CCG Scope Bridge

@cite{steedman-2000}

Connects CCG scope theory (from Theories.Syntax.CCG.Scope) to empirical scope-word-order data (from Phenomena.Quantification.Bruening2001).

Proves that CCG derivation types correctly predict scope availability based on verb order (verb raising vs. verb projection raising).

def Phenomena.Quantification.CCGBridge.verbOrderToDerivationType : Bruening2001.VerbOrder → CCG.Scope.DerivationType

Map Phenomena.Quantification.Bruening2001.VerbOrder to CCG derivation type.

Equations

• Phenomena.Quantification.CCGBridge.verbOrderToDerivationType Phenomena.Quantification.Bruening2001.VerbOrder.verbRaising = CCG.Scope.DerivationType.composed
• Phenomena.Quantification.CCGBridge.verbOrderToDerivationType Phenomena.Quantification.Bruening2001.VerbOrder.verbProjectionRaising = CCG.Scope.DerivationType.directApp

def Phenomena.Quantification.CCGBridge.ScopeAvailability.toBinaryScopeAvailability : Bruening2001.ScopeAvailability → ScopeTheory.BinaryScopeAvailability

Helper to convert ScopeAvailability to BinaryScopeAvailability.

Equations

• One or more equations did not get rendered due to their size.
• Phenomena.Quantification.CCGBridge.ScopeAvailability.toBinaryScopeAvailability Phenomena.Quantification.Bruening2001.ScopeAvailability.ambiguous = ScopeTheory.BinaryScopeAvailability.ambiguous

theorem Phenomena.Quantification.CCGBridge.ccg_predicts_verb_raising_scope (vo : Bruening2001.VerbOrder) : CCG.Scope.derivationTypeToAvailability (verbOrderToDerivationType vo) = ScopeAvailability.toBinaryScopeAvailability (Bruening2001.wordOrderToAvailability vo)

CCG prediction matches observed scope availability.