Documentation

Linglib.Phenomena.Questions.Studies.Holmberg2016

Holmberg (2016): The Syntax of Yes and No #

@cite{holmberg-2016}

Core Contribution #

A cross-linguistic typology of polar question answering. The central parameter is the answering system: truth-based vs polarity-based.

Key Claims Formalized #

  1. Hamblin ↔ [±Pol]: Hamblin's polar p yields exactly two answer cells, corresponding to [+Pol] and [-Pol] valuations.

  2. Answering system divergence: Truth-based and polarity-based systems give opposite answers to negative questions.

  3. Polarity reversal: Languages like Swedish (jo), German (doch), and French (si) have a dedicated particle that assigns [+Pol] while contradicting a negative context.

Connection to Existing Infrastructure #

A polar question ?p = {p, pᶜ} (substrate Core.Question.polar) corresponds to an unvalued [±Pol] feature. Each alternative cell values the feature: - p → [+Pol] (affirmative) - pᶜ → [-Pol] (negative)

The two alternatives are the "positive cell" and "negative cell"
of the partition induced by the question.
source
theorem Holmberg2016.both_alternatives_in_polar {W : Type u_1} {p : Set W} (hne : p ≠ ∅) (hnu : p ≠ Set.univ) :
p ∈ (Core.Question.polar p).alt ∧ pᶜ ∈ (Core.Question.polar p).alt

Both alternatives p and pᶜ lie in alt (polar p) (under nontriviality). Substrate identification of the two-cell answer partition.

source
def Holmberg2016.positiveToPolFeature :
Minimalist.Polarity.PolFeature

The positive answer maps to [+Pol] (valued positive).

Equations
Instances For
    source
    def Holmberg2016.negativeToPolFeature :
    Minimalist.Polarity.PolFeature

    The negative answer maps to [-Pol] (valued negative).

    Equations
    Instances For
      source
      theorem Holmberg2016.positive_valuation :
      Minimalist.Polarity.PolFeature.unvalued.value Features.Polarity.positive = some positiveToPolFeature

      Valuing [uPol] as positive gives [+Pol].

      source
      theorem Holmberg2016.negative_valuation :
      Minimalist.Polarity.PolFeature.unvalued.value Features.Polarity.negative = some negativeToPolFeature

      Valuing [uPol] as negative gives [-Pol].

      source
      theorem Holmberg2016.diagnostic_prediction :
      Features.AnsweringSystem.truthBased.yesToNegativeQuestion = Features.Polarity.negative ∧ Features.AnsweringSystem.polarityBased.yesToNegativeQuestion = Features.Polarity.positive

      The central diagnostic: "Doesn't he drink?" → "Yes" means...

      • Truth-based: "He doesn't drink" (negative polarity)
      • Polarity-based: "He does drink" (positive polarity)
      source
      theorem Holmberg2016.english_swedish_same_system :
      Phenomena.Questions.PolarAnswerStructure.englishProfile.system = Phenomena.Questions.PolarAnswerStructure.swedishProfile.system

      English and Swedish are both polarity-based.

      source
      theorem Holmberg2016.japanese_mandarin_same_system :
      Phenomena.Questions.PolarAnswerStructure.japaneseProfile.system = Phenomena.Questions.PolarAnswerStructure.mandarinProfile.system

      Japanese and Mandarin are both truth-based.

      source
      theorem Holmberg2016.english_japanese_differ :
      Phenomena.Questions.PolarAnswerStructure.englishProfile.system ≠ Phenomena.Questions.PolarAnswerStructure.japaneseProfile.system

      English and Japanese differ in answering system.

      source
      theorem Holmberg2016.swedish_reversal_english_not :
      Phenomena.Questions.PolarAnswerStructure.swedishProfile.hasPolarityReversal = true ∧ Phenomena.Questions.PolarAnswerStructure.englishProfile.hasPolarityReversal = false

      Swedish has polarity reversal; English does not.

      source
      theorem Holmberg2016.system_strategy_orthogonal :
      Phenomena.Questions.PolarAnswerStructure.englishProfile.strategy = Phenomena.Questions.PolarAnswerStructure.japaneseProfile.strategy ∧ Phenomena.Questions.PolarAnswerStructure.englishProfile.system ≠ Phenomena.Questions.PolarAnswerStructure.japaneseProfile.system

      The answering system and answer strategy are orthogonal: both truth-based and polarity-based systems can use particles.

      source
      theorem Holmberg2016.japanese_negation_height_predicts :
      Features.NegationHeight.low.predictedSystem = Phenomena.Questions.PolarAnswerStructure.japaneseProfile.system

      Japanese has low negation → truth-based predicted, matches actual profile.

      source
      theorem Holmberg2016.mandarin_negation_height_predicts :
      Features.NegationHeight.low.predictedSystem = Phenomena.Questions.PolarAnswerStructure.mandarinProfile.system

      Mandarin has low negation → truth-based predicted, matches actual profile.

      source
      theorem Holmberg2016.english_negation_height_predicts :
      Features.NegationHeight.middle.predictedSystem = Phenomena.Questions.PolarAnswerStructure.englishProfile.system

      English has middle negation → polarity-based predicted, matches actual profile.

      source
      theorem Holmberg2016.swedish_negation_height_predicts :
      Features.NegationHeight.middle.predictedSystem = Phenomena.Questions.PolarAnswerStructure.swedishProfile.system

      Swedish has middle negation (exclusively, no low negation; §4.5) → polarity-based predicted, matches actual profile.

      source
      theorem Holmberg2016.finnish_negation_height_predicts :
      Features.NegationHeight.middle.predictedSystem = Phenomena.Questions.PolarAnswerStructure.finnishProfile.system

      Finnish has middle negation (higher variety of middle; §4.6, p178: "still technically a middle negation position") → polarity-based predicted, matches actual profile.

      source
      theorem Holmberg2016.japanese_endtoend :
      Features.NegationHeight.low.predictedSystem.yesToNegativeQuestion = Phenomena.Questions.PolarAnswerStructure.japanese_hai_to_neg.answerPolarity

      End-to-end: Japanese low negation → truth-based → "yes" to negative question has negative polarity → matches the Japanese hai datum.

      source
      theorem Holmberg2016.english_endtoend :
      Features.NegationHeight.middle.predictedSystem.yesToNegativeQuestion = Phenomena.Questions.PolarAnswerStructure.english_yes_to_neg.answerPolarity

      End-to-end: English middle negation → polarity-based → "yes" to negative question has positive polarity → matches the English "yes" datum.

      source
      theorem Holmberg2016.endtoend_diverge :
      Features.NegationHeight.low.predictedSystem.yesToNegativeQuestion ≠ Features.NegationHeight.middle.predictedSystem.yesToNegativeQuestion

      The end-to-end chains for Japanese and English yield opposite polarities, as predicted by their different negation heights.

      @cite{holmberg-2016} §4.13: languages with a polarity-reversing particle (Swedish jo, German doch, French si) are correlated with the polarity-based system. Truth-based languages do not need a reversing particle because they can always use "no" to disconfirm the negative alternative of a negative question.

      source
      theorem Holmberg2016.truthBased_no_reversal :
      Phenomena.Questions.PolarAnswerStructure.japaneseProfile.hasPolarityReversal = false ∧ Phenomena.Questions.PolarAnswerStructure.mandarinProfile.hasPolarityReversal = false

      Truth-based languages do not have polarity reversal in our profiles. (Japanese and Mandarin both lack a reversing particle.)

      source
      theorem Holmberg2016.polarityBased_reversal_variation :
      Phenomena.Questions.PolarAnswerStructure.swedishProfile.hasPolarityReversal = true ∧ Phenomena.Questions.PolarAnswerStructure.englishProfile.hasPolarityReversal = false

      Among polarity-based languages, reversal is attested but not universal: Swedish has it, English does not.