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Linglib.Phenomena.Quantification.Studies.RSAScopeFreezing

Bridge: RSA Scope Freezing → Quantification Phenomena #

Connects the RSA scope-freezing model to empirical scope availability data from Phenomena.Quantification.Data. The RSA model provides domain types and meaning functions; this bridge file applies them to concrete freezing examples (possessor baseline/frozen) and states rescue/suppression predictions.

Status #

The old getInverseProb and l1Interp functions (which used RSA.Eval) have been removed. Domain types and interpretation priors are preserved. Prediction theorems are stated with sorry pending RSA computation rebuild.

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def RSA.ScopeFreezing.Bridge.interpPriorFromAvailability (avail : Phenomena.Quantification.Data.Availability) (ε : ℚ := 1 / 100) :
Semantics.Scope.ScopeConfig → ℚ

Convert grammatical availability to interpretation prior.

Key assumption: Frozen readings get prior ε > 0, not 0.

This encodes the RSA view that "grammatically unavailable" ≠ "impossible", just "strongly dispreferred." Grammar theories would set ε = 0; RSA sets ε > 0.

This is the core disagreement:

  • Grammar: P(frozen reading) = 0 (categorical)
  • RSA: P(frozen reading) = ε > 0 (gradient, rescuable)

The rescue theorem below only goes through because ε > 0.

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    def RSA.ScopeFreezing.Bridge.interpPriorFromExample (ex : Phenomena.Quantification.Data.Example) :
    Semantics.Scope.ScopeConfig → ℚ

    Interpretation prior from a freezing example (uses grammar's prediction)

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      def RSA.ScopeFreezing.Bridge.baseline :
      Phenomena.Quantification.Data.Example

      Baseline example from phenomena data

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        def RSA.ScopeFreezing.Bridge.frozen :
        Phenomena.Quantification.Data.Example

        Frozen example from phenomena data

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          theorem RSA.ScopeFreezing.Bridge.baseline_inverse_available :
          interpPriorFromExample baseline Semantics.Scope.ScopeConfig.inverse = 1

          Baseline: inverse available

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          theorem RSA.ScopeFreezing.Bridge.frozen_suppresses_inverse :
          interpPriorFromExample frozen Semantics.Scope.ScopeConfig.inverse = 1 / 100

          Frozen: grammar suppresses inverse (prior = ε = 1/100)

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          def RSA.ScopeFreezing.Bridge.grammarInterpPrior :
          Semantics.Scope.ScopeConfig → ℚ

          With ε = 0 (grammar's view), inverse prior is exactly 0

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            theorem RSA.ScopeFreezing.Bridge.grammar_view_zero_inverse :
            grammarInterpPrior Semantics.Scope.ScopeConfig.inverse = 0

            RSA Predictions (pending computation rebuild) #

            The following predictions require RSA L0/S1/L1 computation infrastructure:

            1. Baseline: inverse available - getInverseProb uniformWorldPrior baseline > 1/2
            2. Frozen: grammar suppresses inverse - getInverseProb uniformWorldPrior frozen < 1/10
            3. Rescue: world prior overrides grammar - getInverseProb rescueWorldPrior frozen > 1/2
            4. Grammar view: no rescue possible - getInverseProb rescueWorldPrior grammarInterpPrior = 0

            These depend on L1 marginal computation over interpretation priors, which is being rebuilt in the new RSAConfig framework.

            Connection to Grammar Theories #

            Both Minimalism and CCG predict possessor_frozen.observed =.surfaceOnly:

            RSA takes this grammatical prediction as input (via interpPriorFromExample) and shows that strong world priors can still rescue the frozen reading.

            This distinguishes RSA from categorical grammar accounts: