Ellipsis as Catena-Targeting

@cite{osborne-2019} @cite{osborne-gross-2012}

Formalizes @cite{osborne-2019}'s thesis: ellipsis targets catenae, not constituents. This is the primary empirical motivation for the catena concept — it explains why VP ellipsis, gapping, pseudogapping, sluicing, stripping, and fragment answers all elide connected-but-not-necessarily-complete-subtree material.

Key Insight

In DG, the "VP" is NOT a complete subtree (constituent) because the verb's subject is also its dependent. This means even VP ellipsis targets a catena, not a constituent — making catenae essential.

Bridges

• → Catena.lean: uses isCatena, isConstituent for proofs

inductive DepGrammar.Ellipsis.EllipsisType : Type

Ellipsis types in English (@cite{osborne-2019}, Ch 12–13).

• vpEllipsis : EllipsisType
• gapping : EllipsisType
• pseudogapping : EllipsisType
• stripping : EllipsisType
• sluicing : EllipsisType
• fragmentAnswer : EllipsisType

instance DepGrammar.Ellipsis.instReprEllipsisType : Repr EllipsisType

Equations

• DepGrammar.Ellipsis.instReprEllipsisType = { reprPrec := DepGrammar.Ellipsis.instReprEllipsisType.repr }

def DepGrammar.Ellipsis.instReprEllipsisType.repr : EllipsisType → ℕ → Std.Format

Equations

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

instance DepGrammar.Ellipsis.instDecidableEqEllipsisType : DecidableEq EllipsisType

Equations

• DepGrammar.Ellipsis.instDecidableEqEllipsisType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def DepGrammar.Ellipsis.vpEllipsisTree : DepTree

VP Ellipsis: "She will cook dinner, and he will too" Pre-ellipsis second clause: cook(0) → he(1:nsubj), will(2:aux), dinner(3:obj). Elided = {0, 3} (cook + dinner): connected via obj → catena. Subtree of cook = {0,1,2,3} ≠ {0,3} → NOT constituent. @cite{osborne-2019}.

Equations

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

def DepGrammar.Ellipsis.vpEllipsisElided : List ℕ

Elided nodes in VP ellipsis: {cook, dinner} = {0, 3}.

Equations

• DepGrammar.Ellipsis.vpEllipsisElided = [0, 3]

def DepGrammar.Ellipsis.gappingTree : DepTree

Gapping: "Fred eats beans and Jim rice" Pre-ellipsis second clause: eats(0) → Jim(1:nsubj), rice(2:obj). Elided = {0} (eats only): singleton → catena. Subtree of eats = {0,1,2} ≠ {0} → NOT constituent. @cite{osborne-2019}.

Equations

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

def DepGrammar.Ellipsis.gappingElided : List ℕ

Elided nodes in gapping: {eats} = {0}.

Equations

• DepGrammar.Ellipsis.gappingElided = [0]

def DepGrammar.Ellipsis.pseudogappingTree : DepTree

Pseudogapping: "She has helped him, and he has her too" Pre-ellipsis: helped(0) → he(1:nsubj), has(2:aux), her(3:obj), too(4:advmod). Elided = {0} (helped only): singleton → catena, NOT constituent. @cite{osborne-2019}.

Equations

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

def DepGrammar.Ellipsis.pseudogappingElided : List ℕ

Elided nodes in pseudogapping: {helped} = {0}.

Equations

• DepGrammar.Ellipsis.pseudogappingElided = [0]

def DepGrammar.Ellipsis.sluicingTree : DepTree

Sluicing: "She helped someone, but I don't know who" Embedded clause (pre-ellipsis): helped(0) → she(1:nsubj), someone(2:obj). Elided = {0, 1} (helped + she): connected via nsubj → catena. Subtree of helped = {0,1,2} ≠ {0,1} → NOT constituent. @cite{osborne-2019}.

Equations

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

def DepGrammar.Ellipsis.sluicingElided : List ℕ

Elided nodes in sluicing: {helped, she} = {0, 1}.

Equations

• DepGrammar.Ellipsis.sluicingElided = [0, 1]

def DepGrammar.Ellipsis.fragmentTree : DepTree

Fragment answer: "Who helped? — Him." Full answer: helped(0) → him(1:obj). Elided = {0} (helped): singleton → catena, NOT constituent. @cite{osborne-2019}.

Equations

• DepGrammar.Ellipsis.fragmentTree = { words := [Word.mk' "helped" UD.UPOS.VERB, Word.mk' "him" UD.UPOS.PRON], deps := [{ headIdx := 0, depIdx := 1, depType := UD.DepRel.obj }], rootIdx := 0 }

def DepGrammar.Ellipsis.fragmentElided : List ℕ

Elided nodes in fragment answer: {helped} = {0}.

Equations

• DepGrammar.Ellipsis.fragmentElided = [0]

theorem DepGrammar.Ellipsis.vpEllipsis_elided_is_catena : Catena.isCatena vpEllipsisTree.deps vpEllipsisElided = true

VP ellipsis elided material is a catena.

theorem DepGrammar.Ellipsis.vpEllipsis_elided_not_constituent : Catena.isConstituent vpEllipsisTree.deps 4 vpEllipsisElided = false

VP ellipsis elided material is NOT a constituent (not a complete subtree).

theorem DepGrammar.Ellipsis.gapping_elided_is_catena : Catena.isCatena gappingTree.deps gappingElided = true

Gapping elided material is a catena.

theorem DepGrammar.Ellipsis.gapping_elided_not_constituent : Catena.isConstituent gappingTree.deps 3 gappingElided = false

Gapping elided material is NOT a constituent.

theorem DepGrammar.Ellipsis.pseudogapping_elided_is_catena : Catena.isCatena pseudogappingTree.deps pseudogappingElided = true

Pseudogapping elided material is a catena.

theorem DepGrammar.Ellipsis.pseudogapping_elided_not_constituent : Catena.isConstituent pseudogappingTree.deps 5 pseudogappingElided = false

Pseudogapping elided material is NOT a constituent.

theorem DepGrammar.Ellipsis.sluicing_elided_is_catena : Catena.isCatena sluicingTree.deps sluicingElided = true

Sluicing elided material is a catena.

theorem DepGrammar.Ellipsis.sluicing_elided_not_constituent : Catena.isConstituent sluicingTree.deps 3 sluicingElided = false

Sluicing elided material is NOT a constituent.

theorem DepGrammar.Ellipsis.fragment_elided_is_catena : Catena.isCatena fragmentTree.deps fragmentElided = true

Fragment answer elided material is a catena.

theorem DepGrammar.Ellipsis.fragment_elided_not_constituent : Catena.isConstituent fragmentTree.deps 2 fragmentElided = false

Fragment answer elided material is NOT a constituent.

theorem DepGrammar.Ellipsis.all_ellipsis_targets_catenae : Catena.isCatena vpEllipsisTree.deps vpEllipsisElided = true ∧ Catena.isCatena gappingTree.deps gappingElided = true ∧ Catena.isCatena pseudogappingTree.deps pseudogappingElided = true ∧ Catena.isCatena sluicingTree.deps sluicingElided = true ∧ Catena.isCatena fragmentTree.deps fragmentElided = true

@cite{osborne-2019}: All five types of ellipsis target catenae. Verified for all example trees.

theorem DepGrammar.Ellipsis.all_ellipsis_not_constituent : Catena.isConstituent vpEllipsisTree.deps 4 vpEllipsisElided = false ∧ Catena.isConstituent gappingTree.deps 3 gappingElided = false ∧ Catena.isConstituent pseudogappingTree.deps 5 pseudogappingElided = false ∧ Catena.isConstituent sluicingTree.deps 3 sluicingElided = false ∧ Catena.isConstituent fragmentTree.deps 2 fragmentElided = false

@cite{osborne-2019}: ALL five ellipsis types target non-constituent catenae. This is the empirical advantage of catenae over constituents: a constituent-based theory cannot capture these ellipsis patterns.