Staňková & Šimík (2024): Negation in Czech Polar Questions

@cite{stankova-2025} @cite{gartner-gyuris-2017} @cite{simik-2024}

Experimental data from three naturalness judgment experiments on negation in Czech polar questions (Staňková & Šimík, FASL 32 / JSL 33).

Main experiment (§5)

2×2×2 within-subjects design manipulating:

• Verb position: V1 (interrogative) vs nonV1 (declarative)
• Indefinite: NCI (žádný) vs PPI (nějaký)
• Context: negative (implying ¬p) vs neutral

75 native Czech speakers, Likert 1–7, 32 items (4 per condition).

Key findings

1. FALSUM is preferred in V1 (interrogative) PQs — PPIs preferred over NCIs
2. Declarative word order (nonV1) is preferred in negatively biased contexts
3. Czech FALSUM is compatible with any type of evidential bias (positive, negative, neutral) — broader than English
4. The particle náhodou is licensed by FALSUM — PPIs preferred (§6.1)
5. The particle copak requires contextual evidence — biased contexts preferred (§6.2)

structure Data.CLMMEffect : Type

A Cumulative Link Mixed Model (CLMM) regression result. z-values stored as Int × 1000 for precision without Float.

• name : String

  Human-readable effect name

• z1000 : ℤ

  z-value × 1000 (e.g., -15674 = z = -15.674)

• significant : Bool

  Whether the effect is statistically significant

• pThreshold : String

  p-value threshold (as string for display)

@[implicit_reducible]

instance Data.instReprCLMMEffect : Repr CLMMEffect

Equations

• Data.instReprCLMMEffect = { reprPrec := Data.instReprCLMMEffect.repr }

def Data.instReprCLMMEffect.repr : CLMMEffect → ℕ → Std.Format

Equations

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

def Data.instBEqCLMMEffect.beq : CLMMEffect → CLMMEffect → Bool

Equations

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

@[implicit_reducible]

instance Data.instBEqCLMMEffect : BEq CLMMEffect

Equations

• Data.instBEqCLMMEffect = { beq := Data.instBEqCLMMEffect.beq }

def Data.CLMMEffect.isPositive (e : CLMMEffect) : Bool

Whether a CLMM effect's z-value is positive (higher ratings in the first level of the factor).

Equations

• e.isPositive = decide (e.z1000 > 0)

def Data.CLMMEffect.isNegative (e : CLMMEffect) : Bool

Whether a CLMM effect's z-value is negative.

Equations

• e.isNegative = decide (e.z1000 < 0)

def Data.v1_indefinite : CLMMEffect

V1: Main effect of INDEFINITE (NCI < PPI). PPIs (nějaký) are significantly more natural than NCIs (žádný) in V1 PQs. z = −15.674, p < .001.

Interpretation: V1 negation is interpreted as FALSUM (outer negation), which licenses PPIs but blocks NCIs.

Equations

• Data.v1_indefinite = { name := "V1: INDEFINITE", z1000 := -15674, significant := true, pThreshold := "< .001" }

def Data.v1_context : CLMMEffect

V1: Main effect of CONTEXT (not significant). z = −1.374, p = 0.169.

Interpretation: FALSUM/outer negation is insensitive to contextual evidence — V1 PQs are equally natural in negative and neutral contexts. This is because FALSUM conveys epistemic bias (speaker's possibility assessment), not evidential bias.

Equations

• Data.v1_context = { name := "V1: CONTEXT", z1000 := -1374, significant := false, pThreshold := "= 0.169" }

def Data.v1_interaction : CLMMEffect

V1: CONTEXT × INDEFINITE interaction. z = 2.933, p < 0.01.

Post-hoc: the effect of INDEFINITE is more pronounced in neutral contexts. Simple effect of CONTEXT within PPI: z = −3.522, p < .001. Simple effect of CONTEXT within NCI: z = 1.104, p = .27 (n.s.).

Equations

• Data.v1_interaction = { name := "V1: CONTEXT × INDEFINITE", z1000 := 2933, significant := true, pThreshold := "< 0.01" }

def Data.v1_context_within_ppi : CLMMEffect

Post-hoc: V1, simple effect of CONTEXT within PPI level. z = −3.522, p < .001. PPI V1 PQs are more natural in neutral context.

Equations

• Data.v1_context_within_ppi = { name := "V1: CONTEXT | PPI", z1000 := -3522, significant := true, pThreshold := "< .001" }

def Data.v1_context_within_nci : CLMMEffect

Post-hoc: V1, simple effect of CONTEXT within NCI level. z = 1.104, p = .27 (not significant).

Equations

• Data.v1_context_within_nci = { name := "V1: CONTEXT | NCI", z1000 := 1104, significant := false, pThreshold := "= .27" }

def Data.nonV1_context : CLMMEffect

nonV1: Main effect of CONTEXT. Negative contexts rated significantly more natural than neutral contexts. z = 8.674, p < 0.01.

Interpretation: nonV1 (declarative) PQs are sensitive to evidential bias and preferred in negatively biased contexts.

Equations

• Data.nonV1_context = { name := "nonV1: CONTEXT", z1000 := 8674, significant := true, pThreshold := "< 0.01" }

def Data.nonV1_indefinite : CLMMEffect

nonV1: Main effect of INDEFINITE (NCI > PPI). NCIs (žádný) rated higher than PPIs (nějaký) in nonV1 PQs. z = 6.208, p < 0.01.

Interpretation: inner negation (Op¬) is the preferred reading for nonV1, licensing NCIs.

Equations

• Data.nonV1_indefinite = { name := "nonV1: INDEFINITE", z1000 := 6208, significant := true, pThreshold := "< 0.01" }

theorem Data.v1_ppi_preferred : v1_indefinite.significant = true ∧ v1_indefinite.isNegative = true

V1 PQs: PPIs preferred over NCIs → outer (FALSUM) is the reading.

theorem Data.v1_context_insensitive_confirmed : v1_context.significant = false

V1 PQs: No effect of context → FALSUM is insensitive to evidential bias.

theorem Data.nonV1_context_sensitive_confirmed : nonV1_context.significant = true ∧ nonV1_context.isPositive = true

nonV1 PQs: Negative context preferred → sensitive to evidential bias.

theorem Data.nonV1_nci_preferred : nonV1_indefinite.significant = true ∧ nonV1_indefinite.isPositive = true

nonV1 PQs: NCIs preferred → inner negation is the default reading.

theorem Data.context_asymmetry : v1_context.significant = false ∧ nonV1_context.significant = true

The key asymmetry: V1 is CONTEXT-insensitive (FALSUM = epistemic bias), nonV1 is CONTEXT-sensitive (inner neg = evidential bias).

This matches @cite{stankova-2025}'s claim that inner negation requires contextual evidence while outer negation (FALSUM) does not, and confirms the VerbPosition.requiresContextualEvidence classification.

theorem Data.v1_confirms_outer_neg : v1_indefinite.significant = true ∧ Semantics.Negation.CzechNegation.licenses Semantics.Negation.CzechNegation.NegPosition.outer Semantics.Negation.CzechNegation.Diagnostic.ppiOutscoping = true ∧ Semantics.Negation.CzechNegation.licenses Semantics.Negation.CzechNegation.NegPosition.outer Semantics.Negation.CzechNegation.Diagnostic.nciLicensed = false

V1 forces outer negation. Confirmed by experiment: PPIs strongly preferred in V1 PQs, and only outer negation licenses PPIs.

theorem Data.nonV1_confirms_inner_default : nonV1_indefinite.significant = true ∧ Semantics.Negation.CzechNegation.licenses Semantics.Negation.CzechNegation.NegPosition.inner Semantics.Negation.CzechNegation.Diagnostic.nciLicensed = true ∧ Semantics.Negation.CzechNegation.licenses Semantics.Negation.CzechNegation.NegPosition.inner Semantics.Negation.CzechNegation.Diagnostic.ppiOutscoping = false

nonV1 defaults to inner negation. Confirmed by experiment: NCIs preferred in nonV1 PQs, and only inner negation licenses NCIs.

theorem Data.experiment_matches_verb_position : Phenomena.Negation.CzechThreeWayNegTypologyBridge.VerbPosition.v1.requiresContextualEvidence = false ∧ v1_context.significant = false ∧ Phenomena.Negation.CzechThreeWayNegTypologyBridge.VerbPosition.nonV1.requiresContextualEvidence = true ∧ nonV1_context.significant = true

Context sensitivity matches VerbPosition classification.

structure Data.PositiveEvidenceSubexp : Type

Czech FALSUM with positive evidential bias.

In a subexperiment, V1 PQs were tested in contexts with positive evidence for p (e.g., Eva winning first place → "Didn't Eva win a prize?"). Median rating = 6 (biased) vs 5 (neutral), Likert 1–7.

This confirms Czech outer negation (FALSUM) is compatible with positive evidential bias, unlike English HiNQs.

• medianBiased : ℕ

  Median rating in positively biased context

• medianNeutral : ℕ

  Median rating in neutral context

def Data.positiveEvidence : PositiveEvidenceSubexp

Equations

• Data.positiveEvidence = { medianBiased := 6, medianNeutral := 5 }

theorem Data.positive_evidence_natural : positiveEvidence.medianBiased ≥ positiveEvidence.medianNeutral

V1 PQs with positive evidence rated at least as natural as neutral.

theorem Data.falsum_evidence_compatible : positiveEvidence.medianBiased ≥ 5 ∧ v1_context.significant = false

Czech FALSUM compatible with all three evidence types (positive, negative, neutral). This matches the broad distribution of InterNPQ in @cite{simik-2024}'s bias profile table.

náhodou subexperiment: 2×2 design (Context × Indefinite). All V1 PQs with náhodou. 8 items.

Tests whether náhodou requires FALSUM (outer negation). If so, PPIs (nějaký) should be preferred over NCIs (žádný), because FALSUM licenses PPIs but not NCIs.

def Data.nahodou_indefinite : CLMMEffect

náhodou: Main effect of INDEFINITE (NCI < PPI). PPIs strongly preferred with náhodou. z = −12.845, p < .001.

Interpretation: náhodou requires FALSUM, which only licenses PPIs. "based on this we suggest that náhodou could be used as an overt indicator of the covert FALSUM operator" (S&Š §6.1).

Equations

• Data.nahodou_indefinite = { name := "náhodou: INDEFINITE", z1000 := -12845, significant := true, pThreshold := "< .001" }

theorem Data.nahodou_requires_falsum : nahodou_indefinite.significant = true ∧ nahodou_indefinite.isNegative = true ∧ Semantics.Negation.CzechNegation.licenses Semantics.Negation.CzechNegation.NegPosition.outer Semantics.Negation.CzechNegation.Diagnostic.nahodou = true

náhodou requires FALSUM: confirmed by PPI preference.

theorem Data.nahodou_same_direction_as_v1 : nahodou_indefinite.isNegative = true ∧ v1_indefinite.isNegative = true

náhodou's INDEFINITE effect is in the same direction as V1's, confirming both involve FALSUM (outer negation).

copak subexperiment: 2×2 design (Context × PQ Polarity).

• CONTEXT: biased (matching polarity) vs neutral
• PQ POLARITY: positive (copak + PPI) vs negative (copak + ne- + NCI)

For positive PQs: biased context has evidence for ¬p, speaker believed p. For negative PQs: biased context has evidence for p, speaker believed ¬p. In both cases, copak expresses surprise at the evidence conflicting with the speaker's prior belief.

def Data.copak_context : CLMMEffect

copak: Main effect of CONTEXT. Biased contexts significantly more natural than neutral. z = 9.372, p < .001.

Interpretation: copak requires a conflict between speaker's prior belief and current contextual evidence (evidential bias). "copak is a particle which is used to express speaker's surprise about the current contextual evidence" (S&Š §6.2).

Equations

• Data.copak_context = { name := "copak: CONTEXT", z1000 := 9372, significant := true, pThreshold := "< .001" }

theorem Data.copak_requires_evidential_bias : copak_context.significant = true ∧ copak_context.isPositive = true

copak requires evidential bias (biased context).

theorem Data.nahodou_copak_contrast : v1_context.significant = false ∧ copak_context.significant = true

náhodou vs copak: opposite context sensitivity.

• náhodou (FALSUM-tied): context-insensitive. FALSUM conveys epistemic bias regardless of contextual evidence — V1 PQs are equally natural in any evidential context.
• copak (evidential-bias-tied): context-sensitive. Requires a biased context where speaker's prior belief conflicts with evidence.

This confirms they express different types of bias: náhodou → epistemic bias; copak → evidential bias. (@cite{stankova-2025} §6)

theorem Data.epistemic_vs_evidential_coherence : v1_context.significant = false ∧ Semantics.Negation.CzechNegation.licenses Semantics.Negation.CzechNegation.NegPosition.outer Semantics.Negation.CzechNegation.Diagnostic.nahodou = true ∧ nonV1_context.significant = true ∧ copak_context.significant = true

The V1 context insensitivity and náhodou's FALSUM requirement converge: both reflect that outer negation (FALSUM) is an epistemic-bias phenomenon, not an evidential-bias phenomenon. Conversely, nonV1 context sensitivity and copak's context requirement both reflect evidential bias sensitivity.

structure Data.ExperimentMetadata : Type

• nParticipants : ℕ
• nItems : ℕ
• scale : String
• method : String
• platform : String
• citation : String

@[implicit_reducible]

instance Data.instReprExperimentMetadata : Repr ExperimentMetadata

Equations

• Data.instReprExperimentMetadata = { reprPrec := Data.instReprExperimentMetadata.repr }

def Data.instReprExperimentMetadata.repr : ExperimentMetadata → ℕ → Std.Format

Equations

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

def Data.mainExperiment : ExperimentMetadata

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

def Data.nahodouExperiment : ExperimentMetadata

Equations

• Data.nahodouExperiment = { nParticipants := 75, nItems := 8, scale := "Likert 1–7", method := "CLMM (ordinal package in R)", platform := "L-Rex", citation := "Staňková & Šimík 2024, §6.1" }

def Data.copakExperiment : ExperimentMetadata

Equations

• Data.copakExperiment = { nParticipants := 75, nItems := 8, scale := "Likert 1–7", method := "CLMM (ordinal package in R)", platform := "L-Rex", citation := "Staňková & Šimík 2024, §6.2" }