@cite{schwab-2022}: Lexical Variation in NPI Illusions

@cite{krifka-1995a}

Experimental data from "Lexical variation in NPI illusions" (JML). Core finding: NPI illusions (acceptance of NPIs in non-licensing environments) arise for strengthening NPIs (German "jemals"/ever) but NOT for attenuating NPIs (German "so recht"/all that).

Experimental Design

2×3 factorial design:

• NPI type: strengthening (jemals) vs attenuating (so recht)
• Negation: grammatical (neg) vs illusion (no neg, RC provides pseudo-licensing) vs ungrammatical control

Key Finding

The illusion asymmetry: when an RC creates a pseudo-DE environment, strengthening NPIs show illusory acceptance (Bayes factor > 10 for grammaticality) but attenuating NPIs do not.

Theoretical Account

The illusion arises because the parser applies scalar licensing to the NPI. For strengthening NPIs, the scalar mechanism (ScalAssert) expects the asserted proposition to be STRONGER than alternatives — the RC environment superficially satisfies this. For attenuating NPIs, the mechanism expects WEAKER-than-alternatives — the RC environment does NOT satisfy this, so no illusion arises.

inductive Schwab2022.Condition : Type

Condition in the 2×3 design

• grammatical : Condition
• illusion : Condition
• ungrammatical : Condition

@[implicit_reducible]

instance Schwab2022.instDecidableEqCondition : DecidableEq Condition

Equations

• Schwab2022.instDecidableEqCondition x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Schwab2022.instReprCondition.repr : Condition → ℕ → Std.Format

Equations

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

@[implicit_reducible]

instance Schwab2022.instReprCondition : Repr Condition

Equations

• Schwab2022.instReprCondition = { reprPrec := Schwab2022.instReprCondition.repr }

inductive Schwab2022.NPIType : Type

NPI type tested

• strengthening : NPIType
• attenuating : NPIType

@[implicit_reducible]

instance Schwab2022.instDecidableEqNPIType : DecidableEq NPIType

Equations

• Schwab2022.instDecidableEqNPIType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Schwab2022.instReprNPIType.repr : NPIType → ℕ → Std.Format

Equations

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

@[implicit_reducible]

instance Schwab2022.instReprNPIType : Repr NPIType

Equations

• Schwab2022.instReprNPIType = { reprPrec := Schwab2022.instReprNPIType.repr }

structure Schwab2022.ExperimentalDatum : Type

A single experimental datum.

Acceptance rates and Bayes factors are stored as ℚ (exact rational arithmetic) — Float would prevent any later use in proofs and isn't how mathlib stores measured quantities.

• npiType : NPIType
• condition : Condition
• acceptanceRate : ℚ

  Mean acceptance rate (0–1)

• bayesFactor : ℚ

  Bayes factor for grammaticality (BF₁₀ > 3 = substantial evidence)

• accepted : Bool

  Accepted as grammatical? (BF₁₀ > 3)

@[implicit_reducible]

instance Schwab2022.instReprExperimentalDatum : Repr ExperimentalDatum

Equations

• Schwab2022.instReprExperimentalDatum = { reprPrec := Schwab2022.instReprExperimentalDatum.repr }

def Schwab2022.instReprExperimentalDatum.repr : ExperimentalDatum → ℕ → Std.Format

Equations

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

def Schwab2022.jemals_grammatical : ExperimentalDatum

jemals (strengthening) in grammatical condition

Equations

• Schwab2022.jemals_grammatical = { npiType := Schwab2022.NPIType.strengthening, condition := Schwab2022.Condition.grammatical, acceptanceRate := 85 / 100, bayesFactor := 100, accepted := true }

def Schwab2022.jemals_illusion : ExperimentalDatum

jemals (strengthening) in illusion condition — ACCEPTED (illusion!)

Equations

• Schwab2022.jemals_illusion = { npiType := Schwab2022.NPIType.strengthening, condition := Schwab2022.Condition.illusion, acceptanceRate := 65 / 100, bayesFactor := 15, accepted := true }

def Schwab2022.jemals_ungrammatical : ExperimentalDatum

jemals (strengthening) in ungrammatical condition

Equations

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

def Schwab2022.soRecht_grammatical : ExperimentalDatum

soRecht (attenuating) in grammatical condition

Equations

• Schwab2022.soRecht_grammatical = { npiType := Schwab2022.NPIType.attenuating, condition := Schwab2022.Condition.grammatical, acceptanceRate := 80 / 100, bayesFactor := 80, accepted := true }

def Schwab2022.soRecht_illusion : ExperimentalDatum

soRecht (attenuating) in illusion condition — REJECTED (no illusion!)

Equations

• Schwab2022.soRecht_illusion = { npiType := Schwab2022.NPIType.attenuating, condition := Schwab2022.Condition.illusion, acceptanceRate := 30 / 100, bayesFactor := 1 / 10, accepted := false }

def Schwab2022.soRecht_ungrammatical : ExperimentalDatum

soRecht (attenuating) in ungrammatical condition

Equations

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

def Schwab2022.experimentalData : List ExperimentalDatum

All experimental data

Equations

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

theorem Schwab2022.illusion_asymmetry : jemals_illusion.accepted = true ∧ soRecht_illusion.accepted = false

The illusion asymmetry: strengthening NPIs show illusory acceptance, attenuating NPIs do not.

def Schwab2022.npiTypeToScalarDirection : NPIType → Typology.PolarityItem.ScalarDirection

Map from NPI type to scalar direction

Equations

• Schwab2022.npiTypeToScalarDirection Schwab2022.NPIType.strengthening = Typology.PolarityItem.ScalarDirection.strengthening
• Schwab2022.npiTypeToScalarDirection Schwab2022.NPIType.attenuating = Typology.PolarityItem.ScalarDirection.attenuating

def Schwab2022.predictsIllusion (npi : NPIType) : Bool

Predict whether an NPI type shows illusion based on scalar direction. Only strengthening NPIs show illusion because the RC environment superficially satisfies the "stronger-than-alternatives" licensing condition of ScalAssert.

Equations

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

theorem Schwab2022.prediction_matches_data : predictsIllusion NPIType.strengthening = jemals_illusion.accepted ∧ predictsIllusion NPIType.attenuating = soRecht_illusion.accepted

The theoretical prediction matches the observed data.

theorem Schwab2022.illusion_asymmetry_from_scalar_direction : predictsIllusion NPIType.strengthening = true ∧ predictsIllusion NPIType.attenuating = false

Illusion asymmetry follows from scalar direction: strengthening NPIs are predicted to show illusion, attenuating NPIs are not.