Franke and Bergen (2020): Theory-Driven Statistical Modeling for Semantics and Pragmatics #

Franke and Bergen compare four rational speech act models, in the style of Frank and Goodman, of the nested Aristotelians Q₁ of the aliens drank Q₂ of their water, with none, some and all in each position. An alien's type is the vertex of the triangle of opposition its drinking falls on (Aristotelian.Triangle), none of its water, some but not all, or all, a world state is the nonempty set of types some alien realizes, and a parse is the set of sites, among the whole sentence and the two quantifiers, at which an exhaustivity operator applies. The vanilla model has only the literal parse; lexical uncertainty, after Bergen, Levy and Goodman and Potts et al., fixes a lexicon per speaker; the local- and global-implicature speakers choose an utterance together with a matrix-free or arbitrary parse, one softmax over pairs per world.

Main results #

table1_ss and its siblings: the readings of every utterance under every parse, the paper's Table 1.
vanilla_ss_prefers_wNA, gi_ss_prefers_wNS: the global model corrects the interpretation of some of the aliens drank some of their water that the vanilla model gets wrong.
ss_m_parse_pref, m_ss_singleton: its parse posterior peaks at the matrix-only parse, whose reading singles out the world with none- and some-drinkers only, the paper's explanation of the global model's win.
perParse_ss_prefers_o: under the per-parse normalization the paper rejects, exhaustifying the outer quantifier beats exhaustifying the whole sentence at every rationality.

Implementation notes #

One reading family, ext, generates every model: the vanilla model is its literal member, the speakers of the pooled models choose among utterance–parse pairs and their listeners hear the utterance, and lexical uncertainty, like the rejected per-parse architecture, fixes the latent as an argument of the speaker. Sentential alternatives range over a fourth quantifier, not all, that is never uttered. This is the paper's distinction between grammatical and utterance alternatives, which its model comparison favors over the alternative set of Gotzner and Romoli.
Findings that hold at every rationality are closed by strict stochastic dominance of informativity profiles (Multiset.StrictDominates); the rationality-dependent ones are pinned at the paper's illustrative value of 5, where the comparisons clear to inequalities of naturals.
The paper's cost term for none-initial utterances and its fixed error rate are omitted, and the vanilla preference reverses at the fitted cost. The second-level layer of the lexical-uncertainty model, after Lassiter and Goodman, is omitted; the first-level listener formalized here keeps the preference the paper's second-level listener loses.
The paper's matrix exhaustivity operator is not Fox's innocent exclusion (moi_ss_ne_innocent_exclusion). The distinct matrix reading of none of the aliens drank none of their water comes from the lexical alternative not all of none, after Levinson.

Franke and Bergen (2020): Theory-Driven Statistical Modeling for Semantics and Pragmatics #

Main results #

Implementation notes #

References #

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 #