Maori Negation Fragment

[Mie05] [Has13b] [DH13a]

Maori expresses standard negation with the word kāhore (also written kaahore). WALS classifies the negator's morpheme type as wordUnclear — in this isolating language, it is unclear whether kāhore is a verb or a particle.

Asymmetric A/Fin

WALS classifies Maori negation as asymmetric (A/Fin): the negator functions as a quasi-auxiliary that changes the finiteness structure. In the affirmative, the lexical verb is preceded by a TAM particle (e.g., kei te progressive). Under negation, kāhore takes the position of the TAM particle and the verb appears in a nominalized form with e...ana or bare.

Examples

	Affirmative	Negative
Progressive	Kei te kai ia	Kāhore ia e kai ana
Past	I kai ia	Kāhore ia i kai

def Maori.Negation.kahore : Syntax.Negation.NegMarkerEntry

kāhore — Maori's standard sentential negation word. WALS Ch 112A classifies this as .wordUnclear — in Maori's isolating morphology, kāhore could be analyzed as a verb or a particle. Functions as a quasi-auxiliary that takes the TAM-particle position.

Equations

• Maori.Negation.kahore = { form := "kāhore", morphemeType := Syntax.Negation.NegMorphemeType.wordUnclear, position := Syntax.Negation.NegMarkerPosition.preverbal }

def Maori.Negation.negationSystem : Syntax.Negation.NegationSystem

The Maori negation system: a single quasi-auxiliary word. The Fragment-side joint consumed by Studies/Dryer2013Negation.lean.

Equations

• Maori.Negation.negationSystem = Syntax.Negation.NegationSystem.ofISO "mri" [Maori.Negation.kahore]

structure Maori.Negation.NegExample : Type

A Maori negation example.

• affirmative : String
• negative : String
• glossAff : String
• glossNeg : String
• tamLabel : String
• symmetric : Bool

  Is this construction symmetric?

@[implicit_reducible]

instance Maori.Negation.instReprNegExample : Repr NegExample

Equations

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

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

Equations

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

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

Equations

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

@[implicit_reducible]

instance Maori.Negation.instBEqNegExample : BEq NegExample

Equations

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

def Maori.Negation.progressive : NegExample

Progressive: Kei te kai ia → Kāhore ia e kai ana. Asymmetric: TAM particle replaced by negator, verb nominalized.

Equations

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

def Maori.Negation.past : NegExample

Past: I kai ia → Kāhore ia i kai. Asymmetric: negator replaces TAM position.

Equations

• Maori.Negation.past = { affirmative := "I kai ia", negative := "Kāhore ia i kai", glossAff := "PST eat 3SG", glossNeg := "NEG 3SG PST eat", tamLabel := "past", symmetric := false }

def Maori.Negation.allExamples : List NegExample

Equations

• Maori.Negation.allExamples = [Maori.Negation.progressive, Maori.Negation.past]

Verification

theorem Maori.Negation.all_examples_count : allExamples.length = 2

theorem Maori.Negation.all_asymmetric : (allExamples.all fun (e : NegExample) => !e.symmetric) = true

All constructions are asymmetric (A/Fin).

def Maori.Negation.negationProfile : Syntax.Negation.NegationProfile

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

Equations

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