Finnish Consonant Gradation @cite{karlsson-2017}

@cite{hayes-2009}

Consonant gradation is a morphophonological alternation affecting stops at morpheme-internal syllable boundaries in Finnish (@cite{karlsson-2017}, Chs. 4–5). The strong grade appears in open syllables; the weak grade appears in closed syllables (i.e., before a coda consonant).

Quantitative gradation

Geminate stops shorten:

• pp → p, tt → t, kk → k

Qualitative gradation

Single stops weaken:

• p → v, t → d, k → ∅ (deletion)
• mp → mm, nk → ng, lt → ll, rt → rr (assimilatory weakening)

Formalization

We model the quantitative and qualitative rules as SPE PhonRules. The conditioning environment — closed vs. open syllable — is approximated by right context: a following consonant signals a closed syllable.

def Fragments.Finnish.ConsonantGradation.p_stop : Theories.Phonology.Segment

Voiceless bilabial stop /p/: [−cont, −voice, +labial, −coronal, −dorsal].

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def Fragments.Finnish.ConsonantGradation.t_stop : Theories.Phonology.Segment

Voiceless alveolar stop /t/: [−cont, −voice, +coronal, +anterior].

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def Fragments.Finnish.ConsonantGradation.k_stop : Theories.Phonology.Segment

Voiceless velar stop /k/: [−cont, −voice, +dorsal, −labial, −coronal].

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def Fragments.Finnish.ConsonantGradation.v_fricative : Theories.Phonology.Segment

Voiced labial continuant /v/: [+cont, +voice, +labial].

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def Fragments.Finnish.ConsonantGradation.d_stop : Theories.Phonology.Segment

Voiced alveolar stop /d/: [−cont, +voice, +coronal, +anterior].

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def Fragments.Finnish.ConsonantGradation.consonant : Theories.Phonology.Segment

A consonant: [+cons, −syll] (natural class for right context).

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• Fragments.Finnish.ConsonantGradation.consonant = Theories.Phonology.Segment.ofSpecs [(Theories.Phonology.Feature.consonantal, true), (Theories.Phonology.Feature.syllabic, false)]

def Fragments.Finnish.ConsonantGradation.ppGradation : Theories.Phonology.RuleBased.PhonRule

Quantitative pp → p: geminate voiceless bilabial shortens before a consonant. Modeled as: the second /p/ of a geminate is deleted when followed by a consonant (closed syllable).

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def Fragments.Finnish.ConsonantGradation.ttGradation : Theories.Phonology.RuleBased.PhonRule

Quantitative tt → t: geminate voiceless alveolar shortens.

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def Fragments.Finnish.ConsonantGradation.kkGradation : Theories.Phonology.RuleBased.PhonRule

Quantitative kk → k: geminate voiceless velar shortens.

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def Fragments.Finnish.ConsonantGradation.pGradation : Theories.Phonology.RuleBased.PhonRule

Qualitative p → v: single voiceless bilabial becomes a voiced labial continuant before a consonant.

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def Fragments.Finnish.ConsonantGradation.tGradation : Theories.Phonology.RuleBased.PhonRule

Qualitative t → d: single voiceless alveolar becomes voiced before a consonant.

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def Fragments.Finnish.ConsonantGradation.kGradation : Theories.Phonology.RuleBased.PhonRule

Qualitative k → ∅: single voiceless velar deletes before a consonant.

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inductive Fragments.Finnish.ConsonantGradation.GradationType : Type

Classification of a gradation rule: quantitative (geminate shortening) or qualitative (quality change or deletion).

• quantitative : GradationType
• qualitative : GradationType

instance Fragments.Finnish.ConsonantGradation.instDecidableEqGradationType : DecidableEq GradationType

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• Fragments.Finnish.ConsonantGradation.instDecidableEqGradationType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Fragments.Finnish.ConsonantGradation.instBEqGradationType.beq : GradationType → GradationType → Bool

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• Fragments.Finnish.ConsonantGradation.instBEqGradationType.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Fragments.Finnish.ConsonantGradation.instBEqGradationType : BEq GradationType

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• Fragments.Finnish.ConsonantGradation.instBEqGradationType = { beq := Fragments.Finnish.ConsonantGradation.instBEqGradationType.beq }

instance Fragments.Finnish.ConsonantGradation.instReprGradationType : Repr GradationType

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• Fragments.Finnish.ConsonantGradation.instReprGradationType = { reprPrec := Fragments.Finnish.ConsonantGradation.instReprGradationType.repr }

def Fragments.Finnish.ConsonantGradation.instReprGradationType.repr : GradationType → Nat → Std.Format

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structure Fragments.Finnish.ConsonantGradation.GradationPair : Type

A consonant gradation pair: strong and weak grades with classification.

• strong : String
• weak : String
• gradationType : GradationType

def Fragments.Finnish.ConsonantGradation.instReprGradationPair.repr : GradationPair → Nat → Std.Format

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instance Fragments.Finnish.ConsonantGradation.instReprGradationPair : Repr GradationPair

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• Fragments.Finnish.ConsonantGradation.instReprGradationPair = { reprPrec := Fragments.Finnish.ConsonantGradation.instReprGradationPair.repr }

instance Fragments.Finnish.ConsonantGradation.instBEqGradationPair : BEq GradationPair

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• Fragments.Finnish.ConsonantGradation.instBEqGradationPair = { beq := Fragments.Finnish.ConsonantGradation.instBEqGradationPair.beq }

def Fragments.Finnish.ConsonantGradation.instBEqGradationPair.beq : GradationPair → GradationPair → Bool

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• Fragments.Finnish.ConsonantGradation.instBEqGradationPair.beq x✝¹ x✝ = false

def Fragments.Finnish.ConsonantGradation.principalPairs : List GradationPair

The six principal gradation patterns (Karlsson §4.1).

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theorem Fragments.Finnish.ConsonantGradation.quantitative_count : (List.filter (fun (x : GradationPair) => x.gradationType == GradationType.quantitative) principalPairs).length = 3

There are exactly 3 quantitative gradation pairs.

theorem Fragments.Finnish.ConsonantGradation.qualitative_count : (List.filter (fun (x : GradationPair) => x.gradationType == GradationType.qualitative) principalPairs).length = 3

There are exactly 3 qualitative gradation pairs.

theorem Fragments.Finnish.ConsonantGradation.quantitative_shortening : ((List.filter (fun (x : GradationPair) => x.gradationType == GradationType.quantitative) principalPairs).all fun (p : GradationPair) => p.strong.length == p.weak.length + 1) = true

All quantitative pairs involve geminate shortening (strong form is longer than weak form by exactly 1 character).

theorem Fragments.Finnish.ConsonantGradation.k_deletion_unique : (List.filter (fun (p : GradationPair) => p.weak == "") principalPairs).length = 1

The k → ∅ qualitative alternation is the only deletion (empty weak grade).

theorem Fragments.Finnish.ConsonantGradation.p_gradation_voices : pGradation.effect = Theories.Phonology.RuleBased.RuleEffect.changeFeatures (Theories.Phonology.Segment.ofSpecs [(Theories.Phonology.Feature.continuant, true), (Theories.Phonology.Feature.voice, true)])

p → v rule changes voiceless to voiced + continuant.

theorem Fragments.Finnish.ConsonantGradation.t_gradation_voices : tGradation.effect = Theories.Phonology.RuleBased.RuleEffect.changeFeatures (Theories.Phonology.Segment.ofSpecs [(Theories.Phonology.Feature.voice, true)])

t → d rule changes only voicing.

theorem Fragments.Finnish.ConsonantGradation.k_gradation_deletes : kGradation.effect = Theories.Phonology.RuleBased.RuleEffect.delete

k → ∅ rule deletes.