[CGGP19] — Incremental Iterated Response Model #

Cohn-Gordon, R., Goodman, N. D., & Potts, C. (2019). An Incremental Iterated Response Model of Pragmatics. Proceedings of the Society for Computation in Linguistics (SCiL) 2, 81–90.

The Model #

The incremental RSA model extends the standard RSA framework to word-by-word production. The speaker produces referring expressions incrementally, choosing each word to maximize the listener's posterior probability for the target:

S1^WORD(wₖ | [w₁,...,wₖ₋₁], r) ∝ L0(r | w₁,...,wₖ)^α

The full utterance probability factors via the chain rule:

S1^UTT-IP(w₁,...,wₙ | r) = ∏ₖ S1^WORD(wₖ | [w₁,...,wₖ₋₁], r)

L0 uses extension-based incremental semantics (§2.2): given prefix c,

⟦c⟧(w) = |{u ∈ U : c ⊑ u ∧ ⟦u⟧(w) = 1}| / |{u ∈ U : c ⊑ u ∧ ∃w'. ⟦u⟧(w') = 1}|

where U is the set of complete utterances and ⊑ is the prefix relation.

Formalization via the `IncrementalSemantics` bundle #

Each scene in this file is a single value of RSA.IncrementalSemantics U W (in Pragmatics/RSA/Incremental.lean), specifying just the lexicon (wordApplies), the closed set of complete utterances, and the world set. The file derives the chain-rule speaker (α = 1, no cost, uniform priors) and extension-based L0 from the bundle, so the three scenes (Figure 1, the [Sed07] reference game, the [rubio-fernandez-2016] display) share machinery rather than duplicating it.

The bundle exposes a single deep theorem, l0Utt_ge_inv_card, proving the §2.4 weakly-informative bound generically: any complete utterance true of r ∈ worlds yields a literal posterior at least 1 / worlds.length. The Figure 1 application (greedyUnroll_weakly_informative) below discharges only the r ∈ worlds and uttSem utt r = true premises; the bound follows.

Main results #

adj_first_for_target / noun_after_adj / noun_only_for_r2 / adj_only_for_r3: the Figure 1c word-by-word speaker rows.
uniform_after_red_for_r2: the §2.2 dead-end fallback (Figure 1c's R2 row: 0, ½, ½ over words with viable continuations).
listener_anticipation: hearing "red", L1 favours R3 at 7/11 (Figure 1d) — the anticipatory implicature.
incremental_prefers_bare_noun: the chain-rule product prefers bare "dress" (3/7) over "red dress" (8/21) for R1 (Figure 1e), diverging from global_prefers_red_dress — the paper's central architectural wedge.
sedivy_contrast_inference / cgSedivyLooks_satisfy_contrast_reduces_competitor: the §3.2 contrastive-inference reanalysis, discharging the visual-world paradigm contract under the Bayesian posterior linking hypothesis.

Implementation notes #

Extension counts are natural numbers, so the chain is exact ℚ≥0 with PMF agents via PMF.ofScores. The §2.2 dead-end fallback distributes over words with viable continuations, gated to scene referents (out-of-scene referents keep their zero row). Utterance-level probabilities are chain-rule products of s1 values (eq. 7).

[CGGP19] — Incremental Iterated Response Model #

The Model #

Formalization via the IncrementalSemantics bundle #

Main results #

Implementation notes #

Domain Types (Figure 1a) #

The Figure 1 bundle #

The kernel face over the bundle #

The incremental chain #

Predictions #

Figure 1c: the word-by-word speaker #

Figure 1d: the pragmatic listener #

Figure 1e: utterance-level probabilities #

§2.4 Weakly-Informative Greedy Unrolling #

Global RSA Model + Divergence (§2.4) #

The §3.2 contrastive-inference bridge #

No-contrast companion scene #

Linking hypothesis (load-bearing, editorial) #

Construction #

Rubio-Fernández §3.1 Bridge (English Over-Modification, STOP token) #

Formalization via the `IncrementalSemantics` bundle #