CRDC: Conjunct Referential Dependency Constraint

[OL23]

The Conjunct Referential Dependency Constraint (CRDC), formulated by [OL23] in Folia Linguistica 57(3): 629–659, is a dependency-grammar constraint on co-valuation in sentences that involve coordinate structures.

Paper text, p. 651 (verbatim):

A referentially dependent conjunct valent can be co-valued with a full co-valent, but a referentially dependent full valent can hardly be co-valued with a conjunct co-valent.

The CRDC governs only configurations in which one of the relevant positions sits inside a coordinate structure; non-coordinate binding falls under standard binding-theoretic principles (Conditions A/B/C). The paper is explicit on p. 651: "The CRDC therefore says nothing about [cases where no coordination is involved]."

Marginality is constitutive of the CRDC's empirical content. The paper's crowdsourced acceptability table (p. 630 fn. 3) maps mean scores to markers — ? (1.65–2.29), ?? (2.30–2.94), * (2.95–4.00). The CRDC's prediction is ??, which corresponds to Judgment.questionable in the project's 5-level enum.

Main definitions

• isConjunctValent / isFullValent — the paper's predicate-valent type distinction, operationalised over DepTree via UD.DepRel.isValencyArg from Core/UD.lean.
• crdcPredictedJudgment — the Judgment the CRDC assigns to a candidate co-valuation; .questionable exactly when CRDC fires, .acceptable when CRDC is silent (other binding principles may still apply).

Implementation notes

• "Valent" is operationalised as a direct UD valency-relation dependent of the predicate. This is a deliberate simplification of the paper's catena-based notion (paper §4); the example set does not exercise the distinction.
• getConjuncts is reused from DepGrammar.Coordination rather than reinventing coord-structure traversal. UD's basic-tree convention makes the first conjunct the head of the coordinate structure; the remaining conjuncts attach via .conj.
• The CRDC alone is not a full binding theory — it predicts only the coord-conjunct-vs-full-valent contribution to acceptability. Example (9b) "Max talked about him" is sentence-level .questionable from Condition B, but crdcPredictedJudgment returns .acceptable because the CRDC is silent on non-coordinate cases.

Cross-framework relationship

The standard binding theories formalized elsewhere in linglib — [Cho81] (Studies/Chomsky1981.lean), [Hud90] (Studies/Hudson1990.lean), [PS94] / [SWB03] (Syntax/HPSG/Coreference.lean, Studies/SagWasowBender2003.lean) — make categorical predictions via Bool-valued grammaticalForCoreference. The CRDC contributes a graded prediction (.questionable) that those predicates cannot express in their current shape; the comparison is not a head-to-head bake-off because the two frameworks answer different questions on disjoint stimulus subsets:

• CRDC: graded marginality, coordinate-structure stimuli, silent on non-coordinate cases (paper p. 651 explicit).
• Conditions A/B/C: categorical grammaticality, non-coordinate stimuli (current parsers do not traverse coordinate structures, so any coordinated input categorically returns false — a parser limitation, not a theoretical claim).

A direct CRDC-vs-Conditions-A/B/C bake-off requires (a) extending the binding-theory parsers to coordination and (b) lifting their output to Judgment. Both are out of scope for this study file.

Todo

• Paper §6 counterexamples (e.g. vote-predicate identity split, example (55a) in the JSON) are encoded as data but not yet covered by a CRDC-vs-data theorem; needs integration with a third-party- referent disjunct.
• Paper §7 — coordination-as-phrase-structure vs subordination-as- dependency contrast — is theoretical commentary without formal content here yet.
• Bool→Prop migration of isConjunctValent / isFullValent should happen as part of a unified DepGrammar/* sweep, not piecemeal.
• Cross-framework CRDC-vs-Conditions-A/B/C bake-off blocked on parser/coordination work (see Cross-framework relationship).

Predicate-valent type

def OsborneLi2023.isConjunctValent (t : DepGrammar.DepTree) (predIdx valentIdx : ℕ) : Bool

Word valentIdx is a conjunct valent of predicate predIdx: it is a conjunct of a coordinate structure that fills a valency role of predIdx. Concretely: there is a valency-eligible edge from predIdx to some coord-head c, and valentIdx is in allConjuncts c (the first conjunct, which heads the structure in UD, plus the remaining conjuncts attached via .conj).

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def OsborneLi2023.isFullValent (t : DepGrammar.DepTree) (predIdx valentIdx : ℕ) : Bool

Word valentIdx is a full valent of predIdx: a valent of predIdx that is not a conjunct valent. Matches the paper's definition (p. 651): "a valent of a given predicate is a full valent thereof if it is complete, that is, it is not a conjunct valent." Operationalised as "direct valency-eligible dependent of predIdx AND not a conjunct valent."

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CRDC prediction

def OsborneLi2023.crdcPredictedJudgment (t : DepGrammar.DepTree) (predIdx anaIdx anteIdx : ℕ) : Features.Judgment

The CRDC's predicted judgment for co-valuing anaphor anaIdx with antecedent anteIdx under predicate predIdx in tree t.

Fires (.questionable) exactly when the anaphor is a full valent and the antecedent is a conjunct valent of the same predicate. Otherwise returns .acceptable — CRDC is silent, and other binding principles (Conditions A/B/C) may still apply.

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CRDC-prediction theorems

Each theorem builds a DepTree matching one of the example sentences and checks that crdcPredictedJudgment returns the contribution the CRDC is responsible for. For data points whose sentence-level judgment is set by a different principle (e.g. ex9b by Condition B, ex5a strengthened by both...and), the theorem records that CRDC alone predicts .acceptable or .questionable respectively — separating the CRDC's contribution from other determinants of acceptability.

def OsborneLi2023.ex2a_tree : DepGrammar.DepTree

Tree for "Max and Lucie talked about him." Max(0) and(1) Lucie(2) talked(3) about(4) him(5).

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theorem OsborneLi2023.ex2a_predicts_questionable : crdcPredictedJudgment ex2a_tree 3 5 0 = Features.Judgment.questionable

def OsborneLi2023.ex9a_tree : DepGrammar.DepTree

Tree for "Max talked about himself." — non-coordinate baseline.

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theorem OsborneLi2023.ex9a_predicts_acceptable : crdcPredictedJudgment ex9a_tree 1 3 0 = Features.Judgment.acceptable

def OsborneLi2023.ex9b_tree : DepGrammar.DepTree

Tree for "Max talked about him." — non-coordinate Condition B context. The sentence-level .questionable reading comes from Condition B, not the CRDC; here we record only that the CRDC is silent.

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theorem OsborneLi2023.ex9b_crdc_silent : crdcPredictedJudgment ex9b_tree 1 3 0 = Features.Judgment.acceptable

def OsborneLi2023.ex24a_tree : DepGrammar.DepTree

Tree for "John talked about himself and his mother." — coordinate object. himself heads the coord, so it is a conjunct valent; John is a full valent. CRDC's permitted direction (conjunct anaphor of full antecedent).

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theorem OsborneLi2023.ex24a_predicts_acceptable : crdcPredictedJudgment ex24a_tree 1 3 0 = Features.Judgment.acceptable

def OsborneLi2023.ex5a_tree : DepGrammar.DepTree

Tree for "Both John and Mary love him." — coordinate subject with paired coordinator; pronoun in object position. The CRDC fires. Sentence-level judgment is stronger (.ungrammatical) due to both...and strengthening; the CRDC alone predicts .questionable.

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theorem OsborneLi2023.ex5a_predicts_questionable : crdcPredictedJudgment ex5a_tree 4 5 1 = Features.Judgment.questionable

def OsborneLi2023.ex28d_tree : DepGrammar.DepTree

Tree for "John expected Mary and him to be able to leave soon." Coordinate-object under raising-to-object; John is the matrix subject (full valent), him is a conjunct of the embedded subject coord. Permitted direction; the CRDC is silent on him↔John co-valuation because him is a conjunct valent (not a full valent).

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theorem OsborneLi2023.ex28d_predicts_acceptable : crdcPredictedJudgment ex28d_tree 1 4 0 = Features.Judgment.acceptable

Directionality

The CRDC is asymmetric: full-anaphor-of-conjunct-antecedent triggers marginality (.questionable); the reverse direction (conjunct-anaphor of-full-antecedent) does not. The asymmetry is exhibited on a single tree by swapping anaIdx and anteIdx: only the (full, conjunct) ordering fires the constraint.

theorem OsborneLi2023.direction_asymmetry : crdcPredictedJudgment ex2a_tree 3 5 0 = Features.Judgment.questionable ∧ crdcPredictedJudgment ex2a_tree 3 0 5 = Features.Judgment.acceptable

On ex2a's tree, swapping which index is the anaphor and which is the antecedent flips the verdict — only him (full) over Max (conjunct) triggers the CRDC. The reverse swap is structurally irreflexive of CRDC's prediction function; it does not correspond to a semantically coherent anaphoric reading.