Documentation

Studies.Ronai2024

Ronai (2024): Embedded scalar diversity #

Ronai tests the embedded scalar implicature of every N was P across 42 lexical scales: whether Every soup was warm suggests the strong inference No soup was hot, computed in the scope of the universal, beyond the weak inference Not every soup was hot that a global implicature yields. Experiment 1 has the design of Chemla and Spector and of Gotzner and Romoli with the scale varied, and the responses track how many readings of the sentence entail the judged inference. Experiment 2 replaces the false control by the inference task of van Tiel and Geurts, since the compatible control of Gotzner and Romoli is the negation of the strong inference itself. The paper's argument for alternative-based accounts, including the model of Potts et al., is statistical and stays in prose: semantic distance and boundedness predict the embedded variation as they predict the global rates of van Tiel and Geurts, which a lexical strengthening in the style of Bergen, Levy and Goodman leaves unexplained, and the null result of Sun, Tian and Breheny is put down to the corrective context of P so not Q.

Main results #

Implementation notes #

References #

The inferences judged in Experiment 1 #

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inductive Ronai2024.Inference :
Type

The second sentence of a trial (11) is the true control at least one N was P, the weak inference not every N was Q, the strong inference no N was Q, or the false control not every N was P.

Instances For
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    @[instance_reducible]
    instance Ronai2024.instDecidableEqInference :
    DecidableEq Inference
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    def Ronai2024.instReprInference.repr :
    Inference → ℕ → Std.Format
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      @[instance_reducible]
      instance Ronai2024.instReprInference :
      Repr Inference
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      @[instance_reducible]
      instance Ronai2024.instFintypeInference :
      Fintype Inference
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      def Ronai2024.Inference.den {ι : Type u_1} :
      Inference → (ι → Aristotelian.Triangle) → Prop

      What each inference says of a domain of individuals. The weak inference is the negation of the utterance's only alternative on an unmodified neo-Gricean account, every N was Q.

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        @[instance_reducible]
        instance Ronai2024.instDecidableDenOfFintype {ι : Type u_1} [Fintype ι] (m : ι → Aristotelian.Triangle) (n : Inference) :
        Decidable (n.den m)
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        def Ronai2024.Inference.key :
        Inference → String

        The row key of an inference.

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          def Ronai2024.compatible {ι : Type u_1} (m : ι → Aristotelian.Triangle) :
          Prop

          The sentence Some N was Q (5) is the alternative built by replacing both scalar terms and the compatible control of a second experiment.

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            @[instance_reducible]
            instance Ronai2024.instDecidableCompatibleOfFintype {ι : Type u_1} [Fintype ι] (m : ι → Aristotelian.Triangle) :
            Decidable (compatible m)
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            theorem Ronai2024.compatible_iff_not_strong {ι : Type u_1} (m : ι → Aristotelian.Triangle) :
            compatible m ↔ ¬Inference.strong.den m

            Negating the alternative some N was Q yields the strong inference.

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            theorem Ronai2024.compatible_not_literal :
            ∃ (m : Bool → Aristotelian.Triangle), compatible m ∧ ¬ChemlaSpector2011.Exp1Some.reading ChemlaSpector2011.ReadingLabel.literal m

            Some N was Q does not entail every N was P, as an individual at A beside one at E shows.

            Readings and the inferences they support (§3.4) #

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            def Ronai2024.Supports (ℓ : ChemlaSpector2011.ReadingLabel) (n : Inference) :
            Prop

            A reading supports an inference when it entails it on every nonempty domain.

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              def Ronai2024.supported :
              ChemlaSpector2011.ReadingLabel → Finset Inference

              The literal reading supports the true control alone, the global reading the weak inference too, and the local reading the strong inference too; no reading supports the false control.

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                theorem Ronai2024.supports_iff (ℓ : ChemlaSpector2011.ReadingLabel) (n : Inference) :
                Supports ℓ n ↔ n ∈ supported ℓ
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                @[instance_reducible]
                instance Ronai2024.instDecidableSupports (ℓ : ChemlaSpector2011.ReadingLabel) (n : Inference) :
                Decidable (Supports ℓ n)
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                theorem Ronai2024.supports_strong_iff (ℓ : ChemlaSpector2011.ReadingLabel) :
                Supports ℓ Inference.strong ↔ ℓ = ChemlaSpector2011.ReadingLabel.local_

                Only the local reading supports the strong inference.

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                def Ronai2024.support (n : Inference) :
                ℕ

                The number of readings supporting an inference, which the sliding-scale response tracks.

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                  theorem Ronai2024.strong_admitted {ι : Type u_1} (t : ChemlaSpector2011.Theory) :
                  ChemlaSpector2011.Theory.admits ChemlaSpector2011.Exp1Some.reading t ChemlaSpector2011.ReadingLabel.local_ ↔ t ≠ ChemlaSpector2011.Theory.restrictedGlobalist

                  Every account but the unmodified neo-Gricean one makes the local reading available under a universal, the grammatical theory computing it in the scope of every and a globalist whose alternatives need not be stronger than the utterance reaching it because there it entails the literal reading.

                  The rows #

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                  def Ronai2024.mean (n : Inference) :
                  Option ℕ

                  The mean response to an inference over the 42 scales in Experiment 1 (Figure 1), in percent.

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                  • One or more equations did not get rendered due to their size.
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                    theorem Ronai2024.exp1_monotone :
                    ∃ r₀ ∈ mean Inference.falseControl, ∃ r₁ ∈ mean Inference.strong, ∃ r₂ ∈ mean Inference.weak, ∃ r₃ ∈ mean Inference.trueControl, ChemlaSpector2011.RatingsMonotone [(r₀, support Inference.falseControl), (r₁, support Inference.strong), (r₂, support Inference.weak), (r₃, support Inference.trueControl)]

                    In Figure 1 the responses rise with the readings supporting the inference, true above weak above strong above false across the 42 scales. The strong inference above the false control is the paper's evidence that embedded implicatures are computed, and the weak inference above the strong one reflects that the global reading supports only the former.

                    Experiment 2 (§4) #

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                    theorem Ronai2024.literal_and_compatible :
                    ∃ (m : Unit → Aristotelian.Triangle), ChemlaSpector2011.Exp1Some.reading ChemlaSpector2011.ReadingLabel.literal m ∧ compatible m

                    The compatible control is consistent with the sentence, since a domain of individuals at all verifies both every N was P and some N was Q.

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                    theorem Ronai2024.not_compatible_of_local {ι : Type u_1} {m : ι → Aristotelian.Triangle} (h : ChemlaSpector2011.Exp1Some.reading ChemlaSpector2011.ReadingLabel.local_ m) :
                    ¬compatible m

                    Once the strong inference is computed the compatible control is false, the local reading excluding it, which is why Experiment 2 replaces the baseline by an inference task.