Scontras and Tonhauser (2025): Projection without Lexically-Specified Presupposition #
Scontras and Tonhauser model the projection of the complement of know from under negation
without a lexical presupposition. A world settles whether Cole believes the complement and
whether it is true, know is factive and think is not, and the two questions of the
experiments ask whether Cole believes the complement and whether it is true. A literal listener
interprets the utterance within the speaker's private assumptions, a set of worlds, and answers
the question (L0). The speaker is informative about the answer and pays a cost that doubles for
the complex utterances (S1). The pragmatic listener, who hears the utterance and the question,
inverts the speaker jointly over worlds and assumptions (L1), as in the model of Qing, Goodman
and Lassiter.
Main results #
L1_c_mono: the posterior probability of the complement rises with its prior probability, under every utterance, question, rationality, cost and prior over assumptions.S1_univ_bel_knowNeg_lt_thinkNeg: a speaker without assumptions who addresses whether Cole believes the complement prefers negated think to negated know at a world where he does not.S1_knowNeg_eq_thinkNeg,L0_knowNeg_bel_eq_one: a speaker who assumes the complement finds the two equally informative under either question, and negated know then settles the belief question.S1_bel_congr: under the belief question the speaker's choice depends on the world only through Cole's belief.
Implementation notes #
- The paper's literal listener carries a world prior, but in the released model the literal listener draws worlds uniformly within the assumption set and the world prior enters at the pragmatic listener alone. The file follows the released model, whose predictions the paper reports, and this is what makes the prior effect a theorem. The listener's prior puts the actual world in the assumption set, as the released model does.
- The world prior is a parameter, in the theorems a product of a belief prior and a complement prior. The paper's is such a product, the complement twice as likely as not or half as likely. The prior over assumption sets is a parameter, and the paper's is that of Qing, Goodman and Lassiter.
- A simple utterance costs
kand a complex one2 * k, the paper's cost of a simple utterance doubled.
TODO #
- The sizes of the utterance and question effects are computations at the paper's parameters and are not stated.
- The revised model of the paper's fourth section, which backs off toward the prior by the divergence of the posterior from it, and the experiments' ratings are not formalized.
References #
Equations
- ScontrasTonhauser2025.instDecidableEqUtt x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯
Equations
- One or more equations did not get rendered due to their size.
Equations
A complex utterance embeds the complement under an attitude verb.
Equations
- u.Complex = (u ≠ ScontrasTonhauser2025.Utt.cPos ∧ u ≠ ScontrasTonhauser2025.Utt.cNeg)
Instances For
Equations
- ScontrasTonhauser2025.instDecidablePredUttComplex u = { decide := decide (u ≠ ScontrasTonhauser2025.Utt.cPos) && decide (u ≠ ScontrasTonhauser2025.Utt.cNeg), reflects_decide := ⋯ }
Semantics and questions #
In the literal meanings (4), know is factive and think is not, and the simple utterances assert the complement or its negation.
Equations
- ScontrasTonhauser2025.literal ScontrasTonhauser2025.Utt.knowPos = Factivity.World.Knows
- ScontrasTonhauser2025.literal ScontrasTonhauser2025.Utt.knowNeg = fun (x : Factivity.World) => ¬x.Knows
- ScontrasTonhauser2025.literal ScontrasTonhauser2025.Utt.thinkPos = Factivity.World.Thinks
- ScontrasTonhauser2025.literal ScontrasTonhauser2025.Utt.thinkNeg = fun (x : Factivity.World) => ¬x.Thinks
- ScontrasTonhauser2025.literal ScontrasTonhauser2025.Utt.cPos = fun (x : Factivity.World) => x.complement = true
- ScontrasTonhauser2025.literal ScontrasTonhauser2025.Utt.cNeg = fun (x : Factivity.World) => x.complement = false
Instances For
Equations
- One or more equations did not get rendered due to their size.
The extension of an utterance.
Equations
- ScontrasTonhauser2025.sem u = Finset.filter (ScontrasTonhauser2025.literal u) Finset.univ
Instances For
Negated think is semantically stronger than negated know, since it also excludes the world in which Cole believes a false complement.
The cell of a world under a question holds the worlds giving the same answer.
Equations
- ScontrasTonhauser2025.cell q w = {w' : Factivity.World | q.answer w' = q.answer w}
Instances For
The literal listener within an assumption set (5) #
The literal listener within an assumption set (5) samples a world of the set at which the utterance is true and returns its answer to the question.
Equations
- ScontrasTonhauser2025.L0 A q = (RSA.listener (MeasureTheory.Measure.count.restrict ↑A) (RSA.truthful fun (u : ScontrasTonhauser2025.Utt) => ↑(ScontrasTonhauser2025.sem u))).map q.answer
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The literal listener counts the worlds of the assumption set at which the utterance is true and the question's answer is the world's, over those at which the utterance is true.
Equations
- ScontrasTonhauser2025.l0 A q u w = ({x ∈ A ∩ ScontrasTonhauser2025.sem u | x ∈ ScontrasTonhauser2025.cell q w}.card, (A ∩ ScontrasTonhauser2025.sem u).card)
Instances For
A speaker who assumes the complement interprets negated know and negated think alike, since within the assumption set the belief is false under both.
Under the belief question, a speaker who assumes the complement answers fully with negated know at a world in which Cole does not believe the complement.
Without assumptions, negated think answers the belief question fully at a world in which Cole does not believe the complement.
Without assumptions, negated know leaves the belief question open at such a world, since it is also true where Cole believes a false complement.
The speaker (6) #
A simple utterance costs k and a complex one twice that (6).
Equations
- ScontrasTonhauser2025.cost k u = if u.Complex then 2 * k else k
Instances For
The speaker within an assumption set (6) knows her world's answer to the question and is
informative about the literal listener's belief about it at rationality α, less the cost.
Equations
- ScontrasTonhauser2025.S1 α k A q w = (RSA.speaker α (ScontrasTonhauser2025.cost k) (⇑(ScontrasTonhauser2025.L0 A q)) MeasureTheory.Measure.dirac) (q.answer w)
Instances For
A speaker who assumes the complement produces negated know and negated think alike under either question, since they are equally informative and equally costly.
Without assumptions, a speaker addressing the belief question at a world in which Cole does not believe the complement prefers negated think to negated know, since the stronger utterance is the more informative.
Under the belief question the speaker's choice depends on the world only through Cole's belief, as the question's cells do.
The pragmatic listener (7) #
The listener's prior weighs a world with an assumption set containing it by the world prior and the assumption prior.
Equations
- ScontrasTonhauser2025.pairPrior μ ν = (μ.prod ν).restrict {p : Factivity.World × Finset Factivity.World | p.1 ∈ p.2}
Instances For
The pragmatic listener (7) hears the utterance under a known question and inverts the speaker within each assumption set, over pairs of a world and an assumption set.
Equations
- ScontrasTonhauser2025.L1 α k μ ν q = RSA.listener (ScontrasTonhauser2025.pairPrior μ ν) fun (p : Factivity.World × Finset Factivity.World) => ScontrasTonhauser2025.S1 α k p.2 q p.1
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The prior effect (2b) #
The listener's evidence for a value of the complement is the speaker's production of the utterance at the worlds with that value, weighted by the belief prior and by the assumption prior over the assumption sets containing them. It does not depend on the complement prior.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The posterior probability of the complement (fn. 11) is its prior probability times the evidence for it, over the evidence for either value.
The posterior probability of the complement rises with its prior probability, under every utterance, question, rationality, cost and assumption prior, since the world prior enters the model at the pragmatic listener alone. This is the prior effect (2b).