English Negation Fragment

[Mie05] [Has13b] [DH13a]

English expresses standard negation with the particle not (contracted n't). WALS classifies English as both symmetric and asymmetric (SymAsy):

• Symmetric: with modals, be, and have, negation simply adds not with no structural change: He can swim → He cannot swim.

• Asymmetric (A/Cat): with lexical verbs, negation introduces auxiliary do (do-support): He eats → He does not eat. This is a category-level change — the finite verb becomes an auxiliary, and the lexical verb appears as a bare infinitive.

Negative indefinites (Ch 115)

WALS classifies English as mixed:

• nobody, nothing preclude predicate negation: Nobody came / *Nobody didn't come
• anything, ever require predicate negation: I didn't see anything / *I saw anything

def English.Negation.not : Syntax.Negation.NegMarkerEntry

not — English's standard negation particle. The contracted form n't attaches as a clitic to auxiliaries (isn't, don't, won't); see negContracted for the citation form of that allomorph. With lexical verbs, do-support is required: He does not eat, not *He not eats.

Equations

• English.Negation.not = { form := "not", morphemeType := Syntax.Negation.NegMorphemeType.particle, position := Syntax.Negation.NegMarkerPosition.preverbal }

def English.Negation.negContracted : String

The contracted form n't. Phonologically a clitic on the auxiliary; syntactically the same negation marker as not. Listed for the completeness of the citation forms; downstream consumers should treat not as the canonical entry.

Equations

• English.Negation.negContracted = "n't"

def English.Negation.negationSystem : Syntax.Negation.NegationSystem

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

Equations

• English.Negation.negationSystem = Syntax.Negation.NegationSystem.ofISO "eng" [English.Negation.not]

structure English.Negation.NegExample : Type

An English negation example.

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

  Does this construction require do-support?

• symmetric : Bool

  Is this construction symmetric (neg = aff + neg marker, no other change)?

@[implicit_reducible]

instance English.Negation.instReprNegExample : Repr NegExample

Equations

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

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

Equations

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

@[implicit_reducible]

instance English.Negation.instBEqNegExample : BEq NegExample

Equations

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

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

Equations

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

def English.Negation.modal : NegExample

Modal can: symmetric (no do-support).

Equations

• English.Negation.modal = { affirmative := "he can swim", negative := "he cannot swim", glossAff := "3SG can swim", glossNeg := "3SG can.NEG swim", doSupport := false, symmetric := true }

def English.Negation.copula : NegExample

Copula be: symmetric (no do-support).

Equations

• English.Negation.copula = { affirmative := "she is tall", negative := "she is not tall", glossAff := "3SG be tall", glossNeg := "3SG be NEG tall", doSupport := false, symmetric := true }

def English.Negation.auxHave : NegExample

Auxiliary have: symmetric (no do-support).

Equations

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

def English.Negation.lexicalPresent : NegExample

Lexical verb, present: asymmetric (do-support required).

Equations

• English.Negation.lexicalPresent = { affirmative := "he eats", negative := "he does not eat", glossAff := "3SG eat.3SG", glossNeg := "3SG do.3SG NEG eat", doSupport := true, symmetric := false }

def English.Negation.lexicalPast : NegExample

Lexical verb, past: asymmetric (do-support required).

Equations

• English.Negation.lexicalPast = { affirmative := "he ate", negative := "he did not eat", glossAff := "3SG eat.PST", glossNeg := "3SG do.PST NEG eat", doSupport := true, symmetric := false }

def English.Negation.allExamples : List NegExample

Equations

• English.Negation.allExamples = [English.Negation.modal, English.Negation.copula, English.Negation.auxHave, English.Negation.lexicalPresent, English.Negation.lexicalPast]

Verification

theorem English.Negation.all_examples_count : allExamples.length = 5

theorem English.Negation.symasy_distribution : (List.filter (fun (x : NegExample) => x.symmetric) allExamples).length = 3 ∧ (List.filter (fun (e : NegExample) => !e.symmetric) allExamples).length = 2

3 symmetric + 2 asymmetric = SymAsy.

theorem English.Negation.asymmetric_iff_dosupport : (allExamples.all fun (e : NegExample) => e.symmetric == !e.doSupport) = true

Asymmetric constructions all involve do-support.

theorem English.Negation.symmetric_no_dosupport : ((List.filter (fun (x : NegExample) => x.symmetric) allExamples).all fun (e : NegExample) => !e.doSupport) = true

Symmetric constructions do not involve do-support.

def English.Negation.negationProfile : Syntax.Negation.NegationProfile

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

Equations

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