Breiss, Katsuda & Kawahara (2026): Token frequency modulates optional paradigm uniformity in Japanese voiced velar nasalisation #
@cite{breiss-katsuda-kawahara-2026} @cite{mccarthy-2005} @cite{steriade-2000} @cite{ito-mester-1996} @cite{ito-mester-2003} @cite{hibiya-1995} @cite{coetzee-pater-2008} @cite{paster-2019}
The Japanese velar /g/ → [ŋ] alternation in N1+N2 nominal compounds is optional: speakers vacillate between [g] and [ŋ] for many compounds, and the rate of nasalisation varies across compounds, items, and speakers. The paper's central architectural claim is that this optionality is modulated by token frequency through two opposite-sign channels:
- High token frequency of N2 as a free wordform decreases the rate of nasalisation (negative regression coefficient on N2 token frequency). The free-form [g] is a more accessible paradigm exemplar; paradigm-uniformity pressure preserves it, suppressing [ŋ].
- High token frequency of the compound itself increases the rate of nasalisation (positive regression coefficient on compound token frequency). More-attested compounds drift further from their constituent forms.
Both effects only apply when N2 is morphologically free. When N2 is bound (occurs only inside compounds — no surface [g] paradigm exemplar to anchor to), nasalisation is categorically obligatory. The two-channel frequency story collapses to a single-channel (markedness- only) story in the bound case.
Examples from the paper #
Taken verbatim from @cite{breiss-katsuda-kawahara-2026}:
- (1a) /haigan/ ~ /haiŋan/ "lung cancer" — N2 'cancer' (癌) is free.
- (1b) /noogeka/ ~ /nooŋeka/ "brain surgery" — N2 'surgery' (外科) is free.
- (2a) /dokuga/ ~ /dokuŋa/ "poison moth" — N2 'moth' (蛾) is free.
- (2b) /dokuŋa/ *[dokuga] "poison fang" — N2 'fang' (牙) is bound.
- (3) /gaʒoo/ "main castle" — initial-position [g] never nasalises.
The minimal pair (2a)/(2b) is the paper's central piece of evidence: two compounds with identical surface form /dokuga/ but different free/bound status of the segmentally-identical N2 yield categorically different nasalisation behaviour.
Connection to Paradigm Uniformity #
The architecture is paradigm uniformity (PU) + frequency-conditioned strength. The compound and its free N2 stand in a paradigm relation; PU prefers their shared segments to be alike. The PU pressure is modulated — not just on/off — by the token frequency of the N2. This puts the paper at the intersection of:
- @cite{mccarthy-2005} (PU as the symmetric pairwise lift over members;
see
ParadigmUniformity/OptimalParadigms.lean). - @cite{steriade-2000} Lexical Conservatism (PU pressure is anchored
on attested wordforms; see
ParadigmUniformity/LexicalConservatism.lean). - @cite{coetzee-pater-2008} Frequency-scaled weights (the modulation
channel — token-frequency drives a continuous weight; see
ItemSpecificity/ScaledWeights.lean).
The previous constraint-based account of @cite{ito-mester-1996} / @cite{ito-mester-2003} treats nasalisation as the result of a high-ranked markedness constraint; @cite{hibiya-1995}'s sociolinguistic study established the variable, lexically-modulated character of the alternation. BKK 2026's contribution is the sign of the two frequency channels and the architectural commitment that the two-direction story collapses to one direction in the bound case.
Connection to ItemSpecificity theories #
The companion modelling paper (Breiss, Katsuda & Kawahara,
lingbuzz/009508) fits a MaxEnt grammar with @cite{steriade-2000}'s
Lexical Conservatism. We do not formalise the fitting routine here.
The discrimination this study makes against the four siblings in
Theories/Phonology/ItemSpecificity/:
- ScaledWeights (@cite{coetzee-pater-2008}): consistent with the data, with separate slopes per channel (positive on cpd freq, negative on N2 freq).
- RepresentationStrength (@cite{moore-cantwell-2021}): consistent — high N2 activation preserves the boundary segment.
- UseListed (@cite{zuraw-2000}): ruled out by Experiment 2
(novel compounds show the same N2-frequency gradient as familiar
ones) — see
novel_compounds_show_n2_gradientbelow. - Indexed constraints (@cite{pater-2010}): in principle a multi-stratum approximation could fit, but parsimony favours the continuous accounts.
@cite{paster-2019}'s critique of "counting" patterns in phonology is relevant to BKK Experiment 2's finding that N2 length (not total compound length) matters — undermining a mora-counting analysis and favouring a paradigm-anchored account.
Boundary #
- We formalise the qualitative direction-of-effect predictions, not numerical fits, sample sizes, or specific corpus statistics.
- "Optional" is taken at face value as variable surface realisation; we do not commit to a stochastic OT vs. MaxEnt vs. mixed-effects encoding of the variation. The relevant fact for downstream theory is only that nasalisation rate is monotonic in the relevant log-frequency, with the appropriate sign per channel.
- The wug-test methodological contract lives in
Paradigms/WugTest.lean; this file consumes that paradigm via thenovel_compounds_show_n2_gradientdiscriminator.
hai 'lung' (肺) — N1 of /haigan/ "lung cancer", example (1a).
Equations
- Phenomena.Phonology.Studies.BreissKatsudaKawahara2026.n1_hai = { form := "hai", gloss := "lung", accentMora := some 0, nMorae := 2, tokenLogFreq := 5 }
Instances For
gan 'cancer' (癌) — high-token-frequency free N2. Free-form [g] is well-attested; PU pressure should be strong, suppressing nasalisation. Example (1a).
Equations
- Phenomena.Phonology.Studies.BreissKatsudaKawahara2026.n2_gan = { form := "gan", gloss := "cancer", accentMora := some 0, nMorae := 2, tokenLogFreq := 9 }
Instances For
noo 'brain' (脳) — N1 of /noogeka/ "brain surgery", example (1b).
Equations
- Phenomena.Phonology.Studies.BreissKatsudaKawahara2026.n1_noo = { form := "noo", gloss := "brain", accentMora := some 0, nMorae := 2, tokenLogFreq := 5 }
Instances For
geka 'surgery' (外科) — free N2, mid-frequency. Example (1b).
Equations
- Phenomena.Phonology.Studies.BreissKatsudaKawahara2026.n2_geka = { form := "geka", gloss := "surgery", accentMora := some 0, nMorae := 3, tokenLogFreq := 6 }
Instances For
doku 'poison' (毒) — N1 of both /dokuga/ "poison moth" and /dokuŋa/ "poison fang" — the minimal pair (2a)/(2b).
Equations
- Phenomena.Phonology.Studies.BreissKatsudaKawahara2026.n1_doku = { form := "doku", gloss := "poison", accentMora := some 0, nMorae := 2, tokenLogFreq := 5 }
Instances For
ga 'moth' (蛾) — low-frequency free N2. The free /ga/ standalone supplies the PU anchor. Example (2a).
Equations
- Phenomena.Phonology.Studies.BreissKatsudaKawahara2026.n2_ga_moth = { form := "ga", gloss := "moth", accentMora := some 0, nMorae := 1, tokenLogFreq := 1 }
Instances For
ga 'fang' (牙) — bound N2; never appears as a free wordform.
With no /ga/ anchor, PU pressure is null and nasalisation is
categorical. The minimal-pair partner of n2_ga_moth. Example (2b).
Equations
- Phenomena.Phonology.Studies.BreissKatsudaKawahara2026.n2_ga_fang = { form := "ga", gloss := "fang", accentMora := some 0, nMorae := 1, canStandAlone := false }
Instances For
/haigan/ "lung cancer" — example (1a). High-frequency free N2.
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/noogeka/ "brain surgery" — example (1b). Mid-frequency free N2.
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/dokuga/ "poison moth" — example (2a). Low-frequency free N2; optional nasalisation.
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/dokuŋa/ "poison fang" — example (2b). Bound N2 → categorical [ŋ].
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The bound case: JCompound.nasalisationObligatory returns true.
The free cases: JCompound.nasalisationObligatory returns false
— the compound is in the gradient/optional zone.
The minimal pair (2a)/(2b) has identical surface forms but opposite obligatoriness — the paper's central piece of evidence that bound vs. free is the right dimension.
Two free-N2 compounds are both in the optional zone, regardless of their N2's frequency. The frequency story is within the optional zone, not at its boundary.
The PU paradigm of a compound: the candidate compound surface form plus the attested free N2, when N2 is free; just the compound, when N2 is bound. The free/bound split is encoded as paradigm membership (1 vs. 2 elements), not a separate predicate guard on the constraint — that is what makes the bound-case zero structural rather than stipulated.
Built via lcParadigm from
Theories/Phonology/ParadigmUniformity/LexicalConservatism.lean,
making this file a downstream consumer of the LC anchored-paradigm
primitive. The anchor-presence channel is exactly what
@cite{steriade-2000} introduced, and BKK's bound/free split is the
same architectural channel applied to a new domain.
Equations
- Phenomena.Phonology.Studies.BreissKatsudaKawahara2026.n2Paradigm c = Phonology.ParadigmUniformity.lcParadigm c.form (if c.n2.canStandAlone = true then some c.n2.form else none)
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Surface mismatch between two strings: 0 on the diagonal, 1
off-diagonal. A whole-string identity check; not a velar-
feature comparison. The architecturally faithful version would
be a tier-restricted segment-by-segment comparison at the velar
position routed through Theories/Phonology/Featural/Geometry.lean,
but the qualitative architectural claims (sign of the channel,
bound/free split) do not depend on the specific mismatch metric.
Equations
- Phenomena.Phonology.Studies.BreissKatsudaKawahara2026.stringMismatch a b = if a = b then 0 else 1
Instances For
The PU constraint as a NamedConstraint — derived from
mkLCFaith from
Theories/Phonology/ParadigmUniformity/LexicalConservatism.lean.
The structural connection to @cite{steriade-2000} is by
construction: BKK's PU pressure IS LC-FAITH on the
lcParadigm-built paradigm. The architectural difference from
@cite{mccarthy-2005} (OP) is that LC's paradigm is anchored on
attestation; OP's is symmetric over all members. § 10 below makes
that contrast explicit.
Equations
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Number of PU-FAITH violations on a compound's paradigm.
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Bound case is structurally zero. A bound N2 produces a singleton
paradigm [c.form]; the only ordered pair is (c.form, c.form)
whose mismatch is 0 by definition. The categorical nasalisation in
bound compounds is the structural consequence of the PU channel
contributing nothing.
A free-N2 paradigm with distinct compound and N2 forms produces exactly two off-diagonal pairs, each contributing 1, for a total of 2 violations. The compound and N2 forms differ whenever N1 is non-empty — an empirically generic precondition.
The bound /dokuŋa/ case has zero PU violations — concrete witness.
The free /dokuga/ case has two PU violations — concrete witness.
The N2-frequency-weighted PU pressure on a compound: PU-FAITH
violations multiplied by scaledWeight of the N2 token
log-frequency. Higher N2 frequency → stronger weight → stronger
preservation of [g] → less nasalisation. This is the
negative-on-nasalisation channel (negative regression coefficient
on N2 token frequency in @cite{breiss-katsuda-kawahara-2026}).
Equations
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The compound-frequency-weighted markedness pressure for nasalisation: linear in compound log-frequency. Higher compound frequency → stronger drift away from constituent forms → more nasalisation. This is the positive-on-nasalisation channel (positive regression coefficient on compound token frequency in @cite{breiss-katsuda-kawahara-2026}).
Modelled as a one-parameter linear function of the compound's own
log-frequency, parallel to Scaled.scaledWeight but on the
compound (not lexical-entry) channel.
Equations
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The predicted nasalisation log-odds of a compound: markedness pressure (positive sign on nasalisation) minus PU pressure (negative sign on nasalisation). The sign-inversion of the PU channel is built into the difference — increasing PU monotonically decreases the log-odds.
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Sign-inversion lemma. PU pressure enters nasLogOdds with a
negative sign: holding compound markedness fixed, an increase in
PU pressure strictly decreases the log-odds. This is the formal
source of the negative regression coefficient on N2 token
frequency reported in @cite{breiss-katsuda-kawahara-2026}.
N2-frequency channel monotonicity (the negative-sign channel). For two free-N2 compounds with the same compound frequency and matched PU-violation counts, a higher N2 token log-frequency yields strictly higher PU pressure (when slope is positive).
Compound-frequency channel monotonicity (the positive-sign channel). For two compounds with identical PU pressure but different compound log-frequencies, the higher-compound-frequency compound has strictly higher nasalisation log-odds (when slope is positive).
Bound case: nasLogOdds collapses to pure markedness. Because the PU channel is structurally zero on bound paradigms, the bound-case prediction depends only on the compound-frequency channel — i.e. the bound case has one frequency channel, not two. This is the architectural collapse the paper highlights.
Anti-UseListed discriminator. Even on novel compounds (no
listing entry), the N2-frequency gradient on PU pressure persists,
because PU pressure depends on the N2's free-form attestation, not
the compound's listing status. UseListed (@cite{zuraw-2000})
predicts no frequency-dependent modulation on novel items;
puPressure and hence nasLogOdds show one. This is the formal
content of Experiment 2 of @cite{breiss-katsuda-kawahara-2026}.
Concretely: two novel free-N2 compounds with the same compound
log-frequency and matched PU-violation counts have strictly
different puPressure values when their N2 token frequencies
differ and the slope is strictly positive.
Experiment 2 of @cite{breiss-katsuda-kawahara-2026} is a wug-style study: subjects rate nasalisation on novel compounds whose N2 has real attestation as a free wordform. The N2-frequency gradient in their results is the key evidence against UseListed @cite{zuraw-2000}: a novel compound has no listing entry, so any frequency-driven modulation must come from the N2's lexical attestation, not the compound's.
This section wires BKK to the methodological contract in
Paradigms/WugTest.lean (anchored on @cite{berko-1958} and
@cite{albright-hayes-2003}). The cell type carries:
- a compound (the stimulus),
- a structural proof that N2 is free (so that the LC paradigm has the anchor and PU pressure is non-zero),
- a structural proof that compound and N2 forms differ (so that
cpdPuViolations = 2is forced), - the wug
Attestationfactor (attested vs. novel), - and the N2 token log-frequency.
The first two fields make the cell type non-vacuous in a way that
discharges the cpdPuViolations precondition without per-cell
hypotheses. Concretely: for every WugBKKCell, we prove (not
assume) that PU violations equal 2.
- compound : Fragments.Japanese.Prosody.JCompound
- freeN2 : self.compound.n2.canStandAlone = true
- attestation : Paradigms.WugTest.Attestation
- n2LogFreq : ℝ
Instances For
Every WugBKKCell has exactly two PU violations — a derived
consequence of the structural fields, not a stipulation. This is
the load-bearing fact that lets wugBkkRate exhibit a strict
frequency gradient on novel cells without per-cell side
conditions.
Equations
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Equations
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wugBkkRate is BKK's per-cell numeric prediction expressed in the
shape Paradigms/WugTest.lean requires (Rate Cell ℝ). It exhibits
the N2-frequency gradient on novel cells, satisfying the WugTest
predicate NovelShowsFreqGradient — and hence (by
novelGradient_inconsistent_with_invariance) excluding the UseListed
prediction NovelInvariantInFrequency.
The sign of wugBkkRate is monotone increasing in N2 log-frequency
because it tracks the PU pressure, not the surface nasalisation
rate. PU pressure pushes toward [g] preservation; nasalisation rate
falls as PU pressure rises. The discriminator from WugTest only
cares about non-flatness of the rate function in the frequency
factor, so the sign is irrelevant to the structural exclusion of
UseListed.
The wug-paradigm rate observable for BKK: PU pressure on the
cell's compound, computed via cpdPuViolations (= 2 for every
WugBKKCell) times the N2's frequency-scaled weight.
Equations
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BKK satisfies NovelShowsFreqGradient. For any positive
N2-frequency slope, wugBkkRate is strictly monotone in the
frequency factor on novel cells. The proof uses
WugBKKCell.cpdPuViolations_eq_two to discharge the violation
count without per-cell hypotheses.
This is the structural form of BKK Experiment 2's central finding: even on novel compounds, varying N2 token frequency produces a gradient in the predicted PU pressure.
A concrete non-vacuous WugBKKCell witness: /haigan/ "lung
cancer" used as a wug stimulus. The structural fields are
discharged by rfl / decide. Required for the discriminator
corollary below — novelGradient_inconsistent_with_invariance
needs distinct frequencies, which it gets from 0 < 1.
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Anti-UseListed discriminator (final form). Wired through
Paradigms/WugTest.lean's structural impossibility theorem: BKK's
wugBkkRate cannot satisfy NovelInvariantInFrequency (the
UseListed prediction). Any account on which novel forms have flat
PU pressure across N2 frequencies is ruled out by Experiment 2.
This is novel_compounds_show_n2_gradient re-expressed at the
paradigm-contract level: instead of a per-pair puPressure
inequality, we get a structural impossibility on the rate
function itself.
BKK's docstring cites OP (@cite{mccarthy-2005}) as a sister PU theory; the architectural choice is LC over OP because LC's anchor primitive structurally encodes the bound/free split.
Caveat on the analog. @cite{mccarthy-2005}'s OP, narrowly construed, ranges over the inflected wordforms of a single lexeme — not over a compound and its N2 constituent. Applying OP to N1+N2 compound paradigms is an extended application not licensed by the 2005 paper itself. The point of this section is precisely that extending OP straightforwardly to the compound case loses the bound/free distinction: a compound and its (free or bound) N2 are not in an OP-style inflectional relationship, so the architectural handle LC supplies via attestation-anchored paradigm membership has no natural OP counterpart. This is part of why BKK choose LC rather than OP for the compound domain.
The OP-on-compounds straw-figure formalised below predicts identical PU violations on bound and free compounds with distinct N2 surface forms — losing BKK's categorical bound-case nasalisation as a structural prediction. To recover the empirical pattern, an extended-OP account would need an auxiliary stipulation (a separate constraint, a stratum, or a guard predicate). LC gets it from paradigm membership alone.
The OP paradigm of a compound: symmetric over all members, no distinguished anchor. Because OP does not condition on attestation, both bound and free N2 contribute to the paradigm.
Equations
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The OP-flavoured PU constraint, built from the same liftPairwise
combinator. Differs from puFaith only in the paradigm
construction (cf. lcParadigm vs. unconditional pair).
Equations
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OP-flavoured violation count on a compound.
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OP gives identical violation counts on bound and free
compounds. Whenever c.form ≠ c.n2.form, the OP paradigm
[c.form, c.n2.form] has two off-diagonal pairs each contributing
1, regardless of N2 attestation. This is the structural
consequence of OP's anchor-blindness.
Extended-OP and LC structurally disagree on bound compounds. For any bound-N2 compound with distinct compound and N2 forms, the OP-on-compounds analog predicts 2 violations while LC predicts 0. This is the formal incompatibility motivating BKK's choice of LC over an OP-style account in the compound domain — structural, not parameter-dependent. The empirical categorical bound-case nasalisation supports LC.
NB: see the §10 caveat. McCarthy's OP, narrowly construed, is over inflectional paradigms of one lexeme; the disagreement here is with an extended-OP that applies the symmetric-paradigm architecture to N1+N2 compounds, which BKK take to be the natural OP-style competitor in this domain.
Concrete witness: /dokuŋa/ "poison fang" instantiates the OP/LC disagreement. OP says 2 violations; LC says 0.