Bridge: Minimalist Scope Theory to Quantification Phenomena

Connects Minimalist QR/Scope Economy theory to empirical scope freezing data in Phenomena.Quantification.Data.

Main results

• analyzeFreezingContext: Maps freezing contexts to QR barriers
• predictsFreezing: Minimalist predictions for each context
• possessor_freezes_scope, double_object_freezes_scope, etc.: Verification theorems
• configFromExample, predictAvailability, correctlyPredicts: Per-datum predictions

Superiority from C-Command

Double-object scope freezing is derived from asymmetric c-command in @cite{pylkknen-2008}'s Voice + low-Appl tree (ditransitiveTree), where the goal asymmetrically c-commands the theme.

def Phenomena.Quantification.MinimalismBridge.analyzeFreezingContext : Data.FreezingContext → Option Minimalism.Phenomena.Scope.QRBarrier

Analyze why a freezing context blocks inverse scope in Minimalism.

Equations

• Phenomena.Quantification.MinimalismBridge.analyzeFreezingContext Phenomena.Quantification.Data.FreezingContext.none = none
• Phenomena.Quantification.MinimalismBridge.analyzeFreezingContext Phenomena.Quantification.Data.FreezingContext.possessor = some Minimalism.Phenomena.Scope.QRBarrier.dpPhase
• Phenomena.Quantification.MinimalismBridge.analyzeFreezingContext Phenomena.Quantification.Data.FreezingContext.doubleObject = some Minimalism.Phenomena.Scope.QRBarrier.superiority
• Phenomena.Quantification.MinimalismBridge.analyzeFreezingContext Phenomena.Quantification.Data.FreezingContext.passive = some Minimalism.Phenomena.Scope.QRBarrier.adjunctIsland
• Phenomena.Quantification.MinimalismBridge.analyzeFreezingContext Phenomena.Quantification.Data.FreezingContext.heavyNP = none
• Phenomena.Quantification.MinimalismBridge.analyzeFreezingContext Phenomena.Quantification.Data.FreezingContext.weakCrossover = none
• Phenomena.Quantification.MinimalismBridge.analyzeFreezingContext Phenomena.Quantification.Data.FreezingContext.adjunct = some Minimalism.Phenomena.Scope.QRBarrier.adjunctIsland
• Phenomena.Quantification.MinimalismBridge.analyzeFreezingContext Phenomena.Quantification.Data.FreezingContext.attitude = some Minimalism.Phenomena.Scope.QRBarrier.clauseBoundary

def Phenomena.Quantification.MinimalismBridge.predictsFreezing (ctx : Data.FreezingContext) : Bool

Does Minimalism predict freezing for this context?

Equations

• Phenomena.Quantification.MinimalismBridge.predictsFreezing ctx = (Phenomena.Quantification.MinimalismBridge.analyzeFreezingContext ctx).isSome

structure Phenomena.Quantification.MinimalismBridge.MinimalistScopeConfig : Type

Minimalist representation of a scope configuration.

• q1 : Minimalism.Phenomena.Scope.PositionedQuantifier

  Higher quantifier (typically subject)

• q2 : Minimalism.Phenomena.Scope.PositionedQuantifier

  Lower quantifier (typically object)

• freezingContext : Data.FreezingContext

  Freezing context if any

• tree : Option Minimalism.SyntacticObject

  The tree in which q1 and q2 are positioned. When provided, superiority is derived from c-command rather than stipulated.

instance Phenomena.Quantification.MinimalismBridge.instReprMinimalistScopeConfig : Repr MinimalistScopeConfig

Equations

• Phenomena.Quantification.MinimalismBridge.instReprMinimalistScopeConfig = { reprPrec := Phenomena.Quantification.MinimalismBridge.instReprMinimalistScopeConfig.repr }

def Phenomena.Quantification.MinimalismBridge.instReprMinimalistScopeConfig.repr : MinimalistScopeConfig → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Quantification.MinimalismBridge.superiorityBlocked (config : MinimalistScopeConfig) : Bool

Check if superiority blocks QR in this configuration.

When a tree and SO positions are provided, superiority is DERIVED from asymmetric c-command. Otherwise falls back to the freezing context annotation.

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Quantification.MinimalismBridge.availableReadings (config : MinimalistScopeConfig) : Data.Availability

Compute available scope readings in Minimalism

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Quantification.MinimalismBridge.configFromExample (ex : Data.Example) : MinimalistScopeConfig

Build config from a freezing example (fallback path — no tree).

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Quantification.MinimalismBridge.predictAvailability (ex : Data.Example) : Data.Availability

Minimalism's prediction for an example

Equations

• Phenomena.Quantification.MinimalismBridge.predictAvailability ex = Phenomena.Quantification.MinimalismBridge.availableReadings (Phenomena.Quantification.MinimalismBridge.configFromExample ex)

def Phenomena.Quantification.MinimalismBridge.correctlyPredicts (ex : Data.Example) : Bool

Check if Minimalism correctly predicts the example

Equations

• Phenomena.Quantification.MinimalismBridge.correctlyPredicts ex = (Phenomena.Quantification.MinimalismBridge.predictAvailability ex == ex.observed)

theorem Phenomena.Quantification.MinimalismBridge.possessor_freezes_scope : predictsFreezing Data.FreezingContext.possessor = true

Possessor freezing follows from DP being a phase

theorem Phenomena.Quantification.MinimalismBridge.double_object_freezes_scope : predictsFreezing Data.FreezingContext.doubleObject = true

Double object freezing follows from superiority

theorem Phenomena.Quantification.MinimalismBridge.passive_freezes_scope : predictsFreezing Data.FreezingContext.passive = true

Passive freezing follows from adjunct island

theorem Phenomena.Quantification.MinimalismBridge.heavy_np_not_grammatically_frozen : predictsFreezing Data.FreezingContext.heavyNP = false

Heavy NP is NOT predicted to freeze (it's processing)

theorem Phenomena.Quantification.MinimalismBridge.baseline_is_ambiguous : predictsFreezing Data.FreezingContext.none = false

Baseline (no context) is predicted ambiguous

Superiority derived from c-command

@cite{pylkknen-2008}'s low-Appl tree (ditransitiveTree) produces the DOC structure where V takes ApplP as complement, so the goal in Spec-ApplP asymmetrically c-commands the theme in complement of Appl. QR of the theme over the goal is blocked by superiority, derived from c-command rather than stipulated.

def Phenomena.Quantification.MinimalismBridge.docScopeConfig : MinimalistScopeConfig

DOC scope freezing config with @cite{pylkknen-2008}'s tree: superiority is derived from goal asymmetrically c-commanding theme in the Voice + low-Appl structure.

Equations

• One or more equations did not get rendered due to their size.

theorem Phenomena.Quantification.MinimalismBridge.doc_superiority_from_tree : superiorityBlocked docScopeConfig = true

Superiority in the DOC is DERIVED from c-command in @cite{pylkknen-2008}'s tree: goal (Mary) asymmetrically c-commands theme (a letter) via low Appl, so QR of theme over goal is blocked.

Summary

Freezing Explanations

Context	Minimalist Explanation
Possessor	DP phase blocks QR
Double object	Superiority: goal c-commands theme (@cite{pylkknen-2008} tree)
Passive	Adjunct island
Heavy NP	NOT grammatical (processing)
Attitude	Clause boundary