DG Valency Bridge: @cite{osborne-2019}

@cite{tesniere-1959}

Full derivation chain from DG valency theory to argument structure phenomena, grounded in the English Fragment lexicon.

Three-Way Connection

Fragments/English/Predicates/Verbal (complementType → valence)
    ↓ ↑
DG ArgStr / LexRule / checkVerbSubcat ↔ Phenomena/ArgumentStructure data

Verb valence is DERIVED from each Fragment entry's complementType field via complementToValence, 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)
    ↓ complementToValence
VerbEntry.toWord3sg.features.valence ← intransitive / transitive / ditransitive
    ↓
DepTree instances ← concrete parse trees
    ↓
satisfiesArgStr (ArgStr frames) ← frame satisfaction
    ↓
checkVerbSubcat ← subcategorization verification
    ↓
passiveRule (LexRule) ← valency change derivation
    ↓
isCatena / isConstituent ← structural analysis (Ch 4)
    ↓
Phenomena data match ← grammaticality predictions

theorem Osborne2019.sleep_valence_from_fragment : Osborne2019.sleeps✝.features.valence = some Valence.intransitive

sleep.complementType =.none → intransitive.

theorem Osborne2019.devour_valence_from_fragment : Osborne2019.devours✝.features.valence = some Valence.transitive

devour.complementType =.np → transitive.

theorem Osborne2019.give_valence_from_fragment : Osborne2019.gives✝.features.valence = some Valence.ditransitive

give.complementType =.np_np → ditransitive.

theorem Osborne2019.kick_valence_from_fragment : Osborne2019.kicked✝.features.valence = some Valence.transitive

kick.complementType =.np → transitive (active).

theorem Osborne2019.passive_valence_consistent : Osborne2019.kicked_pass✝.features.valence = some Valence.intransitive ∧ Osborne2019.kicked✝.features.valence = some Valence.transitive ∧ 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 valence (intransitive) is consistent with the passive rule: the rule removes the obj slot from the transitive frame.

def Osborne2019.intransTree : DepGrammar.DepTree

"John sleeps" — intransitive, no object. Matches Subcategorization.data pair 1.

Equations

• Osborne2019.intransTree = DepGrammar.mkSVTree Osborne2019.john✝ Osborne2019.sleeps✝

def Osborne2019.transTree : DepGrammar.DepTree

"John devours pizza" — transitive with object. Matches Subcategorization.data pair 3.

Equations

• Osborne2019.transTree = DepGrammar.mkSVOTree Osborne2019.john✝ Osborne2019.devours✝ Osborne2019.pizza✝

def Osborne2019.ditransTree : DepGrammar.DepTree

"John gives Mary book" — ditransitive with two objects. Matches Subcategorization.data pair 5.

Equations

• Osborne2019.ditransTree = DepGrammar.mkDitransTree Osborne2019.john✝ Osborne2019.gives✝ Osborne2019.mary✝ Osborne2019.book✝

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. Matches Passive.data pair 1.

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. Matches Subcategorization.data pair 1.

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. Matches Subcategorization.data pair 3.

Equations

• Osborne2019.trans_no_obj = DepGrammar.mkSVTree Osborne2019.john✝ Osborne2019.devours✝

def Osborne2019.ditrans_no_obj : DepGrammar.DepTree

"*John gives Mary" — ditransitive missing direct object. Matches Subcategorization.data pair 5.

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. Matches Passive.data pair 1.

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 : Osborne2019.kicked✝.features.valence = some Valence.transitive ∧ 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 → valence = transitive
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_data_match : 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 match all data pairs in Phenomena.ArgumentStructure.Subcategorization.data:

Data pair	Grammatical	Ungrammatical	Valence
1	"John sleeps"	"*John sleeps book"	intransitive
3	"John devours pizza"	"*John devours"	transitive
5	"John gives Mary …"	"*John gives Mary"	ditransitive

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

DG passive predictions match Phenomena.ArgumentStructure.Passive.data:

Data pair	Grammatical	Ungrammatical
1	"the ball was kicked"	"*the ball was kicked the ball"