Documentation

Linglib.Phenomena.Nonliteral.Irony.KaoEtAl2015

@cite{kao-goodman-2015} — Let's Talk (Ironically) About the Weather @cite{kao-goodman-2015} #

@cite{bergen-goodman-2015}

Proceedings of the 37th Annual Meeting of the Cognitive Science Society.

The Model #

Extension of Kao et al.'s (2014) QUD-based RSA to irony. The central claim is that irony emerges from pragmatic reasoning when the listener considers that the speaker may be communicating arousal (emotional intensity) rather than just state or valence. Without an arousal goal, the model produces hyperbole (nonliteral, same valence); with arousal, it produces irony (nonliteral, flipped valence, high arousal).

Domain: 5 weather states (terrible, bad, ok, good, amazing) × 2 valence (negative, positive) × 2 arousal (low, high) = 20 world states. 5 utterances (= weather states). 3 QUDs (state, valence, arousal).

L0: L0(w|u) ∝ P(valence, arousal | state) · ⟦u⟧(w)
S1: QUD-projected: S1(u|q,w) ∝ exp(λ · log[Σ_{w': π(w',q)=π(w,q)} L0(w'|u)])
L1: L1(w|u) ∝ P(w) · Σ_q P(q) · S1(u|q,w)

Fitted parameters: λ = 1, P(q_state) = 0.3, P(q_valence) = 0.3, P(q_arousal) = 0.4 (footnote 5).

Context-Dependence #

The paper's model is evaluated across 9 weather contexts × 5 utterances = 45 conditions (Experiment 1). Each context has different weather state priors P(s), while the affect priors P(A|s) are context-independent.

The key demonstration is context-dependence: the same utterance "terrible" is ironic in pleasant weather (valence flip, high arousal) and literal in terrible weather (no flip). We formalize this with two representative contexts:

Pleasant weather (pleasantCfg): good/amazing weather dominant, terrible rare. "Terrible" is ironic — the listener infers positive valence and high arousal despite the negative literal content.
Terrible weather (terribleCfg): terrible/bad weather dominant, amazing rare. "Terrible" is literal — the listener infers negative valence matching the literal content.

Priors #

Weather priors approximate representative contexts from Experiment 1 (Figure 3). Affect priors are derived from Figure 4's PCA-based valence and arousal curves (Experiment 1). Valence follows an S-curve; arousal follows a symmetric U-curve (high at both extremes, low at neutral).

Qualitative Findings #

#	Finding	Config	Description
1	ironic_nonliteral	pleasantCfg	P(¬terrible \| "terrible") > P(terrible)
2	ironic_valence_flip	pleasantCfg	P(positive \| "terrible") > P(negative)
3	ironic_high_arousal	pleasantCfg	P(high \| "terrible") > P(low)
4	no_irony_without_arousal	pleasant (no q_a)	Valence-only: P(negative) > P(positive)
5	literal_state	terribleCfg	P(terrible \| "terrible") > P(¬terrible)
6	literal_no_flip	terribleCfg	P(negative \| "terrible") > P(positive)

Findings 2 + 4 establish the core mechanistic claim: arousal enables irony. Findings 2 + 6 demonstrate context-dependence: same utterance, opposite valence inference depending on the weather prior.

inductive Phenomena.Nonliteral.Irony.KaoEtAl2015.Weather :

Weather states double as utterance types. 5 states from the paper: terrible, bad, ok (= paper's "neutral"), good, amazing.

terrible : Weather
bad : Weather
ok : Weather
good : Weather
amazing : Weather

Instances For

instance Phenomena.Nonliteral.Irony.KaoEtAl2015.instDecidableEqWeather :

DecidableEq Weather

Equations

Phenomena.Nonliteral.Irony.KaoEtAl2015.instDecidableEqWeather x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Nonliteral.Irony.KaoEtAl2015.instBEqWeather.beq :

Weather → Weather → Bool

Equations

Phenomena.Nonliteral.Irony.KaoEtAl2015.instBEqWeather.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

Instances For

instance Phenomena.Nonliteral.Irony.KaoEtAl2015.instBEqWeather :

Equations

Phenomena.Nonliteral.Irony.KaoEtAl2015.instBEqWeather = { beq := Phenomena.Nonliteral.Irony.KaoEtAl2015.instBEqWeather.beq }

instance Phenomena.Nonliteral.Irony.KaoEtAl2015.instReprWeather :

Equations

Phenomena.Nonliteral.Irony.KaoEtAl2015.instReprWeather = { reprPrec := Phenomena.Nonliteral.Irony.KaoEtAl2015.instReprWeather.repr }

def Phenomena.Nonliteral.Irony.KaoEtAl2015.instReprWeather.repr :

Weather → ℕ → Std.Format

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

Instances For

inductive Phenomena.Nonliteral.Irony.KaoEtAl2015.Goal :

Communicative goals (QUDs). The paper's central claim is that arousal as a QUD is what enables ironic interpretation.

state : Goal
valence : Goal
arousal : Goal

Instances For

instance Phenomena.Nonliteral.Irony.KaoEtAl2015.instDecidableEqGoal :

DecidableEq Goal

Equations

Phenomena.Nonliteral.Irony.KaoEtAl2015.instDecidableEqGoal x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Nonliteral.Irony.KaoEtAl2015.instBEqGoal.beq :

Goal → Goal → Bool

Equations

Phenomena.Nonliteral.Irony.KaoEtAl2015.instBEqGoal.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

Instances For

instance Phenomena.Nonliteral.Irony.KaoEtAl2015.instBEqGoal :

Equations

Phenomena.Nonliteral.Irony.KaoEtAl2015.instBEqGoal = { beq := Phenomena.Nonliteral.Irony.KaoEtAl2015.instBEqGoal.beq }

instance Phenomena.Nonliteral.Irony.KaoEtAl2015.instReprGoal :

Equations

Phenomena.Nonliteral.Irony.KaoEtAl2015.instReprGoal = { reprPrec := Phenomena.Nonliteral.Irony.KaoEtAl2015.instReprGoal.repr }

def Phenomena.Nonliteral.Irony.KaoEtAl2015.instReprGoal.repr :

Goal → ℕ → Std.Format

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

Instances For

@[reducible, inline]

abbrev Phenomena.Nonliteral.Irony.KaoEtAl2015.World :

World = weather × positive? × high arousal?

w.1 : weather state
w.2.1 : true = positive valence, false = negative valence
w.2.2 : true = high arousal, false = low arousal

Equations

Phenomena.Nonliteral.Irony.KaoEtAl2015.World = (Phenomena.Nonliteral.Irony.KaoEtAl2015.Weather × Bool × Bool)

Instances For

instance Phenomena.Nonliteral.Irony.KaoEtAl2015.instFintypeWeather :

Fintype Weather

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instance Phenomena.Nonliteral.Irony.KaoEtAl2015.instFintypeGoal :

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def Phenomena.Nonliteral.Irony.KaoEtAl2015.affectPrior (st : Weather) (positive high : Bool) :

Affect prior: P(valence, arousal | weather state) (unnormalized).

Derived from Experiment 1 (Figure 4). The paper fits beta distributions to participants' emotion ratings projected onto valence and arousal dimensions via PCA (circumplex model of affect, @cite{russell-1980}).

Valence P(positive|s) follows an S-curve across weather states: terrible=1%, bad=15%, ok=50%, good=85%, amazing=99%

Arousal P(high|s) follows a symmetric U-curve (high at both extremes): terrible=90%, bad=40%, ok=10%, good=40%, amazing=90%

Joint = product of independent valence and arousal components. Each state sums to 1000 (unnormalized).

The table is symmetric: terrible ↔ amazing and bad ↔ good (swap positive ↔ negative).

Equations

Instances For

def Phenomena.Nonliteral.Irony.KaoEtAl2015.meaning (_q : Goal) (u : Weather) (w : World) :

L0 meaning: affect prior when utterance matches weather state, 0 otherwise.

L0(w|u) ∝ P(valence, arousal | state) · ⟦u = state⟧. The paper's L0 includes the full state prior P(s) = P(weather) × P(A|weather), but since ⟦u⟧ restricts to a single weather state, P(weather) is constant within L0's normalization and cancels. It enters only at L1 via worldPrior.

Equations

Phenomena.Nonliteral.Irony.KaoEtAl2015.meaning _q u w = if (u == w.1) = true then Phenomena.Nonliteral.Irony.KaoEtAl2015.affectPrior w.1 w.2.1 w.2.2 else 0

Instances For

def Phenomena.Nonliteral.Irony.KaoEtAl2015.project (w : World) (q : Goal) :

Project a world onto the QUD-relevant dimension. Returns a natural number encoding the equivalence class.

Equations

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Phenomena.Nonliteral.Irony.KaoEtAl2015.project w Phenomena.Nonliteral.Irony.KaoEtAl2015.Goal.valence = if w.2.1 = true then 1 else 0
Phenomena.Nonliteral.Irony.KaoEtAl2015.project w Phenomena.Nonliteral.Irony.KaoEtAl2015.Goal.arousal = if w.2.2 = true then 1 else 0

Instances For

noncomputable def Phenomena.Nonliteral.Irony.KaoEtAl2015.qudProject (q : Goal) (f : World → ℝ) (w : World) :

Sum L0 over the QUD equivalence class of w under goal q.

This is the key mechanism: when the QUD is arousal, "terrible" and "amazing" weather states are equivalent (both high arousal), creating a pragmatic pathway from one to the other that crosses the valence boundary.

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@[reducible]

noncomputable def Phenomena.Nonliteral.Irony.KaoEtAl2015.cfg (wp : Weather → ℝ) (gp : Goal → ℝ) (hw : ∀ (s : Weather), 0 ≤ wp s) (hg : ∀ (g : Goal), 0 ≤ gp g) :

RSA.RSAConfig Weather World

Irony model, parametric in weather context and goal prior.

S1 score uses exp(λ · log(projected_L0)). With λ = 1 (fitted), this is just the projected L0 score. The exp/log form matches the reifier's expMulLogSub pattern for efficient native_decide proofs.

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def Phenomena.Nonliteral.Irony.KaoEtAl2015.pleasantWeather :

Weather → ℝ

Pleasant weather context (e.g., "nice day in California"). Approximates a context from Experiment 1 (Figure 3) where good/amazing weather is dominant and terrible weather is rare.

Equations

Instances For

def Phenomena.Nonliteral.Irony.KaoEtAl2015.terribleWeather :

Weather → ℝ

Terrible weather context (e.g., "storm day"). Symmetric to pleasantWeather: terrible/bad dominant, amazing rare.

Equations

Instances For

def Phenomena.Nonliteral.Irony.KaoEtAl2015.fittedGoals :

Fitted QUD prior (footnote 5): P(state) = 0.3, P(valence) = 0.3, P(arousal) = 0.4. Unnormalized integers [3, 3, 4].

Equations

Instances For

def Phenomena.Nonliteral.Irony.KaoEtAl2015.valenceOnlyGoals :

Valence-only ablation: arousal QUD removed. This produces hyperbole but NOT irony — the paper's key mechanistic test (Table 1).

Equations

Instances For

@[reducible, inline]

noncomputable abbrev Phenomena.Nonliteral.Irony.KaoEtAl2015.pleasantCfg :

RSA.RSAConfig Weather World

Full model in pleasant weather context — irony emerges.

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@[reducible, inline]

noncomputable abbrev Phenomena.Nonliteral.Irony.KaoEtAl2015.terribleCfg :

RSA.RSAConfig Weather World

Full model in terrible weather context — literal interpretation.

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@[reducible, inline]

noncomputable abbrev Phenomena.Nonliteral.Irony.KaoEtAl2015.pleasantValenceOnlyCfg :

RSA.RSAConfig Weather World

Ablation: pleasant weather without arousal QUD. Produces hyperbole but not irony (Table 1 comparison).

Equations

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

Instances For

theorem Phenomena.Nonliteral.Irony.KaoEtAl2015.ironic_nonliteral :

(pleasantCfg.L1_marginal Weather.terrible fun (w : World) => w.1 != Weather.terrible) > pleasantCfg.L1_marginal Weather.terrible fun (w : World) => w.1 == Weather.terrible

Nonliteral interpretation: the listener infers the weather is NOT terrible. P(state ≠ terrible | "terrible", pleasant) > P(state = terrible | "terrible", pleasant).

theorem Phenomena.Nonliteral.Irony.KaoEtAl2015.ironic_valence_flip :

(pleasantCfg.L1_marginal Weather.terrible fun (w : World) => w.2.1 == true) > pleasantCfg.L1_marginal Weather.terrible fun (w : World) => w.2.1 == false

Valence flip — the hallmark of irony. Despite "terrible" literally conveying negative affect, the pragmatic listener in a pleasant weather context infers that the speaker actually feels positively. This is the paper's central prediction (Figure 5, Figure 6).

theorem Phenomena.Nonliteral.Irony.KaoEtAl2015.ironic_high_arousal :

(pleasantCfg.L1_marginal Weather.terrible fun (w : World) => w.2.2 == true) > pleasantCfg.L1_marginal Weather.terrible fun (w : World) => w.2.2 == false

Ironic speech carries high arousal — the speaker is emotionally engaged, not flat.

theorem Phenomena.Nonliteral.Irony.KaoEtAl2015.no_irony_without_arousal :

(pleasantValenceOnlyCfg.L1_marginal Weather.terrible fun (w : World) => w.2.1 == false) > pleasantValenceOnlyCfg.L1_marginal Weather.terrible fun (w : World) => w.2.1 == true

Without arousal as a communicative goal, "terrible" does NOT flip valence — the listener infers negative affect (matching the literal content). The model produces hyperbole but not irony.

Combined with ironic_valence_flip, this pair establishes the paper's central argument: arousal is the mechanism that enables the pragmatic pathway from negative to positive valence (Table 1).

theorem Phenomena.Nonliteral.Irony.KaoEtAl2015.literal_state :

(terribleCfg.L1_marginal Weather.terrible fun (w : World) => w.1 == Weather.terrible) > terribleCfg.L1_marginal Weather.terrible fun (w : World) => w.1 != Weather.terrible

In terrible weather, "terrible" is interpreted literally — the listener correctly infers the weather IS terrible. The same utterance that is ironic in pleasant weather (theorem 1) is literal here.

theorem Phenomena.Nonliteral.Irony.KaoEtAl2015.literal_no_flip :

(terribleCfg.L1_marginal Weather.terrible fun (w : World) => w.2.1 == false) > terribleCfg.L1_marginal Weather.terrible fun (w : World) => w.2.1 == true

In terrible weather, "terrible" does NOT flip valence — the listener infers negative affect, matching the literal content. Contrast with ironic_valence_flip where the same utterance produces the opposite inference in pleasant weather.