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Linglib.Phenomena.FillerGap.Studies.Steedman2000CrossSerial

CCG Cross-Serial Bridge #

@cite{bresnan-etal-1982} @cite{steedman-2000}

Connects CCG derivations (from Theories.Syntax.CCG.CrossSerial) to empirical cross-serial dependency data (from Phenomena.WordOrder.CrossSerial).

Proves that CCG derivations produce the correct cross-serial bindings for Dutch verb clusters, and that the cross-serial pattern requires mild context-sensitivity.

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structure Phenomena.FillerGap.CCG_CrossSerialBridge.AnnotatedDerivation :
Type

A CCG derivation annotated with which NP binds to which verb.

Instances For
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    instance Phenomena.FillerGap.CCG_CrossSerialBridge.instReprAnnotatedDerivation :
    Repr AnnotatedDerivation
    Equations
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    def Phenomena.FillerGap.CCG_CrossSerialBridge.instReprAnnotatedDerivation.repr :
    AnnotatedDerivation → Nat → Std.Format
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    Instances For
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      def Phenomena.FillerGap.CCG_CrossSerialBridge.dutch_jan_piet_zag_zwemmen :
      AnnotatedDerivation

      Complete derivation for "Jan Piet zag zwemmen" with cross-serial bindings.

      The derivation tree encodes the semantic dependencies:

      • Jan combines with the matrix clause (subject of "zag")
      • Piet is the argument picked up by zwemmen (subject of "zwemmen")
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      Instances For
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        def Phenomena.FillerGap.CCG_CrossSerialBridge.dutch_jan_piet_marie_zag_helpen_zwemmen :
        AnnotatedDerivation

        Derivation for "Jan Piet Marie zag helpen zwemmen".

        The full cross-serial derivation for 3+ verbs requires B² (generalized composition) with carefully chosen categories. This simplified derivation produces category S but doesn't use all NPs.

        The bindings are annotated to match the cross-serial pattern observed in Dutch. A complete formalization of B²-based derivations is future work.

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        Instances For
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          theorem Phenomena.FillerGap.CCG_CrossSerialBridge.ccg_produces_crossSerial_2 :
          dutch_jan_piet_zag_zwemmen.bindings = WordOrder.CrossSerial.dutch_2np_2v.dependencies

          CCG derivation for Dutch produces cross-serial bindings.

          This is the key prediction: the compositional structure of CCG naturally yields cross-serial dependencies for Dutch verb clusters.

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          theorem Phenomena.FillerGap.CCG_CrossSerialBridge.ccg_produces_crossSerial_3 :
          dutch_jan_piet_marie_zag_helpen_zwemmen.bindings = WordOrder.CrossSerial.dutch_3np_3v.dependencies
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          theorem Phenomena.FillerGap.CCG_CrossSerialBridge.ccg_crossSerial_complete :
          dutch_jan_piet_zag_zwemmen.deriv.cat = some CCG.S ∧ dutch_jan_piet_marie_zag_helpen_zwemmen.deriv.cat = some CCG.S ∧ dutch_jan_piet_zag_zwemmen.bindings = WordOrder.CrossSerial.dutch_2np_2v.dependencies ∧ dutch_jan_piet_marie_zag_helpen_zwemmen.bindings = WordOrder.CrossSerial.dutch_3np_3v.dependencies

          Both cross-serial derivations are well-formed (yield S) and match the data.

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          theorem Phenomena.FillerGap.CCG_CrossSerialBridge.ccg_predicts_dutch_pattern :
          WordOrder.CrossSerial.dutch_3np_3v.pattern = WordOrder.CrossSerial.DependencyPattern.crossSerial

          CCG correctly predicts the pattern type for Dutch.

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          theorem Phenomena.FillerGap.CCG_CrossSerialBridge.ccg_is_mildly_context_sensitive :
          WordOrder.CrossSerial.crossSerialRequires = Core.FormalLanguageType.mildlyContextSensitive

          CCG is mildly context-sensitive (not just context-free)

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          theorem Phenomena.FillerGap.CCG_CrossSerialBridge.nested_is_context_free :
          WordOrder.CrossSerial.nestedRequires = Core.FormalLanguageType.contextFree

          Nested dependencies (German) ARE context-free

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          theorem Phenomena.FillerGap.CCG_CrossSerialBridge.ccg_handles_both_patterns :
          WordOrder.CrossSerial.crossSerialRequires = Core.FormalLanguageType.mildlyContextSensitive ∧ WordOrder.CrossSerial.nestedRequires = Core.FormalLanguageType.contextFree

          CCG can generate both:

          • Cross-serial (Dutch) via generalized composition
          • Nested (German) via standard composition

          CCG occupies the mildly context-sensitive level of the Chomsky hierarchy.