Documentation

Linglib.Phenomena.Gradability.Studies.WaldonEtAl2023

@cite{waldon-etal-2023} #

Waldon, B., Condoravdi, C., Levin, B., & Degen, J. (2023). On the context dependence of artifact noun interpretation. In Proceedings of Sinn und Bedeutung 27, pp. 674–692.

Key Claims #

  1. Goal Sensitivity: policy goals systematically modulate artifact noun category boundaries. A flashlight is more likely to count as an "electronic device" when the goal is limiting distracting light than when it's limiting noise.

  2. Multi-dimensional degree semantics for artifact nouns (eq. 8): ⟦vehicle⟧ = λx. Σ_{f ∈ F(vehicle)} f(x) · W(vehicle, f) where F returns context-relevant measure functions and W weights them. Artifact nouns compose additively (@cite{sassoon-fadlon-2017}), in contrast to natural kinds which compose multiplicatively.

  3. RSA model (companion handout): a signaler (rule-maker) produces rules to advance policy goals; the listener jointly infers which objects are targeted and what the signaler's goal is: L₁(obj, goal | rule) ∝ S(rule | obj, goal) · P_G(goal) · P_CAT(obj) where S ∝ U(goal, obj)^α and U is the utility of prohibiting obj given goal (parameterized by feature attribution norming).

RSAConfig Mapping #

source
inductive Phenomena.Gradability.Studies.WaldonEtAl2023.Object :
Type

Objects in the "No electronic devices" scenario (Fig. 1).

Instances For
    source
    def Phenomena.Gradability.Studies.WaldonEtAl2023.instReprObject.repr :
    Object → ℕ → Std.Format
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      instance Phenomena.Gradability.Studies.WaldonEtAl2023.instReprObject :
      Repr Object
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      instance Phenomena.Gradability.Studies.WaldonEtAl2023.instDecidableEqObject :
      DecidableEq Object
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      def Phenomena.Gradability.Studies.WaldonEtAl2023.instBEqObject.beq :
      Object → Object → Bool
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        instance Phenomena.Gradability.Studies.WaldonEtAl2023.instBEqObject :
        BEq Object
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        instance Phenomena.Gradability.Studies.WaldonEtAl2023.instFintypeObject :
        Fintype Object
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        inductive Phenomena.Gradability.Studies.WaldonEtAl2023.Goal :
        Type

        The signaler's policy goals (Appendix A).

        Instances For
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          instance Phenomena.Gradability.Studies.WaldonEtAl2023.instReprGoal :
          Repr Goal
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          def Phenomena.Gradability.Studies.WaldonEtAl2023.instReprGoal.repr :
          Goal → ℕ → Std.Format
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            instance Phenomena.Gradability.Studies.WaldonEtAl2023.instDecidableEqGoal :
            DecidableEq Goal
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            instance Phenomena.Gradability.Studies.WaldonEtAl2023.instBEqGoal :
            BEq Goal
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            def Phenomena.Gradability.Studies.WaldonEtAl2023.instBEqGoal.beq :
            Goal → Goal → Bool
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            Instances For
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              instance Phenomena.Gradability.Studies.WaldonEtAl2023.instFintypeGoal :
              Fintype Goal
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              inductive Phenomena.Gradability.Studies.WaldonEtAl2023.GoalCondition :
              Type

              Experimental conditions (determines latentPrior over Goals).

              Instances For
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                def Phenomena.Gradability.Studies.WaldonEtAl2023.instReprGoalCondition.repr :
                GoalCondition → ℕ → Std.Format
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                  instance Phenomena.Gradability.Studies.WaldonEtAl2023.instReprGoalCondition :
                  Repr GoalCondition
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                  instance Phenomena.Gradability.Studies.WaldonEtAl2023.instDecidableEqGoalCondition :
                  DecidableEq GoalCondition
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                  instance Phenomena.Gradability.Studies.WaldonEtAl2023.instBEqGoalCondition :
                  BEq GoalCondition
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                  def Phenomena.Gradability.Studies.WaldonEtAl2023.instBEqGoalCondition.beq :
                  GoalCondition → GoalCondition → Bool
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                  Instances For
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                    instance Phenomena.Gradability.Studies.WaldonEtAl2023.instFintypeGoalCondition :
                    Fintype GoalCondition
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                    inductive Phenomena.Gradability.Studies.WaldonEtAl2023.Utterance :
                    Type

                    Utterances: the rule-maker produces the rule or stays silent.

                    Instances For
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                      instance Phenomena.Gradability.Studies.WaldonEtAl2023.instReprUtterance :
                      Repr Utterance
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                      def Phenomena.Gradability.Studies.WaldonEtAl2023.instReprUtterance.repr :
                      Utterance → ℕ → Std.Format
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                        instance Phenomena.Gradability.Studies.WaldonEtAl2023.instDecidableEqUtterance :
                        DecidableEq Utterance
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                        def Phenomena.Gradability.Studies.WaldonEtAl2023.instBEqUtterance.beq :
                        Utterance → Utterance → Bool
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                        Instances For
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                          instance Phenomena.Gradability.Studies.WaldonEtAl2023.instBEqUtterance :
                          BEq Utterance
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                          instance Phenomena.Gradability.Studies.WaldonEtAl2023.instFintypeUtterance :
                          Fintype Utterance
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                          These values are schematic approximations, not from the paper's actual norming data. The paper parameterizes U(goal, obj) and P_CAT(obj) via separate norming studies (feature attribution and category membership, §3.1). The actual values are available at the OSF links cited in the paper. The values below capture the qualitative pattern described in the paper (flashlights emit light but not noise; boomboxes emit noise but not light; etc.) and are sufficient to verify the model's structural predictions.

                          source
                          def Phenomena.Gradability.Studies.WaldonEtAl2023.utility :
                          Goal → Object → ℚ

                          U(goal, obj): utility of prohibiting obj given goal. Higher values = prohibiting this object better advances the goal. From feature attribution norming (schematic).

                          Equations
                          Instances For
                            source
                            def Phenomena.Gradability.Studies.WaldonEtAl2023.catPrior :
                            Object → ℚ

                            P_CAT(obj): prior category membership as "electronic device". From category membership norming (schematic).

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                            Instances For
                              source
                              theorem Phenomena.Gradability.Studies.WaldonEtAl2023.catPrior_pos (o : Object) :
                              0 < catPrior o
                              source
                              def Phenomena.Gradability.Studies.WaldonEtAl2023.goalPrior :
                              GoalCondition → Object → Goal → ℚ

                              P_G(goal | condition): goal plausibility prior. In explicit goal conditions, the prior concentrates on the stated goal. In the neutral condition, all goals are equally plausible.

                              Equations
                              Instances For
                                source
                                def Phenomena.Gradability.Studies.WaldonEtAl2023.rsaMeaning (goal : Goal) (utt : Utterance) (obj : Object) :
                                ℚ

                                RSA meaning function: for a given goal, how consistent is each object with each utterance?

                                • rule: meaning = U(goal, obj) (the utility of prohibiting obj)
                                • silence: meaning = 1 (uninformative — equally consistent with all objects)

                                L0 normalizes across objects, giving a distribution over which objects the rule targets. S1 = L0^α normalizes across utterances, giving the speaker's probability of producing the rule.

                                Model simplification: The companion handout defines U(goal, ¬obj) = 1 − U(goal, obj) for silence, making silence informative (not-prohibiting has utility). Our RSAConfig uses meaning(silence) = 1 (uninformative, uniform L0), a standard RSA convention. This preserves within- and cross-config orderings because S1 is monotone in L0, and L0 is monotone in meaning.

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                                  theorem Phenomena.Gradability.Studies.WaldonEtAl2023.rsaMeaning_nonneg (goal : Goal) (utt : Utterance) (obj : Object) :
                                  0 ≤ rsaMeaning goal utt obj
                                  source
                                  noncomputable def Phenomena.Gradability.Studies.WaldonEtAl2023.mkCfg (condition : GoalCondition) :
                                  RSA.RSAConfig Utterance Object

                                  Build one RSAConfig per experimental condition. Follows the companion handout's architecture: L₁(obj, goal | rule) ∝ S(rule | obj, goal) · P_G(goal) · P_CAT(obj)

                                  Structurally parallel to @cite{lassiter-goodman-2017}'s threshold RSA: both jointly infer world state and a latent parameter (threshold θ in LG2017, policy goal in this model).

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                                  Instances For

                                    Within-config predictions (object ordering) via rsa_predict.

                                    source
                                    theorem Phenomena.Gradability.Studies.WaldonEtAl2023.limitLight_flashlight_gt_candle :
                                    (mkCfg GoalCondition.limitLight).L1 Utterance.rule Object.flashlight > (mkCfg GoalCondition.limitLight).L1 Utterance.rule Object.candle

                                    Under limitLight, the flashlight (edge case) is more likely to be targeted by the rule than the candle (clear non-member).

                                    source
                                    theorem Phenomena.Gradability.Studies.WaldonEtAl2023.limitNoise_boombox_gt_flashlight :
                                    (mkCfg GoalCondition.limitNoise).L1 Utterance.rule Object.boombox > (mkCfg GoalCondition.limitNoise).L1 Utterance.rule Object.flashlight

                                    Under limitNoise, the boombox is the primary target.

                                    source
                                    theorem Phenomena.Gradability.Studies.WaldonEtAl2023.limitLight_tablet_gt_boombox :
                                    (mkCfg GoalCondition.limitLight).L1 Utterance.rule Object.tablet > (mkCfg GoalCondition.limitLight).L1 Utterance.rule Object.boombox

                                    Under limitLight, the tablet (clear member + emits light) outranks the boombox (clear member but doesn't emit light).

                                    Cross-config predictions (goal modulation). The paper's central empirical claim: the same edge-case object receives different L1 scores under different goal conditions. Parallel to @cite{lassiter-goodman-2017}'s basketball_tall_favors_taller, which shows context (prior) modulates L1 across configs.

                                    source
                                    theorem Phenomena.Gradability.Studies.WaldonEtAl2023.goal_sensitivity_flashlight :
                                    (mkCfg GoalCondition.limitLight).L1 Utterance.rule Object.flashlight > (mkCfg GoalCondition.limitNoise).L1 Utterance.rule Object.flashlight

                                    Goal sensitivity for flashlights (the paper's key result, Fig. 1): the flashlight is more likely to be targeted under limitLight than limitNoise, because flashlights emit light but not noise.

                                    source
                                    theorem Phenomena.Gradability.Studies.WaldonEtAl2023.goal_sensitivity_boombox :
                                    (mkCfg GoalCondition.limitNoise).L1 Utterance.rule Object.boombox > (mkCfg GoalCondition.limitLight).L1 Utterance.rule Object.boombox

                                    Goal sensitivity for boomboxes (reverse pattern, Fig. 1): the boombox is more likely to be targeted under limitNoise than limitLight, because boomboxes emit noise but not light.

                                    source
                                    theorem Phenomena.Gradability.Studies.WaldonEtAl2023.goal_sensitivity_tablet :
                                    (mkCfg GoalCondition.preventRecordings).L1 Utterance.rule Object.tablet > (mkCfg GoalCondition.limitNoise).L1 Utterance.rule Object.tablet

                                    Goal sensitivity for tablets under preventRecordings: the tablet is more likely to be targeted under preventRecordings than limitNoise, because tablets can record but are quiet.

                                    Utility-level explanations: WHY the L1 orderings hold. The cross-config L1 ordering follows from the utility ordering because S1 is monotone in L0, which is monotone in meaning.

                                    source
                                    theorem Phenomena.Gradability.Studies.WaldonEtAl2023.flashlight_utility_light_gt_noise :
                                    utility Goal.limitLight Object.flashlight > utility Goal.limitNoise Object.flashlight

                                    The flashlight's utility is much higher under limitLight than limitNoise — the driver of goal_sensitivity_flashlight.

                                    source
                                    theorem Phenomena.Gradability.Studies.WaldonEtAl2023.boombox_utility_noise_gt_light :
                                    utility Goal.limitNoise Object.boombox > utility Goal.limitLight Object.boombox

                                    The boombox's utility is higher under limitNoise than limitLight — the driver of goal_sensitivity_boombox.

                                    The utility function U(goal, obj) is structurally a weighted score over dimensional measures — the same mechanism as weightedScore from Semantics.Degree.Aggregation. In the paper's eq. (8), the artifact noun denotation is Σ_f f(x) · W(noun, f). Here, each goal selects ONE feature dimension (emit-light, emit-noise, or can-record), so the utility reduces to the feature's raw value.

                                    In the general case (eq. 14, neutral condition), the utility is a
weighted sum over multiple features with weights from goal plausibility
norming. This is exactly `weightedScore`.
                                    source
                                    def Phenomena.Gradability.Studies.WaldonEtAl2023.emitLight :
                                    Object → ℚ

                                    Individual feature measures (the components of eq. 8).

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                                    Instances For
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                                      def Phenomena.Gradability.Studies.WaldonEtAl2023.emitNoise :
                                      Object → ℚ
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                                      Instances For
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                                        def Phenomena.Gradability.Studies.WaldonEtAl2023.canRecord :
                                        Object → ℚ
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                                        Instances For
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                                          theorem Phenomena.Gradability.Studies.WaldonEtAl2023.utility_is_feature :
                                          utility Goal.limitLight = emitLight ∧ utility Goal.limitNoise = emitNoise ∧ utility Goal.preventRecordings = canRecord

                                          The utility function for explicit goals equals the raw feature value.

                                          @cite{sassoon-fadlon-2017} contrast artifact nouns (additive: Σ) with natural kinds (multiplicative: Π). Under multiplicative composition, a zero on ANY dimension kills membership. Under additive, other dimensions compensate.

                                          source
                                          def Phenomena.Gradability.Studies.WaldonEtAl2023.allFeatures :
                                          List (Object → ℚ)

                                          All feature measures as a list (for aggregation functions).

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                                            theorem Phenomena.Gradability.Studies.WaldonEtAl2023.flashlight_multiplicative_negligible :
                                            Semantics.Degree.Aggregation.multiplicativeScore allFeatures Object.flashlight < 1 / 100

                                            Under multiplicative composition, the flashlight gets ZERO because emitNoise(flashlight) = canRecord(flashlight) = 1/20 ≈ 0. The product is negligibly small.

                                            source
                                            theorem Phenomena.Gradability.Studies.WaldonEtAl2023.flashlight_additive_positive :
                                            Semantics.Degree.Aggregation.weightedScore [1, 1, 1] allFeatures Object.flashlight > 1 / 2

                                            Under additive composition, the flashlight gets a positive score despite near-zero on noise/recording — emitLight compensates.

                                            source
                                            theorem Phenomena.Gradability.Studies.WaldonEtAl2023.artifact_aggregation_is_utilitarian :
                                            Semantics.Degree.Aggregation.AggregationType.utilitarian ≠ Semantics.Degree.Aggregation.AggregationType.counting

                                            Artifact noun aggregation is utilitarian, not counting — the same point made by @cite{dambrosio-hedden-2024} for multidimensional adjectives. @cite{sassoon-2013}'s binding types (conjunctive, disjunctive, mixed) are all counting aggregation and cannot capture the weighted, continuous-measure structure of artifact noun interpretation.