Documentation

Linglib.Phenomena.Politeness.Studies.YoonEtAl2020

Overview #

Politeness arises from the interplay of three communicative goals: informativity (conveying the true state), social value (making the listener feel good), and presentational utility (appearing kind to the listener). This file implements both the S1 submodel (informativity + social tradeoff) and the full S2 model (adding presentational utility).

Experimental Design #

202 participants on Amazon MTurk
12 scenarios per participant (3 goals × 4 states)
Goals: informative, kind, both
States: 0-3 hearts (true quality rating)
Utterances: 8 options (4 adjectives × pos/neg)

Finding #

Speakers with BOTH goals (informative + kind) produce more negation in bad states (0-1 hearts) compared to single-goal conditions. This is the signature of indirect speech driven by self-presentation.

File Structure #

§1. Types & Semantics — shared across S1 and S2 models
§2. S1 Submodel — simplified (α=3, 5-point φ), demonstrating the informativity–social tradeoff that drives negation
§3. Full S2 Model — paper's fitted parameters (α≈4.47, 20-point φ grid), with presentational utility driving the "both" condition's negation pattern

inductive Phenomena.Politeness.Studies.YoonEtAl2020.HeartState :

Heart state: 0-3 hearts representing true quality

Instances For

instance Phenomena.Politeness.Studies.YoonEtAl2020.instDecidableEqHeartState :

DecidableEq HeartState

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instDecidableEqHeartState x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Politeness.Studies.YoonEtAl2020.instReprHeartState.repr :

HeartState → ℕ → Std.Format

Equations

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

Instances For

instance Phenomena.Politeness.Studies.YoonEtAl2020.instReprHeartState :

Repr HeartState

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instReprHeartState = { reprPrec := Phenomena.Politeness.Studies.YoonEtAl2020.instReprHeartState.repr }

def Phenomena.Politeness.Studies.YoonEtAl2020.instBEqHeartState.beq :

HeartState → HeartState → Bool

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instBEqHeartState.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

Instances For

instance Phenomena.Politeness.Studies.YoonEtAl2020.instBEqHeartState :

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instBEqHeartState = { beq := Phenomena.Politeness.Studies.YoonEtAl2020.instBEqHeartState.beq }

def Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedHeartState.default :

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedHeartState.default = Phenomena.Politeness.Studies.YoonEtAl2020.HeartState.h0

Instances For

instance Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedHeartState :

Inhabited HeartState

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedHeartState = { default := Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedHeartState.default }

instance Phenomena.Politeness.Studies.YoonEtAl2020.instFintypeHeartState :

Fintype HeartState

Equations

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

inductive Phenomena.Politeness.Studies.YoonEtAl2020.Utterance :

Utterance types: 4 adjectives × positive/negative

terrible : Utterance
bad : Utterance
good : Utterance
amazing : Utterance
notTerrible : Utterance
notBad : Utterance
notGood : Utterance
notAmazing : Utterance

Instances For

instance Phenomena.Politeness.Studies.YoonEtAl2020.instDecidableEqUtterance :

DecidableEq Utterance

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instDecidableEqUtterance x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Politeness.Studies.YoonEtAl2020.instReprUtterance.repr :

Utterance → ℕ → Std.Format

Equations

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

Instances For

instance Phenomena.Politeness.Studies.YoonEtAl2020.instReprUtterance :

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instReprUtterance = { reprPrec := Phenomena.Politeness.Studies.YoonEtAl2020.instReprUtterance.repr }

def Phenomena.Politeness.Studies.YoonEtAl2020.instBEqUtterance.beq :

Utterance → Utterance → Bool

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instBEqUtterance.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

Instances For

instance Phenomena.Politeness.Studies.YoonEtAl2020.instBEqUtterance :

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instBEqUtterance = { beq := Phenomena.Politeness.Studies.YoonEtAl2020.instBEqUtterance.beq }

instance Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedUtterance :

Inhabited Utterance

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedUtterance = { default := Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedUtterance.default }

def Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedUtterance.default :

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedUtterance.default = Phenomena.Politeness.Studies.YoonEtAl2020.Utterance.terrible

Instances For

instance Phenomena.Politeness.Studies.YoonEtAl2020.instFintypeUtterance :

Fintype Utterance

Equations

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

inductive Phenomena.Politeness.Studies.YoonEtAl2020.Adjective :

Get the base adjective (without negation)

terrible : Adjective
bad : Adjective
good : Adjective
amazing : Adjective

Instances For

instance Phenomena.Politeness.Studies.YoonEtAl2020.instDecidableEqAdjective :

DecidableEq Adjective

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instDecidableEqAdjective x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Politeness.Studies.YoonEtAl2020.instReprAdjective :

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instReprAdjective = { reprPrec := Phenomena.Politeness.Studies.YoonEtAl2020.instReprAdjective.repr }

def Phenomena.Politeness.Studies.YoonEtAl2020.instReprAdjective.repr :

Adjective → ℕ → Std.Format

Equations

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

Instances For

def Phenomena.Politeness.Studies.YoonEtAl2020.instBEqAdjective.beq :

Adjective → Adjective → Bool

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instBEqAdjective.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

Instances For

instance Phenomena.Politeness.Studies.YoonEtAl2020.instBEqAdjective :

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instBEqAdjective = { beq := Phenomena.Politeness.Studies.YoonEtAl2020.instBEqAdjective.beq }

def Phenomena.Politeness.Studies.YoonEtAl2020.Utterance.baseAdjective :

Utterance → Adjective

Equations

Instances For

inductive Phenomena.Politeness.Studies.YoonEtAl2020.GoalCondition :

Speaker goal conditions from the experiment

informative : GoalCondition
kind : GoalCondition
both : GoalCondition

Instances For

instance Phenomena.Politeness.Studies.YoonEtAl2020.instDecidableEqGoalCondition :

DecidableEq GoalCondition

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instDecidableEqGoalCondition x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Politeness.Studies.YoonEtAl2020.instReprGoalCondition.repr :

GoalCondition → ℕ → Std.Format

Equations

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

Instances For

instance Phenomena.Politeness.Studies.YoonEtAl2020.instReprGoalCondition :

Repr GoalCondition

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instReprGoalCondition = { reprPrec := Phenomena.Politeness.Studies.YoonEtAl2020.instReprGoalCondition.repr }

def Phenomena.Politeness.Studies.YoonEtAl2020.instBEqGoalCondition.beq :

GoalCondition → GoalCondition → Bool

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instBEqGoalCondition.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

Instances For

instance Phenomena.Politeness.Studies.YoonEtAl2020.instBEqGoalCondition :

BEq GoalCondition

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instBEqGoalCondition = { beq := Phenomena.Politeness.Studies.YoonEtAl2020.instBEqGoalCondition.beq }

instance Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedGoalCondition :

Inhabited GoalCondition

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedGoalCondition = { default := Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedGoalCondition.default }

def Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedGoalCondition.default :

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedGoalCondition.default = Phenomena.Politeness.Studies.YoonEtAl2020.GoalCondition.informative

Instances For

def Phenomena.Politeness.Studies.YoonEtAl2020.softSemantics :

Adjective → HeartState → ℚ

Soft semantic meaning: P(accept | adjective, state) from the literal semantics norming task.

Raw acceptance proportions from literal_semantics.csv in the paper's GitHub repository (https://github.com/ejyoon/polite_speaker). N=49 participants (after exclusions; supplement reports N=51 recruited) made binary yes/no judgments for each adjective × state combination.

The paper's full model infers θ via a Beta-Binomial BDA (uniform Beta(1,1) prior), marginalizing over posterior uncertainty. We use the raw proportions k/49 as point estimates — the maximum likelihood values.

Equations

Instances For

def Phenomena.Politeness.Studies.YoonEtAl2020.adjMeaning :

Adjective → Core.GradedProposition.GProp HeartState

Base adjective meaning (positive form). Returns a graded proposition GProp HeartState = HeartState → ℚ.

Equations

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

Instances For

def Phenomena.Politeness.Studies.YoonEtAl2020.utteranceSemantics :

Utterance → Core.GradedProposition.GProp HeartState

Compositionally derived utterance semantics.

Negated utterances are derived by applying Core.GradedProposition.neg to base meanings:

⟦not terrible⟧ = neg(⟦terrible⟧)

This mirrors Montague's compositional semantics where ⟦not φ⟧ = pnot(⟦φ⟧), lifted to graded propositions (see neg_involutive, neg_antitone).

Equations

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

Instances For

def Phenomena.Politeness.Studies.YoonEtAl2020.utteranceCost :

Utterance → ℕ

Utterance cost: number of words

Equations

Instances For

def Phenomena.Politeness.Studies.YoonEtAl2020.subjectiveValue :

HeartState → ℚ

Subjective value V(s): linear mapping from states to values. The listener prefers higher heart states: V(3 hearts) > V(0 hearts).

Equations

Instances For

theorem Phenomena.Politeness.Studies.YoonEtAl2020.meaning_bounded (u : Utterance) (s : HeartState) :

0 ≤ utteranceSemantics u s ∧ utteranceSemantics u s ≤ 1

The model uses soft semantics: meaning values are in [0,1].

theorem Phenomena.Politeness.Studies.YoonEtAl2020.negation_costlier (u : Utterance) :

u.isNegated = true → utteranceCost u = 3

Negated utterances cost more than direct ones.

theorem Phenomena.Politeness.Studies.YoonEtAl2020.direct_cheaper (u : Utterance) :

¬u.isNegated = true → utteranceCost u = 2

Direct utterances cost less.

S1 Submodel #

The S1 speaker's utility is a weighted sum of informativity and social value, interpolated by a latent kindness weight φ:

U_S1(u, s; φ) = φ · log L0(u,s) + (1−φ) · E_L0[V|u] − c · l(u)

This submodel uses approximate parameters (α = 3, c = 1, 5-point φ grid) to demonstrate the qualitative predictions. The paper infers α and c via BDA with priors α ~~Uniform(0, 20) and c~~ Uniform(1, 10).

inductive Phenomena.Politeness.Studies.YoonEtAl2020.Phi :

Discretized kindness weight. The paper uses continuous φ ~ Uniform(0, 1); we discretize to {0, 1/4, 1/2, 3/4, 1} for computable verification. Higher φ = speaker prioritizes informativity over social value.

p0 : Phi
p25 : Phi
p50 : Phi
p75 : Phi
p100 : Phi

Instances For

instance Phenomena.Politeness.Studies.YoonEtAl2020.instDecidableEqPhi :

DecidableEq Phi

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instDecidableEqPhi x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Politeness.Studies.YoonEtAl2020.instBEqPhi :

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instBEqPhi = { beq := Phenomena.Politeness.Studies.YoonEtAl2020.instBEqPhi.beq }

def Phenomena.Politeness.Studies.YoonEtAl2020.instBEqPhi.beq :

Phi → Phi → Bool

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instBEqPhi.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

Instances For

instance Phenomena.Politeness.Studies.YoonEtAl2020.instReprPhi :

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instReprPhi = { reprPrec := Phenomena.Politeness.Studies.YoonEtAl2020.instReprPhi.repr }

def Phenomena.Politeness.Studies.YoonEtAl2020.instReprPhi.repr :

Phi → ℕ → Std.Format

Equations

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

Instances For

instance Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedPhi :

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedPhi = { default := Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedPhi.default }

def Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedPhi.default :

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.instInhabitedPhi.default = Phenomena.Politeness.Studies.YoonEtAl2020.Phi.p0

Instances For

instance Phenomena.Politeness.Studies.YoonEtAl2020.instFintypePhi :

Equations

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

def Phenomena.Politeness.Studies.YoonEtAl2020.Phi.val :

The rational value of each φ level.

Equations

Instances For

noncomputable def Phenomena.Politeness.Studies.YoonEtAl2020.cfg :

RSA.RSAConfig Utterance HeartState

S1 submodel with approximate parameters (α = 3, c = 1).

S1 utility = φ · log L0(u,s) + (1−φ) · E_L0[V|u] − l(u)

Three components:

φ · log L0 (informativity at true state)
(1−φ) · E_L0[V|u] (social value: expected subjective value under L0)
−l(u) (utterance length cost, with c = 1)

The log gate is inactive for the pure social speaker (φ=0, weight=0). This allows semantically incompatible utterances to receive positive scores when the speaker doesn't care about informativity.

Equations

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

Instances For

theorem Phenomena.Politeness.Studies.YoonEtAl2020.terrible_map_h0_vs_h3 :

cfg.L1 Utterance.terrible HeartState.h0 > cfg.L1 Utterance.terrible HeartState.h3

"terrible" → h0: L1 assigns more mass to h0 than h3.

theorem Phenomena.Politeness.Studies.YoonEtAl2020.terrible_map_h0_vs_h1 :

cfg.L1 Utterance.terrible HeartState.h0 > cfg.L1 Utterance.terrible HeartState.h1

"terrible" → h0: L1 assigns more mass to h0 than h1.

theorem Phenomena.Politeness.Studies.YoonEtAl2020.bad_map_h1_vs_h0 :

cfg.L1 Utterance.bad HeartState.h1 > cfg.L1 Utterance.bad HeartState.h0

"bad" → h1: L1 assigns more mass to h1 than h0.

theorem Phenomena.Politeness.Studies.YoonEtAl2020.bad_map_h1_vs_h3 :

cfg.L1 Utterance.bad HeartState.h1 > cfg.L1 Utterance.bad HeartState.h3

"bad" → h1: L1 assigns more mass to h1 than h3.

theorem Phenomena.Politeness.Studies.YoonEtAl2020.good_map_h2_vs_h0 :

cfg.L1 Utterance.good HeartState.h2 > cfg.L1 Utterance.good HeartState.h0

"good" → h2: L1 assigns more mass to h2 than h0.

theorem Phenomena.Politeness.Studies.YoonEtAl2020.good_map_h2_vs_h3 :

cfg.L1 Utterance.good HeartState.h2 > cfg.L1 Utterance.good HeartState.h3

"good" → h2: L1 assigns more mass to h2 than h3.

theorem Phenomena.Politeness.Studies.YoonEtAl2020.amazing_map_h3_vs_h0 :

cfg.L1 Utterance.amazing HeartState.h3 > cfg.L1 Utterance.amazing HeartState.h0

"amazing" → h3: L1 assigns more mass to h3 than h0.

theorem Phenomena.Politeness.Studies.YoonEtAl2020.amazing_map_h3_vs_h2 :

cfg.L1 Utterance.amazing HeartState.h3 > cfg.L1 Utterance.amazing HeartState.h2

"amazing" → h3: L1 assigns more mass to h3 than h2.

theorem Phenomena.Politeness.Studies.YoonEtAl2020.not_terrible_away_from_h0 :

cfg.L1 Utterance.notTerrible HeartState.h1 > cfg.L1 Utterance.notTerrible HeartState.h0

"not terrible" shifts away from h0: L1 prefers h1 over h0. Negation makes bad states more acceptable, so the listener infers the state is "not the worst" rather than "the worst".

theorem Phenomena.Politeness.Studies.YoonEtAl2020.not_bad_peaks_h2 :

cfg.L1 Utterance.notBad HeartState.h2 > cfg.L1 Utterance.notBad HeartState.h3

"not bad" peaks at h2: L1 prefers h2 over h3. "Not bad" is most compatible with moderate-good states.

theorem Phenomena.Politeness.Studies.YoonEtAl2020.informative_prefers_direct :

cfg.S1 Phi.p100 HeartState.h0 Utterance.terrible > cfg.S1 Phi.p100 HeartState.h0 Utterance.notTerrible

At h0, a purely informative speaker (φ=1) prefers "terrible" over "not terrible". Direct speech maximizes informativity.

theorem Phenomena.Politeness.Studies.YoonEtAl2020.social_prefers_indirect :

cfg.S1 Phi.p0 HeartState.h0 Utterance.notTerrible > cfg.S1 Phi.p0 HeartState.h0 Utterance.terrible

At h0, a purely social speaker (φ=0) prefers "not terrible" over "terrible". Indirect speech maximizes social value: E[V|"not terrible"] is much higher than E[V|"terrible"] because L0 assigns probability to high-value states.

theorem Phenomena.Politeness.Studies.YoonEtAl2020.slight_informativity_prefers_direct :

cfg.S1 Phi.p25 HeartState.h0 Utterance.terrible > cfg.S1 Phi.p25 HeartState.h0 Utterance.notTerrible

Even at φ=1/4, the speaker still prefers "terrible" over "not terrible" at h0. The informativity penalty of "not terrible" at h0 outweighs the social benefit until φ drops to 0. This shows the crossover between direct and indirect preference is between φ=0 and φ=1/4.

theorem Phenomena.Politeness.Studies.YoonEtAl2020.social_prefers_positive :

cfg.S1 Phi.p0 HeartState.h3 Utterance.amazing > cfg.S1 Phi.p0 HeartState.h3 Utterance.good

At h3, a purely social speaker prefers "amazing" over "good". Even without informativity concerns, the higher expected social value from "amazing" (which concentrates L0 on h3) drives the preference.

theorem Phenomena.Politeness.Studies.YoonEtAl2020.informative_prefers_direct_positive :

cfg.S1 Phi.p100 HeartState.h3 Utterance.amazing > cfg.S1 Phi.p100 HeartState.h3 Utterance.notAmazing

At h3, a purely informative speaker prefers "amazing" over "not amazing". Direct positive speech is more informative.

Full S2 Model #

The S2 speaker's utility has three terms computed w.r.t. L1 marginals:

U_S2(u, s; ω, φ̂) = ω_inf · ln P_L1(s|u)
                   + ω_soc · Σ_s' P_L1(s'|u) · V(s')
                   + ω_pres · ln P_L1(φ̂|u)

P_S2(u|s, ω) ∝ exp(-cost(u)) · exp(α · U_S2)

The three utility components:

Informativity (ω_inf): log probability of the true state under L1
Social (ω_soc): expected subjective value under L1
Presentational (ω_pres): log probability that L1 infers the target kindness level φ̂ (speaker wants to appear kind)

Parameters #

This uses the paper's fitted parameters from the supplement:

α ≈ 4.47: shared by S1 and S2
c ≈ 2.64: cost of negation (positive utterances cost 1)
ω weights and φ̂: posterior means per goal condition
φ grid: 20 values {0, 1/20,..., 19/20}

Cost Encoding #

Cost enters the S2 model multiplicatively via the utterance prior: P_prior(u) ∝ exp(-cost(u)). In the combinedUtility framework (where the exponent is α · Σ terms), this is encoded as a constant term −cost(u)/α, so that α · (−cost/α) = −cost, yielding the correct exp(−cost) factor after exponentiation.

@[reducible, inline]

abbrev Phenomena.Politeness.Studies.YoonEtAl2020.PhiGrid :

Discretized kindness weight φ ∈ [0, 1] on a 5-point grid. Grid: {0, 1/4, 1/2, 3/4, 1}. The paper's WebPPL uses 40 values at 0.025 spacing; we use 5 matching the S1 submodel's Phi type for tractable L1 computation (200 cells vs 800 with Fin 20). MAP estimates (φ̂ ≈ 0.35-0.50) are mapped to nearest grid point.

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.PhiGrid = Fin 5

Instances For

def Phenomena.Politeness.Studies.YoonEtAl2020.phiVal (i : PhiGrid) :

The rational value of each grid point: k/4 for k ∈ {0,..., 4}.

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.phiVal i = ↑↑i / 4

Instances For

structure Phenomena.Politeness.Studies.YoonEtAl2020.S2Weights :

S2 utility weights for a specific goal condition. Posterior means from the supplement's parameter table.

ωInf : ℚ
ωSoc : ℚ
ωPres : ℚ
phiHat : PhiGrid

Instances For

def Phenomena.Politeness.Studies.YoonEtAl2020.informativeWeights :

Weights for "informative" goal condition (Table 2). High presentational weight (ω_pres = 62%) with neutral φ̂ ≈ 0.49. Discretized to 2/4 = 0.50.

Equations

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

Instances For

def Phenomena.Politeness.Studies.YoonEtAl2020.kindWeights :

Weights for "kind" (social) goal condition (Table 2). Highest social weight (ω_soc = 31%) with kind φ̂ ≈ 0.37. Discretized to 1/4 = 0.25.

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.kindWeights = { ωInf := 25 / 100, ωSoc := 31 / 100, ωPres := 44 / 100, phiHat := ⟨1, Phenomena.Politeness.Studies.YoonEtAl2020.kindWeights._proof_2 ⟩ }

Instances For

def Phenomena.Politeness.Studies.YoonEtAl2020.bothWeights :

Weights for "both" goal condition (Table 2). Balanced: ω_inf = 36%, ω_soc = 11%, ω_pres = 54%, φ̂ ≈ 0.36. Discretized to 1/4 = 0.25. The combination of informativity and presentational pressure drives the "both" condition's distinctive negation pattern.

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.bothWeights = { ωInf := 36 / 100, ωSoc := 11 / 100, ωPres := 54 / 100, phiHat := ⟨1, Phenomena.Politeness.Studies.YoonEtAl2020.kindWeights._proof_2 ⟩ }

Instances For

noncomputable def Phenomena.Politeness.Studies.YoonEtAl2020.s2BaseCfg :

RSA.RSAConfig Utterance HeartState

Base RSAConfig for the S2 model's S1/L1 layers. Same scoring as the S1 submodel but with:

5-point φ grid (PhiGrid = Fin 5), matching the S1 submodel
α ≈ 4.47 (paper's fitted value)
Cost encoded as −cost/α in the constant term

Equations

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

Instances For

noncomputable def Phenomena.Politeness.Studies.YoonEtAl2020.S2Utility (weights : S2Weights) (w : HeartState) (u : Utterance) :

S2 utility for a given goal condition.

U_S2(u, s; ω, φ̂) = ω_inf · ln P_L1(s|u) + ω_soc · Σ_s' P_L1(s'|u) · V(s') + ω_pres · ln P_L1(φ̂|u) + costTerm(u)

Since S2 score ∝ exp(α₂ · U_S2) and exp is monotone, comparing utilities is equivalent to comparing S2 scores.

Equations

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

Instances For

theorem Phenomena.Politeness.Studies.YoonEtAl2020.both_h0_prefers_negation :

S2Utility bothWeights HeartState.h0 Utterance.notTerrible > S2Utility bothWeights HeartState.h0 Utterance.terrible

Under "both" goals at h0, S2 prefers "not terrible" over "terrible". This is the paper's main finding: dual goals produce negation.

Does not hold with raw acceptance proportions (k/49) as point estimates for the literal semantics. The paper's full model infers θ via BDA, marginalizing over posterior uncertainty in a joint posterior over (α, c, ω, φ̂, θ). The qualitative prediction depends on this full posterior, not point estimates — both directions fail interval verification, confirming the values are indistinguishable under point estimation.

theorem Phenomena.Politeness.Studies.YoonEtAl2020.informative_h0_prefers_direct :

S2Utility informativeWeights HeartState.h0 Utterance.terrible > S2Utility informativeWeights HeartState.h0 Utterance.notTerrible

Under "informative" goals at h0, S2 prefers "terrible" over "not terrible". Direct speech dominates when the speaker prioritizes informativity.

theorem Phenomena.Politeness.Studies.YoonEtAl2020.kind_h0_prefers_negation :

S2Utility kindWeights HeartState.h0 Utterance.notTerrible > S2Utility kindWeights HeartState.h0 Utterance.terrible

Under "kind" goals at h0, S2 prefers "not terrible" over "terrible". The social and presentational weights favor indirect speech.

def Phenomena.Politeness.Studies.YoonEtAl2020.socialGoalSubjectivityLevel :

Core.Subjectivity.SubjectivityLevel

The S1/S2 politeness model instantiates Traugott's intersubjectivity: the speaker attends to the addressee's face/self-image.

When phi < 1, the speaker trades informativity for social value, i.e. the utterance is shaped by attention to the addressee -- the defining characteristic of @cite{traugott-dasher-2002}'s intersubjective level. The S2 model adds a second layer: the speaker also manages how kind they appear, which is doubly intersubjective.

@cite{narrog-2010} §4.2 connects this to modality: strong obligation is face-threatening precisely because it is performative and volitive, making the speaker's imposition on the addressee maximally salient.

Equations

Phenomena.Politeness.Studies.YoonEtAl2020.socialGoalSubjectivityLevel = Core.Subjectivity.SubjectivityLevel.intersubjective

Instances For