[DT21]: Prior Beliefs Modulate Projection #

Does a listener's prior belief about a content modulate how strongly that content projects — i.e., how committed the speaker is taken to be to it when it sits under an entailment-canceling operator? The prior literature conflicted: [Mah20] found that politically charged complements project more when a priori more plausible, while [Lor18] found no effect of world knowledge on the projection of the prestate of stop. [DT21] resolve the conflict in favor of modulation: across 20 clause-embedding predicates and 20 contents, higher-prior content projects more, at the group and the individual level.

The deep claim is structural: projection tracks prior credence monotonically. We make that the pivot. An account is prior-sensitive when it is monotone in prior credence (PriorSensitive); such an account predicts the observed per-content modulation by its very shape (sensitive_predicts_modulation), whereas the prior-insensitive null account predicts no modulation at all (priorInsensitive_not_sensitive). This is the account family the paper argues for — projection as a posterior credence in a Bayesian / RSA listener ([QGL16], [GF16]). It is the prior analogue of the at-issueness predictor of projection in [TBD18]: both are gradient Rat01 → Rat01 maps into the same projection space.

Main definitions #

Predicate — the 20 clause-embedding predicates (Figure 1C).
PriorAccount := Rat01 → Rat01 — predict projection strength from prior credence.
PriorSensitive / priorInsensitive — the monotone account family vs. the constant null.
ProjectionByPrior — a per-predicate datum (high/low-prior mean certainty and prior credence), lifted from Data.Examples.DegenTonhauser2021.

Main results #

sensitive_predicts_modulation, priorInsensitive_not_sensitive, priorInsensitive_no_modulation — the modulation is derived from account shape.
#guards over Examples.all build-check that every predicate shows higher prior and higher projection in the high condition (the core finding).
all_predicates_take_clause_complement and the coverage lemmas — every predicate is realized by a Fragment entry taking a finite clause.

Empirical findings (prose, per [DT21]) #

Regression coefficients are documented here, not encoded as theorems. Experiment 1 (within-participant, N = 286): the prior manipulation was successful (β = 0.45, SE = 0.01, t = 31.12), and prior probability predicted projection at every level — categorical high/low fact (β = 0.14, t = 12.24), group-level continuous prior (β = 0.31, t = 12.58), and the participant's own continuous prior (β = 0.28, t = 13.85). Model comparison favored the individual-level predictor decisively (BIC 2291 < group-level 2586 < categorical 2654). The by-predicate projection ranking was highly stable (Spearman r = .991 with prior work), reproducing the predicate-level projection variability documented by [TBD18]. Experiment 2 (between-participant) replicated the effect: prior manipulation β = 0.54 (t = 15.07; Exp 2a, N = 75; prior ratings r = .977 with Exp 1) and projection β = 0.18 categorical / β = 0.34 group-level (t = 12.81 / 13.27; Exp 2b, N = 266). The main-clause control projected at floor (mean certainty 0.21).

Implementation notes #

Per-predicate mean certainty (projection) and prior credence are computed from the authors' data (results/9-prior-projection/data/cd.csv at github.com/judith-tonhauser/projective-probability, n = 286) and stored in Data.Examples.DegenTonhauser2021; degrees use the shared Core.Order.Rat01 projection space. The continuous data is checked by #guard (string-keyed paperFeatures do not kernel-reduce); the provable content is the account-shape theorems. Predicates are bridged to their Fragment lexical entries.

[DT21]: Prior Beliefs Modulate Projection #

Main definitions #

Main results #

Empirical findings (prose, per [DT21]) #

Implementation notes #

The 20 clause-embedding predicates #

Projection as a function of prior credence #

Data: prior modulates projection for every predicate #

Fragment bridge #