DG Valency Bridge: [Osb19]

[Tes59]

Full derivation chain from DG valency theory to subcategorization and passive contrasts, grounded in the English Fragment lexicon.

Each verb's DG frame is DERIVED from its Fragment entry's complementType field via complementToArgStr, not stipulated independently. The DG analysis then verifies that trees built with these Fragment-derived words satisfy the corresponding valency frames.

Derivation Chain

Fragment VerbEntry.complementType ← lexical data (sleep=.none, kick=.np, give=.np_np)
    ↓ complementToArgStr
ArgStr frames (argStr_V0/VN/VNN) → DepTree.frames premises
    ↓
DepTree instances ← concrete parse trees
    ↓
satisfiesArgStr / checkVerbSubcat ← frame satisfaction + subcat verification
    ↓
passiveRule (LexRule) ← valency change derivation
    ↓
isCatena / isConstituent ← structural analysis (Ch 4)
    ↓
grammaticality contrasts ← predictions for the example sentences

theorem Osborne2019.sleep_frame_from_fragment : DepGrammar.complementToArgStr English.Predicates.Verbal.sleep.complementType = some DepGrammar.argStr_V0

sleep.complementType =.none → intransitive frame (V0).

theorem Osborne2019.devour_frame_from_fragment : DepGrammar.complementToArgStr English.Predicates.Verbal.devour.complementType = some DepGrammar.argStr_VN

devour.complementType =.np → transitive frame (VN).

theorem Osborne2019.give_frame_from_fragment : DepGrammar.complementToArgStr English.Predicates.Verbal.give.complementType = some DepGrammar.argStr_VNN

give.complementType =.np_np → ditransitive frame (VNN).

theorem Osborne2019.kick_frame_from_fragment : DepGrammar.complementToArgStr English.Predicates.Verbal.kick.complementType = some DepGrammar.argStr_VN

kick.complementType =.np → transitive frame (VN, active).

theorem Osborne2019.passive_valence_consistent : DepGrammar.complementToArgStr English.Predicates.Verbal.kick.complementType = some DepGrammar.argStr_VN ∧ WordGrammar.passiveRule.applies Osborne2019.lex_kicked✝ = true ∧ ((WordGrammar.passiveRule.transform Osborne2019.lex_kicked✝).argStr.slots.any fun (x : DepGrammar.ArgSlot) => x.depType == UD.DepRel.obj) = false

The passive frame carried on passiveTree.frames is consistent with the passive rule: the rule removes the obj slot from kick's transitive frame.

def Osborne2019.intransTree : DepGrammar.DepTree

"John sleeps" — intransitive, no object.

Equations

• Osborne2019.intransTree = DepGrammar.mkSVTree Osborne2019.john✝ Osborne2019.sleeps✝ (DepGrammar.complementToArgStr English.Predicates.Verbal.sleep.complementType)

def Osborne2019.transTree : DepGrammar.DepTree

"John devours pizza" — transitive with object.

Equations

• Osborne2019.transTree = DepGrammar.mkSVOTree Osborne2019.john✝ Osborne2019.devours✝ Osborne2019.pizza✝ (DepGrammar.complementToArgStr English.Predicates.Verbal.devour.complementType)

def Osborne2019.ditransTree : DepGrammar.DepTree

"John gives Mary book" — ditransitive with two objects.

Equations

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

def Osborne2019.activeTree : DepGrammar.DepTree

"John kicked the ball" — active transitive (for passive derivation).

Equations

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

def Osborne2019.passiveTree : DepGrammar.DepTree

"The ball was kicked" — short passive; the passive analysis derives argStr_VPassive from kick's transitive frame (passive_frame_matches).

Equations

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

def Osborne2019.longPassiveTree : DepGrammar.DepTree

"The ball was kicked by John" — long passive with agent by-phrase.

Equations

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

def Osborne2019.intrans_with_obj : DepGrammar.DepTree

"*John sleeps book" — intransitive with spurious object.

Equations

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

def Osborne2019.trans_no_obj : DepGrammar.DepTree

"*John devours" — transitive missing required object.

Equations

• Osborne2019.trans_no_obj = DepGrammar.mkSVTree Osborne2019.john✝ Osborne2019.devours✝ (DepGrammar.complementToArgStr English.Predicates.Verbal.devour.complementType)

def Osborne2019.ditrans_no_obj : DepGrammar.DepTree

"*John gives Mary" — ditransitive missing direct object.

Equations

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

def Osborne2019.passive_with_obj : DepGrammar.DepTree

"*The ball was kicked the ball" — passive with spurious object.

Equations

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

theorem Osborne2019.intrans_satisfies_V0 : DepGrammar.satisfiesArgStr intransTree 1 DepGrammar.argStr_V0 = true

Intransitive tree satisfies intransitive frame (V0).

theorem Osborne2019.trans_satisfies_VN : DepGrammar.satisfiesArgStr transTree 1 DepGrammar.argStr_VN = true

Transitive tree satisfies transitive frame (VN).

theorem Osborne2019.ditrans_satisfies_VNN : DepGrammar.satisfiesArgStr ditransTree 1 DepGrammar.argStr_VNN = true

Ditransitive tree satisfies ditransitive frame (VNN).

theorem Osborne2019.intrans_not_VN : DepGrammar.satisfiesArgStr intransTree 1 DepGrammar.argStr_VN = false

Intransitive tree does NOT satisfy transitive frame (missing obj).

theorem Osborne2019.trans_noobj_not_VN : DepGrammar.satisfiesArgStr trans_no_obj 1 DepGrammar.argStr_VN = false

Transitive-minus-object tree does NOT satisfy transitive frame.

theorem Osborne2019.intrans_subcat_ok : DepGrammar.checkVerbSubcat intransTree = true

theorem Osborne2019.trans_subcat_ok : DepGrammar.checkVerbSubcat transTree = true

theorem Osborne2019.ditrans_subcat_ok : DepGrammar.checkVerbSubcat ditransTree = true

theorem Osborne2019.intrans_obj_subcat_fail : DepGrammar.checkVerbSubcat intrans_with_obj = false

theorem Osborne2019.trans_noobj_subcat_fail : DepGrammar.checkVerbSubcat trans_no_obj = false

theorem Osborne2019.ditrans_noobj_subcat_fail : DepGrammar.checkVerbSubcat ditrans_no_obj = false

theorem Osborne2019.passive_applies_to_kicked : WordGrammar.passiveRule.applies Osborne2019.lex_kicked✝ = true

The passive rule applies to transitive "kicked".

theorem Osborne2019.passive_removes_obj_adds_obl : ((WordGrammar.passiveRule.transform Osborne2019.lex_kicked✝).argStr.slots.any fun (x : DepGrammar.ArgSlot) => x.depType == UD.DepRel.obj) = false ∧ ((WordGrammar.passiveRule.transform Osborne2019.lex_kicked✝).argStr.slots.any fun (x : DepGrammar.ArgSlot) => x.depType == UD.DepRel.obl) = true

The derived entry removes the obj slot and adds optional obl.

theorem Osborne2019.passive_frame_matches : (WordGrammar.passiveRule.transform Osborne2019.lex_kicked✝).argStr.slots = DepGrammar.argStr_VPassive.slots

The passive rule output matches argStr_VPassive.

theorem Osborne2019.passive_subcat_ok : DepGrammar.checkVerbSubcat passiveTree = true

theorem Osborne2019.long_passive_subcat_ok : DepGrammar.checkVerbSubcat longPassiveTree = true

theorem Osborne2019.passive_obj_subcat_fail : DepGrammar.checkVerbSubcat passive_with_obj = false

theorem Osborne2019.passive_satisfies_VPassive : DepGrammar.satisfiesArgStr passiveTree 3 DepGrammar.argStr_VPassive = true

theorem Osborne2019.long_passive_satisfies_VPassive : DepGrammar.satisfiesArgStr longPassiveTree 3 DepGrammar.argStr_VPassive = true

theorem Osborne2019.svo_complete_is_constituent : DepGrammar.Catena.isConstituent transTree.deps 3 [0, 1, 2] = true

SVO tree: verb + all args {0, 1, 2} is a constituent (complete subtree).

theorem Osborne2019.svo_verb_subj_is_catena : DepGrammar.Catena.isCatena transTree.deps [0, 1] = true

SVO tree: verb + subject {0, 1} is a catena (connected via nsubj).

theorem Osborne2019.svo_verb_subj_not_constituent : DepGrammar.Catena.isConstituent transTree.deps 3 [0, 1] = false

SVO tree: verb + subject {0, 1} is NOT a constituent (missing obj).

theorem Osborne2019.ditrans_complete_is_constituent : DepGrammar.Catena.isConstituent ditransTree.deps 4 [0, 1, 2, 3] = true

Ditransitive: verb + all args {0, 1, 2, 3} is a constituent.

theorem Osborne2019.ditrans_verb_obj_catena_not_constituent : DepGrammar.Catena.isCatena ditransTree.deps [1, 3] = true ∧ DepGrammar.Catena.isConstituent ditransTree.deps 4 [1, 3] = false

Ditransitive: verb + just obj {1, 3} is a catena but not constituent.

theorem Osborne2019.valency_derivation_chain : DepGrammar.complementToArgStr English.Predicates.Verbal.kick.complementType = some DepGrammar.argStr_VN ∧ DepGrammar.satisfiesArgStr activeTree 1 DepGrammar.argStr_VN = true ∧ DepGrammar.checkVerbSubcat activeTree = true ∧ WordGrammar.passiveRule.applies Osborne2019.lex_kicked✝ = true ∧ ((WordGrammar.passiveRule.transform Osborne2019.lex_kicked✝).argStr.slots.any fun (x : DepGrammar.ArgSlot) => x.depType == UD.DepRel.obj) = false ∧ DepGrammar.satisfiesArgStr passiveTree 3 DepGrammar.argStr_VPassive = true ∧ DepGrammar.checkVerbSubcat passiveTree = true ∧ DepGrammar.checkVerbSubcat passive_with_obj = false

Full valency derivation chain: from Fragment lexicon through DG theory to grammaticality predictions.

1. Fragment kick.complementType =.np → transitive frame (argStr_VN)
2. Active tree satisfies transitive frame (argStr_VN) ✓
3. checkVerbSubcat validates the active tree ✓
4. Passive rule applies and removes obj slot ✓
5. Passive tree satisfies derived frame (argStr_VPassive) ✓
6. checkVerbSubcat validates the passive tree ✓
7. Passive + spurious obj correctly rejected ✗

theorem Osborne2019.subcategorization_contrasts : DepGrammar.checkVerbSubcat intransTree = true ∧ DepGrammar.checkVerbSubcat intrans_with_obj = false ∧ DepGrammar.checkVerbSubcat transTree = true ∧ DepGrammar.checkVerbSubcat trans_no_obj = false ∧ DepGrammar.checkVerbSubcat ditransTree = true ∧ DepGrammar.checkVerbSubcat ditrans_no_obj = false

DG subcategorization predictions capture the textbook contrasts:

Grammatical	Ungrammatical	Frame
"John sleeps"	"*John sleeps book"	argStr_V0
"John devours pizza"	"*John devours"	argStr_VN
"John gives Mary …"	"*John gives Mary"	argStr_VNN

theorem Osborne2019.passive_contrasts : DepGrammar.checkVerbSubcat passiveTree = true ∧ DepGrammar.checkVerbSubcat passive_with_obj = false

DG passive prediction captures the contrast "the ball was kicked" / "*the ball was kicked the ball".