Rose & Walker (2004) @cite{rose-walker-2004} #
A Typology of Consonant Agreement as Correspondence. Language 80(3): 475–531.
@cite{rose-walker-2004} present a typology of long-distance consonant agreement (LDCA) — covering nasal, laryngeal, liquid, coronal, and dorsal harmonies — and analyze it within Optimality Theory using a correspondence-theoretic apparatus: pairs of similar consonants in the output stand in a CORR-CC correspondence relation, and IDENT-CC[F] constraints require corresponding consonants to share the value of feature [F]. Their architecture predicts that agreement is more likely between more similar consonants and that intervening dissimilar material is "neutral" rather than blocking.
What this file formalizes (and what it does not) #
We do not formalize Rose & Walker's correspondence apparatus (CORR-CC, IDENT-CC[F], the similarity-based ranking) — that is a constraint architecture in OT and lives outside the subregular layer. What we formalize here is the surface stringset of one of their core case studies — Kikongo nasal harmony, the paper's leading example — as a tier-based strictly 2-local language, following the Heinz/Rogers/Hansson subregular tradition (@cite{hansson-2010}, @cite{mcmullin-2016}).
The framing is: Rose & Walker's correspondence analysis derives the surface generalization; the TSL_2 description characterizes the surface stringset that their derivation produces. The two analyses operate at different levels and are not in competition for the same explanatory work.
The function-level subregular substrate at
Core/Computability/Subregular/Function/ provides a separate axis of
classification for the map (UR → SR) rather than the stringset; LDCA
maps are typically Tier-Subsequential (specifically Right-Tier-Subsequential
per @cite{hansson-2010}'s anticipatory directionality argument). We
keep the language-level TSL_2 statement here because the directionality
argument is upstream of the surface filter formalised in this file.
Kikongo nasal harmony is asymmetric: the forbidden tier-adjacent pair
is (nasal, voiced-stop), not the reverse. This is a strict instance of
the generic TSLGrammar.ofForbiddenPairs constructor and does not
factor through either TSLGrammar.ocp (R := (· = ·)) or
TSLGrammar.agree (R := (· ≠ ·)); the AGREE specialization captures
symmetric harmony (e.g. Navajo sibilant harmony in Hansson2010.lean).
The asymmetry here tracks the morphological geometry (stem→suffix
direction), not a feature-symmetric agreement relation.
Design boundary #
Things this formalization is silent on, by design:
- Similarity-scaled correspondence: in ABC, harmony probability depends gradiently on featural similarity. The TSL_2 stringset is sharp — a pair either is or is not forbidden.
- Trigger/target asymmetry: the OT derivation distinguishes the feature source from its target; the surface phonotactic does not.
- Transparency vs blocking by similarity: ABC predicts that
intervening segments behave differently depending on how similar
they are to the harmonizing pair. Single-tier TSL with a fixed
tier predicate cannot express this — see the design-boundary
docstring on
tierProjectnon-monotonicity inForbiddenPairs.lean. Cases where transparency is similarity-graded (e.g. the Sanskrit n-retroflexion pattern Rose & Walker discuss) require richer formalisms (multi-tier strictly local; ITSL).
Kikongo nasal harmony — the paper's leading case #
@cite{rose-walker-2004} open with Kikongo (Bantu): a voiced oral stop
in the suffix is realized as a nasal stop when the stem contains a
preceding nasal consonant. For example, the suffix -idi alternates
to -ini after a nasal. Equivalently, the surface phonotactic is:
no nasal consonant may be followed at any consonantal distance by a
voiced oral stop within the relevant morphological domain.
The TSL_2 description: project the harmonizing-class tier (only nasal
consonants and voiced oral stops project; neutral consonants and vowels
are transparent), then forbid any tier-adjacent pair (C₁, C₂) where
C₁ is [+nasal] and C₂ is a voiced oral stop.
A minimal alphabet sufficient to demonstrate Kikongo nasal harmony as a TSL_2 stringset. We do not model the full Kikongo inventory — just enough segment classes to distinguish the relevant natural classes (nasal consonants, voiced oral stops, neutral consonants, vowels).
- nasalC : KSeg
A nasal consonant ([+nasal, +cons], e.g. /n/, /m/, /ŋ/).
- voicedStop : KSeg
A voiced oral stop ([+voice, −nasal, +cons, −cont], e.g. /b/, /d/, /g/).
- neutralC : KSeg
A neutral (non-nasal, non-voiced-stop) consonant ([+cons], e.g. /s/, /k/, /t/).
- vowel : KSeg
A vowel ([−cons]) — transparent for nasal harmony.
Instances For
Equations
- Phonology.Studies.RoseWalker2004.instDecidableEqKSeg x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
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The harmonizing-class tier predicate: nasal consonants and voiced
oral stops are on-tier. Neutral consonants and vowels are transparent
(off-tier). This corresponds to the long-distance reading of the
@cite{rose-walker-2004} typology — only the segments participating in
the agreement form the relevant locality domain. The tier choice is the
substantive theoretical commitment (cf. the design-boundary docstring
on tierProject non-monotonicity in ForbiddenPairs.lean).
Equations
Instances For
Equations
- Phonology.Studies.RoseWalker2004.instDecidablePredKSegOnTier Phonology.Studies.RoseWalker2004.KSeg.nasalC = isTrue trivial
- Phonology.Studies.RoseWalker2004.instDecidablePredKSegOnTier Phonology.Studies.RoseWalker2004.KSeg.voicedStop = isTrue trivial
- Phonology.Studies.RoseWalker2004.instDecidablePredKSegOnTier Phonology.Studies.RoseWalker2004.KSeg.neutralC = isFalse not_false
- Phonology.Studies.RoseWalker2004.instDecidablePredKSegOnTier Phonology.Studies.RoseWalker2004.KSeg.vowel = isFalse not_false
The forbidden-pair relation: a nasal consonant immediately followed on the harmonizing-class tier by a voiced oral stop. Asymmetric: the surface phonotactic emerges from a stem→suffix morphological geometry, in which only the (nasal stem, voiced-stop suffix) configuration arises. The reverse order (voiced stop then nasal) is unattested in the relevant domain rather than independently licit; the asymmetry tracks the morphological geometry, not a separately stipulated directionality of agreement.
Equations
Instances For
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- Phonology.Studies.RoseWalker2004.instDecidableRelKSegForbidNasalStop Phonology.Studies.RoseWalker2004.KSeg.nasalC Phonology.Studies.RoseWalker2004.KSeg.voicedStop = isTrue trivial
- Phonology.Studies.RoseWalker2004.instDecidableRelKSegForbidNasalStop Phonology.Studies.RoseWalker2004.KSeg.nasalC Phonology.Studies.RoseWalker2004.KSeg.nasalC = isFalse not_false
- Phonology.Studies.RoseWalker2004.instDecidableRelKSegForbidNasalStop Phonology.Studies.RoseWalker2004.KSeg.nasalC Phonology.Studies.RoseWalker2004.KSeg.neutralC = isFalse not_false
- Phonology.Studies.RoseWalker2004.instDecidableRelKSegForbidNasalStop Phonology.Studies.RoseWalker2004.KSeg.nasalC Phonology.Studies.RoseWalker2004.KSeg.vowel = isFalse not_false
- Phonology.Studies.RoseWalker2004.instDecidableRelKSegForbidNasalStop Phonology.Studies.RoseWalker2004.KSeg.voicedStop x✝ = isFalse not_false
- Phonology.Studies.RoseWalker2004.instDecidableRelKSegForbidNasalStop Phonology.Studies.RoseWalker2004.KSeg.neutralC x✝ = isFalse not_false
- Phonology.Studies.RoseWalker2004.instDecidableRelKSegForbidNasalStop Phonology.Studies.RoseWalker2004.KSeg.vowel x✝ = isFalse not_false
The Kikongo nasal-harmony grammar as a tier-based strictly 2-local
language: project to the harmonizing-class tier (nasals + voiced stops),
forbid nasalC-then-voicedStop adjacency on the tier.
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A schematic pre-harmony form: a nasal stem consonant followed (across vowels and a neutral coda) by a voiced oral stop in the suffix. Illustrates the offending input configuration that Kikongo harmony resolves; not a verbatim Kikongo lexical item.
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The corresponding post-harmony surface form: the suffix voiced stop has been realized as a nasal. Illustrates the resolved configuration; not a verbatim Kikongo lexical item.
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A schematic control form with no nasal trigger: the voiced stop is
licit because no preceding tier element is nasalC.
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The pre-harmony underlying form is rejected: it contains a
tier-adjacent nasalC-voicedStop pair.
The post-harmony surface form is accepted: every tier-adjacent pair is licit.
Forms with no nasal trigger are accepted even if they contain voiced stops — the constraint is conditional on a preceding tier- adjacent nasal.
The OT markedness constraint corresponding to the Kikongo nasal-harmony
phonotactic: AGREE-style markedness penalizing each tier-adjacent
nasalC-voicedStop pair on the harmonizing-class tier. The OT-side
counterpart of kikongoNasalHarmony — same forbidden-pair relation,
same tier predicate, packaged as a NamedConstraint. The TSL grammar
characterizes the language; this constraint evaluates it.
This case does not use mkAgreeOnTier (the symmetric R := (· ≠ ·)
specialization) because Kikongo's forbidden pair is asymmetric — see the
"What this file formalizes" docstring above.
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kikongoAgree is a markedness constraint by construction.
Bridge: kikongoAgree evaluates to zero on a candidate iff the
candidate is in the TSL_2 language. The "OT-side" and "subregular-side"
characterizations of the same Kikongo phonotactic coincide — making the
co-extensiveness of the two analyses true by construction rather than a
separately-proved equivalence.
TSL_2 witness: Kikongo nasal harmony is tier-strictly-local at window-size 2.
BTSL_2 corollary (via IsTierStrictlyLocal.toIsBTSL in
Core.Computability.Subregular.Multitier): Kikongo nasal harmony is in
the multitier closure of strictly local languages, hence consumed by
the @cite{lambert-2026} BTC framework.