Documentation

Linglib.Studies.DegenTonhauser2021

[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.

A prior-sensitive account is one monotone in prior credence (PriorSensitive); it predicts the modulation by its shape (sensitive_predicts_modulation), while the prior-insensitive null account predicts none (priorInsensitive_not_sensitive). This is the account family the paper argues for — projection as a posterior credence in a Bayesian / RSA listener ([QGL16], [GF16]) — and the prior analogue of the at-issueness predictor of [TBD18]. The experiment 1 by-predicate means realize the modulation for every predicate (prior_modulates_projection), and the predicates are bridged to their Fragment entries (all_predicates_take_clause_complement).

The regression coefficients are recorded as prose, not 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).

The 20 clause-embedding predicates #

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inductive DegenTonhauser2021.Predicate :
Type

The 20 clause-embedding predicates of [DT21], listed alphabetically as in Figure 1C. For the traditional classification see DegenTonhauser2022.traditionalClass.

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    @[instance_reducible]
    instance DegenTonhauser2021.instDecidableEqPredicate :
    DecidableEq Predicate
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    @[instance_reducible]
    instance DegenTonhauser2021.instFintypePredicate :
    Fintype Predicate
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    @[instance_reducible]
    instance DegenTonhauser2021.instReprPredicate :
    Repr Predicate
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    def DegenTonhauser2021.instReprPredicate.repr :
    Predicate → ℕ → Std.Format
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      Projection as a function of prior credence #

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      @[reducible, inline]
      abbrev DegenTonhauser2021.PriorAccount :
      Type

      A predictor of projection strength from prior credence in the complement.

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        def DegenTonhauser2021.priorInsensitive (c : ↑(Set.Icc 0 1)) :
        PriorAccount

        The prior-insensitive null account: projection is constant in prior credence.

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          def DegenTonhauser2021.PriorSensitive (acc : PriorAccount) :
          Prop

          An account is prior-sensitive when projection is strictly monotone in prior credence.

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            theorem DegenTonhauser2021.priorInsensitive_no_modulation (c p q : ↑(Set.Icc 0 1)) :
            priorInsensitive c p = priorInsensitive c q

            The null account predicts identical projection for any two priors.

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            theorem DegenTonhauser2021.priorInsensitive_not_sensitive (c : ↑(Set.Icc 0 1)) :
            ¬PriorSensitive (priorInsensitive c)

            The null account is not prior-sensitive.

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            theorem DegenTonhauser2021.sensitive_predicts_modulation {acc : PriorAccount} (h : PriorSensitive acc) {p q : ↑(Set.Icc 0 1)} (hpq : p < q) :
            acc p < acc q

            A prior-sensitive account predicts stronger projection for higher-prior content.

            Data: prior modulates projection for every predicate #

            Experiment 1 by-predicate means from results/9-prior-projection/data/cd.csv at github.com/judith-tonhauser/projective-probability (n = 286), rounded to two decimals; prior means average over the contents each predicate was randomly paired with.

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            def DegenTonhauser2021.certaintyHigh :
            Predicate → ℚ

            Mean certainty rating (projection) under the higher-probability fact (Figure 3; nonprojective main-clause control mean 0.21).

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              def DegenTonhauser2021.certaintyLow :
              Predicate → ℚ

              Mean certainty rating under the lower-probability fact.

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                def DegenTonhauser2021.priorHigh :
                Predicate → ℚ

                Mean prior probability rating of the complement content given the higher-probability fact.

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                  def DegenTonhauser2021.priorLow :
                  Predicate → ℚ

                  Mean prior probability rating given the lower-probability fact.

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                    theorem DegenTonhauser2021.prior_modulates_projection (p : Predicate) :
                    priorLow p < priorHigh p ∧ certaintyLow p < certaintyHigh p

                    Prior credence and certainty are both higher under the higher-probability fact for every predicate (Figure 3) — the pattern a prior-sensitive account predicts and the null account rules out.

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                    theorem DegenTonhauser2021.certaintyLow_ne_certaintyHigh (p : Predicate) :
                    certaintyLow p ≠ certaintyHigh p

                    The observed certainties differ across the manipulation, contra the null account (priorInsensitive_no_modulation).

                    Fragment bridge #

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                    def DegenTonhauser2021.toVerbEntry :
                    Predicate → Option English.Predicates.Verbal.VerbEntry

                    Map each predicate to its Fragment verb entry (18 of 20; beAnnoyed and beRight are copular — use toPredicateCore for full coverage).

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                      theorem DegenTonhauser2021.toVerbEntry_eq_none_iff (p : Predicate) :
                      toVerbEntry p = none ↔ p = Predicate.beAnnoyed ∨ p = Predicate.beRight

                      The two copular predicates are exactly the ones without a VerbEntry.

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                      def DegenTonhauser2021.toPredicateCore :
                      Predicate → Verb

                      Map each predicate to its Verb — the semantic spine shared by verbal and copular entries. Covers all 20; copular entries go through ClauseEmbeddingAdjective.toVerb.

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                        theorem DegenTonhauser2021.all_predicates_take_clause_complement (p : Predicate) :
                        (toPredicateCore p).complementType = ComplementType.finiteClause ∨ (toPredicateCore p).altComplementType = some ComplementType.finiteClause

                        Every predicate takes a finite clause complement (as primary or alternate frame), matching the experimental design.