Franke & Bergen 2020: grammatically generated implicature readings #

[FB20b] compares four RSA models ([FG12]) of the nested Aristotelians "Q₁ of the aliens drank Q₂ of their water" (Q ∈ {none, some, all}). An alien's drinking amount is a SomeAllWorld; a world state is the nonempty set of amounts realized by at least one alien (7 states); a parse is the set of EXH insertion sites among matrix/outer/inner (8 parses); the readings are the paper's Table 1 (the table1_* lemmas, one per row, each characterized by a membership predicate). The models differ in where the parse enters the speaker: vanilla (§3.1) has only the literal parse; LU (§3.2) fixes a lexicon l ∈ {lit, OI} per speaker — the parse an argument of the speaker (eq. 11) and a latent the listener marginalizes ([BLG16], [PLLF16]); the LI (§3.3) and GI (§3.4) speakers instead choose an (utterance, parse) pair (eqs. 18a/21a), over the 4 matrix-free parses resp. all 8 — one softmax over pairs per world, heard through the RSA.Scenario observation map.

We show that GI corrects the SS interpretation vanilla gets wrong (vanilla_ss_prefers_wNA vs gi_ss_prefers_wNS), and that its parse posterior for SS peaks at the matrix-only parse (ss_m_parse_pref), whose reading ⟦SS⟧^M = {wNS} "uniquely singles out this world state" (eq. 22, m_ss_singleton) and is unavailable to LI and LU (li_excludes_matrix, lu_excludes_matrix) — the paper's explanation of GI's win in its Bayesian model comparison (posterior 0.956 vs LI 0.033, LU 0.01, vanilla 0; Table 2). The M-advantage exists because the pooled speaker normalizes over pairs: under the per-parse normalization the paper rejects (p. e85), O beats M at every rationality (perParse_ss_prefers_o). LI and LU still derive the embedded enrichments (li_ss_outer_exh, li_ss_prefers_wNS, lu_ss_prefers_wNS).

Main results #

table1_* — the paper's Table 1, one lemma per row, including NN's distinct matrix row (fn. 7) from the none ~ not all lexical alternative ([Lev00]).
ss_m_parse_pref vs perParse_ss_prefers_o — the architectural headline: pooled (utterance, parse) choice peaks at M (α = 5), per-parse normalization prefers O for every rationality. With RSA.Scenario.pool_L0 (identical weights), the pair locates GI's win purely in the position of the latent parameter (p. e86).
moi_ss_ne_innocent_exclusion — the paper's matrix operator (eq. A2) is not Fox-style innocent exclusion ([Fox07]).

Implementation notes #

One reading family (readings) generates every model: vanilla is its literal member, GI and LI pool (utterance, parse) pairs into the choice space (RSA.Scenario.pool, eqs. 18a/21a), and LU — like the rejected per-parse architecture — fixes the latent as a speaker argument (RSA.Scenario.familySpeaker, eq. 11). Sentential alternatives (A3a) range over a fourth quantifier notAll that is never an utterance — the paper's grammatical-vs-utterance alternatives distinction (its comparison with [GR18]'s alternative set favors this one by a Bayes factor of ~1,530). Findings come in two registers, both closed by decide: Multiset.StrictDominates certificates — strict stochastic dominance of informativity profiles — hold for every rationality α > 0, while genuinely α-dependent findings are pinned at the paper's illustrative α = 5, where comparisons clear to ℕ inequalities via Multiset.divPowSum. We omit the paper's cost term for none-initial utterances and fixed error ε = 0.045 (eqs. 25–28); vanilla_ss_prefers_wNA reverses at the fitted cost. The paper's S2/L2 layer for LU ([LG17], eqs. 14a–14b) is also omitted: our L1-only LU keeps wNS over wNA at every rationality, though the paper's LU-L2 concentrates on wNSA (eq. 15).

Franke & Bergen 2020: grammatically generated implicature readings #

Main results #

Implementation notes #

The grammar of readings #

Domain #

Alternative quantifiers #

Compositional semantics #

Compositional exhaustification #

Truth-table verification (the paper's Table 1) #

The models #

The reading family and the pooled models #

Lexical uncertainty: the latent as a speaker argument #

The rejected architecture: per-parse normalization #

The findings #

Exhaustified interpretation #

The model comparison #

The position of the latent parameter #