Cartner, Kogan, Webster, Wagers & Sichel (2026)

@cite{cartner-et-al-2026}

Subject islands do not reduce to construction-specific discourse function. Cognition 271, 106467.

Core Result

Three acceptability judgment experiments test whether subject islands arise from an information-structural clash (the Focus Background Constraint of @cite{abeille-et-al-2020}) or from an abstract syntactic constraint on movement. Using a super-additive factorial design (@cite{sprouse-2007}, @cite{sprouse-et-al-2012}), the paper isolates subject island effects across wh-questions, relative clauses, and topicalization — three constructions that share the filler-gap mechanism but differ in the IS profile of the filler.

Finding: Subject island effects are present in all three constructions, with remarkably invariant magnitude. This falsifies the FBC (and its revised formulation in @cite{winckel-et-al-2025}), which predict island effects only for wh-questions. The paper explicitly notes (§8) that the results do NOT falsify direct backgroundedness approaches (@cite{cuneo-goldberg-2023}), only the constructional IS profile account.

Formalization

1. IS profiles per construction, with structural uniformity/variance theorems
2. Original FBC (@cite{abeille-et-al-2020}) and revised FBC (@cite{winckel-et-al-2025}) as predicates over IS profiles
3. Both FBCs' predictions derived, then falsified by experimental DD scores
4. Explicit distinction from direct backgroundedness (BCI), which is NOT falsified (connecting to BackgroundedIslands.lean)
5. Cross-constructional invariance of the island effect
6. Bridge to constraintSource .subject = .syntactic
7. End-to-end argument chain

Each filler-gap construction assigns distinct IS roles to its filler (the displaced element) and its extraction domain. These profiles determine whether the FBC predicts an IS clash.

For the FBC, what matters is whether the filler is focused. WHQ fillers are focused (at-issue, introducing new information); RC and TOP fillers are not (the paper says both are "given" — RC heads are presupposed, topics are discourse-old). The specific non-focused status (.given vs .new) is immaterial: the FBC fires only on .focused.

def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.fillerIS : FGDConstruction → Core.InformationStructure.DiscourseStatus

IS status of the filler in each construction. @cite{abeille-et-al-2020}, §2; @cite{winckel-et-al-2025}.

Equations

• Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.fillerIS FGDConstruction.whQuestion = Core.InformationStructure.DiscourseStatus.focused
• Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.fillerIS FGDConstruction.relativeClause = Core.InformationStructure.DiscourseStatus.given
• Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.fillerIS FGDConstruction.topicalization = Core.InformationStructure.DiscourseStatus.given

def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.subjectIS : FGDConstruction → Core.InformationStructure.DiscourseStatus

IS status of the extraction domain (subject position). Subjects are typically backgrounded across all three constructions.

Equations

• Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.subjectIS FGDConstruction.whQuestion = Core.InformationStructure.DiscourseStatus.given
• Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.subjectIS FGDConstruction.relativeClause = Core.InformationStructure.DiscourseStatus.given
• Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.subjectIS FGDConstruction.topicalization = Core.InformationStructure.DiscourseStatus.given

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.subjectIS_uniform : subjectIS FGDConstruction.whQuestion = subjectIS FGDConstruction.relativeClause ∧ subjectIS FGDConstruction.relativeClause = subjectIS FGDConstruction.topicalization

Subjects have uniform IS status across all constructions. This uniformity is what makes the cross-constructional comparison informative: the extraction domain is held constant while the filler's IS status varies.

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.fillerIS_varies : fillerIS FGDConstruction.whQuestion ≠ fillerIS FGDConstruction.relativeClause ∧ fillerIS FGDConstruction.whQuestion ≠ fillerIS FGDConstruction.topicalization

Fillers differ in IS status across constructions. WHQ fillers are focused; RC and TOP fillers are given. This is the variable that the FBC claims should modulate island effects.

def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.fbcViolation (fillerStatus domainStatus : Core.InformationStructure.DiscourseStatus) : Bool

The FBC (constraint (8) of @cite{abeille-et-al-2020}):

"A focused element should not be part of a backgrounded constituent."

A violation occurs when a focused filler is extracted from a backgrounded domain. The FBC is relational: it depends on the IS profiles of both the filler and the extraction domain.

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def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.fbcPredictsIsland (c : FGDConstruction) : Bool

The FBC predicts a subject island effect for a given construction iff extracting from a subject creates an IS clash.

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def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.fbcRevisedViolation (extractedStatus governorStatus : Core.InformationStructure.DiscourseStatus) : Bool

The revised FBC (formulation (11) of @cite{winckel-et-al-2025}):

"An extracted element should not be more focused than its (non-local)
governor."

This is gradient: the greater the focus difference between filler and governor, the more degraded the dependency. Uses DiscourseStatus.rank from Core/Discourse/InformationStructure.lean.

Equations

• Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.fbcRevisedViolation extractedStatus governorStatus = decide (extractedStatus.rank > governorStatus.rank)

def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.fbcRevisedPredictsIsland (c : FGDConstruction) : Bool

Revised FBC predicts a subject island effect for a given construction iff the filler is more focused than the subject governor.

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theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.fbc_predicts_whq_island : fbcPredictsIsland FGDConstruction.whQuestion = true

The FBC predicts a subject island effect for wh-questions: the wh-phrase is focused, the subject is backgrounded → clash.

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.fbc_predicts_no_rc_island : fbcPredictsIsland FGDConstruction.relativeClause = false

The FBC predicts NO subject island effect for relative clauses.

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.fbc_predicts_no_top_island : fbcPredictsIsland FGDConstruction.topicalization = false

The FBC predicts NO subject island effect for topicalization.

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.both_fbcs_same_predictions : fbcPredictsIsland FGDConstruction.whQuestion = fbcRevisedPredictsIsland FGDConstruction.whQuestion ∧ fbcPredictsIsland FGDConstruction.relativeClause = fbcRevisedPredictsIsland FGDConstruction.relativeClause ∧ fbcPredictsIsland FGDConstruction.topicalization = fbcRevisedPredictsIsland FGDConstruction.topicalization

The revised FBC makes the same predictions as the original.

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.fbc_predicts_construction_dependence : fbcPredictsIsland FGDConstruction.whQuestion = true ∧ fbcPredictsIsland FGDConstruction.relativeClause = false ∧ fbcPredictsIsland FGDConstruction.topicalization = false

Both FBCs predict construction-dependent island effects: only WHQs should show subject islands.

structure Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.DDScore : Type

A super-additive DD (Differences-in-Differences) score. Isolates the island effect by factoring out independent costs of DP complexity and extraction. DD > 0 indicates a super-additive penalty — the hallmark of an island effect.

Scores are z-scored by participant, rounded to ×100 integer encoding.

• construction : FGDConstruction
• position : ExtractionPosition
• dd : ℤ

  DD score × 100 (z-scored). Positive = super-additive penalty.

• citation : String

def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instReprDDScore.repr : DDScore → ℕ → Std.Format

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instance Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instReprDDScore : Repr DDScore

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• Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instReprDDScore = { reprPrec := Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instReprDDScore.repr }

def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.whqSubjectDD : DDScore

Experiment 1: Wh-questions (Fig. 1, n = 72). Three-way interaction β = −0.94, 95%CrI = (−1.54, −0.32), Pr(β < 0) = 0.99.

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def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.whqObjectDD : DDScore

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def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.rcSubjectDD : DDScore

Experiment 2: Relative clauses (Fig. 2, n = 72). Three-way interaction β = −0.58, 95%CrI = (−1.17, 0), Pr(β < 0) = 0.98.

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def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.rcObjectDD : DDScore

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def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.topSubjectDD : DDScore

Experiment 3: Topicalization (Fig. 3, n = 72). Three-way interaction β = −1.24, 95%CrI = (−1.90, −0.59), Pr(β < 0) = 0.99.

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def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.topObjectDD : DDScore

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theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.subject_gt_object_whq : whqSubjectDD.dd > whqObjectDD.dd

Subject sub-extraction cost exceeds object sub-extraction cost in ALL three constructions — not just wh-questions.

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.subject_gt_object_rc : rcSubjectDD.dd > rcObjectDD.dd

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.subject_gt_object_top : topSubjectDD.dd > topObjectDD.dd

def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.islandEffect (c : FGDConstruction) : ℤ

The subject island effect (Subject DD − Object DD) per construction.

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theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.island_effect_positive_whq : islandEffect FGDConstruction.whQuestion > 0

The island effect is positive for all three constructions.

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.island_effect_positive_rc : islandEffect FGDConstruction.relativeClause > 0

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.island_effect_positive_top : islandEffect FGDConstruction.topicalization > 0

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.island_effect_invariance : have whq := islandEffect FGDConstruction.whQuestion; have rc := islandEffect FGDConstruction.relativeClause; have top := islandEffect FGDConstruction.topicalization; whq > 0 ∧ rc > 0 ∧ top > 0 ∧ 2 * whq ≤ 3 * rc ∧ 2 * rc ≤ 3 * whq ∧ 2 * whq ≤ 3 * top ∧ 2 * top ≤ 3 * whq ∧ 2 * rc ≤ 3 * top ∧ 2 * top ≤ 3 * rc

Cross-constructional invariance: The island effect magnitudes are of similar order across all three constructions (34–48 on the ×100 z-score scale), despite the constructions having distinct IS profiles. Each effect is within 3/2 of every other.

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.fbc_falsified_for_rc : fbcPredictsIsland FGDConstruction.relativeClause = false ∧ islandEffect FGDConstruction.relativeClause > 0

The FBC is falsified for RCs: It predicts no island effect for relative clauses, but the data shows a robust subject island effect.

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.fbc_falsified_for_top : fbcPredictsIsland FGDConstruction.topicalization = false ∧ islandEffect FGDConstruction.topicalization > 0

The FBC is falsified for TOPs: It predicts no island effect for topicalization, but the data shows a robust subject island effect.

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.fbc_revised_falsified_for_rc : fbcRevisedPredictsIsland FGDConstruction.relativeClause = false ∧ islandEffect FGDConstruction.relativeClause > 0

The revised FBC (@cite{winckel-et-al-2025}) is equally falsified.

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.fbc_revised_falsified_for_top : fbcRevisedPredictsIsland FGDConstruction.topicalization = false ∧ islandEffect FGDConstruction.topicalization > 0

The paper explicitly notes (§8, p.12):

"We note that our results only speak to the FBC, and do not contradict
direct backgroundedness approaches (Cuneo & Goldberg, 2023)."

The constructional IS profile account (FBC) attributes islands to the interaction of the construction's IS profile with the filler's IS status. The direct backgroundedness account (BCI, @cite{cuneo-goldberg-2023}) attributes islands to the degree of backgroundedness of the extraction domain itself, independent of the filler's IS profile.

Since subjects were systematically more backgrounded than objects across all three constructions tested, direct backgroundedness could in principle capture the results. The paper did not manipulate backgroundedness directly, so the BCI remains unfalsified.

This matters for linglib integration: BackgroundedIslands.lean formalizes the direct backgroundedness account (for MoS verbs, via QUD-determined backgroundedness). That formalization is NOT undermined by Cartner et al.'s findings — they target a different theory.

inductive Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.DiscourseIslandTheory : Type

Discourse-based island theories distinguished by what drives the prediction: the construction's IS profile (FBC) or the extraction domain's backgroundedness (BCI).

• constructionalISProfile : DiscourseIslandTheory

  Island status depends on IS profile of the construction (filler status interacts with domain status). @cite{abeille-et-al-2020}.

• directBackgroundedness : DiscourseIslandTheory

  Island status depends on the degree of backgroundedness of the extraction domain, independent of construction type. @cite{cuneo-goldberg-2023}.

instance Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instDecidableEqDiscourseIslandTheory : DecidableEq DiscourseIslandTheory

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• Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instDecidableEqDiscourseIslandTheory x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instReprDiscourseIslandTheory : Repr DiscourseIslandTheory

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• Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instReprDiscourseIslandTheory = { reprPrec := Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instReprDiscourseIslandTheory.repr }

def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instReprDiscourseIslandTheory.repr : DiscourseIslandTheory → ℕ → Std.Format

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instance Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instBEqDiscourseIslandTheory : BEq DiscourseIslandTheory

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• Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instBEqDiscourseIslandTheory = { beq := Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instBEqDiscourseIslandTheory.beq }

def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instBEqDiscourseIslandTheory.beq : DiscourseIslandTheory → DiscourseIslandTheory → Bool

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• Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instBEqDiscourseIslandTheory.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.cartnerTestsTheory : DiscourseIslandTheory → Bool

Cartner et al.'s experiments test the constructional IS profile account (by varying construction type while holding domain backgroundedness constant), NOT the direct backgroundedness account.

Equations

• Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.cartnerTestsTheory Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.DiscourseIslandTheory.constructionalISProfile = true
• Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.cartnerTestsTheory Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.DiscourseIslandTheory.directBackgroundedness = false

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.bci_not_falsified : cartnerTestsTheory DiscourseIslandTheory.directBackgroundedness = false

The direct backgroundedness account (BCI) is untouched by these results. This connects to the existing formalization in Theories/Semantics/Focus/BackgroundedIslands.lean, which models QUD-determined backgroundedness for MoS islands — a different phenomenon that these experiments do not address.

def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.predictsInvariance : IslandSource → Bool

An island source predicts construction-invariance iff it attributes the island to a mechanism shared across all filler-gap constructions.

The syntactic account (Subject Condition) attributes subject islands to the abstract movement operation, shared by WHQs, RCs, and TOPs → predicts invariance. The discourse account (FBC) attributes subject islands to an IS clash, which varies by construction → predicts variance.

Equations

• Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.predictsInvariance IslandSource.syntactic = true
• Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.predictsInvariance IslandSource.processing = true
• Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.predictsInvariance IslandSource.discourse = false

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.syntactic_predicts_invariance : predictsInvariance (constraintSource ConstraintType.subject) = true

The syntactic classification of subject islands in Data.lean predicts construction-invariant island effects — consistent with the data.

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.discourse_predicts_variance : predictsInvariance IslandSource.discourse = false

The discourse source would predict construction-dependent effects — inconsistent with the data.

structure Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.SubExtractionCost : Type

Sub-extraction cost relative to full extraction, from the cross- constructional posterior analysis (Section 7, Fig. 5). Values × 100.

These are (sub-extraction cost) − (full extraction cost) for subjects, estimated from ordinal mixed-effects regression posteriors with 95% HPDIs.

• construction : FGDConstruction
• cost : ℕ

  Point estimate × 100

• hpdiLo : ℕ

  95% HPDI lower bound × 100

• hpdiHi : ℕ

  95% HPDI upper bound × 100

• citation : String

def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instReprSubExtractionCost.repr : SubExtractionCost → ℕ → Std.Format

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instance Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instReprSubExtractionCost : Repr SubExtractionCost

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• Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instReprSubExtractionCost = { reprPrec := Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.instReprSubExtractionCost.repr }

def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.whqSubjectSubExCost : SubExtractionCost

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def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.rcSubjectSubExCost : SubExtractionCost

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def Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.topSubjectSubExCost : SubExtractionCost

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theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.all_hpdis_exclude_zero : whqSubjectSubExCost.hpdiLo > 0 ∧ rcSubjectSubExCost.hpdiLo > 0 ∧ topSubjectSubExCost.hpdiLo > 0

All three 95% HPDIs exclude zero — each construction shows a reliable additional sub-extraction cost for subjects.

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.hpdis_overlap : whqSubjectSubExCost.hpdiLo < rcSubjectSubExCost.hpdiHi ∧ rcSubjectSubExCost.hpdiLo < whqSubjectSubExCost.hpdiHi ∧ whqSubjectSubExCost.hpdiLo < topSubjectSubExCost.hpdiHi ∧ topSubjectSubExCost.hpdiLo < whqSubjectSubExCost.hpdiHi ∧ rcSubjectSubExCost.hpdiLo < topSubjectSubExCost.hpdiHi ∧ topSubjectSubExCost.hpdiLo < rcSubjectSubExCost.hpdiHi

The 95% HPDIs largely overlap across constructions, consistent with a single underlying constraint of stable magnitude.

theorem Phenomena.FillerGap.Islands.Studies.CartnerEtAl2026.argument_chain : subjectIS FGDConstruction.whQuestion = subjectIS FGDConstruction.relativeClause ∧ subjectIS FGDConstruction.relativeClause = subjectIS FGDConstruction.topicalization ∧ fillerIS FGDConstruction.whQuestion ≠ fillerIS FGDConstruction.relativeClause ∧ fbcPredictsIsland FGDConstruction.whQuestion = true ∧ fbcPredictsIsland FGDConstruction.relativeClause = false ∧ fbcPredictsIsland FGDConstruction.topicalization = false ∧ fbcPredictsIsland FGDConstruction.whQuestion = fbcRevisedPredictsIsland FGDConstruction.whQuestion ∧ fbcPredictsIsland FGDConstruction.relativeClause = fbcRevisedPredictsIsland FGDConstruction.relativeClause ∧ fbcPredictsIsland FGDConstruction.topicalization = fbcRevisedPredictsIsland FGDConstruction.topicalization ∧ islandEffect FGDConstruction.whQuestion > 0 ∧ islandEffect FGDConstruction.relativeClause > 0 ∧ islandEffect FGDConstruction.topicalization > 0 ∧ constraintSource ConstraintType.subject = IslandSource.syntactic ∧ predictsInvariance (constraintSource ConstraintType.subject) = true ∧ predictsInvariance IslandSource.discourse = false ∧ cartnerTestsTheory DiscourseIslandTheory.directBackgroundedness = false

The paper's complete argument in one theorem.

Premises:

• Subjects have uniform IS across constructions (the controlled variable)
• Fillers differ in IS across constructions (the manipulated variable)
• Both FBC formulations predict only WHQs show subject islands
• All three constructions show subject island effects (the data)

Conclusions:

• The FBC is falsified (it predicts construction-dependence; data shows construction-invariance)
• The syntactic account is corroborated (it predicts invariance)
• The direct backgroundedness account (BCI) is not tested