Connection to RSA Theory

@cite{bergen-goodman-2015} @cite{merchant-2004}

This phenomenon is modeled by @cite{bergen-goodman-2015}'s noisy channel RSA. See Phenomena.Ellipsis.Studies.BergenGoodman2015 for the noisy channel RSA model that derives fragment interpretation from noise inference.

Connection to unified noise theory: Theories/RSA/Core/Noise.lean

structure Phenomena.Ellipsis.FragmentAnswers.FragmentDatum : Type

A fragment answer datum

• question : String

  The question context

• fragment : String

  The fragment utterance

• interpretation : String

  The full sentence it's interpreted as

• category : String

  Syntactic category of fragment

• available : Bool

  Is this interpretation available?

• notes : String

  Notes

• source : String

  Source

instance Phenomena.Ellipsis.FragmentAnswers.instReprFragmentDatum : Repr FragmentDatum

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• Phenomena.Ellipsis.FragmentAnswers.instReprFragmentDatum = { reprPrec := Phenomena.Ellipsis.FragmentAnswers.instReprFragmentDatum.repr }

def Phenomena.Ellipsis.FragmentAnswers.instReprFragmentDatum.repr : FragmentDatum → Nat → Std.Format

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def Phenomena.Ellipsis.FragmentAnswers.fragmentSubject : FragmentDatum

Subject fragment answer

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def Phenomena.Ellipsis.FragmentAnswers.fragmentObject : FragmentDatum

Object fragment answer

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def Phenomena.Ellipsis.FragmentAnswers.fragmentNobody : FragmentDatum

Negative quantifier fragment

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def Phenomena.Ellipsis.FragmentAnswers.fragmentPP : FragmentDatum

PP fragment answer

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def Phenomena.Ellipsis.FragmentAnswers.fragmentTemporal : FragmentDatum

Temporal adverb fragment

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def Phenomena.Ellipsis.FragmentAnswers.fragmentPredicate : FragmentDatum

Predicate fragment (less common)

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structure Phenomena.Ellipsis.FragmentAnswers.NonQuestionFragmentDatum : Type

Fragment in non-question context (Stainton's examples)

• context : String

  The preceding context

• fragment : String

  The fragment utterance

• interpretation : String

  The interpretation

• notes : String

  Notes

• source : String

  Source

instance Phenomena.Ellipsis.FragmentAnswers.instReprNonQuestionFragmentDatum : Repr NonQuestionFragmentDatum

Equations

• Phenomena.Ellipsis.FragmentAnswers.instReprNonQuestionFragmentDatum = { reprPrec := Phenomena.Ellipsis.FragmentAnswers.instReprNonQuestionFragmentDatum.repr }

def Phenomena.Ellipsis.FragmentAnswers.instReprNonQuestionFragmentDatum.repr : NonQuestionFragmentDatum → Nat → Std.Format

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def Phenomena.Ellipsis.FragmentAnswers.fragmentAssertion : NonQuestionFragmentDatum

Assertion context

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def Phenomena.Ellipsis.FragmentAnswers.fragmentTopic : NonQuestionFragmentDatum

Topic continuation

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def Phenomena.Ellipsis.FragmentAnswers.fragmentPointing : NonQuestionFragmentDatum

Pointing context

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structure Phenomena.Ellipsis.FragmentAnswers.FragmentConstraintDatum : Type

When fragments are NOT acceptable

• question : String

  The question

• fragment : String

  The attempted fragment

• acceptable : Bool

  Is it acceptable?

• explanation : String

  Why (not) acceptable

• source : String

  Source

def Phenomena.Ellipsis.FragmentAnswers.instReprFragmentConstraintDatum.repr : FragmentConstraintDatum → Nat → Std.Format

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instance Phenomena.Ellipsis.FragmentAnswers.instReprFragmentConstraintDatum : Repr FragmentConstraintDatum

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• Phenomena.Ellipsis.FragmentAnswers.instReprFragmentConstraintDatum = { reprPrec := Phenomena.Ellipsis.FragmentAnswers.instReprFragmentConstraintDatum.repr }

def Phenomena.Ellipsis.FragmentAnswers.categoryMismatch : FragmentConstraintDatum

Category mismatch

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def Phenomena.Ellipsis.FragmentAnswers.focusMismatch : FragmentConstraintDatum

Focus mismatch

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def Phenomena.Ellipsis.FragmentAnswers.semanticMismatch : FragmentConstraintDatum

Semantic mismatch

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def Phenomena.Ellipsis.FragmentAnswers.basicFragments : List FragmentDatum

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def Phenomena.Ellipsis.FragmentAnswers.nonQuestionFragments : List NonQuestionFragmentDatum

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def Phenomena.Ellipsis.FragmentAnswers.fragmentConstraints : List FragmentConstraintDatum

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Noisy Channel Account

The noisy channel model explains fragment interpretation via:

1. Noise assumption: Words can be deleted in transmission
2. Rational inference: Listener infers what was deleted
3. Most probable reconstruction: "Bob" → "Bob went to the movies"

Key prediction: Fragment interpretation is robust to noise rate. Even with very low actual noise, fragments work because:

• Conditional on hearing a fragment, listener knows something was deleted
• Most likely deletion recovers the correct full sentence

See Phenomena.Ellipsis.Studies.BergenGoodman2015 for proofs.

Proven Results

• EllipsisModel.l0_fragment_correct: L0 assigns prob 1 to "Bob went"
• EllipsisModel.l0_fragment_robust: works for any δ > 0 (parametric)
• EllipsisModel.l1_fragment_correct: L1 also correctly interprets fragments

Alternative Accounts

1. Syntactic ellipsis (Merchant): Fragments have unpronounced structure

   • Predicts island sensitivity, case matching
   • See: Phenomena/Ellipsis/Sluicing.lean for related data

2. Direct interpretation (Stainton): No hidden structure

   • Fragments are genuinely sub-sentential
   • Interpretation via pragmatic type-shifting