Cross-Linguistic Quantifier Typology

@cite{barwise-cooper-1981} @cite{peters-westerstahl-2006} @cite{shimoyama-2006} @cite{nakanishi-2007} @cite{kuo-yu-2012} @cite{tsai-2015}

Empirical quantifier inventories from three languages (three families) mapped to a common QuantifierInventory structure, following the pattern established in Phenomena.Modality.Typology for modal inventories.

Mapping conventions

• Force, monotonicity, and strength values are taken from the Fragment entries (English QuantifierEntry, Mandarin MandarinQuantEntry, Japanese JapaneseQuantEntry)
• Each inventory is derived from its Fragment (single source of truth)

Data sources

• English: @cite{barwise-cooper-1981}
• Mandarin: @cite{kuo-yu-2012}, @cite{tsai-2015} (GQ inventory + strong/weak classification)
• Japanese: @cite{shimoyama-2006}, @cite{nakanishi-2007}

structure Phenomena.Quantification.Typology.QuantifierEntry : Type

A quantifier entry in the common typological format.

• form : String
• qforce : Fragments.English.Determiners.QForce
• monotonicity : Fragments.English.Determiners.Monotonicity
• strength : Fragments.English.Determiners.Strength

instance Phenomena.Quantification.Typology.instBEqQuantifierEntry : BEq QuantifierEntry

Equations

• Phenomena.Quantification.Typology.instBEqQuantifierEntry = { beq := Phenomena.Quantification.Typology.instBEqQuantifierEntry.beq }

def Phenomena.Quantification.Typology.instBEqQuantifierEntry.beq : QuantifierEntry → QuantifierEntry → Bool

Equations

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• Phenomena.Quantification.Typology.instBEqQuantifierEntry.beq x✝¹ x✝ = false

def Phenomena.Quantification.Typology.instReprQuantifierEntry.repr : QuantifierEntry → ℕ → Std.Format

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instance Phenomena.Quantification.Typology.instReprQuantifierEntry : Repr QuantifierEntry

Equations

• Phenomena.Quantification.Typology.instReprQuantifierEntry = { reprPrec := Phenomena.Quantification.Typology.instReprQuantifierEntry.repr }

structure Phenomena.Quantification.Typology.QuantifierInventory : Type

A language's quantifier inventory.

• language : String
• family : String
• source : String
• entries : List QuantifierEntry

instance Phenomena.Quantification.Typology.instReprQuantifierInventory : Repr QuantifierInventory

Equations

• Phenomena.Quantification.Typology.instReprQuantifierInventory = { reprPrec := Phenomena.Quantification.Typology.instReprQuantifierInventory.repr }

def Phenomena.Quantification.Typology.instReprQuantifierInventory.repr : QuantifierInventory → ℕ → Std.Format

Equations

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def Phenomena.Quantification.Typology.QuantifierInventory.size (inv : QuantifierInventory) : ℕ

Equations

• inv.size = inv.entries.length

def Phenomena.Quantification.Typology.english : QuantifierInventory

English quantifier inventory, derived from the QuantityWord fragment. Uses the 6-word scale: none, few, some, half, most, all.

Equations

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theorem Phenomena.Quantification.Typology.english_size : english.entries.length = 6

theorem Phenomena.Quantification.Typology.english_has_weak : (english.entries.any fun (x : QuantifierEntry) => x.strength == Fragments.English.Determiners.Strength.weak) = true

theorem Phenomena.Quantification.Typology.english_has_strong : (english.entries.any fun (x : QuantifierEntry) => x.strength == Fragments.English.Determiners.Strength.strong) = true

def Phenomena.Quantification.Typology.mandarin : QuantifierInventory

Mandarin quantifier inventory, derived from the MandarinQuantEntry fragment. 5 entries per @cite{tsai-2015} §5.3: měi, suǒyǒu, quánbù, hěnduō, dà-bùfèn.

Equations

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theorem Phenomena.Quantification.Typology.mandarin_size : mandarin.entries.length = 5

theorem Phenomena.Quantification.Typology.mandarin_no_definiteness : (mandarin.entries.all fun (x : QuantifierEntry) => x.qforce != Fragments.English.Determiners.QForce.definite) = true

theorem Phenomena.Quantification.Typology.mandarin_has_weak : (mandarin.entries.any fun (x : QuantifierEntry) => x.strength == Fragments.English.Determiners.Strength.weak) = true

theorem Phenomena.Quantification.Typology.mandarin_has_strong : (mandarin.entries.any fun (x : QuantifierEntry) => x.strength == Fragments.English.Determiners.Strength.strong) = true

def Phenomena.Quantification.Typology.japanese : QuantifierInventory

Japanese quantifier inventory, derived from the JapaneseQuantEntry fragment. 7 entries: subete, dono-N-mo, dare-ka, dare-mo, nan-nin-ka, hotondo, ryōhō.

Equations

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theorem Phenomena.Quantification.Typology.japanese_size : japanese.entries.length = 7

theorem Phenomena.Quantification.Typology.japanese_no_definiteness : (japanese.entries.all fun (x : QuantifierEntry) => x.qforce != Fragments.English.Determiners.QForce.definite) = true

theorem Phenomena.Quantification.Typology.japanese_has_weak : (japanese.entries.any fun (x : QuantifierEntry) => x.strength == Fragments.English.Determiners.Strength.weak) = true

theorem Phenomena.Quantification.Typology.japanese_has_strong : (japanese.entries.any fun (x : QuantifierEntry) => x.strength == Fragments.English.Determiners.Strength.strong) = true

def Phenomena.Quantification.Typology.allInventories : List QuantifierInventory

Equations

• Phenomena.Quantification.Typology.allInventories = [Phenomena.Quantification.Typology.english, Phenomena.Quantification.Typology.mandarin, Phenomena.Quantification.Typology.japanese]

theorem Phenomena.Quantification.Typology.all_have_weak_strong : (allInventories.all fun (inv : QuantifierInventory) => (inv.entries.any fun (x : QuantifierEntry) => x.strength == Fragments.English.Determiners.Strength.weak) && inv.entries.any fun (x : QuantifierEntry) => x.strength == Fragments.English.Determiners.Strength.strong) = true

All three languages have both weak and strong quantifiers.

theorem Phenomena.Quantification.Typology.all_have_universals : (allInventories.all fun (inv : QuantifierInventory) => inv.entries.any fun (x : QuantifierEntry) => x.qforce == Fragments.English.Determiners.QForce.universal) = true

All three languages have universal quantifiers.

theorem Phenomena.Quantification.Typology.no_articles_east_asian : ([mandarin, japanese].all fun (inv : QuantifierInventory) => inv.entries.all fun (x : QuantifierEntry) => x.qforce != Fragments.English.Determiners.QForce.definite) = true

Neither Mandarin nor Japanese has definite determiners (no articles).