Documentation

Linglib.Phenomena.Modality.ModalConcord.Data

Modal Concord Data — @cite{rotter-liu-2025} #

@cite{rotter-liu-2025} @cite{zeijlstra-2007}

Empirical data from "A Register Approach to Modal Non-Concord in English: An Experimental Study of Linguistic and Social Meaning."

Key finding #

Stacked necessity modals (must have to VP) yield a single-necessity reading (concord), not the compositionally expected double-necessity. The stacked form receives intermediate formality ratings (between must and have to) and carries social meaning (perceived as less educated, non-standard dialect).

Experiments #

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inductive Phenomena.Modality.ModalConcord.Condition :
Type

Experimental conditions: the three modal constructions under study.

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    instance Phenomena.Modality.ModalConcord.instDecidableEqCondition :
    DecidableEq Condition
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    instance Phenomena.Modality.ModalConcord.instBEqCondition :
    BEq Condition
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    def Phenomena.Modality.ModalConcord.instBEqCondition.beq :
    Condition → Condition → Bool
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      instance Phenomena.Modality.ModalConcord.instReprCondition :
      Repr Condition
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      def Phenomena.Modality.ModalConcord.instReprCondition.repr :
      Condition → ℕ → Std.Format
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      • One or more equations did not get rendered due to their size.
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        instance Phenomena.Modality.ModalConcord.instInhabitedCondition :
        Inhabited Condition
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        def Phenomena.Modality.ModalConcord.instInhabitedCondition.default :
        Condition
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          inductive Phenomena.Modality.ModalConcord.SocialDimension :
          Type

          Dimensions of social meaning measured in Experiment 2.

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            instance Phenomena.Modality.ModalConcord.instDecidableEqSocialDimension :
            DecidableEq SocialDimension
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            def Phenomena.Modality.ModalConcord.instBEqSocialDimension.beq :
            SocialDimension → SocialDimension → Bool
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              instance Phenomena.Modality.ModalConcord.instBEqSocialDimension :
              BEq SocialDimension
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              def Phenomena.Modality.ModalConcord.instReprSocialDimension.repr :
              SocialDimension → ℕ → Std.Format
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                instance Phenomena.Modality.ModalConcord.instReprSocialDimension :
                Repr SocialDimension
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                structure Phenomena.Modality.ModalConcord.LikertRating :
                Type

                A Likert-scale rating (mean on a 7-point scale).

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                  instance Phenomena.Modality.ModalConcord.instReprLikertRating :
                  Repr LikertRating
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                  def Phenomena.Modality.ModalConcord.instReprLikertRating.repr :
                  LikertRating → ℕ → Std.Format
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                    Experiment 1: Formality and Meaning Strength #

                    76 native English speakers rated sentences on 7-point Likert scales for formality and meaning strength (paraphrase matching with have to).

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                    def Phenomena.Modality.ModalConcord.formalityRating :
                    Condition → LikertRating

                    Experiment 1 formality ratings (7-point Likert, 1=very informal, 7=very formal). F(2, 140.09) = 54.0, p < .001. All pairwise comparisons significant after Bonferroni correction.

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                      def Phenomena.Modality.ModalConcord.meaningRating :
                      Condition → LikertRating

                      Experiment 1 meaning strength ratings (7-point Likert). "How well does [have to paraphrase] capture the meaning of the sentence?" F(2, 140.28) = 6.5, p < .01. Post-hoc: only have to vs must have to significant (p = .003); neither differs reliably from must.

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                        Key Experiment 1 empirical generalizations #

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                        theorem Phenomena.Modality.ModalConcord.formality_gradient :
                        (formalityRating Condition.must).mean > (formalityRating Condition.mustHaveTo).mean ∧ (formalityRating Condition.mustHaveTo).mean > (formalityRating Condition.haveTo).mean

                        Formality gradient: must > must_have_to > have_to. All three pairwise comparisons significant after Bonferroni correction.

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                        theorem Phenomena.Modality.ModalConcord.intermediate_formality :
                        (formalityRating Condition.haveTo).mean < (formalityRating Condition.mustHaveTo).mean ∧ (formalityRating Condition.mustHaveTo).mean < (formalityRating Condition.must).mean

                        Intermediate formality: The stacked form is strictly between the two single-modal forms. This is the key prediction of the register approach (@cite{rotter-liu-2025} §4) and is NOT predicted by the syntactic agreement approach, which treats one modal as semantically vacuous.

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                        theorem Phenomena.Modality.ModalConcord.meaning_above_midpoint :
                        (meaningRating Condition.must).mean > 4 ∧ (meaningRating Condition.haveTo).mean > 4 ∧ (meaningRating Condition.mustHaveTo).mean > 4

                        Meaning strength comparable: All three conditions receive high meaning ratings (above scale midpoint 4), indicating concord (single necessity) rather than double necessity.

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                        theorem Phenomena.Modality.ModalConcord.meaning_must_close_to_mustHaveTo :
                        (meaningRating Condition.must).mean - (meaningRating Condition.mustHaveTo).mean < 1 / 2

                        No reliable meaning difference between must and must_have_to: Post-hoc comparison not significant. The concord reading (single necessity) is the dominant interpretation.

                        Experiment 2: Social Meaning #

                        89 native English speakers rated the speaker (not the sentence) on four social dimensions after hearing sentences in each condition.

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                        def Phenomena.Modality.ModalConcord.socialRating :
                        Condition → SocialDimension → LikertRating

                        Experiment 2 social meaning ratings (7-point Likert).

                        Significant effects:

                        • Educated: F(2, 175.22) = 5.0, p = .008
                        • Standard dialect: F(2, 175.20) = 12.32, p < .001

                        Non-significant effects:

                        • Friendly: F(2, 174.96) = 2.1, p = .13
                        • Attractive: F(2, 175.23) = 1.2, p = .30
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                          Key Experiment 2 empirical generalizations #

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                          theorem Phenomena.Modality.ModalConcord.education_must_gt_mustHaveTo :
                          (socialRating Condition.must SocialDimension.educated).mean > (socialRating Condition.mustHaveTo SocialDimension.educated).mean

                          Education effect: must speakers perceived as more educated than must have to speakers. Post-hoc: must vs must_have_to significant.

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                          theorem Phenomena.Modality.ModalConcord.dialect_gradient :
                          (socialRating Condition.must SocialDimension.standardDialect).mean > (socialRating Condition.haveTo SocialDimension.standardDialect).mean ∧ (socialRating Condition.haveTo SocialDimension.standardDialect).mean > (socialRating Condition.mustHaveTo SocialDimension.standardDialect).mean

                          Dialect standardness gradient: must > have_to > must_have_to. Post-hoc: must vs have_to and must vs must_have_to both significant.

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                          theorem Phenomena.Modality.ModalConcord.social_meaning_selective :
                          (socialRating Condition.must SocialDimension.educated).mean - (socialRating Condition.mustHaveTo SocialDimension.educated).mean > 4 / 10 ∧ (socialRating Condition.must SocialDimension.standardDialect).mean - (socialRating Condition.mustHaveTo SocialDimension.standardDialect).mean > 4 / 10

                          Social meaning is selective: Education and dialect show effects (> 0.4 point spread), while friendliness and attractiveness do not. Register mixing affects perceived competence, not warmth.

                          Cross-cutting empirical generalizations #

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                          theorem Phenomena.Modality.ModalConcord.concord_with_social_cost :
                          (meaningRating Condition.must).mean - (meaningRating Condition.mustHaveTo).mean < 1 / 2 ∧ (socialRating Condition.must SocialDimension.educated).mean > (socialRating Condition.mustHaveTo SocialDimension.educated).mean ∧ (socialRating Condition.must SocialDimension.standardDialect).mean > (socialRating Condition.mustHaveTo SocialDimension.standardDialect).mean

                          Concord with social cost: must have to preserves the meaning of single-modal necessity (comparable meaning ratings) while incurring a social cost (lower education and dialect ratings).