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Linglib.Phenomena.Ellipsis.Studies.Steedman2000Gapping

CCG Gapping Bridge #

@cite{ross-1970} @cite{steedman-2000}

Connects CCG category theory (from Theories.Syntax.CCG.Gapping) to empirical gapping data (from Phenomena.Ellipsis.Gapping).

Proves that:

  1. Gapping direction follows from lexical verb categories and word order
  2. Ross's generalization emerges from CCG's Principles of Consistency and Inheritance
  3. Dutch allows both gapping directions due to mixed word order
source
def Phenomena.Ellipsis.CCG_GappingBridge.HasBackwardRaising :
Gapping.WordOrder → Prop

Can arguments type-raise to backward categories (T(T/NP))? This requires VSO/SVO verbs in the language.

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    @[implicit_reducible]
    instance Phenomena.Ellipsis.CCG_GappingBridge.instDecidablePredWordOrderHasBackwardRaising :
    DecidablePred HasBackwardRaising
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    def Phenomena.Ellipsis.CCG_GappingBridge.HasForwardRaising :
    Gapping.WordOrder → Prop

    Can arguments type-raise to forward categories (T/(T\NP))? This requires SOV/OVS verbs in the language.

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      @[implicit_reducible]
      instance Phenomena.Ellipsis.CCG_GappingBridge.instDecidablePredWordOrderHasForwardRaising :
      DecidablePred HasForwardRaising
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      def Phenomena.Ellipsis.CCG_GappingBridge.predictedGappingPattern (order : Gapping.WordOrder) :
      Gapping.GappingPattern

      Gapping direction follows from available type-raised categories.

      Forward gapping: gapped conjunct is leftward-looking (needs verb to left) -> requires backward type-raising (T(T/NP)) -> requires VSO/SVO verbs

      Backward gapping: gapped conjunct is rightward-looking (needs verb to right) -> requires forward type-raising (T/(T\NP)) -> requires SOV verbs

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        theorem Phenomena.Ellipsis.CCG_GappingBridge.ross_from_ccg_principles (order : Gapping.WordOrder) :
        ((predictedGappingPattern order).allowsForward ↔ (Gapping.rossOriginal order).allowsForward) ∧ ((predictedGappingPattern order).allowsBackward ↔ (Gapping.rossOriginal order).allowsBackward)

        Ross's generalization emerges from CCG's Principles of Consistency and Inheritance: the predicted pattern allows the same directions as Ross's original generalization.

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        theorem Phenomena.Ellipsis.CCG_GappingBridge.svo_patterns_with_vso :
        ((predictedGappingPattern Gapping.WordOrder.SVO).allowsForward ↔ (predictedGappingPattern Gapping.WordOrder.VSO).allowsForward) ∧ ((predictedGappingPattern Gapping.WordOrder.SVO).allowsBackward ↔ (predictedGappingPattern Gapping.WordOrder.VSO).allowsBackward)

        SVO patterns with VSO (forward gapping), not SOV (backward gapping): both license forward but not backward.

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        theorem Phenomena.Ellipsis.CCG_GappingBridge.no_backward_gapping_in_english :
        ¬HasForwardRaising Gapping.WordOrder.SVO

        English has no SOV verb category, so forward type-raising is not available.

        Without T/(T\NP), we cannot build a rightward-looking gapped conjunct. Hence "*Warren, potatoes and Dexter ate bread" is ungrammatical.

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        def Phenomena.Ellipsis.CCG_GappingBridge.dutchProfile :
        Gapping.WordOrderProfile

        Dutch has both VSO main verbs and SOV subordinate verbs. Therefore, Dutch licenses both type-raising directions.

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          theorem Phenomena.Ellipsis.CCG_GappingBridge.dutch_allows_both_gapping :
          (Gapping.rossRevised dutchProfile).allowsForward ∧ (Gapping.rossRevised dutchProfile).allowsBackward

          Dutch allows both forward and backward gapping.