DG Control/Raising Bridge: @cite{osborne-2019}

@cite{de-marneffe-nivre-2019} @cite{noonan-2007} @cite{osborne-2019}

Derivation chain from DG enhanced dependency analysis to complementation phenomena, grounded in the English Fragment lexicon.

Key Insight

In DG, control and raising verbs both take xcomp complements. The basic tree enforces unique heads, so the controlled/raised subject appears as a dependent of the matrix verb ONLY. The predicate-argument relation to the embedded verb is lost in the basic tree but recovered in the enhanced dependency graph.

Three Control Types

Type	Example	Propagation
Subject control	"John managed to sleep"	matrix nsubj → embedded nsubj
Object control	"John persuaded Mary to run"	matrix obj → embedded nsubj
Raising	"John seems to sleep"	Same structure as subject control

Derivation Chain

Fragment VerbEntry.controlType ← lexical data (manage=.subjectControl, etc.)
    ↓
DG basic tree (xcomp relation) ← subject attached to matrix verb only
    ↓
DG enhanced graph ← shared nsubj edge added
    ↓
hasUnrepresentedArg = true ← basic tree loses embedded subject
    ↓
classifyEnhancement =.controlSubject ← enhanced edge classified
    ↓
CTPDatum.hasEquiDeletion ← matches @cite{noonan-2007}'s observations

theorem DepGrammar.ControlBridge.manage_is_subject_control : Fragments.English.Predicates.Verbal.manage.controlType = Core.Verbs.ControlType.subjectControl

manage is subject control in the Fragment.

theorem DepGrammar.ControlBridge.persuade_is_object_control : Fragments.English.Predicates.Verbal.persuade.controlType = Core.Verbs.ControlType.objectControl

persuade is object control in the Fragment.

theorem DepGrammar.ControlBridge.seem_is_raising : Fragments.English.Predicates.Verbal.seem.controlType = Core.Verbs.ControlType.raising

seem is raising in the Fragment.

def DepGrammar.ControlBridge.subjControlBasic : DepTree

Basic tree: John is nsubj of manages only.

Equations

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

def DepGrammar.ControlBridge.subjControlEnhanced : DepGraph

Enhanced graph: John is also nsubj of sleep (shared dependent).

Equations

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

def DepGrammar.ControlBridge.objControlBasic : DepTree

Basic tree: Mary is obj of persuaded only.

Equations

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

def DepGrammar.ControlBridge.objControlEnhanced : DepGraph

Enhanced graph: Mary is also nsubj of run (shared dependent).

Equations

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

def DepGrammar.ControlBridge.raisingBasic : DepTree

Basic tree: John is nsubj of seems only.

Equations

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

def DepGrammar.ControlBridge.raisingEnhanced : DepGraph

Enhanced graph: John is also nsubj of sleep.

Equations

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

theorem DepGrammar.ControlBridge.subjControl_loses_embedded_subject : EnhancedDependencies.hasUnrepresentedArg subjControlBasic subjControlEnhanced 0 = true

Subject control: John (idx 0) has an unrepresented argument in the basic tree. He is semantically nsubj of sleep (3), but the tree only attaches him to manages (1).

theorem DepGrammar.ControlBridge.objControl_loses_embedded_subject : EnhancedDependencies.hasUnrepresentedArg objControlBasic objControlEnhanced 2 = true

Object control: Mary (idx 2) has an unrepresented argument in the basic tree. She is semantically nsubj of run (4), but the tree only attaches her to persuaded (1).

theorem DepGrammar.ControlBridge.raising_loses_embedded_subject : EnhancedDependencies.hasUnrepresentedArg raisingBasic raisingEnhanced 0 = true

Raising: John (idx 0) has an unrepresented argument in the basic tree. He is semantically nsubj of sleep (3), but the tree only attaches him to seems (1).

theorem DepGrammar.ControlBridge.subjControl_enhanced_recovers : subjControlEnhanced.deps.length > subjControlBasic.deps.length

Enhanced graph for subject control has more edges than basic tree.

theorem DepGrammar.ControlBridge.objControl_enhanced_recovers : objControlEnhanced.deps.length > objControlBasic.deps.length

Enhanced graph for object control has more edges than basic tree.

theorem DepGrammar.ControlBridge.raising_enhanced_recovers : raisingEnhanced.deps.length > raisingBasic.deps.length

Enhanced graph for raising has more edges than basic tree.

theorem DepGrammar.ControlBridge.subjControl_basic_is_tree : hasUniqueHeads subjControlBasic = true

Subject control basic tree IS a tree (unique heads).

theorem DepGrammar.ControlBridge.subjControl_enhanced_not_tree : hasUniqueHeads { words := subjControlEnhanced.words, deps := subjControlEnhanced.deps, rootIdx := subjControlEnhanced.rootIdx } = false

Subject control enhanced graph violates unique heads (John has two nsubj edges).

theorem DepGrammar.ControlBridge.objControl_basic_is_tree : hasUniqueHeads objControlBasic = true

Object control basic tree IS a tree.

theorem DepGrammar.ControlBridge.objControl_enhanced_not_tree : hasUniqueHeads { words := objControlEnhanced.words, deps := objControlEnhanced.deps, rootIdx := objControlEnhanced.rootIdx } = false

Object control enhanced graph violates unique heads (Mary has two incoming edges).

theorem DepGrammar.ControlBridge.subjControl_classified : EnhancedDependencies.classifyEnhancement subjControlBasic.deps { headIdx := 3, depIdx := 0, depType := UD.DepRel.nsubj } = some EnhancedDependencies.EnhancementType.controlSubject

Subject control enhanced edge is classified as controlSubject.

theorem DepGrammar.ControlBridge.objControl_classified : EnhancedDependencies.classifyEnhancement objControlBasic.deps { headIdx := 4, depIdx := 2, depType := UD.DepRel.nsubj } = some EnhancedDependencies.EnhancementType.controlSubject

Object control enhanced edge is classified as controlSubject. Even though the controller is the matrix OBJ (Mary), the enhanced edge is an nsubj relation → classified as controlSubject.

theorem DepGrammar.ControlBridge.raising_classified : EnhancedDependencies.classifyEnhancement raisingBasic.deps { headIdx := 3, depIdx := 0, depType := UD.DepRel.nsubj } = some EnhancedDependencies.EnhancementType.controlSubject

Raising enhanced edge is classified as controlSubject. Structurally identical to subject control — the DG tree doesn't distinguish control from raising. The distinction is semantic (theta role assignment, captured in Fragment controlType).

theorem DepGrammar.ControlBridge.control_raising_same_deps : subjControlBasic.deps = raisingBasic.deps

Subject control and raising produce structurally identical basic trees. (Same word positions, same dependency relations — only the words differ.)

theorem DepGrammar.ControlBridge.control_raising_same_enhancement : subjControlEnhanced.deps.length = raisingEnhanced.deps.length

Both produce the same enhanced edge pattern.

theorem DepGrammar.ControlBridge.control_predicts_equi_deletion : Fragments.English.Predicates.Verbal.manage.controlType = Core.Verbs.ControlType.subjectControl ∧ Fragments.English.Predicates.Verbal.persuade.controlType = Core.Verbs.ControlType.objectControl ∧ Fragments.English.Predicates.Verbal.want.controlType = Core.Verbs.ControlType.subjectControl ∧ Fragments.English.Predicates.Verbal.hope.altControlType = Core.Verbs.ControlType.subjectControl ∧ Fragments.English.Predicates.Verbal.stop.controlType = Core.Verbs.ControlType.subjectControl ∧ Fragments.English.Predicates.Verbal.start.controlType = Core.Verbs.ControlType.subjectControl ∧ Fragments.English.Predicates.Verbal.continue_.controlType = Core.Verbs.ControlType.subjectControl ∧ Phenomena.Complementation.Typology.english_manage.hasEquiDeletion = true ∧ Phenomena.Complementation.Typology.english_persuade.hasEquiDeletion = true ∧ Phenomena.Complementation.Typology.english_want.hasEquiDeletion = true ∧ Phenomena.Complementation.Typology.english_hope.hasEquiDeletion = true ∧ Phenomena.Complementation.Typology.english_stop.hasEquiDeletion = true ∧ Phenomena.Complementation.Typology.english_start.hasEquiDeletion = true ∧ Phenomena.Complementation.Typology.english_continue.hasEquiDeletion = true

Control verbs in the Fragment have corresponding CTPDatum entries with hasEquiDeletion = true (@cite{noonan-2007} §2.1).

This connects three independently specified data sources:

1. Fragment controlType / altControlType (lexical annotation)
2. DG enhanced dependencies (structural analysis)
3. CTPDatum hasEquiDeletion (typological observation)

Note: "hope" has complementType =.finiteClause (primary frame) but altComplementType =.infinitival with altControlType =.subjectControl. The equi-deletion corresponds to the infinitival frame.

theorem DepGrammar.ControlBridge.seem_is_raising_not_ctp : Fragments.English.Predicates.Verbal.seem.controlType = Core.Verbs.ControlType.raising

The raising verb "seem" is NOT marked for equi-deletion in the typology. seem does not appear in allEnglishCTPData — it's a purely syntactic phenomenon, not a CTP in Noonan's semantic classification.

theorem DepGrammar.ControlBridge.control_derivation_chain : Fragments.English.Predicates.Verbal.manage.controlType = Core.Verbs.ControlType.subjectControl ∧ hasUniqueHeads subjControlBasic = true ∧ EnhancedDependencies.hasUnrepresentedArg subjControlBasic subjControlEnhanced 0 = true ∧ subjControlEnhanced.deps.length > subjControlBasic.deps.length ∧ EnhancedDependencies.classifyEnhancement subjControlBasic.deps { headIdx := 3, depIdx := 0, depType := UD.DepRel.nsubj } = some EnhancedDependencies.EnhancementType.controlSubject ∧ Phenomena.Complementation.Typology.english_manage.hasEquiDeletion = true

Full control derivation chain: from Fragment lexicon through DG enhanced dependency analysis to complementation typology.

1. Fragment manage.controlType =.subjectControl ✓
2. Basic tree attaches John to manages only ✓
3. Basic tree LOSES John as argument of sleep ✓
4. Enhanced graph RECOVERS John as nsubj of sleep ✓
5. Enhanced edge classified as controlSubject ✓
6. CTPDatum english_manage.hasEquiDeletion = true ✓

The chain is cumulative: changing manage's controlType in the Fragment breaks the grounding theorem; changing the tree structure breaks the information-loss proof; changing the CTPDatum breaks the bridge.

theorem DepGrammar.ControlBridge.object_control_derivation_chain : Fragments.English.Predicates.Verbal.persuade.controlType = Core.Verbs.ControlType.objectControl ∧ hasUniqueHeads objControlBasic = true ∧ EnhancedDependencies.hasUnrepresentedArg objControlBasic objControlEnhanced 2 = true ∧ objControlEnhanced.deps.length > objControlBasic.deps.length ∧ EnhancedDependencies.classifyEnhancement objControlBasic.deps { headIdx := 4, depIdx := 2, depType := UD.DepRel.nsubj } = some EnhancedDependencies.EnhancementType.controlSubject ∧ Phenomena.Complementation.Typology.english_persuade.hasEquiDeletion = true

Full object control derivation chain: persuade variant.

1. Fragment persuade.controlType =.objectControl ✓
2. Basic tree attaches Mary to persuaded only ✓
3. Basic tree LOSES Mary as argument of run ✓
4. Enhanced graph RECOVERS Mary as nsubj of run ✓
5. Enhanced edge classified as controlSubject ✓
6. CTPDatum english_persuade.hasEquiDeletion = true ✓