Documentation

Linglib.Phenomena.SocialMeaning.Studies.Burnett2019

@cite{burnett-2019} — Signalling Games, Sociolinguistic Variation, and #

the Construction of Style

Linguistics and Philosophy 42: 419–450.

Overview #

Social Meaning Games (SMGs) model how sociolinguistic variant choice conveys social information. A speaker's use of -ing vs -in' induces listener inferences about persona traits (competent, friendly, etc.). The framework combines @cite{lewis-1969}'s signalling games with RSA-style Bayesian reasoning to derive both style shifting (intra-speaker variation across contexts) and social stratification (inter-speaker variation across classes) from the same principles.

Architecture #

The meaning function is grounded in the Eckert–Montague lift from EckertMontague.emMeaningMI: each variant's Eckert field (a set of indexed properties) is lifted to persona compatibility via intersection semantics. The grounding theorem ingMeaning_eq_emMeaningMI verifies that the study's meaning function matches the theory-layer derivation.

Each context is an RSAConfig INGVariant Persona with beliefBased S1 scoring (S1(v|π) ∝ L0(π|v)^α, α=6) and context-specific worldPrior. All predictions are verified by rsa_predict.

Key predictions #

Per-persona variant preference: cool-guy prefers -in' ~69%
Style shifting: casual→careful flips the cool-guy's preference
Stern-leader exclusion: -in' is incompatible with stern leader
Listener interpretation: Rice/Pelosi/Bush /t/ release predictions
Bulletproofing: strong prior overwhelms variant effects (Bush)
Cross-reference: model predictions close to @cite{labov-2012} data

inductive Phenomena.SocialMeaning.Studies.Burnett2019.PersonaTrait :

Social properties (Burnett example (5)). Two bipolar dimensions: competence (competent/incompetent) and warmth (friendly/aloof).

competent : PersonaTrait
incompetent : PersonaTrait
friendly : PersonaTrait
aloof : PersonaTrait

Instances For

instance Phenomena.SocialMeaning.Studies.Burnett2019.instDecidableEqPersonaTrait :

DecidableEq PersonaTrait

Equations

Phenomena.SocialMeaning.Studies.Burnett2019.instDecidableEqPersonaTrait x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.SocialMeaning.Studies.Burnett2019.instBEqPersonaTrait.beq :

PersonaTrait → PersonaTrait → Bool

Equations

Phenomena.SocialMeaning.Studies.Burnett2019.instBEqPersonaTrait.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

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instance Phenomena.SocialMeaning.Studies.Burnett2019.instBEqPersonaTrait :

BEq PersonaTrait

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Phenomena.SocialMeaning.Studies.Burnett2019.instBEqPersonaTrait = { beq := Phenomena.SocialMeaning.Studies.Burnett2019.instBEqPersonaTrait.beq }

def Phenomena.SocialMeaning.Studies.Burnett2019.instReprPersonaTrait.repr :

PersonaTrait → ℕ → Std.Format

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instance Phenomena.SocialMeaning.Studies.Burnett2019.instReprPersonaTrait :

Repr PersonaTrait

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Phenomena.SocialMeaning.Studies.Burnett2019.instReprPersonaTrait = { reprPrec := Phenomena.SocialMeaning.Studies.Burnett2019.instReprPersonaTrait.repr }

instance Phenomena.SocialMeaning.Studies.Burnett2019.instFintypePersonaTrait :

Fintype PersonaTrait

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inductive Phenomena.SocialMeaning.Studies.Burnett2019.Persona :

The four personae: maximally consistent subsets (Burnett example (6)). Each selects one pole per dimension.

coolGuy : Persona
sternLeader : Persona
doofus : Persona
asshole : Persona

Instances For

instance Phenomena.SocialMeaning.Studies.Burnett2019.instDecidableEqPersona :

DecidableEq Persona

Equations

Phenomena.SocialMeaning.Studies.Burnett2019.instDecidableEqPersona x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.SocialMeaning.Studies.Burnett2019.instBEqPersona.beq :

Persona → Persona → Bool

Equations

Phenomena.SocialMeaning.Studies.Burnett2019.instBEqPersona.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

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instance Phenomena.SocialMeaning.Studies.Burnett2019.instBEqPersona :

Equations

Phenomena.SocialMeaning.Studies.Burnett2019.instBEqPersona = { beq := Phenomena.SocialMeaning.Studies.Burnett2019.instBEqPersona.beq }

instance Phenomena.SocialMeaning.Studies.Burnett2019.instReprPersona :

Equations

Phenomena.SocialMeaning.Studies.Burnett2019.instReprPersona = { reprPrec := Phenomena.SocialMeaning.Studies.Burnett2019.instReprPersona.repr }

def Phenomena.SocialMeaning.Studies.Burnett2019.instReprPersona.repr :

Persona → ℕ → Std.Format

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instance Phenomena.SocialMeaning.Studies.Burnett2019.instFintypePersona :

Fintype Persona

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inductive Phenomena.SocialMeaning.Studies.Burnett2019.INGVariant :

ING variants (Burnett example (8)).

ing : INGVariant
in' : INGVariant

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instance Phenomena.SocialMeaning.Studies.Burnett2019.instDecidableEqINGVariant :

DecidableEq INGVariant

Equations

Phenomena.SocialMeaning.Studies.Burnett2019.instDecidableEqINGVariant x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.SocialMeaning.Studies.Burnett2019.instBEqINGVariant.beq :

INGVariant → INGVariant → Bool

Equations

Phenomena.SocialMeaning.Studies.Burnett2019.instBEqINGVariant.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

Instances For

instance Phenomena.SocialMeaning.Studies.Burnett2019.instBEqINGVariant :

Equations

Phenomena.SocialMeaning.Studies.Burnett2019.instBEqINGVariant = { beq := Phenomena.SocialMeaning.Studies.Burnett2019.instBEqINGVariant.beq }

instance Phenomena.SocialMeaning.Studies.Burnett2019.instReprINGVariant :

Repr INGVariant

Equations

Phenomena.SocialMeaning.Studies.Burnett2019.instReprINGVariant = { reprPrec := Phenomena.SocialMeaning.Studies.Burnett2019.instReprINGVariant.repr }

def Phenomena.SocialMeaning.Studies.Burnett2019.instReprINGVariant.repr :

INGVariant → ℕ → Std.Format

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instance Phenomena.SocialMeaning.Studies.Burnett2019.instFintypeINGVariant :

Fintype INGVariant

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Eckert fields (Burnett example (10)):

[-ing] = {competent, aloof}
[-in'] = {incompetent, friendly}

The meaning function is derived via the Montagovian Individual / intersection semantics (Burnett footnote 14, Table 1): persona p is compatible with variant v iff p shares at least one property with v's Eckert field.

def Phenomena.SocialMeaning.Studies.Burnett2019.burnettSpace :

Sociolinguistics.PropertySpace

The property space for Burnett's simplified example.

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def Phenomena.SocialMeaning.Studies.Burnett2019.Persona.toFinset :

Persona → Finset PersonaTrait

Persona membership as a Finset.

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def Phenomena.SocialMeaning.Studies.Burnett2019.ingEckertField :

INGVariant → Finset PersonaTrait

Eckert fields for (ING) (Burnett example (10)).

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def Phenomena.SocialMeaning.Studies.Burnett2019.ingField :

Sociolinguistics.EckertMontague.GroundedField INGVariant burnettSpace

The ING grounded field: both Eckert fields are consistent.

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def Phenomena.SocialMeaning.Studies.Burnett2019.ingMeaning :

INGVariant → Persona → Bool

Meaning via the EM intersection lift: persona p is compatible with variant v iff p shares ≥1 property with v's Eckert field.

Equations

Instances For

theorem Phenomena.SocialMeaning.Studies.Burnett2019.ingMeaning_eq_emMeaningMI (v : INGVariant) (p : Persona) :

ingMeaning v p = Sociolinguistics.EckertMontague.emMeaningMI ingField v p.toFinset

Grounding theorem: the inline meaning function equals the theory-layer emMeaningMI applied to the ING Eckert fields.

theorem Phenomena.SocialMeaning.Studies.Burnett2019.ing_compat_count :

{p : Persona | ingMeaning INGVariant.ing p = true}.card = 3

-ing is compatible with 3 personae (Table 1: excludes doofus).

theorem Phenomena.SocialMeaning.Studies.Burnett2019.in'_compat_count :

{p : Persona | ingMeaning INGVariant.in' p = true}.card = 3

-in' is compatible with 3 personae (Table 1: excludes stern leader).

Each social context is an RSAConfig INGVariant Persona:

Worlds = personae (what the listener infers)
Utterances = variants (what the speaker chooses)
Meaning = EM intersection lift
S1 scoring = beliefBased: S1(v|p) ∝ L0(p|v)^α
α = 6 (Burnett p. 435)
worldPrior = context-dependent belief about the speaker

@[reducible, inline]

noncomputable abbrev Phenomena.SocialMeaning.Studies.Burnett2019.mkSMG (prior : Persona → ℚ) (h : ∀ (p : Persona), 0 ≤ prior p) :

RSA.RSAConfig INGVariant Persona

Construct an SMG as an RSAConfig with context-specific prior.

The meaning function incorporates the prior so that L0 matches Burnett's naive listener: L₀(π|v) ∝ Pr(π) · ⟦v⟧(π). Without the prior in meaning, L0 would be uniform over compatible personae (1/3 for all), erasing the context-dependence that drives style shifting.

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def Phenomena.SocialMeaning.Studies.Burnett2019.casualPrior :

Persona → ℚ

Casual-context prior (Burnett Table 2): voters at the barbecue think Obama is aloof (personae with aloof get more weight).

Equations

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@[reducible, inline]

noncomputable abbrev Phenomena.SocialMeaning.Studies.Burnett2019.casualCfg :

RSA.RSAConfig INGVariant Persona

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def Phenomena.SocialMeaning.Studies.Burnett2019.carefulPrior :

Persona → ℚ

Careful-context prior (Burnett Table 5): journalists think Obama is incompetent (incompetent personae get more weight).

Equations

Instances For

@[reducible, inline]

noncomputable abbrev Phenomena.SocialMeaning.Studies.Burnett2019.carefulCfg :

RSA.RSAConfig INGVariant Persona

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def Phenomena.SocialMeaning.Studies.Burnett2019.ricePrior :

Persona → ℚ

Rice: uniform prior — unfamiliar politician (Burnett Table 10).

Equations

Phenomena.SocialMeaning.Studies.Burnett2019.ricePrior x✝ = 1 / 4

Instances For

@[reducible, inline]

noncomputable abbrev Phenomena.SocialMeaning.Studies.Burnett2019.riceCfg :

RSA.RSAConfig INGVariant Persona

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def Phenomena.SocialMeaning.Studies.Burnett2019.pelosiPrior :

Persona → ℚ

Pelosi: listeners believe she is inarticulate (Burnett Table 13).

Equations

Instances For

@[reducible, inline]

noncomputable abbrev Phenomena.SocialMeaning.Studies.Burnett2019.pelosiCfg :

RSA.RSAConfig INGVariant Persona

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def Phenomena.SocialMeaning.Studies.Burnett2019.bushPrior :

Persona → ℚ

Bush: listeners almost certain he is {inarticulate, aloof} (Burnett Table 15).

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Instances For

@[reducible, inline]

noncomputable abbrev Phenomena.SocialMeaning.Studies.Burnett2019.bushCfg :

RSA.RSAConfig INGVariant Persona

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theorem Phenomena.SocialMeaning.Studies.Burnett2019.casual_coolGuy_prefers_in' :

casualCfg.S1 () Persona.coolGuy INGVariant.in' > casualCfg.S1 () Persona.coolGuy INGVariant.ing

Cool-guy at the barbecue prefers -in' over -ing (~69% vs ~31%). Burnett (p. 435): "we predict that Obama will use -in' around 69% of the time [...] which is close to what Labov found" (72%).

theorem Phenomena.SocialMeaning.Studies.Burnett2019.casual_sternLeader_prefers_ing :

casualCfg.S1 () Persona.sternLeader INGVariant.ing > casualCfg.S1 () Persona.sternLeader INGVariant.in'

Stern leader only uses -ing: -in' is incompatible (Table 1). This predicts ~0% -in' in formal contexts where Obama constructs the stern leader.

theorem Phenomena.SocialMeaning.Studies.Burnett2019.casual_doofus_prefers_in' :

casualCfg.S1 () Persona.doofus INGVariant.in' > casualCfg.S1 () Persona.doofus INGVariant.ing

The doofus only uses -in': -ing is incompatible (Table 1).

theorem Phenomena.SocialMeaning.Studies.Burnett2019.careful_coolGuy_prefers_ing :

carefulCfg.S1 () Persona.coolGuy INGVariant.ing > carefulCfg.S1 () Persona.coolGuy INGVariant.in'

In the careful context, the cool-guy now prefers -ing over -in'. The prior shift reverses the informativity ranking.

The /t/ release variable has the same mathematical structure as (ING). Relabeling: articulate↔competent, inarticulate↔incompetent (same friendly/aloof). Variants: released [tʰ]↔-ing, flapped [ɾ]↔-in'. The Eckert fields are structurally identical (Burnett example (19)): [tʰ] = {articulate, aloof}, [ɾ] = {inarticulate, friendly}.

We reuse the same types and meaning function, since the math is isomorphic. The personae reinterpret as: coolGuy ↔ {articulate, friendly}, sternLeader ↔ {articulate, aloof}, doofus ↔ {inarticulate, friendly}, asshole ↔ {inarticulate, aloof}.

theorem Phenomena.SocialMeaning.Studies.Burnett2019.casual_asshole_prefers_in' :

casualCfg.S1 () Persona.asshole INGVariant.in' > casualCfg.S1 () Persona.asshole INGVariant.ing

The asshole prefers -in' in the casual context (both variants are compatible, but -in' is more informative given the prior).

theorem Phenomena.SocialMeaning.Studies.Burnett2019.rice_released_sternLeader :

riceCfg.L1 INGVariant.ing Persona.sternLeader > riceCfg.L1 INGVariant.ing Persona.coolGuy

Rice: released /t/ triggers {articulate, aloof} = stern leader (Burnett Table 11). With uniform prior, the exclusive variant (only -ing compatible) gets double the L1 weight.

theorem Phenomena.SocialMeaning.Studies.Burnett2019.rice_flapped_doofus :

riceCfg.L1 INGVariant.in' Persona.doofus > riceCfg.L1 INGVariant.in' Persona.coolGuy

Rice: flapped /t/ triggers {inarticulate, friendly} = doofus (Burnett Table 11). Symmetric to the released case.

theorem Phenomena.SocialMeaning.Studies.Burnett2019.pelosi_released_inarticAloof :

pelosiCfg.L1 INGVariant.ing Persona.asshole > pelosiCfg.L1 INGVariant.ing Persona.sternLeader

Pelosi: released /t/ predominantly triggers {inarticulate, aloof} — the strong prior that she is inarticulate overwhelms the released /t/ association with articulateness (Burnett Table 14).

theorem Phenomena.SocialMeaning.Studies.Burnett2019.pelosi_flapped_friendly :

pelosiCfg.L1 INGVariant.in' Persona.doofus > pelosiCfg.L1 INGVariant.in' Persona.asshole

Pelosi: flapped /t/ triggers {inarticulate, friendly} (Table 14).

theorem Phenomena.SocialMeaning.Studies.Burnett2019.bush_bulletproofing :

bushCfg.L1 INGVariant.ing Persona.asshole > 9 / 10 ∧ bushCfg.L1 INGVariant.in' Persona.asshole > 9 / 10

Bush "bulletproofing" (Burnett p. 444, Table 16): the prior is so extreme that variant choice has no practical effect. Both released and flapped /t/ yield >90% {inarticulate, aloof}.