Imbabura Quechua Negation Fragment

[Mie05] [Has13b] [DH13a]

Imbabura Quechua expresses standard negation with the preverbal particle mana, optionally reinforced by the suffix -chu on the verb.

SymAsy: Symmetric and Asymmetric (A/NonReal)

WALS classifies Imbabura Quechua as both symmetric and asymmetric:

• Symmetric: in some constructions, mana simply negates without further structural change.

• Asymmetric (A/NonReal): in other constructions, negation triggers obligatory -chu marking on the verb. -chu is a validator enclitic that also appears in polar interrogatives; it expresses assertion authority and certainty ([Mie05] p. 158). Its use in negatives introduces a non-realized category absent from affirmatives.

The A/NonReal asymmetry is paradigmatic: the negative paradigm obligatorily includes a validator category (-chu) that the affirmative lacks. The clause structure itself does not change (no constructional asymmetry).

def Quechua.Negation.mana : Syntax.Negation.NegMarkerEntry

mana — Imbabura Quechua's standard preverbal negation particle. The load-bearing element of the negation construction; the -chu enclitic is a separate validator (also used in polar interrogatives) whose obligatory appearance under negation drives the WALS A/NonReal asymmetry classification.

Equations

• Quechua.Negation.mana = { form := "mana", morphemeType := Syntax.Negation.NegMorphemeType.particle, position := Syntax.Negation.NegMarkerPosition.preverbal }

def Quechua.Negation.chuSuffix : String

The validator enclitic -chu, triggered in negative and interrogative contexts. Glossed as VAL (validator); shared with polar questions. Not a negation marker — its appearance under negation is what distinguishes the asymmetric Quechua negative paradigm ([Mie05] p. 158).

Equations

• Quechua.Negation.chuSuffix = "-chu"

def Quechua.Negation.negationSystem : Syntax.Negation.NegationSystem

The Imbabura Quechua negation system: a single preverbal particle. The Fragment-side joint consumed by Studies/Dryer2013Negation.lean.

Equations

• Quechua.Negation.negationSystem = Syntax.Negation.NegationSystem.ofISO "qvi" [Quechua.Negation.mana]

structure Quechua.Negation.NegExample : Type

An Imbabura Quechua negation example.

• affirmative : String
• negative : String
• glossAff : String
• glossNeg : String
• requiresChu : Bool

  Does this construction require -chu?

• symmetric : Bool

  Is this construction symmetric?

def Quechua.Negation.instReprNegExample.repr : NegExample → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[implicit_reducible]

instance Quechua.Negation.instReprNegExample : Repr NegExample

Equations

• Quechua.Negation.instReprNegExample = { reprPrec := Quechua.Negation.instReprNegExample.repr }

@[implicit_reducible]

instance Quechua.Negation.instBEqNegExample : BEq NegExample

Equations

• Quechua.Negation.instBEqNegExample = { beq := Quechua.Negation.instBEqNegExample.beq }

def Quechua.Negation.instBEqNegExample.beq : NegExample → NegExample → Bool

Equations

• One or more equations did not get rendered due to their size.
• Quechua.Negation.instBEqNegExample.beq x✝¹ x✝ = false

def Quechua.Negation.present : NegExample

Simple present: asymmetric (requires -chu, A/NonReal).

Equations

• Quechua.Negation.present = { affirmative := "shamuni", negative := "mana shamu-ni-chu", glossAff := "come-1SG", glossNeg := "NEG come-1SG-VAL", requiresChu := true, symmetric := false }

def Quechua.Negation.progressive : NegExample

Progressive: symmetric (mana alone suffices).

Equations

• One or more equations did not get rendered due to their size.

def Quechua.Negation.past : NegExample

Past: asymmetric (requires -chu).

Equations

• Quechua.Negation.past = { affirmative := "shamurca", negative := "mana shamurca-chu", glossAff := "come-PST", glossNeg := "NEG come-PST-VAL", requiresChu := true, symmetric := false }

def Quechua.Negation.allExamples : List NegExample

Equations

• Quechua.Negation.allExamples = [Quechua.Negation.present, Quechua.Negation.progressive, Quechua.Negation.past]

Verification

theorem Quechua.Negation.example_count : allExamples.length = 3

theorem Quechua.Negation.symasy_distribution : (List.filter (fun (x : NegExample) => x.symmetric) allExamples).length = 1 ∧ (List.filter (fun (e : NegExample) => !e.symmetric) allExamples).length = 2

Mixed: some symmetric, some asymmetric = SymAsy.

theorem Quechua.Negation.asymmetric_iff_chu : (allExamples.all fun (e : NegExample) => e.symmetric == !e.requiresChu) = true

Asymmetric constructions are exactly those requiring -chu.

def Quechua.Negation.negationProfile : Syntax.Negation.NegationProfile

Quechua (Imbabura) negation profile (WALS Ch 112-115 + Greco/JinKoenig fields).

Equations

• One or more equations did not get rendered due to their size.