Osborne & Groß (2012): Constructions Are Catenae — Data

Dependency trees from Osborne & Groß (2012), "Constructions are catenae: Construction Grammar meets Dependency Grammar" (Cognitive Linguistics 23(1):165–216).

Each tree is a concrete linguistic example analyzed with dependency structure. The catena proofs connecting these trees to the paper's theoretical claims are in DG_OsborneGross2012Bridge.lean.

Construction Types

The paper demonstrates catenae across five construction types:

1. Idioms (§3): fixed V+N combinations where the idiomatic words form a catena skipping the determiner
2. Light verb constructions (§4): semantically bleached verb + meaningful noun, same dependency pattern as idioms
3. Verb chains (§5): auxiliary hierarchies forming connected chains
4. Displacement (§7): topicalized element + governor connected despite linear separation
5. Comparative correlative (§6): each correlative clause forms a catena

inductive Phenomena.Constructions.Studies.OsborneGross2012.ConstructionType : Type

The five construction types analyzed in @cite{osborne-gross-2012}.

• idiom : ConstructionType
• lightVerbConstruction : ConstructionType
• verbChain : ConstructionType
• displacement : ConstructionType
• comparativeCorrelative : ConstructionType

instance Phenomena.Constructions.Studies.OsborneGross2012.instReprConstructionType : Repr ConstructionType

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• Phenomena.Constructions.Studies.OsborneGross2012.instReprConstructionType = { reprPrec := Phenomena.Constructions.Studies.OsborneGross2012.instReprConstructionType.repr }

def Phenomena.Constructions.Studies.OsborneGross2012.instReprConstructionType.repr : ConstructionType → ℕ → Std.Format

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instance Phenomena.Constructions.Studies.OsborneGross2012.instDecidableEqConstructionType : DecidableEq ConstructionType

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• Phenomena.Constructions.Studies.OsborneGross2012.instDecidableEqConstructionType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Constructions.Studies.OsborneGross2012.instBEqConstructionType : BEq ConstructionType

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• Phenomena.Constructions.Studies.OsborneGross2012.instBEqConstructionType = { beq := Phenomena.Constructions.Studies.OsborneGross2012.instBEqConstructionType.beq }

def Phenomena.Constructions.Studies.OsborneGross2012.instBEqConstructionType.beq : ConstructionType → ConstructionType → Bool

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• Phenomena.Constructions.Studies.OsborneGross2012.instBEqConstructionType.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

def Phenomena.Constructions.Studies.OsborneGross2012.spillTheBeans : DepGrammar.DepTree

"spill the beans" (p. 181) — idiom {spill, beans} skips determiner.

Words: spill(0) the(1) beans(2) Deps: spill(0) → beans(2:obj), beans(2) → the(1:det) Construction nodes: {0, 2}

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def Phenomena.Constructions.Studies.OsborneGross2012.giveTheSack : DepGrammar.DepTree

"give the sack" (p. 183) — same V-det-N pattern.

Words: give(0) the(1) sack(2) Deps: give(0) → sack(2:obj), sack(2) → the(1:det) Construction nodes: {0, 2}

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def Phenomena.Constructions.Studies.OsborneGross2012.kickTheBucket : DepGrammar.DepTree

"kick the bucket" (p. 181) — decoding idiom (FKO1988 §1.1.1).

Words: kick(0) the(1) bucket(2) Deps: kick(0) → bucket(2:obj), bucket(2) → the(1:det) Construction nodes: {0, 2}

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def Phenomena.Constructions.Studies.OsborneGross2012.pullSomeStrings : DepGrammar.DepTree

"pull some strings" (p. 183) — idiom {pull, strings} skips quantifier.

Cf. Catena.pulledSomeStrings for the past-tense variant.

Words: pull(0) some(1) strings(2) Deps: pull(0) → strings(2:obj), strings(2) → some(1:det) Construction nodes: {0, 2}

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def Phenomena.Constructions.Studies.OsborneGross2012.takeABath : DepGrammar.DepTree

"take a bath" (p. 187) — LVC {take, bath} skips determiner.

The verb is semantically bleached; the V+N combination carries idiosyncratic meaning not predictable from its parts.

Words: take(0) a(1) bath(2) Deps: take(0) → bath(2:obj), bath(2) → a(1:det) Construction nodes: {0, 2}

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def Phenomena.Constructions.Studies.OsborneGross2012.haveALook : DepGrammar.DepTree

"have a look" (p. 187) — same LVC pattern.

Words: have(0) a(1) look(2) Deps: have(0) → look(2:obj), look(2) → a(1:det) Construction nodes: {0, 2}

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def Phenomena.Constructions.Studies.OsborneGross2012.giveAYell : DepGrammar.DepTree

"give a yell" (p. 187) — same LVC pattern.

Words: give(0) a(1) yell(2) Deps: give(0) → yell(2:obj), yell(2) → a(1:det) Construction nodes: {0, 2}

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def Phenomena.Constructions.Studies.OsborneGross2012.heWillHaveHelped : DepGrammar.DepTree

"He will have helped" — 3-element verb chain (p. 190).

In Osborne's DG, auxiliaries form a hierarchical chain (not UD-flat): will governs have, have governs helped. The verb chain is a catena but NOT a constituent — the subtree of will includes "he".

Words: he(0) will(1) have(2) helped(3) Deps: will(1) → he(0:nsubj), will(1) → have(2:dep), have(2) → helped(3:dep) Construction nodes: {1, 2, 3}

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def Phenomena.Constructions.Studies.OsborneGross2012.sheWillHaveBeenDoingIt : DepGrammar.DepTree

"She will have been doing it" — 4-element verb chain (p. 190, ex. 19b).

The full chain {will, have, been, doing} = {1,2,3,4} is a catena. The subject "she" and object "it" break it up linearly, but the chain remains connected in the dependency tree.

Words: she(0) will(1) have(2) been(3) doing(4) it(5) Deps: will(1) → she(0:nsubj), will(1) → have(2:dep), have(2) → been(3:dep), been(3) → doing(4:dep), doing(4) → it(5:obj) Construction nodes: {1, 2, 3, 4}

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def Phenomena.Constructions.Studies.OsborneGross2012.beansSheSpilled : DepGrammar.DepTree

"Beans she spilled" — topicalization (p. 200).

The displaced element "beans" and its governor "spilled" form a catena despite being separated by "she" in the linear string. This is also a risen catena (see Discontinuity.lean): connected in the dependency tree but non-contiguous in linear order.

Words: beans(0) she(1) spilled(2) Deps: spilled(2) → beans(0:obj), spilled(2) → she(1:nsubj) Construction nodes: {0, 2}

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def Phenomena.Constructions.Studies.OsborneGross2012.theMoreTheFatter : DepGrammar.DepTree

"The more you eat the fatter you get" — comparative correlative (p. 194, ex. 23a).

The CC is a formal idiom (FKO1988 §1.1.3): a productive syntactic pattern with non-compositional semantics. Each correlative clause forms a catena, and the apodosis is NOT a constituent.

Words: the(0) more(1) you(2) eat(3) the(4) fatter(5) you(6) get(7) Deps: get(7) → eat(3:advcl), eat(3) → you(2:nsubj), eat(3) → more(1:advmod), more(1) → the(0:det), get(7) → you(6:nsubj), get(7) → fatter(5:xcomp), fatter(5) → the(4:det) Protasis nodes: {0, 1, 2, 3} Apodosis nodes: {4, 5, 6, 7}

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Bridge content (merged from DG_OsborneGross2012Bridge.lean)

Bridge: Osborne & Groß (2012) DG Catenae → CxG Constructions

@cite{fillmore-kay-oconnor-1988} @cite{osborne-gross-2012}

Connects the dependency trees from Studies/OsborneGross2012/Data.lean to the catena theory from Catena.lean and the CxG types from ConstructionGrammar.Basic and FillmoreKayOConnor1988.

Verified Claims

Claim 1 (p. 176): Every construction type — idioms, LVCs, verb chains, displacement, comparative correlatives — corresponds to a catena. All 10 example trees are verified. All non-trivial constructions are non-constituent catenae, demonstrating that the catena concept is needed.

Claim 2 (p. 176): When a more fixed construct (idiom, LVC) is broken up by a less fixed one (NP), both form catenae. Verified for all 7 V-det-N examples and the CC's two clauses.

CxG ↔ DG Bridge

Four CatenalCx instances covering the full specificity spectrum (lexicallySpecified → partiallyOpen → fullyAbstract), connecting CxG Construction descriptions to DG catena witnesses.

FKO1988 IdiomType classification is bridged to catena verification: substantive decoding idioms ("kick the bucket") and formal idioms (the comparative correlative) are both catenae.

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.spillTheBeans_catena : DepGrammar.Catena.isCatena spillTheBeans.deps [0, 2] = true

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.spillTheBeans_not_constituent : DepGrammar.Catena.isConstituent spillTheBeans.deps 3 [0, 2] = false

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.giveTheSack_catena : DepGrammar.Catena.isCatena giveTheSack.deps [0, 2] = true

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.giveTheSack_not_constituent : DepGrammar.Catena.isConstituent giveTheSack.deps 3 [0, 2] = false

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.kickTheBucket_catena : DepGrammar.Catena.isCatena kickTheBucket.deps [0, 2] = true

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.kickTheBucket_not_constituent : DepGrammar.Catena.isConstituent kickTheBucket.deps 3 [0, 2] = false

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.pullSomeStrings_catena : DepGrammar.Catena.isCatena pullSomeStrings.deps [0, 2] = true

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.pullSomeStrings_not_constituent : DepGrammar.Catena.isConstituent pullSomeStrings.deps 3 [0, 2] = false

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.takeABath_catena : DepGrammar.Catena.isCatena takeABath.deps [0, 2] = true

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.takeABath_not_constituent : DepGrammar.Catena.isConstituent takeABath.deps 3 [0, 2] = false

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.haveALook_catena : DepGrammar.Catena.isCatena haveALook.deps [0, 2] = true

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.haveALook_not_constituent : DepGrammar.Catena.isConstituent haveALook.deps 3 [0, 2] = false

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.giveAYell_catena : DepGrammar.Catena.isCatena giveAYell.deps [0, 2] = true

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.giveAYell_not_constituent : DepGrammar.Catena.isConstituent giveAYell.deps 3 [0, 2] = false

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.verbChain3_catena : DepGrammar.Catena.isCatena heWillHaveHelped.deps [1, 2, 3] = true

3-element chain {will, have, helped} = {1,2,3}.

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.verbChain3_not_constituent : DepGrammar.Catena.isConstituent heWillHaveHelped.deps 4 [1, 2, 3] = false

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.verbChain4_catena : DepGrammar.Catena.isCatena sheWillHaveBeenDoingIt.deps [1, 2, 3, 4] = true

4-element chain {will, have, been, doing} = {1,2,3,4}.

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.verbChain4_not_constituent : DepGrammar.Catena.isConstituent sheWillHaveBeenDoingIt.deps 6 [1, 2, 3, 4] = false

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.fullVP_catena : DepGrammar.Catena.isCatena sheWillHaveBeenDoingIt.deps [1, 2, 3, 4, 5] = true

The full VP {will, have, been, doing, it} = {1,2,3,4,5} is a catena but not a constituent — the subject "she" prevents it.

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.fullVP_not_constituent : DepGrammar.Catena.isConstituent sheWillHaveBeenDoingIt.deps 6 [1, 2, 3, 4, 5] = false

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.displacement_catena : DepGrammar.Catena.isCatena beansSheSpilled.deps [0, 2] = true

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.displacement_not_constituent : DepGrammar.Catena.isConstituent beansSheSpilled.deps 3 [0, 2] = false

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.cc_protasis_catena : DepGrammar.Catena.isCatena theMoreTheFatter.deps [0, 1, 2, 3] = true

Protasis = {the, more, you, eat} = {0,1,2,3}.

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.cc_apodosis_catena : DepGrammar.Catena.isCatena theMoreTheFatter.deps [4, 5, 6, 7] = true

Apodosis = {the, fatter, you, get} = {4,5,6,7}.

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.cc_apodosis_not_constituent : DepGrammar.Catena.isConstituent theMoreTheFatter.deps 8 [4, 5, 6, 7] = false

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.cc_protasis_is_constituent : DepGrammar.Catena.isConstituent theMoreTheFatter.deps 8 [0, 1, 2, 3] = true

Protasis IS a constituent (subtree of eat = {eat, you, more, the}).

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.cc_degree_markers_catenae : DepGrammar.Catena.isCatena theMoreTheFatter.deps [0, 1] = true ∧ DepGrammar.Catena.isCatena theMoreTheFatter.deps [4, 5] = true

Degree markers {the, more} and {the, fatter} each form catenae.

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.claim1_constructions_are_catenae : DepGrammar.Catena.isCatena spillTheBeans.deps [0, 2] = true ∧ DepGrammar.Catena.isCatena giveTheSack.deps [0, 2] = true ∧ DepGrammar.Catena.isCatena kickTheBucket.deps [0, 2] = true ∧ DepGrammar.Catena.isCatena pullSomeStrings.deps [0, 2] = true ∧ DepGrammar.Catena.isCatena takeABath.deps [0, 2] = true ∧ DepGrammar.Catena.isCatena haveALook.deps [0, 2] = true ∧ DepGrammar.Catena.isCatena giveAYell.deps [0, 2] = true ∧ DepGrammar.Catena.isCatena heWillHaveHelped.deps [1, 2, 3] = true ∧ DepGrammar.Catena.isCatena sheWillHaveBeenDoingIt.deps [1, 2, 3, 4] = true ∧ DepGrammar.Catena.isCatena beansSheSpilled.deps [0, 2] = true ∧ DepGrammar.Catena.isCatena theMoreTheFatter.deps [0, 1, 2, 3] = true ∧ DepGrammar.Catena.isCatena theMoreTheFatter.deps [4, 5, 6, 7] = true

Claim 1 (Osborne & Groß 2012, p. 176): Constructions are catenae.

Verified across all five construction types, 10 example trees total.

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.all_constructions_not_constituent : DepGrammar.Catena.isConstituent spillTheBeans.deps 3 [0, 2] = false ∧ DepGrammar.Catena.isConstituent giveTheSack.deps 3 [0, 2] = false ∧ DepGrammar.Catena.isConstituent kickTheBucket.deps 3 [0, 2] = false ∧ DepGrammar.Catena.isConstituent pullSomeStrings.deps 3 [0, 2] = false ∧ DepGrammar.Catena.isConstituent takeABath.deps 3 [0, 2] = false ∧ DepGrammar.Catena.isConstituent haveALook.deps 3 [0, 2] = false ∧ DepGrammar.Catena.isConstituent giveAYell.deps 3 [0, 2] = false ∧ DepGrammar.Catena.isConstituent heWillHaveHelped.deps 4 [1, 2, 3] = false ∧ DepGrammar.Catena.isConstituent sheWillHaveBeenDoingIt.deps 6 [1, 2, 3, 4] = false ∧ DepGrammar.Catena.isConstituent beansSheSpilled.deps 3 [0, 2] = false ∧ DepGrammar.Catena.isConstituent theMoreTheFatter.deps 8 [4, 5, 6, 7] = false

All non-constituent constructions: these require the catena concept — a constituent-based framework cannot represent any of them.

Claim 2: when a more fixed construct (idiom, LVC) is broken up by a less fixed one (NP), the words of both always form catenae.

In each V-det-N tree, the construction {V, N} = {0, 2} is a catena AND the intervening NP {det, N} = {1, 2} is also a catena. The NP breaks up the construction, but catena-hood is preserved for both participants.

For the CC, the protasis and apodosis interleave at the sentence level: the apodosis depends on the protasis (advcl), yet both form catenae.

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.claim2_interleaving_preserves_catenae : DepGrammar.Catena.isCatena spillTheBeans.deps [0, 2] = true ∧ DepGrammar.Catena.isCatena spillTheBeans.deps [1, 2] = true ∧ DepGrammar.Catena.isCatena giveTheSack.deps [0, 2] = true ∧ DepGrammar.Catena.isCatena giveTheSack.deps [1, 2] = true ∧ DepGrammar.Catena.isCatena kickTheBucket.deps [0, 2] = true ∧ DepGrammar.Catena.isCatena kickTheBucket.deps [1, 2] = true ∧ DepGrammar.Catena.isCatena pullSomeStrings.deps [0, 2] = true ∧ DepGrammar.Catena.isCatena pullSomeStrings.deps [1, 2] = true ∧ DepGrammar.Catena.isCatena takeABath.deps [0, 2] = true ∧ DepGrammar.Catena.isCatena takeABath.deps [1, 2] = true ∧ DepGrammar.Catena.isCatena haveALook.deps [0, 2] = true ∧ DepGrammar.Catena.isCatena haveALook.deps [1, 2] = true ∧ DepGrammar.Catena.isCatena giveAYell.deps [0, 2] = true ∧ DepGrammar.Catena.isCatena giveAYell.deps [1, 2] = true ∧ DepGrammar.Catena.isCatena theMoreTheFatter.deps [0, 1, 2, 3] = true ∧ DepGrammar.Catena.isCatena theMoreTheFatter.deps [4, 5, 6, 7] = true

Claim 2 (Osborne & Groß 2012, p. 176): When a more fixed construct is broken up by a less fixed one, both form catenae.

Verified for all 7 V-det-N examples (idioms + LVCs) and the CC's two clauses. Each pair shows: construction catena ∧ intervening catena.

Each construction type is represented as a CatenalCx: a CxG Construction description paired with a DG tree and catena proof.

def Phenomena.Constructions.Studies.OsborneGross2012.Bridge.idiomCx : DepGrammar.CatenalConstruction.CatenalCx

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def Phenomena.Constructions.Studies.OsborneGross2012.Bridge.lvcCx : DepGrammar.CatenalConstruction.CatenalCx

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def Phenomena.Constructions.Studies.OsborneGross2012.Bridge.verbChainCx : DepGrammar.CatenalConstruction.CatenalCx

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def Phenomena.Constructions.Studies.OsborneGross2012.Bridge.displacementCx : DepGrammar.CatenalConstruction.CatenalCx

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theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.catenal_specificity_coverage : idiomCx.construction.specificity = ConstructionGrammar.Specificity.lexicallySpecified ∧ lvcCx.construction.specificity = ConstructionGrammar.Specificity.partiallyOpen ∧ verbChainCx.construction.specificity = ConstructionGrammar.Specificity.fullyAbstract ∧ displacementCx.construction.specificity = ConstructionGrammar.Specificity.fullyAbstract

CatenalCx instances cover the full specificity spectrum.

FKO1988's IdiomType classification (interpretability × grammaticality × formality) is bridged to catena verification. Both ends of the formality spectrum — substantive idioms and formal idioms — are catenae.

def Phenomena.Constructions.Studies.OsborneGross2012.Bridge.kickTheBucketIdiomType : ConstructionGrammar.Studies.FillmoreKayOConnor1988.IdiomType

"kick the bucket" is a substantive decoding idiom in FKO1988's typology.

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def Phenomena.Constructions.Studies.OsborneGross2012.Bridge.ccIdiomType : ConstructionGrammar.Studies.FillmoreKayOConnor1988.IdiomType

The CC is a formal idiom in FKO1988's typology (§1.2.1).

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theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.fko1988_idiom_types_are_catenae : kickTheBucketIdiomType.formality = ConstructionGrammar.Studies.FillmoreKayOConnor1988.IdiomFormality.substantive ∧ DepGrammar.Catena.isCatena kickTheBucket.deps [0, 2] = true ∧ ccIdiomType.formality = ConstructionGrammar.Studies.FillmoreKayOConnor1988.IdiomFormality.formal ∧ DepGrammar.Catena.isCatena theMoreTheFatter.deps [0, 1, 2, 3] = true

Both substantive and formal idioms are catenae: the idiom classification does not affect catena-hood. Substantive idiom {kick, bucket} and formal idiom protasis {the, more, you, eat} are both catenae.

theorem Phenomena.Constructions.Studies.OsborneGross2012.Bridge.cc_matches_fko1988 : ConstructionGrammar.Studies.FillmoreKayOConnor1988.comparativeCorrelative.name = "the X-er the Y-er" ∧ ConstructionGrammar.Studies.FillmoreKayOConnor1988.comparativeCorrelative.specificity = ConstructionGrammar.Specificity.partiallyOpen ∧ DepGrammar.Catena.isCatena theMoreTheFatter.deps [0, 1, 2, 3] = true ∧ DepGrammar.Catena.isCatena theMoreTheFatter.deps [4, 5, 6, 7] = true

Bridge to FKO1988 CC: the comparativeCorrelative construction from FKO1988 matches the CC tree verified here. Both describe the same formal idiom — FKO1988 provides the CxG description, Osborne & Groß provide the DG catena analysis.