Spinoso-@cite{spinoso-di-piano-etal-2025} — (RSA)² @cite{spinoso-di-piano-etal-2025} @cite{kao-goodman-2015} #

@cite{bergen-goodman-2015}

(RSA)²: A Rhetorical-Strategy-Aware Rational Speech Act Framework for Figurative Language Understanding.

The Model #

Replaces RSA's literal meaning indicator with a rhetorical function f_r(c, m, u) parameterized by strategy r ∈ {literal, ironic}. The strategy is a latent variable marginalized at L1, yielding the paper's title: (RSA)².

L0: L0(m|c,u,r) ∝ f_r(c, m, u) · P(m|c) (Eq 4)
- literal: f_literal(c, m, u) = ⟦m = meaning(u)⟧
- ironic: f_ironic(c, m, u) = ⟦m = opposite(meaning(u))⟧
S1: S1(u|m,c,r) ∝ L0(m|c,u,r)^α · P(u|c) (Eq 5)
L1: L1(m|c,u,r) ∝ S1(u|m,c,r) · P(m|c) (Eq 6)
Marginalization: L1(m|c,u) = Σ_r L1(m|c,u,r) · P(r|c,u) (Eq 7)

Parameters: α = 1 (paper's default), uniform P(u|c), uniform P(r).

What We Formalize #

We formalize the conceptual hand-specified model from Section 3.2 of the paper, where f_r is a deterministic indicator (0/1). The paper's experimental results use a neural network to approximate f_r from human data; that quantitative fit is outside our scope.

For indicator meanings with one matching world per (u,r) pair, P(m|c) drops out of L0 normalization, so our RSAConfig (which puts worldPrior only in L1) produces equivalent predictions. Similarly, uniform P(u|c) drops out of S1. The joint marginalization in RSAConfig is algebraically equivalent to the paper's per-strategy normalization then mixing (Eq 7).

Comparison to @cite{kao-goodman-2015} #

Both models derive irony from context-dependent pragmatic inference over the same weather domain. The key difference:

Dimension	@cite{kao-goodman-2015}	Spinoso-@cite{spinoso-di-piano-etal-2025}
Latent	QUD (state/valence/arousal)	Strategy (literal/ironic)
World	Weather × Valence × Arousal (20 states)	Weather only (5 states)
Mechanism	Arousal QUD enables valence flip	Antonym mapping enables flip
Claim	Affect (arousal) is necessary	Affect is unnecessary

The simplification IS the result: irony emerges from strategy inference alone, without modeling affect dimensions, matching the same qualitative predictions.

Verified Predictions #

#	Theorem	Config	Description
1	ironic_reading	terribleCfg	"amazing" → terrible weather (Fig 3)
2	literal_reading	pleasantCfg	"amazing" → amazing weather
3	infer_ironic	terribleCfg	"amazing" → ironic strategy
4	infer_literal	pleasantCfg	"amazing" → literal strategy
5	terrible_ironic	pleasantCfg	"terrible" → amazing weather
6	terrible_literal	terribleCfg	"terrible" → terrible weather
7	ok_strategy_neutral	terribleCfg	"ok" → strategies equiprobable
8	bad_ironic	pleasantCfg	"bad" → good weather (interior scale)
9	good_ironic	terribleCfg	"good" → bad weather (interior scale)
10	ok_strategy_neutral_pleasant	pleasantCfg	"ok" → strategies equiprobable

Theorems 1+2 and 5+6 demonstrate context-dependence (same utterance, opposite interpretation). Theorems 3+4 are unique to (RSA)² — the strategy posterior is directly observable, unlike the QUD posterior in @cite{kao-goodman-2015}. Theorems 7+10 test a boundary case: since opposite(ok) = ok, the ironic and literal strategies produce identical L0 distributions for "ok" in BOTH contexts, making L1's strategy inference uninformative. Theorems 8+9 test interior scale positions (bad/good rather than endpoints terrible/amazing).

Structural Properties #

rhetoricalMeaning_swap captures the core mechanism algebraically: ironic meaning at world w equals literal meaning at the antonym world opposite(w). This follows from opposite being an involution and grounds the ironic strategy as "literal interpretation in the opposite world."

irony_iff_prior_favors_antonym is the deepest result: the (RSA)² model's entire behavior reduces to comparing the world prior at two points. Irony emerges iff worldPrior(opposite(u.toWeather)) > worldPrior(u.toWeather). This is a much stronger claim than individual prediction theorems — it explains WHY the cross-model agreement with @cite{kao-goodman-2015} holds: both models agree whenever the weather prior is sufficiently asymmetric, because (RSA)²'s prediction IS just a prior comparison.

Implementation Note #

The paper uses U = W = Weather (utterances are weather descriptions, worlds are weather states). RSAConfig requires distinct types, so we use a thin Utterance wrapper with an explicit toWeather conversion.