Italian Number–Gender Interaction @cite{adamson-2024}

Standard Italian has a small class of nouns — mostly body parts — whose plural form changes gender from masculine to feminine. These are the -a plurals: braccio (m.sg) → braccia (f.pl) 'arm/arms'.

@cite{adamson-2024} §5.1 analyzes this as evidence for the GLH's prediction about number position: the -a plural involves low number (number on n, within nP), which can interact with gender. Regular -i plurals involve high number (number on Num, outside nP), which cannot.

This is the same locality logic as possession–gender interaction: features within nP can condition gender; features outside nP cannot.

inductive Fragments.Italian.NumberGender.PluralClass : Type

Italian plural classes, distinguished by where the number feature sits in the nominal spine.

• -a plurals: number on n (low/derivational). These can change gender from masculine to feminine because the number feature is nP-internal, local to gender on n.
• Regular plurals (-i, -e): number on Num (high/inflectional). These preserve gender because the number feature is outside nP.

• aPlural : PluralClass
• regular : PluralClass

instance Fragments.Italian.NumberGender.instDecidableEqPluralClass : DecidableEq PluralClass

Equations

• Fragments.Italian.NumberGender.instDecidableEqPluralClass x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Fragments.Italian.NumberGender.instBEqPluralClass.beq : PluralClass → PluralClass → Bool

Equations

• Fragments.Italian.NumberGender.instBEqPluralClass.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Fragments.Italian.NumberGender.instBEqPluralClass : BEq PluralClass

Equations

• Fragments.Italian.NumberGender.instBEqPluralClass = { beq := Fragments.Italian.NumberGender.instBEqPluralClass.beq }

instance Fragments.Italian.NumberGender.instReprPluralClass : Repr PluralClass

Equations

• Fragments.Italian.NumberGender.instReprPluralClass = { reprPrec := Fragments.Italian.NumberGender.instReprPluralClass.repr }

def Fragments.Italian.NumberGender.instReprPluralClass.repr : PluralClass → ℕ → Std.Format

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def Fragments.Italian.NumberGender.PluralClass.toNumberPosition : PluralClass → Morphology.DM.NumberPosition

Map plural class to number position in the nominal spine.

Equations

• Fragments.Italian.NumberGender.PluralClass.aPlural.toNumberPosition = Morphology.DM.NumberPosition.onN
• Fragments.Italian.NumberGender.PluralClass.regular.toNumberPosition = Morphology.DM.NumberPosition.onNum

def Fragments.Italian.NumberGender.PluralClass.canAffectGender (pc : PluralClass) : Bool

Can this plural class's number feature interact with gender? Derived from the number position via the GLH — not stipulated.

Equations

• pc.canAffectGender = Morphology.DM.genderLocalityHypothesis pc.toNumberPosition.toNominalPosition

structure Fragments.Italian.NumberGender.NumberGenderNoun : Type

An Italian noun with explicit singular and plural gender tracking. The plural gender is derived from the singular gender and plural class, not stored independently.

• formSg : String
• formPl : String
• gloss : String
• sgGender : Nouns.Gender
• pluralClass : PluralClass

instance Fragments.Italian.NumberGender.instDecidableEqNumberGenderNoun : DecidableEq NumberGenderNoun

Equations

• Fragments.Italian.NumberGender.instDecidableEqNumberGenderNoun = Fragments.Italian.NumberGender.instDecidableEqNumberGenderNoun.decEq

def Fragments.Italian.NumberGender.instDecidableEqNumberGenderNoun.decEq (x✝ x✝¹ : NumberGenderNoun) : Decidable (x✝ = x✝¹)

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def Fragments.Italian.NumberGender.instBEqNumberGenderNoun.beq : NumberGenderNoun → NumberGenderNoun → Bool

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• Fragments.Italian.NumberGender.instBEqNumberGenderNoun.beq x✝¹ x✝ = false

instance Fragments.Italian.NumberGender.instBEqNumberGenderNoun : BEq NumberGenderNoun

Equations

• Fragments.Italian.NumberGender.instBEqNumberGenderNoun = { beq := Fragments.Italian.NumberGender.instBEqNumberGenderNoun.beq }

instance Fragments.Italian.NumberGender.instReprNumberGenderNoun : Repr NumberGenderNoun

Equations

• Fragments.Italian.NumberGender.instReprNumberGenderNoun = { reprPrec := Fragments.Italian.NumberGender.instReprNumberGenderNoun.repr }

def Fragments.Italian.NumberGender.instReprNumberGenderNoun.repr : NumberGenderNoun → ℕ → Std.Format

Equations

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def Fragments.Italian.NumberGender.NumberGenderNoun.plGender (n : NumberGenderNoun) : Nouns.Gender

Plural gender: -a plurals are always feminine; regular plurals preserve the singular gender.

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def Fragments.Italian.NumberGender.NumberGenderNoun.genderChanges (n : NumberGenderNoun) : Bool

Does this noun's gender change between singular and plural?

Equations

• n.genderChanges = (n.sgGender != n.plGender)

-a plural body parts (masc.sg → fem.pl)

These are the canonical examples of low-number gender interaction. The body-part semantics parallels the Teop/Jarawara data: body parts interact with n in special ways across languages.

def Fragments.Italian.NumberGender.braccio : NumberGenderNoun

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def Fragments.Italian.NumberGender.dito : NumberGenderNoun

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def Fragments.Italian.NumberGender.ginocchio : NumberGenderNoun

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def Fragments.Italian.NumberGender.labbro : NumberGenderNoun

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def Fragments.Italian.NumberGender.osso : NumberGenderNoun

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def Fragments.Italian.NumberGender.sopracciglio : NumberGenderNoun

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-a plural non-body parts

def Fragments.Italian.NumberGender.uovo : NumberGenderNoun

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def Fragments.Italian.NumberGender.paio : NumberGenderNoun

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def Fragments.Italian.NumberGender.miglio : NumberGenderNoun

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Regular plurals (gender-preserving)

def Fragments.Italian.NumberGender.libroNG : NumberGenderNoun

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def Fragments.Italian.NumberGender.ragazzoNG : NumberGenderNoun

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def Fragments.Italian.NumberGender.casaNG : NumberGenderNoun

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def Fragments.Italian.NumberGender.ragazzaNG : NumberGenderNoun

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def Fragments.Italian.NumberGender.aPluralNouns : List NumberGenderNoun

All -a plural nouns.

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def Fragments.Italian.NumberGender.regularNouns : List NumberGenderNoun

All regular-plural nouns (for contrast).

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def Fragments.Italian.NumberGender.allNouns : List NumberGenderNoun

All nouns in the inventory.

Equations

• Fragments.Italian.NumberGender.allNouns = Fragments.Italian.NumberGender.aPluralNouns ++ Fragments.Italian.NumberGender.regularNouns

theorem Fragments.Italian.NumberGender.braccio_changes : braccio.genderChanges = true

theorem Fragments.Italian.NumberGender.dito_changes : dito.genderChanges = true

theorem Fragments.Italian.NumberGender.ginocchio_changes : ginocchio.genderChanges = true

theorem Fragments.Italian.NumberGender.labbro_changes : labbro.genderChanges = true

theorem Fragments.Italian.NumberGender.osso_changes : osso.genderChanges = true

theorem Fragments.Italian.NumberGender.uovo_changes : uovo.genderChanges = true

theorem Fragments.Italian.NumberGender.libro_preserves : libroNG.genderChanges = false

theorem Fragments.Italian.NumberGender.ragazzo_preserves : ragazzoNG.genderChanges = false

theorem Fragments.Italian.NumberGender.casa_preserves : casaNG.genderChanges = false

theorem Fragments.Italian.NumberGender.ragazza_preserves : ragazzaNG.genderChanges = false

theorem Fragments.Italian.NumberGender.braccio_pl_fem : braccio.plGender = Nouns.Gender.fem

theorem Fragments.Italian.NumberGender.libro_pl_masc : libroNG.plGender = Nouns.Gender.masc

theorem Fragments.Italian.NumberGender.casa_pl_fem : casaNG.plGender = Nouns.Gender.fem

def Fragments.Italian.NumberGender.numberGenderPipeline (pc : PluralClass) : Bool

The GLH pipeline for number–gender interaction: PluralClass → NumberPosition → NominalPosition → GLH evaluation. Each stage feeds the next.

Equations

• Fragments.Italian.NumberGender.numberGenderPipeline pc = Morphology.DM.genderLocalityHypothesis pc.toNumberPosition.toNominalPosition

theorem Fragments.Italian.NumberGender.aPlural_can_affect : numberGenderPipeline PluralClass.aPlural = true

theorem Fragments.Italian.NumberGender.regular_cannot_affect : numberGenderPipeline PluralClass.regular = false

theorem Fragments.Italian.NumberGender.gender_change_tracks_glh : (allNouns.all fun (n : NumberGenderNoun) => n.genderChanges == n.pluralClass.canAffectGender) = true

Gender changes in the plural iff the GLH permits number–gender interaction. Verified over the full inventory.

theorem Fragments.Italian.NumberGender.aPlural_always_masc_sg : (aPluralNouns.all fun (n : NumberGenderNoun) => n.sgGender == Nouns.Gender.masc) = true

All -a plural nouns are masculine in the singular. The gender change is always masc → fem, never fem → masc.

theorem Fragments.Italian.NumberGender.aPlural_body_part_count : (List.filter (fun (n : NumberGenderNoun) => ["arm", "finger", "knee", "lip", "bone", "eyebrow"].contains n.gloss) aPluralNouns).length = 6

The -a plural class is exclusively body parts and measure nouns. 6 of 9 are body parts — the same semantic class that drives possession–gender interaction in Teop and Jarawara.