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Linglib.Theories.Syntax.CCG.Gapping

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def CCG.Gapping.GappedTV :
Cat

Category for a gapped subject+object cluster (e.g., "Warren, potatoes").

This is built by:

  1. Type-raising each NP: NP → T(T/NP)
  2. Backward composing: T(T/NP₁) ∘ T(T/NP₂) → T((T/NP₂)/NP₁)

The result needs a VSO transitive verb ((S/NP)/NP) to its LEFT.

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    def CCG.Gapping.GappedSubj :
    Cat

    Category for a gapped subject alone (stripping: "and Warren (too)").

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      def CCG.Gapping.BackwardRaisedNP :
      Cat

      Backward type-raised NP (for SVO/VSO gapping). T(T/NP) - combines with verbs to the LEFT.

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        def CCG.Gapping.ForwardRaisedNP :
        Cat

        Forward type-raised NP (for SOV argument clusters). T/(T\NP) - combines with verbs to the RIGHT.

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          def CCG.Gapping.BackwardGappedTV :
          Cat

          The potential backward-gapped conjunct would need category S/((S\NP)/NP). But this requires forward composition of forward type-raised NPs. English doesn't license T/(T\NP) categories.

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            theorem CCG.Gapping.inheritance_determines_gapping :
            GappedTV = S.lslash ((S.rslash NP).rslash NP)

            The Principle of Inheritance ensures composed functions inherit directionality.

            When we backward-compose two T(T/NP) categories: T(T/NP₁) ∘ T(T/NP₂) → T((T/NP₂)/NP₁)

            The result is still leftward-looking (backslash on top). Hence it can only combine with a verb to its left.

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            theorem CCG.Gapping.gapped_tv_is_leftward :
            match GappedTV with | a.lslash a_1 => true = true | x => false = true

            The gapped conjunct S((S/NP)/NP) is leftward-looking.

            The backslash on the outside means it seeks an argument to its left. Forward gapping (verb left, gap right) works in SVO for this reason.

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            theorem CCG.Gapping.backward_gapped_tv_is_rightward :
            match BackwardGappedTV with | a.rslash a_1 => true = true | x => false = true

            The backward-gapped conjunct S/((S\NP)/NP) would be rightward-looking.

            The slash on the outside means it seeks an argument to its right. This would require backward gapping (gap LEFT, verb RIGHT). But SVO doesn't license this category.

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            def CCG.Gapping.strippingCategory :
            Cat

            Stripping is gapping with a single remnant.

            "Dexter ran away, and Warren (too)" Warren = S(S/NP)

            This is just a type-raised subject coordinating with a decomposed sentence.

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              theorem CCG.Gapping.stripping_has_correct_category :
              strippingCategory = GappedSubj
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              theorem CCG.Gapping.stripping_same_constraints_as_gapping :
              GappedSubj = BackwardRaisedNP

              Stripping shares the same word-order constraints as gapping. This is because both use the same type-raised categories.