[FB20b] — GI-RSA for Nested Aristotelians #

[FB20b] [Fox07] [Fra11]

"Theory-driven statistical modeling for semantics and pragmatics: A case study on grammatically generated implicature readings"

The Model #

Domain: Nested Aristotelian sentences "Q₁ of the aliens drank Q₂ of their water" with Q₁, Q₂ ∈ {none, some, all}. 7 world states based on which alien types exist (none-drinkers, some-drinkers, all-drinkers). 8 grammatical parses (subsets of {M, O, I} EXH positions) as latent variables.

The Global Intentions (GI) model treats the parse as a latent variable: the speaker chooses both an utterance and a parse, the listener marginalizes over parses to recover the world state.

L0: L0(w|u,g) ∝ ⟦u⟧ᵍ(w) (meaning under parse g)
S1: S1(u,g|w) ∝ L0(w|u,g)^α · P(g)
L1: L1(w|u) ∝ P(w) · Σ_g S1(u,g|w)

Exhaustification uses compositional enrichment at inner/outer quantifier positions: Exh(Q) conjoins Q with the negation of all strictly stronger lexical alternatives on the {some, all} scale ([Fox07]). Only Exh(some) = "some but not all" is non-vacuous; Exh(all) and Exh(none) have no strictly stronger alternative.

At matrix position, EXH uses exh_MW (eq. A2): negate the LITERAL meanings of sentential alternatives that are strictly stronger than the sub-matrix enriched meaning, with a noncontradictory fallback. Sentential alternatives are the cross-product of scale-mate substitutions ({some, all}) for each on-scale quantifier. "none" is treated as off-scale; the paper notes (fn. 7) that including "not all" as an alternative to "none" has negligible effect on predictions.

Parameters: α = 2 (modeling choice; the paper estimates α jointly with cost and error parameters, reporting MLE ≈ 1.3 for GI), uniform priors. The paper's cost term c(u) for "none"-initial utterances and error term ε are omitted; the qualitative predictions below are robust to these simplifications.

Qualitative Findings #

#	Finding	Theorem
1	SS exhaustifies inner Q	`ss_inner_exh`
2	SS exhaustifies outer Q	`ss_outer_exh`
3	AA identifies unique world	`aa_identifies`
4	AS exhaustifies inner Q	`as_inner_exh`
5	Full EXH preferred for SS	`ss_parse_pref`
6	Vanilla gets SS wrong (prefers wNA)	`vanilla_ss_prefers_wNA`
7	GI gets SS right (prefers wNS)	`gi_ss_prefers_wNS`
8	LU gets SS→wNS right	`lu_ss_prefers_wNS`
9	LI derives outer exh for SS	`li_ss_outer_exh`
10	LI also gets SS→wNS right	`li_ss_prefers_wNS`

Model Comparison #

All four models share one per-parse speaker S(w, p) (the softmax at exponent α = 2 of the parse-p literal listener), because the speaker at a (world, parse) state depends only on that parse's Boolean meaning. They differ only in the latent space the pragmatic listener marginalises over — a joint PMF (World × Latent) posterior (RSA.Canonical.L1) with a uniform prior:

Vanilla (§3.1): latent Unit — literal parse only (S(·, .none))
LU (§3.2): latent LULex (2 lexica) — simplified to L1 (the paper adds an S2/L2 layer following [PLLF16]; our L1-only approximation suffices for qualitative predictions)
LI (§3.3): latent LIParse (4 parses) — speaker chooses parse
GI (§3.4): latent Parse (8 parses) — full parse space

The listener predictions are decided by exact PMF evaluation: each speaker mass S(w, p) u is a rational ENNReal.ofReal value (s_* lemmas below), and each theorem reduces via RSA.Canonical.L1_world_prefers_iff (or _latent_prefers_iff) to a comparison of pooled speaker sums over the latent.

Bayesian model comparison: GI achieves 0.956 posterior probability, LI = 0.033, LU = 0.010, vanilla = 0.

[FB20b] — GI-RSA for Nested Aristotelians #

The Model #

Qualitative Findings #

Model Comparison #

wNS partition and speaker masses (SS) #

wNSA partition and speaker masses (SS) #

wS partition and speaker masses (SS and AS) #

wNA, wSA, wA partitions and speaker masses #

Pooled speaker sums for the remaining worlds #

Latent pooling over worlds (parse-preference) #

LU / LI pooling over the smaller latent spaces #

Listener-preference reductions #

Marginal-nonzero witnesses #

The ten qualitative findings #

Connection to [PLLF16] #

Connection to [CWS23] #

Connection to [Fra11] #

Connection to [Fox07] #

Why GI wins (§6) #

`wNS` partition and speaker masses (SS) #

`wNSA` partition and speaker masses (SS) #

`wS` partition and speaker masses (SS and AS) #

`wNA`, `wSA`, `wA` partitions and speaker masses #