Pronoun interpretation: coherence vs. centering [KR13]

[KR13] reconcile [Hob79]'s coherence-driven account of pronoun interpretation with the centering-driven account of [GJW95] through a Bayesian decomposition, P(referent | pronoun) ∝ P(pronoun | referent) × P(referent). The prior P(referent) is a coherence-driven next-mention bias; the likelihood P(pronoun | referent) is a centering-driven topichood (production) bias. The two components are empirically dissociable across five passage-completion experiments with transfer-of-possession and implicit-causality verbs.

Main declarations

• NextMentionModel, NextMentionModel.sourceBias: the coherence-marginalized prior P(Source) = Σ_CR P(CR) · P(Source | CR) (the paper's Eq. (9)).
• topichood, TopichoodLevel: voice and surface position to topichood, the centering-driven likelihood term.
• bayesianPrediction: Bayesian inversion to P(Subject | pronoun) (Eq. (13)).
• NextMentionModel.toBias: coarsening of the prior to the two-point Discourse.NextMentionBias, with expectancy_reversed_under_voice refuting the expectancy hypothesis the substrate's predictedForm encodes.
• cb_topichood_dissociation_under_voice: Centering's backward-looking center is voice-blind where topichood is voice-sensitive.
• she_ambiguous_over_stimuli: the φ-design premise — both same-gender characters are candidate antecedents (Proform.CandidateAntecedent) of the prompt pronoun, so the φ-filter cannot resolve the reference the Bayesian model competes over.

Implementation notes

Probabilities are exact rationals (ℚ) on a 0–100 percentage scale; empirical values are quoted from the paper's Tables 1–10. sourceBias marginalizes over CoherenceRelation.all, so adding a coherence relation forces the mixture to be revisited (via CoherenceRelation.mem_all) rather than silently dropping it.

References

[Hob79] [Keh02] [Dav84] [Kam86] [GJW95]

Experimental design

inductive KehlerRohde2013.PromptType : Type

Prompt type in passage completion experiments.

• pronoun : PromptType
• noPronoun : PromptType

@[instance_reducible]

instance KehlerRohde2013.instDecidableEqPromptType : DecidableEq PromptType

Equations

• KehlerRohde2013.instDecidableEqPromptType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance KehlerRohde2013.instReprPromptType : Repr PromptType

Equations

• KehlerRohde2013.instReprPromptType = { reprPrec := KehlerRohde2013.instReprPromptType.repr }

def KehlerRohde2013.instReprPromptType.repr : PromptType → ℕ → Std.Format

Equations

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

inductive KehlerRohde2013.InstructionCond : Type

Instruction condition (transfer-of-possession experiments).

• whatNext : InstructionCond
• why : InstructionCond

@[instance_reducible]

instance KehlerRohde2013.instDecidableEqInstructionCond : DecidableEq InstructionCond

Equations

• KehlerRohde2013.instDecidableEqInstructionCond x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance KehlerRohde2013.instReprInstructionCond : Repr InstructionCond

Equations

• KehlerRohde2013.instReprInstructionCond = { reprPrec := KehlerRohde2013.instReprInstructionCond.repr }

def KehlerRohde2013.instReprInstructionCond.repr : InstructionCond → ℕ → Std.Format

Equations

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

The Bayesian model

structure KehlerRohde2013.NextMentionModel : Type

The coherence-marginalized next-mention bias (the paper's Eq. (9)): P(referent) = Σ_CR P(CR) × P(referent | CR), a mixture of CR-specific biases weighted by the prior over coherence relations — the coherence-driven prior. Probabilities are percentages (0–100).

• pCR : Discourse.Coherence.CoherenceRelation → ℚ

  P(CR): prior probability of coherence relation (%)

• pSourceGivenCR : Discourse.Coherence.CoherenceRelation → ℚ

  P(referent = Source | CR): Source bias given CR (%)

inductive KehlerRohde2013.TopichoodLevel : Type

Topichood level, determined by grammatical construction. Passive subjects signal stronger topichood than active subjects, since a marked construction placing an entity in subject position is a stronger topic indicator ([Dav84]). The likelihood P(pronoun | referent) tracks this level, not grammatical role per se.

• strong : TopichoodLevel
• default_ : TopichoodLevel
• low : TopichoodLevel

@[instance_reducible]

instance KehlerRohde2013.instDecidableEqTopichoodLevel : DecidableEq TopichoodLevel

Equations

• KehlerRohde2013.instDecidableEqTopichoodLevel x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def KehlerRohde2013.instReprTopichoodLevel.repr : TopichoodLevel → ℕ → Std.Format

Equations

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

@[instance_reducible]

instance KehlerRohde2013.instReprTopichoodLevel : Repr TopichoodLevel

Equations

• KehlerRohde2013.instReprTopichoodLevel = { reprPrec := KehlerRohde2013.instReprTopichoodLevel.repr }

def KehlerRohde2013.topichood (voice : UD.Voice) (isSubject : Bool) : TopichoodLevel

Compute topichood from voice and surface position.

Equations

• KehlerRohde2013.topichood voice false = KehlerRohde2013.TopichoodLevel.low
• KehlerRohde2013.topichood UD.Voice.Pass true = KehlerRohde2013.TopichoodLevel.strong
• KehlerRohde2013.topichood voice true = KehlerRohde2013.TopichoodLevel.default_

Aspect manipulation

def KehlerRohde2013.sourceInterpPerfective : ℚ

Table 1: Source interpretation rate by aspect. Imperfective focuses on the ongoing event (Source still central); perfective focuses on the end state (Goal = endpoint of transfer).

Equations

• KehlerRohde2013.sourceInterpPerfective = 57

def KehlerRohde2013.sourceInterpImperfective : ℚ

Equations

• KehlerRohde2013.sourceInterpImperfective = 80

theorem KehlerRohde2013.imperfective_more_source : sourceInterpImperfective > sourceInterpPerfective

Imperfective yields more Source interpretations than perfective.

Coherence relation analysis

structure KehlerRohde2013.CRDatum : Type

Coherence relation frequency and bias data from Table 2 (perfective condition, transfer-of-possession verbs). The paper's "Violated Expectation" is modelled as CoherenceRelation.contrast: it is a denial-of-expectation relation, which [Umb04] classes with contrast, though [Keh02] alternatively files it under cause-effect. No theorem here depends on its coherence class.

• cr : Discourse.Coherence.CoherenceRelation
• freqPct : ℚ
• sourceGivenCR : ℚ

def KehlerRohde2013.instReprCRDatum.repr : CRDatum → ℕ → Std.Format

Equations

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

@[instance_reducible]

instance KehlerRohde2013.instReprCRDatum : Repr CRDatum

Equations

• KehlerRohde2013.instReprCRDatum = { reprPrec := KehlerRohde2013.instReprCRDatum.repr }

def KehlerRohde2013.crOccasion : CRDatum

Equations

• KehlerRohde2013.crOccasion = { cr := Discourse.Coherence.CoherenceRelation.occasion, freqPct := 38, sourceGivenCR := 18 }

def KehlerRohde2013.crElaboration : CRDatum

Equations

• KehlerRohde2013.crElaboration = { cr := Discourse.Coherence.CoherenceRelation.elaboration, freqPct := 28, sourceGivenCR := 98 }

def KehlerRohde2013.crExplanation : CRDatum

Equations

• KehlerRohde2013.crExplanation = { cr := Discourse.Coherence.CoherenceRelation.explanation, freqPct := 18, sourceGivenCR := 80 }

def KehlerRohde2013.crViolatedExp : CRDatum

Equations

• KehlerRohde2013.crViolatedExp = { cr := Discourse.Coherence.CoherenceRelation.contrast, freqPct := 8, sourceGivenCR := 76 }

def KehlerRohde2013.crResult : CRDatum

Equations

• KehlerRohde2013.crResult = { cr := Discourse.Coherence.CoherenceRelation.result, freqPct := 6, sourceGivenCR := 8 }

theorem KehlerRohde2013.goal_biased_crs : crOccasion.sourceGivenCR < 50 ∧ crResult.sourceGivenCR < 50

Occasion and Result are Goal-biased (Source < 50%).

theorem KehlerRohde2013.source_biased_crs : crElaboration.sourceGivenCR > 50 ∧ crExplanation.sourceGivenCR > 50 ∧ crViolatedExp.sourceGivenCR > 50

Elaboration, Explanation, and Violated Expectation are Source-biased.

theorem KehlerRohde2013.biases_masked_by_mixture : crOccasion.sourceGivenCR < 50 ∧ crElaboration.sourceGivenCR > 50 ∧ crOccasion.freqPct > crElaboration.freqPct

The overall ~57/43 Source/Goal split masks strong CR-conditioned biases: Occasion is most common (.38) and Goal-biased (.18 Source); Elaboration is second (.28) and strongly Source-biased (.98).

Instruction manipulation: P(CR) shift

def KehlerRohde2013.whatNextOccasionPct : ℚ

Table 3: "What happened next?" yields Occasion-dominated completions; "Why?" yields Explanation-dominated ones. Instructions shift P(CR) without changing the stimuli.

Equations

• KehlerRohde2013.whatNextOccasionPct = 71

def KehlerRohde2013.whatNextExplanationPct : ℚ

Equations

• KehlerRohde2013.whatNextExplanationPct = 1

def KehlerRohde2013.whyOccasionPct : ℚ

Equations

• KehlerRohde2013.whyOccasionPct = 1

def KehlerRohde2013.whyExplanationPct : ℚ

Equations

• KehlerRohde2013.whyExplanationPct = 91

theorem KehlerRohde2013.instructions_shift_pCR : whatNextOccasionPct > whyOccasionPct ∧ whyExplanationPct > whatNextExplanationPct

def KehlerRohde2013.whatNextSourcePct : ℚ

Table 5: Source interpretation by instruction condition (perfective). Shifting P(CR) shifts P(referent), as predicted by the mixture (Eq. (9)).

Equations

• KehlerRohde2013.whatNextSourcePct = 34

def KehlerRohde2013.whySourcePct : ℚ

Equations

• KehlerRohde2013.whySourcePct = 82

theorem KehlerRohde2013.instructions_shift_interpretation : whySourcePct > whatNextSourcePct

theorem KehlerRohde2013.instruction_effect_magnitude : whySourcePct - whatNextSourcePct > 40

The instruction effect is 48 pp on identical stimuli — no morphosyntactic heuristic can account for it.

Bias stability: P(ref | CR) invariance

structure KehlerRohde2013.StabilityDatum : Type

Table 4: P(Source | CR) is stable across the original experiment and the instruction manipulation, supporting the structural claim that CR-conditioned biases are properties of the coherence relation itself, not the experimental context.

• cr : Discourse.Coherence.CoherenceRelation
• originalPct : ℚ
• instructionPct : ℚ

@[instance_reducible]

instance KehlerRohde2013.instReprStabilityDatum : Repr StabilityDatum

Equations

• KehlerRohde2013.instReprStabilityDatum = { reprPrec := KehlerRohde2013.instReprStabilityDatum.repr }

def KehlerRohde2013.instReprStabilityDatum.repr : StabilityDatum → ℕ → Std.Format

Equations

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

def KehlerRohde2013.stabElaboration : StabilityDatum

Equations

• KehlerRohde2013.stabElaboration = { cr := Discourse.Coherence.CoherenceRelation.elaboration, originalPct := 98, instructionPct := 100 }

def KehlerRohde2013.stabExplanation : StabilityDatum

Equations

• KehlerRohde2013.stabExplanation = { cr := Discourse.Coherence.CoherenceRelation.explanation, originalPct := 80, instructionPct := 82 }

def KehlerRohde2013.stabOccasion : StabilityDatum

Equations

• KehlerRohde2013.stabOccasion = { cr := Discourse.Coherence.CoherenceRelation.occasion, originalPct := 18, instructionPct := 27 }

def KehlerRohde2013.stabResult : StabilityDatum

Equations

• KehlerRohde2013.stabResult = { cr := Discourse.Coherence.CoherenceRelation.result, originalPct := 8, instructionPct := 9 }

theorem KehlerRohde2013.bias_direction_stable : (stabElaboration.originalPct > 50 ∧ stabElaboration.instructionPct > 50) ∧ (stabExplanation.originalPct > 50 ∧ stabExplanation.instructionPct > 50) ∧ (stabOccasion.originalPct < 50 ∧ stabOccasion.instructionPct < 50) ∧ stabResult.originalPct < 50 ∧ stabResult.instructionPct < 50

Bias direction (above/below 50%) is preserved for all five CRs across conditions: P(CR) can shift independently of P(ref | CR).

Bidirectionality: pronoun → coherence

structure KehlerRohde2013.PromptCRDatum : Type

Table 6: CR distribution by prompt type. The mere presence of an ambiguous pronoun shifts coherence expectations toward Source-biased relations. This bidirectionality — coreference affects coherence, not just vice versa — is predicted by Bayes (Eq. (12)) but not by Hobbs (pronouns are inert free variables) or Centering (does not model coherence).

• prompt : PromptType
• cr : Discourse.Coherence.CoherenceRelation
• freqPct : ℚ

def KehlerRohde2013.instReprPromptCRDatum.repr : PromptCRDatum → ℕ → Std.Format

Equations

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

@[instance_reducible]

instance KehlerRohde2013.instReprPromptCRDatum : Repr PromptCRDatum

Equations

• KehlerRohde2013.instReprPromptCRDatum = { reprPrec := KehlerRohde2013.instReprPromptCRDatum.repr }

def KehlerRohde2013.npElaboration : PromptCRDatum

Equations

• KehlerRohde2013.npElaboration = { prompt := KehlerRohde2013.PromptType.noPronoun, cr := Discourse.Coherence.CoherenceRelation.elaboration, freqPct := 6 }

def KehlerRohde2013.npExplanation : PromptCRDatum

Equations

• KehlerRohde2013.npExplanation = { prompt := KehlerRohde2013.PromptType.noPronoun, cr := Discourse.Coherence.CoherenceRelation.explanation, freqPct := 20 }

def KehlerRohde2013.npOccasion : PromptCRDatum

Equations

• KehlerRohde2013.npOccasion = { prompt := KehlerRohde2013.PromptType.noPronoun, cr := Discourse.Coherence.CoherenceRelation.occasion, freqPct := 36 }

def KehlerRohde2013.npResult : PromptCRDatum

Equations

• KehlerRohde2013.npResult = { prompt := KehlerRohde2013.PromptType.noPronoun, cr := Discourse.Coherence.CoherenceRelation.result, freqPct := 13 }

def KehlerRohde2013.ppElaboration : PromptCRDatum

Equations

• KehlerRohde2013.ppElaboration = { prompt := KehlerRohde2013.PromptType.pronoun, cr := Discourse.Coherence.CoherenceRelation.elaboration, freqPct := 20 }

def KehlerRohde2013.ppExplanation : PromptCRDatum

Equations

• KehlerRohde2013.ppExplanation = { prompt := KehlerRohde2013.PromptType.pronoun, cr := Discourse.Coherence.CoherenceRelation.explanation, freqPct := 28 }

def KehlerRohde2013.ppOccasion : PromptCRDatum

Equations

• KehlerRohde2013.ppOccasion = { prompt := KehlerRohde2013.PromptType.pronoun, cr := Discourse.Coherence.CoherenceRelation.occasion, freqPct := 28 }

def KehlerRohde2013.ppResult : PromptCRDatum

Equations

• KehlerRohde2013.ppResult = { prompt := KehlerRohde2013.PromptType.pronoun, cr := Discourse.Coherence.CoherenceRelation.result, freqPct := 5 }

theorem KehlerRohde2013.pronoun_boosts_source_CRs : ppElaboration.freqPct > npElaboration.freqPct ∧ ppExplanation.freqPct > npExplanation.freqPct

Pronoun prompt increases Source-biased CRs.

theorem KehlerRohde2013.pronoun_reduces_goal_CRs : ppOccasion.freqPct < npOccasion.freqPct ∧ ppResult.freqPct < npResult.freqPct

Pronoun prompt decreases Goal-biased CRs.

Voice manipulation: implicit-causality verbs

def KehlerRohde2013.nmActivePron : ℚ

Equations

• KehlerRohde2013.nmActivePron = 77

def KehlerRohde2013.nmActiveNoPron : ℚ

Equations

• KehlerRohde2013.nmActiveNoPron = 59

def KehlerRohde2013.nmPassivePron : ℚ

Equations

• KehlerRohde2013.nmPassivePron = 42

def KehlerRohde2013.nmPassiveNoPron : ℚ

Equations

• KehlerRohde2013.nmPassiveNoPron = 76

theorem KehlerRohde2013.voice_affects_nextMention : nmActivePron > nmPassivePron

Voice affects next-mention in the pronoun condition: active (.77) vs. passive (.42). Passivization moves the causally-implicated referent out of subject position — same proposition, different bias.

theorem KehlerRohde2013.noPronoun_pattern_reverses : nmPassiveNoPron > nmActiveNoPron

In the no-pronoun condition the pattern reverses: passive (.76) > active (.59). By-phrases are optional in English, so their inclusion signals the referent will be re-mentioned.

def KehlerRohde2013.explActivePron : ℚ

Equations

• KehlerRohde2013.explActivePron = 75

def KehlerRohde2013.explPassivePron : ℚ

Equations

• KehlerRohde2013.explPassivePron = 52

theorem KehlerRohde2013.voice_affects_coherence : explActivePron > explPassivePron

Voice affects coherence in the pronoun condition: active produces more Explanations than passive. Since the propositions are identical, this is mediated by the shift in pronominal reference — bidirectional coherence–coreference dependency.

def KehlerRohde2013.pronActiveSubj : ℚ

Equations

• KehlerRohde2013.pronActiveSubj = 62

def KehlerRohde2013.pronActiveNonSubj : ℚ

Equations

• KehlerRohde2013.pronActiveNonSubj = 24

def KehlerRohde2013.pronPassiveSubj : ℚ

Equations

• KehlerRohde2013.pronPassiveSubj = 87

def KehlerRohde2013.pronPassiveNonSubj : ℚ

Equations

• KehlerRohde2013.pronPassiveNonSubj = 23

theorem KehlerRohde2013.passive_subj_more_pronominalized : pronPassiveSubj > pronActiveSubj

Passive subjects are pronominalized more than active subjects (87% vs. 62%). Both are subjects, so this is not explicable by grammatical role; it reflects the stronger topichood signal of the passive — the key evidence that P(pronoun | referent) tracks topichood, not subjecthood.

theorem KehlerRohde2013.nonSubj_pron_invariant : pronActiveNonSubj - pronPassiveNonSubj ≤ 1

Non-subject pronominalization is invariant across voice (24% vs. 23%): at the same (low) topichood level, the voice manipulation has no effect on pronominalization rate. This is the Independence Hypothesis — P(pronoun | referent) does not depend on coherence-driven factors.

theorem KehlerRohde2013.subject_advantage_both_voices : pronActiveSubj > pronActiveNonSubj ∧ pronPassiveSubj > pronPassiveNonSubj

Subjects are pronominalized more than non-subjects in both voices — the centering-derived component.

theorem KehlerRohde2013.topichood_monotone : pronPassiveSubj > pronActiveSubj ∧ pronActiveSubj > pronActiveNonSubj

Topichood monotonically predicts pronominalization: strong (passive subject, 87%) > default (active subject, 62%) > low (non-subject, ~24%).

def KehlerRohde2013.predictedActiveSubj : ℚ

Equations

• KehlerRohde2013.predictedActiveSubj = 81

def KehlerRohde2013.actualActiveSubj : ℚ

Equations

• KehlerRohde2013.actualActiveSubj = 74

def KehlerRohde2013.predictedPassiveSubj : ℚ

Equations

• KehlerRohde2013.predictedPassiveSubj = 59

def KehlerRohde2013.actualPassiveSubj : ℚ

Equations

• KehlerRohde2013.actualPassiveSubj = 60

theorem KehlerRohde2013.bayesian_directionally_correct : predictedActiveSubj > predictedPassiveSubj ∧ actualActiveSubj > actualPassiveSubj

Bayesian predictions are directionally correct: active > passive in both predicted and actual biases.

theorem KehlerRohde2013.passive_prediction_accurate : actualPassiveSubj - predictedPassiveSubj ≤ 1

The passive prediction is highly accurate (59% vs. 60%).

Mixture derivation (Eq. (9))

def KehlerRohde2013.NextMentionModel.sourceBias (m : NextMentionModel) : ℚ

The coherence-marginalized Source bias of a NextMentionModel. This is the paper's Eq. (9), P(Source) = Σ_CR P(CR) × P(Source | CR), as a percentage — marginalizing over CoherenceRelation.all.

Equations

• m.sourceBias = List.foldl (fun (acc : ℚ) (cr : Discourse.Coherence.CoherenceRelation) => acc + m.pCR cr * m.pSourceGivenCR cr) 0 Discourse.Coherence.CoherenceRelation.all / 100

def KehlerRohde2013.whatNextModel : NextMentionModel

Equations

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

def KehlerRohde2013.whyModel : NextMentionModel

Equations

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

theorem KehlerRohde2013.instruction_models_share_bias : whatNextModel.pSourceGivenCR = whyModel.pSourceGivenCR

The two instruction models share their CR-conditioned biases: the instruction manipulation changes P(CR) while holding P(ref | CR) constant (Table 4).

theorem KehlerRohde2013.eq9_why_exceeds_whatNext : whyModel.sourceBias > whatNextModel.sourceBias

The "Why?" mixture exceeds the "What next?" mixture, derived from the model rather than read off Table 5: Explanation (Source-biased at 82%) dominates the "Why?" mixture at 91% P(CR).

theorem KehlerRohde2013.eq9_mixtures_approximate_table5 : whyModel.sourceBias > 80 ∧ whatNextModel.sourceBias < 40

The computed mixtures track Table 5: "Why?" → ~84% Source, "What next?" → ~36% Source (vs. observed 82% and 34%), the small gap from integer rounding and the "Other" CR category.

Bayesian inversion (Eq. (13))

def KehlerRohde2013.bayesianPrediction (pSubj pPronSubj pPronNonSubj : ℚ) : ℚ

P(Subject | pronoun) via Bayes' rule (Eq. (13)), from P(Subject next-mentioned) (no-pronoun data) and P(pronoun | position) (pronominalization rates). Result is a percentage.

Equations

• KehlerRohde2013.bayesianPrediction pSubj pPronSubj pPronNonSubj = pPronSubj * pSubj * 100 / (pPronSubj * pSubj + pPronNonSubj * (100 - pSubj))

theorem KehlerRohde2013.eq13_active_prediction : bayesianPrediction nmActiveNoPron pronActiveSubj pronActiveNonSubj > 50

Active voice: from P(Subject) = 59% (Table 7), P(pronoun | Subject) = 62%, P(pronoun | NonSubject) = 24% (Table 9), Bayes' rule yields ≈ 78% (the paper reports 81% from unrounded data; the direction matches).

theorem KehlerRohde2013.eq13_passive_prediction : bayesianPrediction (100 - nmPassiveNoPron) pronPassiveSubj pronPassiveNonSubj > 50

Passive voice: from P(Subject) = 100 − 76 = 24% (Table 7), P(pronoun | Subject) = 87%, P(pronoun | NonSubject) = 23% (Table 9), Bayes' rule yields ≈ 54%.

theorem KehlerRohde2013.eq13_active_exceeds_passive : bayesianPrediction nmActiveNoPron pronActiveSubj pronActiveNonSubj > bayesianPrediction (100 - nmPassiveNoPron) pronPassiveSubj pronPassiveNonSubj

Bayes' rule derives active > passive for P(Subject | pronoun) even though passive subjects are pronominalized more (87% vs. 62%): the lower passive prior P(Subject) (24% vs. 59%) dominates, reversing the production bias.

Expectancy coarsening

def KehlerRohde2013.biasOfRate (p : ℚ) : Discourse.NextMentionBias

Coarsen a next-mention rate (a percentage) to the two-point Discourse.NextMentionBias by thresholding at 50%.

Equations

• KehlerRohde2013.biasOfRate p = if 50 < p then Discourse.NextMentionBias.high else Discourse.NextMentionBias.low

def KehlerRohde2013.NextMentionModel.toBias (m : NextMentionModel) : Discourse.NextMentionBias

The Bayesian prior coarsened to the two-point substrate bias: Discourse.NextMentionBias is the sign of sourceBias − 50.

Equations

• m.toBias = KehlerRohde2013.biasOfRate m.sourceBias

theorem KehlerRohde2013.whyModel_toBias : whyModel.toBias = Discourse.NextMentionBias.high

The "Why?" mixture coarsens to .high (Source-biased).

theorem KehlerRohde2013.whatNextModel_toBias : whatNextModel.toBias = Discourse.NextMentionBias.low

The "What next?" mixture coarsens to .low (Goal-biased).

theorem KehlerRohde2013.expectancy_reversed_under_voice : (biasOfRate nmPassiveNoPron).predictedForm.rank > (biasOfRate (100 - nmPassiveNoPron)).predictedForm.rank ∧ pronPassiveNonSubj < pronPassiveSubj

Expectancy refuted at the voice manipulation. Thresholding the no-pronoun next-mention rates (Table 7, passive) gives the by-phrase referent a .high bias and the passive subject a .low bias, so the expectancy hypothesis — encoded in the substrate as Discourse.NextMentionBias.predictedForm — predicts the by-phrase referent surfaces in the more reduced form. The observed pronominalization rates (Table 9) run the other way: 23% for the by-phrase vs. 87% for the subject. Production tracks topichood (topichood_monotone), not next-mention bias.

Coherence–referent bridge

theorem KehlerRohde2013.goal_biased_crs_are_endpoint_focused : crOccasion.cr.toClass = Discourse.Coherence.CoherenceClass.contiguity ∧ crResult.cr.toClass = Discourse.Coherence.CoherenceClass.causeEffect ∧ crOccasion.sourceGivenCR < 50 ∧ crResult.sourceGivenCR < 50

The two Goal-biased CRs (Occasion, Result) both focus on what happens after the prior event; for transfer verbs the endpoint is the Goal.

theorem KehlerRohde2013.explanation_source_and_backward : crExplanation.cr.selectsCause ∧ crExplanation.sourceGivenCR > 50

Explanation is Source-biased and selects for causes (backward causal). For transfer verbs the Source is the cause; for IC verbs the stimulus is — the bridge to IC bias studies.

theorem KehlerRohde2013.contiguity_class_splits : crOccasion.cr.toClass = crElaboration.cr.toClass ∧ crOccasion.sourceGivenCR < 50 ∧ crElaboration.sourceGivenCR > 50

The contiguity class does not uniformly predict bias: Occasion (18% Source) and Elaboration (98% Source) are both contiguity relations with opposite biases. Occasion focuses on the end state (Goal); Elaboration redescribes the same event (Source). Bias is set by the relation, not the class.

Centering substrate connection

[KR13] is the Bayesian–Centering reconciliation paper, so this section grounds the file's topichood/bayesianPrediction apparatus in the Discourse/Centering/ substrate (cb, cp, CbPronominalized). Under the standard grammatical-role Cf ranking (SUBJECT > OBJECT > OTHER, [Kam86]), the CB is invariant under voice — both (Amanda, SUBJ) (Brittany, OBJ) and (Amanda, SUBJ) (Brittany, OTHER-by-phrase) make Amanda the most-preferred Cf — yet topichood distinguishes them (passive subject .strong, active subject .default_). The voice-induced pronominalization gradient (87% vs. 62%) lives in the topichood signal, not the CB signal.

The φ-design premise

The Bayesian competition presupposes that morphology underdetermines the referent: the passages pair same-gender characters, so the prompt pronoun φ-agrees with both candidates and P(referent | pronoun) must come from the coherence prior and the topichood likelihood. The premise is checked against the English Fragment entry rather than stipulated.

def KehlerRohde2013.amanda : Morphology.Word

The two characters of the running example ("Amanda amazed Brittany"), both third-person singular feminine.

Equations

• KehlerRohde2013.amanda = { form := "Amanda", cat := UD.UPOS.PROPN, features := { number := some UD.Number.Sing, gender := some UD.Gender.Fem, person := some UD.Person.third } }

def KehlerRohde2013.brittany : Morphology.Word

Equations

• KehlerRohde2013.brittany = { form := "Brittany", cat := UD.UPOS.PROPN, features := { number := some UD.Number.Sing, gender := some UD.Gender.Fem, person := some UD.Person.third } }

def KehlerRohde2013.masculineFoil : Morphology.Word

A masculine token (a counterfactual foil, not a K&R stimulus).

Equations

• KehlerRohde2013.masculineFoil = { form := "Bill", cat := UD.UPOS.PROPN, features := { number := some UD.Number.Sing, gender := some UD.Gender.Masc, person := some UD.Person.third } }

theorem KehlerRohde2013.she_ambiguous_over_stimuli : Proform.CandidateAntecedent English.Pronouns.she amanda ∧ Proform.CandidateAntecedent English.Pronouns.she brittany

Both characters are candidate antecedents for the prompt She (the English Fragment entry), so the φ-filter cannot resolve the reference.

theorem KehlerRohde2013.she_resolved_against_masculine : Proform.CandidateAntecedent English.Pronouns.she amanda ∧ ¬Proform.CandidateAntecedent English.Pronouns.she masculineFoil

Against a mixed-gender pair the candidate set is a singleton; the same-gender design is what forces the Bayesian competition.

def KehlerRohde2013.prevAmandaActive : Discourse.Centering.Utterance Morphology.Word Discourse.Centering.GrammaticalRole

Prior "Amanda V'd Brittany": Amanda SUBJ, Brittany OBJ. Under Kameyama's role ranking the forward-looking centers are [Amanda, Brittany] with Amanda Cp.

Equations

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

def KehlerRohde2013.curActive : Discourse.Centering.Utterance Morphology.Word Discourse.Centering.GrammaticalRole

Active continuation "She V'd her" — Amanda still SUBJ, both pronouns.

Equations

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

def KehlerRohde2013.curPassive : Discourse.Centering.Utterance Morphology.Word Discourse.Centering.GrammaticalRole

Passive continuation "Amanda was V'd by Brittany" — Amanda promoted to SUBJ by the marked passive; Brittany now in the by-phrase (OTHER). The proposition is identical; only the construction differs.

Equations

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

theorem KehlerRohde2013.cp_prev_is_amanda : prevAmandaActive.cp = some amanda

Cp of the prior utterance is Amanda (SUBJ outranks OBJ).

theorem KehlerRohde2013.cb_invariant_under_voice : Discourse.Centering.cb prevAmandaActive curActive = Discourse.Centering.cb prevAmandaActive curPassive

CB is invariant under voice: both continuations have CB = Amanda, since Amanda is in prev.cf and realized in both, and the grammatical-role ranker cannot see voice — both subjects rank equally as .subject.

theorem KehlerRohde2013.cb_is_amanda_in_both_voices : Discourse.Centering.cb prevAmandaActive curActive = some amanda ∧ Discourse.Centering.cb prevAmandaActive curPassive = some amanda

Both voice variants have CB = Amanda specifically.

theorem KehlerRohde2013.topichood_distinguishes_voice : topichood UD.Voice.Pass true ≠ topichood UD.Voice.Act true

KR2013's topichood is voice-sensitive: the same subject-position Amanda is .strong under passive marking but .default_ under active — the gradient driving the 87% vs. 62% pronominalization difference (Table 9).

theorem KehlerRohde2013.cb_topichood_dissociation_under_voice : Discourse.Centering.cb prevAmandaActive curActive = Discourse.Centering.cb prevAmandaActive curPassive ∧ topichood UD.Voice.Pass true ≠ topichood UD.Voice.Act true

The dissociation: Centering's CB and KR2013's topichood diverge on the voice manipulation. CB is the same in both (Amanda); topichood differs (.strong vs. .default_). The 25-pp pronominalization gap (Table 9) lives in the topichood signal, not the CB signal — "P(pronoun | referent) tracks topichood, not subjecthood."

theorem KehlerRohde2013.rule1_gordon_satisfied_both_voices : Discourse.Centering.CbPronominalized prevAmandaActive curActive ∧ Discourse.Centering.CbPronominalized prevAmandaActive curPassive

Rule 1 (Gordon) is satisfied in both voice variants — both Amanda-realizations are pronominal — so the substrate Rule 1 constraint is voice-insensitive too. KR2013's contribution is the gradient it averages over: among Rule 1-satisfying utterances, passive-subject ones pronominalize 87% of the time vs. 62% for active (Table 9).

theorem KehlerRohde2013.topichood_rates_monotone_in_table9 : pronPassiveSubj > pronActiveSubj ∧ pronActiveSubj > pronActiveNonSubj

Centering as the qualitative skeleton of KR2013's likelihood: where CbPronominalized says "the CB should be pronominalized" (yes/no), the likelihood P(pronoun | referent) says "at a rate proportional to topichood" (gradient). The 87% / 62% / ~24% rates (Table 9) monotonically track the .strong / .default_ / .low levels (topichood_monotone).