Cartner et al. 2026: subject islands do not reduce to discourse function

Cartner et al. argue against information-structural accounts of the subject island. On the Focus Background Constraint of Abeillé et al. a subject island is a clash between a focused filler and a backgrounded extraction domain, so the effect should appear where the filler is focused and not otherwise: in wh-questions but not in relative clauses or topicalization, whose fillers are not focused. Three factorial acceptability experiments in Sprouse's design find the effect in all three constructions and at comparable magnitude, which no reading of the constraint accommodates. The constraint compares the filler and the extraction domain on one scale, a backgrounded constituent being an unfocused one, so both statuses are a Focus.Mark. Its gradient statement, (44) of Abeillé et al., makes focus monotone along containment: the more focused an element, the more focused the constituent it is part of. The revision of Winckel et al., the paper's (11), states it as the strict inequality, an extracted element being no more focused than its governor (FBCPredictsIsland), and on binary marks the categorical constraint, the paper's (10), is that inequality (fbcViolation_iff_lt).

The design holds the extraction domain constant and varies the filler, so it bears only on accounts that read the filler. An account whose prediction is a function of the domain alone, such as the direct backgroundedness of Cuneo and Goldberg or a structural constraint on the configuration, predicts the same verdict in every construction and is untouched by the result, as the paper notes (§8). Direct backgroundedness is not the constraint with a different filler: its foregrounded constituents include topics, which the Focus Background Constraint counts as backgrounded, and it assumes that every filler-gap construction foregrounds a constituent (p. 4), so it reads the domain alone.

Main definitions

• FGDConstruction, fillerFocus, subjectFocus — the three constructions, the filler's focus, which the design manipulates, and the subject's, which it holds fixed
• FBCViolation — the categorical constraint (10)
• FBCPredictsIsland — the constraint's prediction, the filler more focused than the subject

Main results

• fbcViolation_iff_lt — on binary marks the categorical constraint is the strict inequality
• fbc_predicts_construction_dependence — the constraint makes the effect turn on construction
• fbc_falsified — an effect in relative clauses refutes it, in either formulation
• domain_only_predicts_invariance — an account reading only the domain predicts invariance, so the experiments leave it standing

References

• [CKW+26]
• [AHWG20]
• [WAHG25]
• [CG23]
• [Spr07]
• [SWP12]

Filler-gap constructions and their information structure

inductive CartnerEtAl2026.FGDConstruction : Type

The three filler-gap constructions the experiments compare. They share the movement mechanism and differ in the information-structural status of the filler.

• whQuestion : FGDConstruction
• relativeClause : FGDConstruction
• topicalization : FGDConstruction

@[instance_reducible]

instance CartnerEtAl2026.instDecidableEqFGDConstruction : DecidableEq FGDConstruction

Equations

• CartnerEtAl2026.instDecidableEqFGDConstruction x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance CartnerEtAl2026.instReprFGDConstruction : Repr FGDConstruction

Equations

• CartnerEtAl2026.instReprFGDConstruction = { reprPrec := CartnerEtAl2026.instReprFGDConstruction.repr }

def CartnerEtAl2026.instReprFGDConstruction.repr : FGDConstruction → ℕ → Std.Format

Equations

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

def CartnerEtAl2026.fillerFocus : FGDConstruction → Focus.Mark

The focus marking of the filler. A wh-phrase is focused, a topicalized constituent is already backgrounded in the discourse (§2), and relativization assigns its head no focus ([AHWG20]).

Equations

• CartnerEtAl2026.fillerFocus CartnerEtAl2026.FGDConstruction.whQuestion = Focus.Mark.focused
• CartnerEtAl2026.fillerFocus CartnerEtAl2026.FGDConstruction.relativeClause = Focus.Mark.unfeatured
• CartnerEtAl2026.fillerFocus CartnerEtAl2026.FGDConstruction.topicalization = Focus.Mark.unfeatured

def CartnerEtAl2026.subjectFocus : FGDConstruction → Focus.Mark

Focus marking of the subject, the constituent containing the gap. Subjects are backgrounded, that is unfocused, in all three constructions, which is what the design holds constant.

Equations

• CartnerEtAl2026.subjectFocus x✝ = Focus.Mark.unfeatured

theorem CartnerEtAl2026.subjectFocus_uniform (c c' : FGDConstruction) : subjectFocus c = subjectFocus c'

The extraction domain is uniform across the three constructions, so any difference between them is a difference in the filler.

theorem CartnerEtAl2026.fillerFocus_varies : fillerFocus FGDConstruction.whQuestion ≠ fillerFocus FGDConstruction.relativeClause ∧ fillerFocus FGDConstruction.whQuestion ≠ fillerFocus FGDConstruction.topicalization

The filler is not: only the wh-question's is focused. This is the variable the constraint claims should modulate the island effect.

The Focus Background Constraint

def CartnerEtAl2026.FBCViolation (filler domain : Focus.Mark) : Prop

The categorical Focus Background Constraint of [AHWG20], the paper's (10): a focused element should not be part of an unfocused, backgrounded constituent.

Equations

• CartnerEtAl2026.FBCViolation filler domain = (filler = Focus.Mark.focused ∧ domain = Focus.Mark.unfeatured)

@[instance_reducible]

instance CartnerEtAl2026.instDecidableRelMarkFBCViolation : DecidableRel FBCViolation

Equations

• CartnerEtAl2026.instDecidableRelMarkFBCViolation x✝¹ x✝ = { decide := decide (x✝¹ = Focus.Mark.focused) && decide (x✝ = Focus.Mark.unfeatured), reflects_decide := ⋯ }

theorem CartnerEtAl2026.fbcViolation_iff_lt (filler domain : Focus.Mark) : FBCViolation filler domain ↔ domain < filler

On binary marks the categorical constraint is the strict inequality of (11): in a two-element scale the only strict pair is the unfocused below the focused.

def CartnerEtAl2026.FBCPredictsIsland (c : FGDConstruction) : Prop

The constraint predicts an island in a construction whose filler is strictly more focused than the subject containing its gap, against the monotonicity of [AHWG20]'s (44) and the revision (11).

Equations

• CartnerEtAl2026.FBCPredictsIsland c = (CartnerEtAl2026.subjectFocus c < CartnerEtAl2026.fillerFocus c)

@[instance_reducible]

instance CartnerEtAl2026.instDecidablePredFGDConstructionFBCPredictsIsland : DecidablePred FBCPredictsIsland

Equations

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

theorem CartnerEtAl2026.fbcPredictsIsland_iff (c : FGDConstruction) : FBCPredictsIsland c ↔ FBCViolation (fillerFocus c) (subjectFocus c)

The categorical constraint predicts the same.

theorem CartnerEtAl2026.fbc_predicts_construction_dependence : FBCPredictsIsland FGDConstruction.whQuestion ∧ ¬FBCPredictsIsland FGDConstruction.relativeClause ∧ ¬FBCPredictsIsland FGDConstruction.topicalization

The constraint makes the island effect turn on the construction: present in wh-questions, absent in relative clauses and topicalization.

What the experiments show

All three experiments find a super-additive penalty for sub-extraction from a subject, and the cross-constructional analysis puts the three penalties at comparable magnitude with overlapping 95% HPDIs (§7). Taking Island to be the effect's distribution over constructions, the finding is that it holds of a construction whose filler is not focused.

theorem CartnerEtAl2026.fbc_falsified (Island : FGDConstruction → Prop) (hfbc : ∀ (c : FGDConstruction), Island c ↔ FBCPredictsIsland c) (h : Island FGDConstruction.relativeClause) : False

An island effect in relative clauses refutes the Focus Background Constraint, in either formulation (fbcPredictsIsland_iff), which ties the effect to a focused filler.

theorem CartnerEtAl2026.domain_only_predicts_invariance (P : Focus.Mark → Prop) (c c' : FGDConstruction) : P (subjectFocus c) ↔ P (subjectFocus c')

The limit of the result. An account whose prediction reads only the extraction domain gives the same verdict in every construction, since the design holds the domain fixed — so construction-invariant effects are what it predicts, and the experiments do not bear on it.