Documentation

Linglib.Phenomena.Modality.ModalConcord.LiuRotter2025

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

Empirical data from "Non-redundant modal concord: Evidence from speaker commitment and social meaning."

Key finding #

Modal concord (MC) is not semantically vacuous: necessity MC (must certainly) strengthens speaker commitment, while possibility MC (may possibly) weakens it. This FORCE × NUMBER interaction is not predicted by syntactic agreement, semantic identity, or the register approach.

MC also carries social meaning: necessity MC signals competence (higher SES, education, formality, confidence), while possibility MC signals warmth (higher friendliness, warmth). The social meaning mirrors the commitment direction.

Experiments #

Experiment 1 (n=160): 2 (FORCE: necessity/possibility) × 2 (NUMBER: single/concord) between-subjects. DV: speaker commitment (7-point Likert).
Experiment 2 (n=160): Same design. DVs: 7 social meaning dimensions.

Stimuli #

Necessity SM: must/should/have to VP
Necessity MC: must certainly/should definitely/have to necessarily VP
Possibility SM: may/might/could VP
Possibility MC: may possibly/might perhaps/could potentially VP

Experimental design #

inductive Phenomena.Modality.ModalConcord.LiuRotter2025.Doubling :

NUMBER factor: single modal vs modal concord (doubled).

single : Doubling
concord : Doubling

Instances For

instance Phenomena.Modality.ModalConcord.LiuRotter2025.instDecidableEqDoubling :

DecidableEq Doubling

Equations

Phenomena.Modality.ModalConcord.LiuRotter2025.instDecidableEqDoubling x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqDoubling :

Equations

Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqDoubling = { beq := Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqDoubling.beq }

def Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqDoubling.beq :

Doubling → Doubling → Bool

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Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqDoubling.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

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def Phenomena.Modality.ModalConcord.LiuRotter2025.instReprDoubling.repr :

Doubling → ℕ → Std.Format

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instance Phenomena.Modality.ModalConcord.LiuRotter2025.instReprDoubling :

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Phenomena.Modality.ModalConcord.LiuRotter2025.instReprDoubling = { reprPrec := Phenomena.Modality.ModalConcord.LiuRotter2025.instReprDoubling.repr }

structure Phenomena.Modality.ModalConcord.LiuRotter2025.Condition :

Experimental condition: FORCE × NUMBER.

force : Core.Modality.ModalForce
doubling : Doubling

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def Phenomena.Modality.ModalConcord.LiuRotter2025.instDecidableEqCondition.decEq (x✝ x✝¹ : Condition) :

Decidable (x✝ = x✝¹)

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instance Phenomena.Modality.ModalConcord.LiuRotter2025.instDecidableEqCondition :

DecidableEq Condition

Equations

Phenomena.Modality.ModalConcord.LiuRotter2025.instDecidableEqCondition = Phenomena.Modality.ModalConcord.LiuRotter2025.instDecidableEqCondition.decEq

instance Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqCondition :

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Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqCondition = { beq := Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqCondition.beq }

def Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqCondition.beq :

Condition → Condition → Bool

Equations

Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqCondition.beq { force := a, doubling := a_1 } { force := b, doubling := b_1 } = (a == b && a_1 == b_1)
Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqCondition.beq x✝¹ x✝ = false

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def Phenomena.Modality.ModalConcord.LiuRotter2025.instReprCondition.repr :

Condition → ℕ → Std.Format

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instance Phenomena.Modality.ModalConcord.LiuRotter2025.instReprCondition :

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Phenomena.Modality.ModalConcord.LiuRotter2025.instReprCondition = { reprPrec := Phenomena.Modality.ModalConcord.LiuRotter2025.instReprCondition.repr }

def Phenomena.Modality.ModalConcord.LiuRotter2025.necSM :

Equations

Phenomena.Modality.ModalConcord.LiuRotter2025.necSM = { force := Core.Modality.ModalForce.necessity, doubling := Phenomena.Modality.ModalConcord.LiuRotter2025.Doubling.single }

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def Phenomena.Modality.ModalConcord.LiuRotter2025.necMC :

Equations

Phenomena.Modality.ModalConcord.LiuRotter2025.necMC = { force := Core.Modality.ModalForce.necessity, doubling := Phenomena.Modality.ModalConcord.LiuRotter2025.Doubling.concord }

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def Phenomena.Modality.ModalConcord.LiuRotter2025.posSM :

Equations

Phenomena.Modality.ModalConcord.LiuRotter2025.posSM = { force := Core.Modality.ModalForce.possibility, doubling := Phenomena.Modality.ModalConcord.LiuRotter2025.Doubling.single }

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def Phenomena.Modality.ModalConcord.LiuRotter2025.posMC :

Equations

Phenomena.Modality.ModalConcord.LiuRotter2025.posMC = { force := Core.Modality.ModalForce.possibility, doubling := Phenomena.Modality.ModalConcord.LiuRotter2025.Doubling.concord }

Instances For

Experiment 1: Speaker commitment #

160 participants (40 per condition) rated speaker commitment on a 7-point Likert scale ("How certain is the speaker that...").

FORCE × NUMBER interaction: β = 0.56, SE = 0.17, t = 3.31, p = .001.

def Phenomena.Modality.ModalConcord.LiuRotter2025.commitmentRating :

Condition → LikertRating

Speaker commitment ratings (7-point Likert, 1=not at all certain, 7=completely certain).

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Key Experiment 1 empirical generalizations #

theorem Phenomena.Modality.ModalConcord.LiuRotter2025.necessity_mc_strengthens :

(commitmentRating necMC).mean > (commitmentRating necSM).mean

Necessity MC strengthens commitment: must certainly is rated higher in speaker commitment than bare must (p = .03).

theorem Phenomena.Modality.ModalConcord.LiuRotter2025.possibility_mc_weakens :

(commitmentRating posMC).mean < (commitmentRating posSM).mean

Possibility MC weakens commitment: may possibly is rated lower in speaker commitment than bare may (p = .04).

theorem Phenomena.Modality.ModalConcord.LiuRotter2025.force_number_interaction :

(commitmentRating necMC).mean > (commitmentRating necSM).mean ∧ (commitmentRating posMC).mean < (commitmentRating posSM).mean

FORCE × NUMBER interaction: The direction of the concord effect reverses with force. Necessity MC strengthens, possibility MC weakens. This is the paper's central finding (β = 0.56, p = .001).

theorem Phenomena.Modality.ModalConcord.LiuRotter2025.mc_not_vacuous :

(commitmentRating necMC).mean ≠ (commitmentRating necSM).mean ∧ (commitmentRating posMC).mean ≠ (commitmentRating posSM).mean

MC is semantically non-vacuous: Both necessity and possibility MC differ from their single-modal counterparts. The syntactic agreement approach, which treats one modal as semantically vacuous, incorrectly predicts MC = SM.

theorem Phenomena.Modality.ModalConcord.LiuRotter2025.necessity_above_possibility :

(commitmentRating necSM).mean > (commitmentRating posSM).mean ∧ (commitmentRating necMC).mean > (commitmentRating posMC).mean

Necessity above possibility: Both SM and MC show higher commitment for necessity than possibility.

theorem Phenomena.Modality.ModalConcord.LiuRotter2025.no_main_effect_of_number :

have smMean := ((commitmentRating necSM).mean + (commitmentRating posSM).mean) / 2; have mcMean := ((commitmentRating necMC).mean + (commitmentRating posMC).mean) / 2; smMean - mcMean > -1 / 10 ∧ smMean - mcMean < 1 / 10

No main effect of NUMBER: Grand means of SM and MC are close (within 0.1 points). The concord effect appears only as an interaction with FORCE (β = −0.03, p = .86).

160 participants (40 per condition) rated speakers on 7 social dimensions (7-point Likert scale) after hearing sentences.

inductive Phenomena.Modality.ModalConcord.LiuRotter2025.SocialDimension :

Social meaning dimensions (Experiment 2).

ses : SocialDimension
education : SocialDimension
formality : SocialDimension
confidence : SocialDimension
friendliness : SocialDimension
warmth : SocialDimension
coolness : SocialDimension

Instances For

instance Phenomena.Modality.ModalConcord.LiuRotter2025.instDecidableEqSocialDimension :

DecidableEq SocialDimension

Equations

Phenomena.Modality.ModalConcord.LiuRotter2025.instDecidableEqSocialDimension x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqSocialDimension.beq :

SocialDimension → SocialDimension → Bool

Equations

Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqSocialDimension.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

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instance Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqSocialDimension :

BEq SocialDimension

Equations

Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqSocialDimension = { beq := Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqSocialDimension.beq }

def Phenomena.Modality.ModalConcord.LiuRotter2025.instReprSocialDimension.repr :

SocialDimension → ℕ → Std.Format

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instance Phenomena.Modality.ModalConcord.LiuRotter2025.instReprSocialDimension :

Repr SocialDimension

Equations

Phenomena.Modality.ModalConcord.LiuRotter2025.instReprSocialDimension = { reprPrec := Phenomena.Modality.ModalConcord.LiuRotter2025.instReprSocialDimension.repr }

inductive Phenomena.Modality.ModalConcord.LiuRotter2025.DimensionClass :

Competence/warmth classification. Necessity MC increases competence dimensions, decreases warmth. Possibility MC does the reverse.

competence : DimensionClass
warmth : DimensionClass

Instances For

instance Phenomena.Modality.ModalConcord.LiuRotter2025.instDecidableEqDimensionClass :

DecidableEq DimensionClass

Equations

Phenomena.Modality.ModalConcord.LiuRotter2025.instDecidableEqDimensionClass x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqDimensionClass.beq :

DimensionClass → DimensionClass → Bool

Equations

Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqDimensionClass.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

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instance Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqDimensionClass :

BEq DimensionClass

Equations

Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqDimensionClass = { beq := Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqDimensionClass.beq }

def Phenomena.Modality.ModalConcord.LiuRotter2025.instReprDimensionClass.repr :

DimensionClass → ℕ → Std.Format

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instance Phenomena.Modality.ModalConcord.LiuRotter2025.instReprDimensionClass :

Repr DimensionClass

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Phenomena.Modality.ModalConcord.LiuRotter2025.instReprDimensionClass = { reprPrec := Phenomena.Modality.ModalConcord.LiuRotter2025.instReprDimensionClass.repr }

def Phenomena.Modality.ModalConcord.LiuRotter2025.SocialDimension.dimClass :

SocialDimension → DimensionClass

Classify each social dimension as competence or warmth.

Equations

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def Phenomena.Modality.ModalConcord.LiuRotter2025.SocialDimension.all :

List SocialDimension

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structure Phenomena.Modality.ModalConcord.LiuRotter2025.InteractionEffect :

FORCE × NUMBER interaction on a social dimension. Positive β: necessity MC scores higher (competence pattern). Negative β: necessity MC scores lower (warmth pattern).

beta : ℚ
se : ℚ
significant : Bool

Instances For

instance Phenomena.Modality.ModalConcord.LiuRotter2025.instReprInteractionEffect :

Repr InteractionEffect

Equations

Phenomena.Modality.ModalConcord.LiuRotter2025.instReprInteractionEffect = { reprPrec := Phenomena.Modality.ModalConcord.LiuRotter2025.instReprInteractionEffect.repr }

def Phenomena.Modality.ModalConcord.LiuRotter2025.instReprInteractionEffect.repr :

InteractionEffect → ℕ → Std.Format

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instance Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqInteractionEffect :

BEq InteractionEffect

Equations

Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqInteractionEffect = { beq := Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqInteractionEffect.beq }

def Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqInteractionEffect.beq :

InteractionEffect → InteractionEffect → Bool

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Phenomena.Modality.ModalConcord.LiuRotter2025.instBEqInteractionEffect.beq x✝¹ x✝ = false

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def Phenomena.Modality.ModalConcord.LiuRotter2025.socialInteraction :

SocialDimension → InteractionEffect

FORCE × NUMBER interaction results per social dimension. All 7 dimensions show significant interactions (p < .05).

Equations

One or more equations did not get rendered due to their size.
Phenomena.Modality.ModalConcord.LiuRotter2025.socialInteraction Phenomena.Modality.ModalConcord.LiuRotter2025.SocialDimension.ses = { beta := 41 / 100, se := 16 / 100, significant := true }
Phenomena.Modality.ModalConcord.LiuRotter2025.socialInteraction Phenomena.Modality.ModalConcord.LiuRotter2025.SocialDimension.warmth = { beta := -30 / 100, se := 15 / 100, significant := true }

Instances For

Key Experiment 2 empirical generalizations #

Competence dimensions have positive interaction: Necessity MC increases perceived competence (SES, education, formality, confidence, coolness).

theorem Phenomena.Modality.ModalConcord.LiuRotter2025.warmth_negative :

(socialInteraction SocialDimension.friendliness).beta < 0 ∧ (socialInteraction SocialDimension.warmth).beta < 0

Warmth dimensions have negative interaction: Necessity MC decreases perceived warmth (friendliness, warmth).

Social meaning mirrors commitment: Competence dimensions have positive β (matching necessity strengthening), warmth dimensions have negative β (matching possibility weakening). This parallel suggests the social meaning drives the commitment effect.

Formality shows the strongest interaction among all social dimensions (β = 0.51), consistent with the register approach to modal concord.