basis-it is hard to sustain enough transglottal airpressure drop to maintain glottal vibration during long geminate closure (Ohala 1983;Hayes & Steriade 2004;Kawahara 2006).For this reason, this constraint is active in many other languages (Hayes & Steriade 2004).Ultimately, then, it may not be desirable to eliminate the constraint *[+voice, -son, +gem] in favor of *[っ X゛].In that case, Japanese has two ways to represent voicing, [+voice] and dakuten diacritics, only the latter of which form a natural class diacritic with han-dakuten.Kawahara & Sano (2016) consulted the P-Base (Mielke 2007) (http://pbase.brohan.ca/query) to examine whether /p/-driven geminate devoicing exists in other languages.The search did not find any example of devoicing that was caused by /p/ at a distance.The P-Base contains 7318 phonological patterns from 629 languages, indicating that /p/-driven devoicing is a very rare process cross-linguistically.The orthographic theory explains why this phenomenon is limited to Japanese-it is because Japanese (and only Japanese), for a historical reason, marks /p/ with a diacritic.Admittedly, I did not check whether the rest of the languages in the P-base do not mark /p/ with the same or similar diacritic as voiced obstruents, because the P-Base does not provide orthographic information for these languages, but it seems to be a safe assumption to make.Of course, if there is a language with an orthographic system that is similar to Japanese, the prediction is that /p/-driven geminate devoicing would be possible in that language.Neither OCP(Infrequent) nor OCP(LaryngeallyMarked) makes this connection between the language's orthography system and /p/-driven geminate devoicing.
There are specific problems with these alternative analyses as well; as for OCP(Infrequent), if it is the infrequency of singleton [p] that causes devoicing of geminates, it could be that other infrequent segments or segmental sequences like [ɸi] or [ti/tu] can cause devoicing.Sequences like [ɸi] or [ti/tu] are infrequent in Japanese just like [p], as they appear only in recent loanwords, but to the best of my knowledge, these segments do not trigger devoicing of geminates.In general, the constraint OCP(Infrequent) allows any two infrequent items to interact, but this sort of interaction does not seem to happen.Note that OCP(Infrequent) is predicted to cause not only devoicing, but also other phonological processes.For example, it predicts the existence of a pattern in which [ti] undergoes affrication-a process obligatory in the native phonology of Japanese-if and only if there is [ɸi] elsewhere in the same word.Such alternations do not occur, at least in Japanese.
OCP(LaryngeallyMarked) comes with its own problems.It predicts for example that there could be a constraint like OCP(Manner-wiseMarked), which for instance predicts a co-occurrence restriction on fricatives and clicks, assuming that fricatives and clicks are marked in terms of their manner of articulation.Likewise, OCP(Place-wiseMarked) can prohibit a co-occurrence of a labial consonant and a dorsal consonant (assuming that coronal is the least marked place of assimilation: Prince & Smolensky 2004;de Lacy 2006).These co-occurrence restrictions do not seem to be observed in natural languages.In short, both OCP(Infrequent) and OCP(MarkedInSomePhonol ogicalDimension) predict a range of interactions that are unlikely to occur in natural languages.

Can phonology refer to other orthographic information?
The overall proposal of this paper is that phonological systems can refer to orthographic information.A question that naturally arises is whether other orthographic representations can be referred to in phonology.There is evidence from Japanese phonology that OCP(diacritic) may not actually be an isolated example in which phonological constraints refer to orthographic information.Based on patterns of loanword adaptation, Ito & Mester (2003a: 49-50) propose that Japanese prohibits two instances of geminates within a word, and hence OCP(gem) is active.Their evidence comes from the observation that gemination in loanword adaptation does not occur twice within a word, as in (2a-c); the examples in (2d-f) show that word-medial gemination is possible, when there are no other geminable consonants in the word.This constraint OCP(gem) can easily be reformulated as OCP(っ), where っ is an orthographic marker for gemination.Ito et al. (2017) recently reiterate the argument for OCP(gem) (which should be formalized as OCP(っ), if the current proposal is on the right track).'pipette' d. [pikkoro] 'piccolo' e. [zukkiini] 'zucchini' f. [rokkuɸooru] 'Roquefort' Therefore, it may be that phonological constraints referring to orthographic information are not as rare as we think, once we accept the view that orthography can influence phonology in non-trivial ways.This prediction should certainly be tested in languages other than Japanese.A possible candidate for an orthography-based constraint outside of Japanese is found in Slovak, in which long vowels are not allowed in adjacent syllables (Kenstowicz & Rubach 1987).In the Slovak writing system, the length of vowels is represented by an acute accent mark on the vowels.Slovak may thus have OCP(AcuteAccentMark).
Going beyond, can there be a constraint like OCP(umlaut), which prohibits two front rounded vowels?Can there be a constraint like OCP(diareses), which prohibits two nondiphthongal pronunciations of vowel sequences within a morpheme?There are likely to be limits on how much orthographic information phonology has access to, and there should be a principled way to impose such a restriction.However, it is beyond the scope of this paper to explore and examine the general properties and limitations of the phonologyorthography interaction.The problem is that we only know a few cases, including the current case, that involve the interaction between phonology and orthography.Only after accumulation of cross-linguistics studies do we understand what kinds of restrictions should be imposed on the orthography-phonology interface.It is sincerely hoped that this paper piques other researchers' interests in looking at potential cases of phonological patterns that make reference to orthographic information, which will allow us to uncover some principled restrictions on how much orthographic information phonology can refer to.
Hence, we need to conduct extensive cross-linguistic investigation to explore the connection between orthography and phonology in further detail.In doing so, there is one crucial distinction that needs to be made when studying potential orthography-phonology interaction: phonological patterns that require direct reference to "inherently orthographic information" vs. "phonological representation informed by orthographic information". 13t is not very hard to look for examples of the second kind.For example, take an English minimal pair like latter vs. ladder.Without orthographic information, there is no way for (North American) English speakers to know that the first word contains word-medial /t/, whereas the latter word contains word-medial /d/.Adult English speakers presumably know the difference between the two words, because when they hyper-articulate, their underlying /t/ and /d/, which would otherwise be neutralized as a flap, can be pronounced as such.However, from their surface sounds alone, it is very difficult to learn that latter contains /t/ and ladder contains /d/ in their underlying representation.14Nevertheless, synchronically speaking, the underlying representations themselves do not have to rely on orthography directly, i.e., they need to be learned based on orthographic information, but they themselves can be purely phonological (see also Taft 2006).
Another example, discussed by Ito et al. (1996), is how the syntax term SPECshortening of specifier-is read with final [k].It is unlikely that /s/ in specifier becomes [k] when truncated (although it is not unimaginable given Velar Softening proposed in SPE: Chomsky & Halle 1968).Ito et al. (1996) thus argue that this [k] is informed by the orthography, i.e., word-final C.However, once the word SPEC is lexicalized with the help of orthography, English speakers can store its underlying representation as /spɛk/, which can be purely phonological.
Similarly, many studies of loanword adaptation have shown that the role of orthography is non-negligible (Silverman 1992;Vendelin & Peperkamp 2006;Smith 2007;Daland et al. 2015).To take an example from Japanese, the English word manager is borrowed as [maneeʑaa] in Japanese.Note that the second vowel in the original manager is a schwa in English, and there is no reason that it had to be borrowed as a long vowel /ee/ in Japanese (p.c.Junko Ito, Oct. 2016).In this example, the orthography "a" in the original English word, and knowledge that this letter sometimes represents a diphthong in English (as in "ape") may have led Japanese speakers to borrow it as a long vowel.See Smith (2007) for other examples of the influence of orthography in loanword adaptation in Japanese.Again, although underlying representations of such words may need to be informed by orthographic consideration, synchronically there are no reasons to doubt that underlying forms of these words are purely phonological.

Universality of constraints?
To recapitulate, the current proposal is that Japanese has OCP(diacritic).This constraint, taken literally, must be specific to Japanese (hence not universal), because "diacritic" here specifically refers to the diacritic marks in the Japanese orthography system.This postulation may at first sight seem to contradict one of the important theses of OT (Prince & Smolensky 2004) that a set of constraints (i.e. the content of CON) is universal.While this concern is legitimate to some extent, the current proposal may not constitute a large departure from the original formulation of Optimality Theory, as presented in Prince & Smolensky (2004).The reason is that OT, from its inception, admits morpheme-specific constraints-for example, Prince & Smolensky (2004: 42) use an alignment constraint that is specific to a morpheme /-um/ in Tagalog (Edgemost(um; L)).This constraint cannot be a universal constraint, because /-um/ is not a morpheme used by every language.
Thus, one way to reconcile the current proposal and the claim that constraints are universal is that Universal Grammar provides templates of constraint schemata, such as alignment constraints and OCP, but arguments for these constraints can be filled in on a language-specific basis (like "diacritics" and "/-um/").For arguments that CON should provide systematic schemata of constraints (rather than a random set of constraints), see McCarthy (2002;2003a), Potts & Pullum (2002), Smith (2002), Gouskova (2004), Kawahara (2008), Flack (2009), among many others.

Rendaku is also sensitive to phonology
Even if the current proposal is on the right track, we need to make sure not to throw the baby out with the bathwater; i.e. banishing rendaku and Lyman's Law from the field of phonology entirely.As summarized in the introduction, recent work shows that orthographic knowledge may have a deep connection with our linguistic knowledge (Ito et al. 1996;Taft 2006;Nagano & Shimada 2014;Shaw et al. 2014).Likewise, it is unlikely that every aspect of rendaku can be reduced to orthography.Rendaku, for instance, interacts with several kinds of linguistic information, such as branching structures and morphosyntactic categories (Kubozono 2005;Vance & Irwin 2016), which cannot be reduced to orthography.Rendaku is also blocked by Identity Avoidance constraints (Kawahara & Sano 2014a;2014b;Tanaka 2017), as well as by OCP(labial) (Kawahara et al. 2006;Kumagai 2017).It also interacts with pitch accent, in such a way that rendaku often correlates with unaccentedness in compounding (Sugito 1965;Zamma 2005;Kurisu 2010).
It is also important to note that in the loanword devoicing pattern discussed in section 3.2, only voiced geminates, not singletons, can get devoiced in response to Lyman's Law, as shown in Figure 1-i.e.devoicing due to Lyman's Law is delineated by a grammatical distinction like singletons vs. geminates (Kawahara 2006;2016).Therefore, a grammatical consideration comes into play, even if the trigger of devoicing is defined in terms of orthography, i.e., OCP(diacritic).It thus seems most productive to consider an interplay between orthography and other grammatical principles in order to explain our linguistic behavior.Japanese speakers should have an orthographic representation as part of their linguistic knowledge (Nagano & Shimada 2014), and that representation can affect their speech behavior, in tandem with phonological and other linguistic representations.

Overall conclusion
Recent work has shown that both phonological knowledge and orthographic knowledge influence our linguistic behavior.This paper has shown that many properties of rendaku and Lyman's Law automatically follow, if we take the orthographic patterns of Japanese into consideration.First, at the surface phonetic level, rendaku is not a simple matter of "voicing the target consonant", but involves different sets of more complicated pairings.However, in terms of orthography, rendaku can be characterized as an addition of dakuten.Second, postulating Lyman's Law as OCP(diacritic) explains why /p/ can cause devoicing of geminates.Third, this theory explains why Lyman's Law ignores the voicing of sonorants.Fourth, it explains why /ɡ/ blocks rendaku, after it turns into [ŋ].However, some aspects of rendaku are undoubtedly phonological, which suggest that rendaku is phonological as much as it is orthographic.Taken together, then, we should develop a model of phonology in which phonological operations and constraints can refer to orthographic information.
One interesting prediction that the current proposal makes about rendaku is that preliterate children should not be able to apply rendaku productively, and that as their orthographic knowledge develops, so does their knowledge of rendaku and Lyman's Law.This prediction has to be tested independently (for evidence that rendaku is acquired gradually, see Sugimoto 2013, who unfortunately does not report the development of the children's orthographic knowledge).A related question is how OCP(diacritic) is learned by Japanese children, because obviously, OCP(diacritic) cannot be an innate constraint.The most obvious candidate is that it is learned based on Japanese phonotactics.How existing theories of phonotactic learning, such as the one proposed by Hayes & Wilson (2008), can extend to OCP(diacritic) and how that prediction aligns with the actual acquisition processes would be a very important line of future research.

Figure 1 :
Figure 1: Devoicability of each type of consonant.Based on Kawahara & Sano (2016).Reprinted with the permission from the editor and the publisher.

Table 3 :
A derivational analysis of the opacity.One may argue that natural languages do show (Duke-of-York) opacity, and hence phonological grammar must be powerful enough to deal with opacity (e.g.Idsardi 2000;