@cite{turco-braun-dimroth-2014} — Polarity Marking in Dutch and German

@cite{turco-braun-dimroth-2014}

Cross-linguistic production study comparing how Dutch and German speakers mark polarity switches (negation → affirmation) in two discourse contexts: polarity contrast (different topic situations) and polarity correction (same topic situation, mutually exclusive claims).

Key Findings

1. Dutch uses the affirmative particle wel as its dominant strategy (~88% in contrast, ~63% in correction).
2. German uses Verum focus (pitch accent on finite verb) as its dominant strategy (~82% in contrast, ~78% in correction).
3. German has zero sentence-internal polarity particles.
4. Correction contexts elicit more prosodic prominence than contrast contexts in both languages.
5. Dutch wel accent type varies by context: downstepped fall (!HL L%) in contrast, plain fall (HL L%) in correction.

Theoretical contribution

@cite{turco-braun-dimroth-2014} (p. 104, following Blühdorn 2012) argue that VF and wel operate at different semantic levels: VF targets the assertion operator (the element carrying the assertive relation between topic and comment), while wel targets the polarity operator ([±Pol]). Both achieve polarity contrast/correction pragmatically, but they are structurally distinct. See PolarityLevel.lean for the formal theory.

Data Sources

• Fig. 2: Dutch production strategy distribution
• Fig. 3: Dutch wel accent rate by context
• Fig. 5: Dutch wel accent type by context
• Fig. 6: German production strategy distribution
• p. 102: German VF pitch range statistics

Note: Production percentages are approximate (read from bar charts).

Types

inductive TurcoBraunDimroth2014.Language : Type

Languages compared in the study.

• dutch : Language
• german : Language

@[implicit_reducible]

instance TurcoBraunDimroth2014.instDecidableEqLanguage : DecidableEq Language

Equations

• TurcoBraunDimroth2014.instDecidableEqLanguage x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance TurcoBraunDimroth2014.instReprLanguage : Repr Language

Equations

• TurcoBraunDimroth2014.instReprLanguage = { reprPrec := TurcoBraunDimroth2014.instReprLanguage.repr }

def TurcoBraunDimroth2014.instReprLanguage.repr : Language → ℕ → Std.Format

Equations

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

structure TurcoBraunDimroth2014.ProductionDatum : Type

A production-strategy distribution datum (percentages as rationals). The distribution is keyed by Strategy, so adding a strategy constructor forces updating every datum.

• language : Language
• context : Core.Discourse.Coherence.CoherenceRelation
• pctByStrategy : Typology.PolarityMarking.Strategy → ℚ

  Percentage of trials per strategy (approximate, from bar charts)

structure TurcoBraunDimroth2014.ProminenceDatum : Type

A prosodic prominence datum (pitch range in semitones).

• context : Core.Discourse.Coherence.CoherenceRelation
• pitchRangeST : ℚ

  Pitch range in semitones

• beta : ℚ

  Regression coefficient (contrast relative to correction baseline)

• se : ℚ

  Standard error

• pValue : ℚ

  p-value (encoded as rational for decidable comparison)

@[implicit_reducible]

instance TurcoBraunDimroth2014.instReprProminenceDatum : Repr ProminenceDatum

Equations

• TurcoBraunDimroth2014.instReprProminenceDatum = { reprPrec := TurcoBraunDimroth2014.instReprProminenceDatum.repr }

def TurcoBraunDimroth2014.instReprProminenceDatum.repr : ProminenceDatum → ℕ → Std.Format

Equations

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def TurcoBraunDimroth2014.instBEqProminenceDatum.beq : ProminenceDatum → ProminenceDatum → Bool

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• One or more equations did not get rendered due to their size.
• TurcoBraunDimroth2014.instBEqProminenceDatum.beq x✝¹ x✝ = false

@[implicit_reducible]

instance TurcoBraunDimroth2014.instBEqProminenceDatum : BEq ProminenceDatum

Equations

• TurcoBraunDimroth2014.instBEqProminenceDatum = { beq := TurcoBraunDimroth2014.instBEqProminenceDatum.beq }

structure TurcoBraunDimroth2014.AccentRateDatum : Type

An accent-rate datum for Dutch wel (Fig. 3).

• context : Core.Discourse.Coherence.CoherenceRelation
• pctAccented : ℚ

  Percentage of wel tokens that were accented

def TurcoBraunDimroth2014.instReprAccentRateDatum.repr : AccentRateDatum → ℕ → Std.Format

Equations

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

@[implicit_reducible]

instance TurcoBraunDimroth2014.instReprAccentRateDatum : Repr AccentRateDatum

Equations

• TurcoBraunDimroth2014.instReprAccentRateDatum = { reprPrec := TurcoBraunDimroth2014.instReprAccentRateDatum.repr }

def TurcoBraunDimroth2014.instBEqAccentRateDatum.beq : AccentRateDatum → AccentRateDatum → Bool

Equations

• TurcoBraunDimroth2014.instBEqAccentRateDatum.beq { context := a, pctAccented := a_1 } { context := b, pctAccented := b_1 } = (a == b && a_1 == b_1)
• TurcoBraunDimroth2014.instBEqAccentRateDatum.beq x✝¹ x✝ = false

@[implicit_reducible]

instance TurcoBraunDimroth2014.instBEqAccentRateDatum : BEq AccentRateDatum

Equations

• TurcoBraunDimroth2014.instBEqAccentRateDatum = { beq := TurcoBraunDimroth2014.instBEqAccentRateDatum.beq }

structure TurcoBraunDimroth2014.AccentTypeDatum : Type

Accent type distribution on Dutch wel (Fig. 5). ToDI annotation: !HL L% (downstepped fall) vs HL L% (fall).

• context : Core.Discourse.Coherence.CoherenceRelation
• pctDownsteppedFall : ℚ

  Percentage realized as downstepped fall (!H*L L%)

• pctFall : ℚ

  Percentage realized as plain fall (H*L L%)

• pctOther : ℚ

  Percentage other realizations

@[implicit_reducible]

instance TurcoBraunDimroth2014.instReprAccentTypeDatum : Repr AccentTypeDatum

Equations

• TurcoBraunDimroth2014.instReprAccentTypeDatum = { reprPrec := TurcoBraunDimroth2014.instReprAccentTypeDatum.repr }

def TurcoBraunDimroth2014.instReprAccentTypeDatum.repr : AccentTypeDatum → ℕ → Std.Format

Equations

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

@[implicit_reducible]

instance TurcoBraunDimroth2014.instBEqAccentTypeDatum : BEq AccentTypeDatum

Equations

• TurcoBraunDimroth2014.instBEqAccentTypeDatum = { beq := TurcoBraunDimroth2014.instBEqAccentTypeDatum.beq }

def TurcoBraunDimroth2014.instBEqAccentTypeDatum.beq : AccentTypeDatum → AccentTypeDatum → Bool

Equations

• One or more equations did not get rendered due to their size.
• TurcoBraunDimroth2014.instBEqAccentTypeDatum.beq x✝¹ x✝ = false

Production Strategy Data (Fig. 2: Dutch, Fig. 6: German)

def TurcoBraunDimroth2014.dutchContrast : ProductionDatum

Dutch contrast: ~88% particle, 0% VF, ~5% other, ~7% unmarked

Equations

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def TurcoBraunDimroth2014.dutchCorrection : ProductionDatum

Dutch correction: ~63% particle, ~5% VF, ~7% other, ~25% unmarked

Equations

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

def TurcoBraunDimroth2014.germanContrast : ProductionDatum

German contrast: 0% particle, ~82% VF, 0% other, ~18% unmarked. "Others" in the paper's coding = doch pre-utterance + VF combinations; these occur only in correction (p. 102).

Equations

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def TurcoBraunDimroth2014.germanCorrection : ProductionDatum

German correction: 0% particle, ~78% VF, ~8% other, ~14% unmarked. The ~8% "other" = doch pre-utterance followed by VF (p. 102): "always followed by a Verum focus utterance."

Equations

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

def TurcoBraunDimroth2014.allProductionData : List ProductionDatum

Equations

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

Dutch wel Accent Data (Fig. 3)

def TurcoBraunDimroth2014.welAccentContrast : AccentRateDatum

Wel is accented ~93% of the time in contrast contexts.

Equations

• TurcoBraunDimroth2014.welAccentContrast = { context := Core.Discourse.Coherence.CoherenceRelation.contrast, pctAccented := 93 }

def TurcoBraunDimroth2014.welAccentCorrection : AccentRateDatum

Wel is accented ~97% of the time in correction contexts.

Equations

• TurcoBraunDimroth2014.welAccentCorrection = { context := Core.Discourse.Coherence.CoherenceRelation.correction, pctAccented := 97 }

Dutch wel Accent Type Data (Fig. 5)

ToDI annotation (Gussenhoven 2005): in contrast, wel is mostly realized as a downstepped fall (!HL L%); in correction, as a plain fall (HL L%). The plain fall is more prominent.

def TurcoBraunDimroth2014.welTypeContrast : AccentTypeDatum

Contrast: ~60% downstepped fall, ~30% fall, ~10% other

Equations

• TurcoBraunDimroth2014.welTypeContrast = { context := Core.Discourse.Coherence.CoherenceRelation.contrast, pctDownsteppedFall := 60, pctFall := 30, pctOther := 10 }

def TurcoBraunDimroth2014.welTypeCorrection : AccentTypeDatum

Correction: ~30% downstepped fall, ~60% fall, ~10% other

Equations

• TurcoBraunDimroth2014.welTypeCorrection = { context := Core.Discourse.Coherence.CoherenceRelation.correction, pctDownsteppedFall := 30, pctFall := 60, pctOther := 10 }

Prosodic Prominence Data (p. 102)

def TurcoBraunDimroth2014.germanVFContrast : ProminenceDatum

German VF pitch range in contrast: 3.1 semitones. β = −1.85 (contrast is 1.85 ST below correction baseline), SE = 0.39, p < .0001. The regression coefficient is for the contrast condition relative to the correction baseline (correction is the reference level).

Equations

• TurcoBraunDimroth2014.germanVFContrast = { context := Core.Discourse.Coherence.CoherenceRelation.contrast, pitchRangeST := 31 / 10, beta := -185 / 100, se := 39 / 100, pValue := 1 / 10000 }

def TurcoBraunDimroth2014.germanVFCorrection : ProminenceDatum

German VF pitch range in correction: 5.3 semitones. This is the reference level (baseline) in the regression model.

Equations

• TurcoBraunDimroth2014.germanVFCorrection = { context := Core.Discourse.Coherence.CoherenceRelation.correction, pitchRangeST := 53 / 10, beta := 0, se := 0, pValue := 1 }

Verification Theorems — Dominant Strategies

theorem TurcoBraunDimroth2014.dutch_contrast_particle_dominant (s : Typology.PolarityMarking.Strategy) : s ≠ Typology.PolarityMarking.Strategy.particle → dutchContrast.pctByStrategy Typology.PolarityMarking.Strategy.particle > dutchContrast.pctByStrategy s

Dutch dominant strategy is particles in contrast.

theorem TurcoBraunDimroth2014.dutch_correction_particle_dominant (s : Typology.PolarityMarking.Strategy) : s ≠ Typology.PolarityMarking.Strategy.particle → dutchCorrection.pctByStrategy Typology.PolarityMarking.Strategy.particle > dutchCorrection.pctByStrategy s

Dutch dominant strategy is particles in correction.

theorem TurcoBraunDimroth2014.german_contrast_vf_dominant (s : Typology.PolarityMarking.Strategy) : s ≠ Typology.PolarityMarking.Strategy.verumFocus → germanContrast.pctByStrategy Typology.PolarityMarking.Strategy.verumFocus > germanContrast.pctByStrategy s

German dominant strategy is Verum focus in contrast.

theorem TurcoBraunDimroth2014.german_correction_vf_dominant (s : Typology.PolarityMarking.Strategy) : s ≠ Typology.PolarityMarking.Strategy.verumFocus → germanCorrection.pctByStrategy Typology.PolarityMarking.Strategy.verumFocus > germanCorrection.pctByStrategy s

German dominant strategy is Verum focus in correction.

Verification Theorems — German Zero Particles

theorem TurcoBraunDimroth2014.german_contrast_no_particles : germanContrast.pctByStrategy Typology.PolarityMarking.Strategy.particle = 0

German has zero sentence-internal particles in contrast.

theorem TurcoBraunDimroth2014.german_correction_no_particles : germanCorrection.pctByStrategy Typology.PolarityMarking.Strategy.particle = 0

German has zero sentence-internal particles in correction.

Verification Theorems — Dutch VF Asymmetry

theorem TurcoBraunDimroth2014.dutch_contrast_no_vf : dutchContrast.pctByStrategy Typology.PolarityMarking.Strategy.verumFocus = 0

Dutch speakers never use VF in polarity contrast (0%).

theorem TurcoBraunDimroth2014.dutch_vf_correction_only : dutchContrast.pctByStrategy Typology.PolarityMarking.Strategy.verumFocus = 0 ∧ dutchCorrection.pctByStrategy Typology.PolarityMarking.Strategy.verumFocus > 0

Dutch speakers occasionally use VF in polarity correction (~5%), but never in contrast — an asymmetry the paper notes (p. 102) but does not explain.

Verification Theorems — German doch Correction-Only

The "others" category in German is exclusively doch+VF combinations (p. 102). These appear only in correction, consistent with Env.contrast ∉ dochPreUtterance.environments in the Fragment.

theorem TurcoBraunDimroth2014.german_doch_vf_correction_only : germanContrast.pctByStrategy Typology.PolarityMarking.Strategy.other = 0 ∧ germanCorrection.pctByStrategy Typology.PolarityMarking.Strategy.other > 0

German "others" (doch+VF) appears only in correction, never contrast.

theorem TurcoBraunDimroth2014.german_doch_production_matches_fragment : Typology.PolarityMarking.Env.contrast ∉ Fragments.German.PolarityMarking.dochPreUtterance.environments ∧ germanContrast.pctByStrategy Typology.PolarityMarking.Strategy.other = 0

The production data matches the Fragment: doch is correction-only.

Verification Theorems — Dutch wel Accent

theorem TurcoBraunDimroth2014.wel_mostly_accented : welAccentContrast.pctAccented > 90 ∧ welAccentCorrection.pctAccented > 90

Wel is accented in >90% of tokens in both contexts.

theorem TurcoBraunDimroth2014.correction_favors_fall : welTypeCorrection.pctFall > welTypeCorrection.pctDownsteppedFall ∧ welTypeContrast.pctDownsteppedFall > welTypeContrast.pctFall

Accent type shifts between contexts: correction favors plain fall (HL) over downstepped fall (!HL). The plain fall is more prominent, consistent with the cross-linguistic pattern that correction elicits more prosodic prominence.

Verification Theorems — Prosodic Prominence

theorem TurcoBraunDimroth2014.correction_more_prominent : germanVFCorrection.pitchRangeST > germanVFContrast.pitchRangeST

Correction elicits more prosodic prominence than contrast on German VF.

theorem TurcoBraunDimroth2014.correction_prominence_significant : germanVFContrast.pValue < 5 / 100

The correction–contrast difference is significant (p < .05).

Bridge Theorems — Fragment Connections

theorem TurcoBraunDimroth2014.dominant_strategies_both_marked : Fragments.Dutch.Particles.wel.strategy ≠ Typology.PolarityMarking.Strategy.unmarked ∧ Fragments.German.PolarityMarking.verumFocus.strategy ≠ Typology.PolarityMarking.Strategy.unmarked

Neither Dutch wel nor German VF maps to .unmarked: both languages have overt polarity-marking strategies.

theorem TurcoBraunDimroth2014.strategies_differ : Fragments.Dutch.Particles.wel.strategy ≠ Fragments.German.PolarityMarking.verumFocus.strategy

Dutch wel and German VF instantiate different strategy types.

theorem TurcoBraunDimroth2014.dutch_particle_internal_german_doch_not : Typology.PolarityMarking.Env.sentenceInternal ∈ Fragments.Dutch.Particles.wel.environments ∧ Typology.PolarityMarking.Env.sentenceInternal ∉ Fragments.German.PolarityMarking.dochPreUtterance.environments

Dutch wel is sentence-internal; German doch is not. This captures the key typological contrast: Dutch has a sentence-internal particle for polarity switches, German does not.

theorem TurcoBraunDimroth2014.both_strategies_context_general : (Typology.PolarityMarking.Env.contrast ∈ Fragments.Dutch.Particles.wel.environments ∧ Typology.PolarityMarking.Env.correction ∈ Fragments.Dutch.Particles.wel.environments) ∧ Typology.PolarityMarking.Env.contrast ∈ Fragments.German.PolarityMarking.verumFocus.environments ∧ Typology.PolarityMarking.Env.correction ∈ Fragments.German.PolarityMarking.verumFocus.environments

Both Dutch wel and German VF are available in both contexts.

Bridge Theorems — Polarity-Marking Levels

Blühdorn (2012): Dutch wel targets [±Pol] (polarity level); German VF targets the assertion operator (assertion level). This explains why VF can co-occur with negation (emphatic denial) while wel cannot.

theorem TurcoBraunDimroth2014.wel_targets_polarity : Semantics.Focus.PolarityLevel.strategyLevel Fragments.Dutch.Particles.wel.strategy = some Semantics.Focus.PolarityLevel.PolarityMarkingLevel.polarity

Dutch wel targets the polarity level.

theorem TurcoBraunDimroth2014.vf_targets_assertion : Semantics.Focus.PolarityLevel.strategyLevel Fragments.German.PolarityMarking.verumFocus.strategy = some Semantics.Focus.PolarityLevel.PolarityMarkingLevel.assertion

German VF targets the assertion level.

theorem TurcoBraunDimroth2014.strategies_target_different_levels : Semantics.Focus.PolarityLevel.strategyLevel Fragments.Dutch.Particles.wel.strategy ≠ Semantics.Focus.PolarityLevel.strategyLevel Fragments.German.PolarityMarking.verumFocus.strategy

The two dominant strategies operate at different semantic levels. This is the paper's key theoretical claim (p. 104).

Cross-Linguistic Extension

@cite{turco-braun-dimroth-2014} compare Dutch and German; the analysis naturally extends to other Western European languages with comparable polarity-marking inventories: English (emphatic do), French (si), Swedish (jo), Spanish (sí (que)), Italian (sì che). See also @cite{holmberg-2016}, @cite{batllori-hernanz-2013}, @cite{wilder-2013}, @cite{garassino-jacob-2018}.

We aggregate the seven-language sample and verify the strategy–level, correction-only, context-general, and sentence-internality generalizations as quantified statements over the inventory rather than as individual per-entry rfls.

def TurcoBraunDimroth2014.allEntries : List Typology.PolarityMarking.Entry

All polarity-marking entries across the seven-language sample.

Equations

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

theorem TurcoBraunDimroth2014.strategy_level_partition (e : Typology.PolarityMarking.Entry) : e ∈ allEntries → (e.strategy = Typology.PolarityMarking.Strategy.particle ∨ e.strategy = Typology.PolarityMarking.Strategy.polarityReversal → Semantics.Focus.PolarityLevel.strategyLevel e.strategy = some Semantics.Focus.PolarityLevel.PolarityMarkingLevel.polarity) ∧ (e.strategy = Typology.PolarityMarking.Strategy.verumFocus → Semantics.Focus.PolarityLevel.strategyLevel e.strategy = some Semantics.Focus.PolarityLevel.PolarityMarkingLevel.assertion)

Generalization 1 — Strategy/level mapping. Every particle and polarity-reversal entry targets the polarity level; every Verum-focus entry targets the assertion level.

theorem TurcoBraunDimroth2014.all_reversal_license_correction (e : Typology.PolarityMarking.Entry) : e ∈ allEntries → e.strategy = Typology.PolarityMarking.Strategy.polarityReversal → Typology.PolarityMarking.Env.correction ∈ e.environments

Generalization 2 — Reversal particles license correction. Every polarity-reversal entry has .correction present in environments. The earlier "correction-only" version of this generalization (also asserting .contrast ∉ e.environments) was falsified by Italian sì che and Spanish sí que per @cite{garassino-jacob-2018} ex. 17 + @cite{batllori-hernanz-2013} ex. 4-5 (both license non-contradictory contrast contexts). The surviving cross-linguistic generalization is the correction direction only.

theorem TurcoBraunDimroth2014.all_nonreversal_context_general (e : Typology.PolarityMarking.Entry) : e ∈ allEntries → e.strategy = Typology.PolarityMarking.Strategy.particle ∨ e.strategy = Typology.PolarityMarking.Strategy.verumFocus → Typology.PolarityMarking.Env.contrast ∈ e.environments ∧ Typology.PolarityMarking.Env.correction ∈ e.environments

Generalization 3 — Non-reversal strategies are context-general. Every particle or Verum-focus entry has both .contrast and .correction present in environments.

theorem TurcoBraunDimroth2014.sentence_internality_by_strategy (e : Typology.PolarityMarking.Entry) : e ∈ allEntries → (e.strategy = Typology.PolarityMarking.Strategy.polarityReversal → Typology.PolarityMarking.Env.sentenceInternal ∉ e.environments) ∧ (e.strategy = Typology.PolarityMarking.Strategy.particle ∨ e.strategy = Typology.PolarityMarking.Strategy.verumFocus → Typology.PolarityMarking.Env.sentenceInternal ∈ e.environments)

Generalization 4 — Sentence-internality splits by strategy type. Polarity-reversal entries are not sentence-internal; particles and Verum-focus entries are.