Rosa and Arnold (2017): Predictability affects production

This file formalizes [RA17]'s test of whether the predictability of a referent affects the speaker's choice of a pronoun. Transfer verbs separate thematic role from grammatical role, since get and take put the goal in subject position while give and hand put it in a nonsubject position, so the design crosses the role of the continued character with its grammatical role and with the gender contrast of the character pair, and a rating study finds the goal expected as the next mention well above the source while subjects are not expected above nonsubjects. The expectancy hypothesis of [Arn01] predicts more pronouns for goals; the topicality account of [KR13] and [FvG10] predicts that thematic role leaves the production probability untouched once grammatical role is fixed. The production probability is a logistic model over the design, the paper's regression with its two main effects: topical_iff states the topicality account as the vanishing of the thematic effect, and source_subject_gt_goal_iff shows that a subject source pronominalized above a nonsubject goal, the earlier finding taken as evidence against predictability, is consistent with a positive thematic effect whenever the subject effect exceeds it. The pronoun rates of the three experiments and the rating study are Data/Experiments/RosaArnold2017; topical_not_fits reads the Experiment 1 contrast at fixed grammatical role and goal_expected the rating study. The effect sizes, the marginal amplification of the goal effect under Occasion and Result continuations in Experiment 2, and the shorter latencies for goal continuations stay in prose.

Implementation notes

• A model fits a table of rates when its log-odds order the cells as the rates do, which the logistic link guarantees for population rates.
• The gender contrast of an item is derived from the characters' φ-features: a pronoun is ambiguous exactly when the two characters agree.

References

• [RA17]
• [Arn01]
• [KR13]
• [FvG10]

The design

structure RosaArnold2017.Cell : Type

A cell of the design.

• role : Role
• gram : Gram
• gender : Gender

def RosaArnold2017.instDecidableEqCell.decEq (x✝ x✝¹ : Cell) : Decidable (x✝ = x✝¹)

Equations

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

@[instance_reducible]

instance RosaArnold2017.instDecidableEqCell : DecidableEq Cell

Equations

• RosaArnold2017.instDecidableEqCell = RosaArnold2017.instDecidableEqCell.decEq

def RosaArnold2017.instReprCell.repr : Cell → ℕ → Std.Format

Equations

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

@[instance_reducible]

instance RosaArnold2017.instReprCell : Repr Cell

Equations

• RosaArnold2017.instReprCell = { reprPrec := RosaArnold2017.instReprCell.repr }

@[instance_reducible]

instance RosaArnold2017.instFintypeCell : Fintype Cell

Equations

• RosaArnold2017.instFintypeCell = Fintype.ofEquiv ((_ : RosaArnold2017.Role) × (_ : RosaArnold2017.Gram) × RosaArnold2017.Gender) RosaArnold2017.Cell.proxyTypeEquiv

def RosaArnold2017.Gender.ofPair (w₁ w₂ : Morphology.Word) : Gender

The gender contrast of a pair of characters: same exactly when their φ-features agree, the pairs a third-person singular pronoun cannot tell apart.

Equations

• RosaArnold2017.Gender.ofPair w₁ w₂ = if w₁.Agree w₂ then RosaArnold2017.Gender.same else RosaArnold2017.Gender.different

def RosaArnold2017.lisa : Morphology.Word

Lisa, of Lisa gave the leftover pie to Brendan.

Equations

• RosaArnold2017.lisa = { form := "Lisa", cat := UD.UPOS.PROPN, features := Morphology.Features.of (some Person.third) (some Number.singular) (some Gender.feminine) }

def RosaArnold2017.brendan : Morphology.Word

Brendan.

Equations

• RosaArnold2017.brendan = { form := "Brendan", cat := UD.UPOS.PROPN, features := Morphology.Features.of (some Person.third) (some Number.singular) (some Gender.masculine) }

theorem RosaArnold2017.lisa_brendan : Gender.ofPair lisa brendan = Gender.different ∧ English.Pronouns.she.CandidateAntecedent lisa ∧ ¬English.Pronouns.she.CandidateAntecedent brendan

The running example is a different-gender item: she has Lisa as its only candidate antecedent.

The production model

The regressions predict the log-odds of a pronoun from subjecthood and thematic role.

structure RosaArnold2017.Model : Type

A logistic production model over the design: the log-odds of a pronoun as a baseline plus a subject effect and a goal effect.

• base : ℚ
• subject : ℚ
• goal : ℚ

def RosaArnold2017.Model.logit (M : Model) (c : Cell) : ℚ

The log-odds of a pronoun in a cell.

Equations

• M.logit c = (M.base + if c.gram = RosaArnold2017.Gram.subject then M.subject else 0) + if c.role = RosaArnold2017.Role.goal then M.goal else 0

def RosaArnold2017.Model.Topical (M : Model) : Prop

The topicality account: production is insensitive to thematic role.

Equations

• M.Topical = (M.goal = 0)

theorem RosaArnold2017.topical_iff (M : Model) : M.Topical ↔ ∀ (g : Gram) (d : Gender), M.logit { role := Role.goal, gram := g, gender := d } = M.logit { role := Role.source, gram := g, gender := d }

The topicality account is the claim that goals and sources are pronominalized alike at every grammatical role and gender.

theorem RosaArnold2017.source_subject_gt_goal_iff (M : Model) (d : Gender) : M.logit { role := Role.goal, gram := Gram.nonsubject, gender := d } < M.logit { role := Role.source, gram := Gram.subject, gender := d } ↔ M.goal < M.subject

A subject source pronominalized above a nonsubject goal, the earlier finding read as evidence that production ignores predictability, holds exactly when the subject effect exceeds the goal effect, so it leaves a positive goal effect untested.

def RosaArnold2017.Model.Fits (M : Model) (r : Cell → ℕ) : Prop

A model fits a table of rates when its log-odds order the cells as the rates do.

Equations

• M.Fits r = ∀ (c c' : RosaArnold2017.Cell), M.logit c < M.logit c' ↔ r c < r c'

The findings

def RosaArnold2017.rate (x : Experiment) (c : Cell) : ℕ

The rate of pronoun production in a cell of an experiment (Tables 1, 4, 7), in percent.

Equations

• RosaArnold2017.rate x c = (RosaArnold2017.rates x c.gender c.gram c.role).pronouns

theorem RosaArnold2017.goal_expected : 50 < goalNextMention ∧ subjectNextMention < goalNextMention

Goals are expected as the next mention above sources, and above subjects.

theorem RosaArnold2017.topical_not_fits (M : Model) (hM : M.Topical) : ¬M.Fits (rate Experiment.retelling)

Experiment 1 at fixed grammatical role refutes the topicality account: goals in subject position are pronominalized above sources in subject position, which no model without a thematic effect fits.