@cite{bale-etal-2025} — Competence by Default

Bale, A. C., Noguchi, H., Rolland, M. & Barner, D. (2025). Competence by default: Do listeners assume that speakers are knowledgeable when computing conversational inferences? Journal of Semantics 42(1–2): 39–55.

Core Contribution

Tests whether the competence assumption in scalar implicature derivation (step 5 of @cite{soames-1982} / @cite{horn-1989} / @cite{sauerland-2004}) is a cognitive default or must be contextually licensed. The 5-step derivation:

1. Speaker said φ (e.g., "some of the marbles are red")
2. There exists a stronger alternative ψ (e.g., "all of the marbles are red")
3. Speaker didn't say ψ (Quantity)
4. Therefore ¬Bel_S(ψ) — weak implicature
5. With competence (Bel_S(ψ) ∨ Bel_S(¬ψ)), derive Bel_S(¬ψ) — strong SI

Step 5 depends on the competence assumption: the listener assumes the speaker knows whether ψ. Three hypotheses about when this is applied:

• Competence-by-default: competence is assumed by default; cancellation requires effortful integration of contextual evidence
• SSI-by-default: the entire SSI is a default; load disrupts SI computation itself
• Contextual licensing: competence must be contextually justified; it is not a default

Experimental Design

Dual-task paradigm with 2 × 2 design:

• Between-subjects: cognitive load (load vs. no load), n = 30 per group
• Within-subjects: speaker knowledge (full knowledge = FK vs. partial knowledge = PK)
• Trials: FK+All (control), FK+Some, PK+Some
• Response: 3-way forced choice ("Yes" / "No" / "I don't know")
• Key DV: proportion of "No" responses on some trials (= SSI computed)

Key Finding

GLMM reveals a significant Knowledge × Load interaction (β = 2.62, SE = 0.86, χ²(1) = 11.3, P < .001): load increases SSI rate in the PK (ignorant) condition (10% → 23.3%) while non-significantly decreasing it in the FK (competent) condition (65.6% → 56.7%). This crossover supports competence-by-default: load impairs effortful cancellation of the default competence assumption.

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.nTotal : Nat

Total participants (N = 60, n = 30 per load group).

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.nTotal = 60

Experimental Conditions

inductive Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.SpeakerKnowledge : Type

Speaker's epistemic state regarding the stronger alternative ψ.

Manipulated via cover story: speaker either looked in all sections of a box (full knowledge) or only some sections (partial knowledge).

• fullKnowledge : SpeakerKnowledge

  Full Knowledge: speaker inspected all sections, knows whether ψ

• partialKnowledge : SpeakerKnowledge

  Partial Knowledge: speaker inspected only some sections, ignorant of ψ

instance Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instDecidableEqSpeakerKnowledge : DecidableEq SpeakerKnowledge

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instDecidableEqSpeakerKnowledge x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqSpeakerKnowledge.beq : SpeakerKnowledge → SpeakerKnowledge → Bool

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqSpeakerKnowledge.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqSpeakerKnowledge : BEq SpeakerKnowledge

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqSpeakerKnowledge = { beq := Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqSpeakerKnowledge.beq }

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprSpeakerKnowledge.repr : SpeakerKnowledge → Nat → Std.Format

Equations

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

instance Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprSpeakerKnowledge : Repr SpeakerKnowledge

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprSpeakerKnowledge = { reprPrec := Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprSpeakerKnowledge.repr }

inductive Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.LoadCondition : Type

Cognitive load manipulation (between-subjects).

• noLoad : LoadCondition

  No concurrent task

• load : LoadCondition

  Dual-task: memorize a dot pattern while processing utterance

instance Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instDecidableEqLoadCondition : DecidableEq LoadCondition

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instDecidableEqLoadCondition x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqLoadCondition.beq : LoadCondition → LoadCondition → Bool

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqLoadCondition.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqLoadCondition : BEq LoadCondition

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqLoadCondition = { beq := Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqLoadCondition.beq }

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprLoadCondition.repr : LoadCondition → Nat → Std.Format

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

instance Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprLoadCondition : Repr LoadCondition

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprLoadCondition = { reprPrec := Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprLoadCondition.repr }

structure Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.ExperimentalCondition : Type

A full experimental condition: speaker knowledge × cognitive load.

• knowledge : SpeakerKnowledge
• load : LoadCondition

instance Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instDecidableEqExperimentalCondition : DecidableEq ExperimentalCondition

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instDecidableEqExperimentalCondition = Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instDecidableEqExperimentalCondition.decEq

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instDecidableEqExperimentalCondition.decEq (x✝ x✝¹ : ExperimentalCondition) : Decidable (x✝ = x✝¹)

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

instance Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqExperimentalCondition : BEq ExperimentalCondition

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqExperimentalCondition = { beq := Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqExperimentalCondition.beq }

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqExperimentalCondition.beq : ExperimentalCondition → ExperimentalCondition → Bool

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqExperimentalCondition.beq { knowledge := a, load := a_1 } { knowledge := b, load := b_1 } = (a == b && a_1 == b_1)
• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqExperimentalCondition.beq x✝¹ x✝ = false

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprExperimentalCondition.repr : ExperimentalCondition → Nat → Std.Format

Equations

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

instance Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprExperimentalCondition : Repr ExperimentalCondition

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprExperimentalCondition = { reprPrec := Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprExperimentalCondition.repr }

Observed SSI Rates

Rates are stored in tenths of a percent to preserve the one-decimal-place
precision reported in the paper (e.g., 233 = 23.3%). 

structure Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.SSIRate : Type

Observed strong scalar implicature rate for one condition.

• condition : ExperimentalCondition

  The experimental condition

• rateTenths : Nat

  SSI rate in tenths of a percent (e.g., 233 = 23.3%)

• n : Nat

  Number of participants in this load group

instance Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprSSIRate : Repr SSIRate

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprSSIRate = { reprPrec := Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprSSIRate.repr }

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprSSIRate.repr : SSIRate → Nat → Std.Format

Equations

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

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.fk_noLoad : SSIRate

FK + No Load: 65.6% SSI rate (baseline for competent speaker).

Equations

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

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.fk_load : SSIRate

FK + Load: 56.7% SSI rate (non-significant decrease, P = .22).

Equations

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

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.pk_noLoad : SSIRate

PK + No Load: 10.0% SSI rate (competence properly canceled).

Equations

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

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.pk_load : SSIRate

PK + Load: 23.3% SSI rate — the key finding. Load impairs cancellation of the default competence assumption, yielding more SSIs despite speaker ignorance.

Equations

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

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.allConditions : List SSIRate

All four conditions.

Equations

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

Interaction Test

The key statistical test: Knowledge × Load interaction in a GLMM. 

structure Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.InteractionTest : Type

Result of the Knowledge × Load interaction test (GLMM, logistic).

• beta : Float

  Interaction coefficient

• se : Float

  Standard error

• chiSq : Float

  Chi-squared statistic (likelihood ratio, 1 df)

• p : Float

  p-value

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprInteractionTest.repr : InteractionTest → Nat → Std.Format

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

instance Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprInteractionTest : Repr InteractionTest

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprInteractionTest = { reprPrec := Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprInteractionTest.repr }

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.knowledgeLoadInteraction : InteractionTest

The observed interaction: β = 2.62, χ²(1) = 11.3, P < .001.

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.knowledgeLoadInteraction = { beta := 2.62, se := 0.86, chiSq := 11.3, p := 1e-3 }

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.interaction_significant : knowledgeLoadInteraction.p < 5e-2

The interaction is significant (P < .05).

Load Effects by Condition

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.loadEffect (k : SpeakerKnowledge) : Int

Signed load effect in tenths of a percent. Positive = load increases SSI rate; negative = load decreases.

Equations

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

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.crossover_interaction : loadEffect SpeakerKnowledge.partialKnowledge > 0 ∧ loadEffect SpeakerKnowledge.fullKnowledge < 0

The crossover interaction: load increases SSIs for PK speakers but decreases SSIs for FK speakers.

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.pk_load_increase : pk_load.rateTenths > pk_noLoad.rateTenths

Load increases SSI rate in PK condition by 13.3 percentage points.

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.interaction_magnitude : loadEffect SpeakerKnowledge.partialKnowledge - loadEffect SpeakerKnowledge.fullKnowledge > 0

The interaction magnitude: the difference in load effects across knowledge conditions is positive (PK effect > FK effect).

Competing Hypotheses

inductive Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.CompetenceHypothesis : Type

Three hypotheses about the status of the competence assumption.

• competenceByDefault : CompetenceHypothesis

  Competence is assumed by default; cancellation requires effortful processing. Load impairs cancellation → more SSIs when speaker is actually ignorant.

• ssiByDefault : CompetenceHypothesis

  The entire SI derivation is a default; load disrupts SI computation itself. Predicts load decreases SSI rates.

• contextualLicensing : CompetenceHypothesis

  Competence must be contextually licensed; it is not a default. Load should not increase SSI rates for ignorant speakers — competence was never assumed, so there is nothing to fail to cancel.

instance Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instDecidableEqCompetenceHypothesis : DecidableEq CompetenceHypothesis

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instDecidableEqCompetenceHypothesis x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqCompetenceHypothesis.beq : CompetenceHypothesis → CompetenceHypothesis → Bool

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqCompetenceHypothesis.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqCompetenceHypothesis : BEq CompetenceHypothesis

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqCompetenceHypothesis = { beq := Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instBEqCompetenceHypothesis.beq }

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprCompetenceHypothesis.repr : CompetenceHypothesis → Nat → Std.Format

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

instance Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprCompetenceHypothesis : Repr CompetenceHypothesis

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprCompetenceHypothesis = { reprPrec := Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.instReprCompetenceHypothesis.repr }

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.predictsPositiveInteraction : CompetenceHypothesis → Bool

Whether a hypothesis predicts a positive Knowledge × Load interaction (i.e., load increases SSI more — or decreases it less — in PK than FK).

This is the key discriminating prediction: only competence-by-default predicts a positive interaction.

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.predictsPositiveInteraction Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.CompetenceHypothesis.competenceByDefault = true
• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.predictsPositiveInteraction Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.CompetenceHypothesis.ssiByDefault = false
• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.predictsPositiveInteraction Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.CompetenceHypothesis.contextualLicensing = false

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.only_competenceByDefault_predicts_interaction : List.filter predictsPositiveInteraction [CompetenceHypothesis.competenceByDefault, CompetenceHypothesis.ssiByDefault, CompetenceHypothesis.contextualLicensing] = [CompetenceHypothesis.competenceByDefault]

Competence-by-default is the only hypothesis predicting a positive interaction, matching the observed data.

Connects the experimental findings to the NeoGricean competence formalization in Theories.Pragmatics.Implicature.Core.

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.toBeliefState : SpeakerKnowledge → Implicature.BeliefState

Map speaker knowledge to NeoGricean belief state about the stronger alternative ψ. FK speaker knows ¬ψ; PK speaker has no opinion.

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.toBeliefState Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.SpeakerKnowledge.fullKnowledge = Implicature.BeliefState.disbelief
• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.toBeliefState Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.SpeakerKnowledge.partialKnowledge = Implicature.BeliefState.noOpinion

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.fk_competent : Implicature.competent (toBeliefState SpeakerKnowledge.fullKnowledge) = true

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.pk_not_competent : Implicature.competent (toBeliefState SpeakerKnowledge.partialKnowledge) = false

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.fk_yields_strong : have p := Implicature.Competence.processAlternative true (toBeliefState SpeakerKnowledge.fullKnowledge); p.weakHolds = true ∧ p.competenceAssumed = true ∧ p.strongDerived = true

FK speaker: processAlternative yields a strong SI.

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.pk_yields_weak_only : have p := Implicature.Competence.processAlternative true (toBeliefState SpeakerKnowledge.partialKnowledge); p.weakHolds = true ∧ p.competenceAssumed = false ∧ p.strongDerived = false

PK speaker (correctly identified): weak-only SI.

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.defaultBeliefState : Implicature.BeliefState

The default belief state: listeners assume speakers are competent.

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.defaultBeliefState = Implicature.BeliefState.disbelief

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.canIntegrateContext : LoadCondition → Bool

Context integration: no load → yes; load → no.

Equations

• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.canIntegrateContext Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.LoadCondition.noLoad = true
• Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.canIntegrateContext Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.LoadCondition.load = false

def Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.effectiveBeliefState (k : SpeakerKnowledge) (l : LoadCondition) : Implicature.BeliefState

The effective belief state after (possibly failed) context integration.

Equations

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

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.noLoad_fk_correct : effectiveBeliefState SpeakerKnowledge.fullKnowledge LoadCondition.noLoad = Implicature.BeliefState.disbelief

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.noLoad_pk_correct : effectiveBeliefState SpeakerKnowledge.partialKnowledge LoadCondition.noLoad = Implicature.BeliefState.noOpinion

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.load_fk_default : effectiveBeliefState SpeakerKnowledge.fullKnowledge LoadCondition.load = Implicature.BeliefState.disbelief

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.load_pk_defaults_to_competent : effectiveBeliefState SpeakerKnowledge.partialKnowledge LoadCondition.load = Implicature.BeliefState.disbelief

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.load_pk_yields_strong : have b := effectiveBeliefState SpeakerKnowledge.partialKnowledge LoadCondition.load; have p := Implicature.Competence.processAlternative true b; p.strongDerived = true

Under load + PK, the default competence yields a strong SI (10% → 23.3%).

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.noLoad_pk_yields_weak : have b := effectiveBeliefState SpeakerKnowledge.partialKnowledge LoadCondition.noLoad; have p := Implicature.Competence.processAlternative true b; p.strongDerived = false

Under no-load + PK, correct context integration yields weak-only (10%).

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.crossover_prediction : have pk_noLoad := Implicature.Competence.processAlternative true (effectiveBeliefState SpeakerKnowledge.partialKnowledge LoadCondition.noLoad); have pk_load := Implicature.Competence.processAlternative true (effectiveBeliefState SpeakerKnowledge.partialKnowledge LoadCondition.load); have fk_noLoad := Implicature.Competence.processAlternative true (effectiveBeliefState SpeakerKnowledge.fullKnowledge LoadCondition.noLoad); have fk_load := Implicature.Competence.processAlternative true (effectiveBeliefState SpeakerKnowledge.fullKnowledge LoadCondition.load); pk_noLoad.strongDerived = false ∧ pk_load.strongDerived = true ∧ fk_noLoad.strongDerived = true ∧ fk_load.strongDerived = true

The crossover prediction: load flips PK from weak to strong, but leaves FK unchanged.

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.simpleAssertion_assumes_competence : Implicature.Competence.shouldAssumeCompetence Implicature.Competence.CompetenceContext.simpleAssertion = true

Simple assertion context = competence assumed by default.

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.default_matches_competent_disbelief : defaultBeliefState = Implicature.BeliefState.disbelief

theorem Phenomena.ScalarImplicatures.Studies.BaleEtAl2025.competence_default_is_simpleAssertion : Implicature.Competence.shouldAssumeCompetence Implicature.Competence.CompetenceContext.simpleAssertion = true ∧ Implicature.Competence.shouldAssumeCompetence Implicature.Competence.CompetenceContext.uncertain = false

Bale et al. validate .simpleAssertion as the cognitive default.