Cognitive Constraints and Island Effects

@cite{hofmeister-sag-2010}

@cite{hofmeister-sag-2010} argue that island effects are gradient along multiple dimensions and that acceptability varies systematically with nonstructural manipulations (filler complexity, referential load) that leave island configurations intact. This challenges every categorical island constraint proposed: Subjacency, Complex NP Constraint, Barriers, and the Minimal Link Condition.

Key findings

1. More complex fillers (which-N phrases) improve acceptability inside islands relative to bare wh-words (who, what) — counterintuitively, richer representations resist interference and aid memory retrieval.
2. Indefinite/plural island NPs improve acceptability relative to definite NPs, consistent with lower referential processing cost.
3. Even the best island condition remains below non-island baselines: islands are ameliorated, not eliminated.

The cross-theory comparison (competence vs. performance vs. discourse) lives in Phenomena.FillerGap.Studies.LuPanDegen2025, which integrates these findings with @cite{lu-pan-degen-2025}'s discourse-based account.

inductive Phenomena.Islands.Studies.HofmeisterSag2010.ProcessingFactor : Type

Processing factors that independently contribute to the difficulty of filler-gap dependencies inside islands.

• locality : ProcessingFactor

  Distance between filler and gap increases memory load (section 3.1). Confirmed by processing studies.

• referentialLoad : ProcessingFactor

  Referential processing of intervening constituents depletes resources (section 3.2). Definites trigger referent search; proper names > definites > indefinites > pronouns in processing cost.

• clauseBoundary : ProcessingFactor

  Clause boundaries impose processing cost independent of extraction (section 3.3). Even in yes-no questions, different complementizers elicit different neurological responses and acceptability.

• fillerComplexity : ProcessingFactor

  Syntactic/semantic complexity of the filler phrase affects retrieval (section 3.4). Counterintuitively, MORE complex fillers REDUCE processing difficulty because richer representations resist interference and aid retrieval.

def Phenomena.Islands.Studies.HofmeisterSag2010.instReprProcessingFactor.repr : ProcessingFactor → ℕ → Std.Format

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@[implicit_reducible]

instance Phenomena.Islands.Studies.HofmeisterSag2010.instReprProcessingFactor : Repr ProcessingFactor

Equations

• Phenomena.Islands.Studies.HofmeisterSag2010.instReprProcessingFactor = { reprPrec := Phenomena.Islands.Studies.HofmeisterSag2010.instReprProcessingFactor.repr }

@[implicit_reducible]

instance Phenomena.Islands.Studies.HofmeisterSag2010.instDecidableEqProcessingFactor : DecidableEq ProcessingFactor

Equations

• Phenomena.Islands.Studies.HofmeisterSag2010.instDecidableEqProcessingFactor x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

inductive Phenomena.Islands.Studies.HofmeisterSag2010.FillerType : Type

Complexity of the displaced wh-phrase. More complex fillers (which-N phrases) facilitate processing inside islands, because richer representations aid memory retrieval (section 3.4).

• bare : FillerType

  Bare wh-word: who, what

• whichN : FillerType

  Complex wh-phrase: which convict, which employee

def Phenomena.Islands.Studies.HofmeisterSag2010.instReprFillerType.repr : FillerType → ℕ → Std.Format

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@[implicit_reducible]

instance Phenomena.Islands.Studies.HofmeisterSag2010.instReprFillerType : Repr FillerType

Equations

• Phenomena.Islands.Studies.HofmeisterSag2010.instReprFillerType = { reprPrec := Phenomena.Islands.Studies.HofmeisterSag2010.instReprFillerType.repr }

@[implicit_reducible]

instance Phenomena.Islands.Studies.HofmeisterSag2010.instDecidableEqFillerType : DecidableEq FillerType

Equations

• Phenomena.Islands.Studies.HofmeisterSag2010.instDecidableEqFillerType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

inductive Phenomena.Islands.Studies.HofmeisterSag2010.IslandNPType : Type

Type of the island-forming NP (Experiment 1 only). Definite NPs trigger referent search and presupposition accommodation, consuming resources needed for dependency resolution (section 3.2).

• definite : IslandNPType

  Definite singular: the report

• plural : IslandNPType

  Indefinite plural: reports

• indefinite : IslandNPType

  Indefinite singular: a report

def Phenomena.Islands.Studies.HofmeisterSag2010.instReprIslandNPType.repr : IslandNPType → ℕ → Std.Format

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

@[implicit_reducible]

instance Phenomena.Islands.Studies.HofmeisterSag2010.instReprIslandNPType : Repr IslandNPType

Equations

• Phenomena.Islands.Studies.HofmeisterSag2010.instReprIslandNPType = { reprPrec := Phenomena.Islands.Studies.HofmeisterSag2010.instReprIslandNPType.repr }

@[implicit_reducible]

instance Phenomena.Islands.Studies.HofmeisterSag2010.instDecidableEqIslandNPType : DecidableEq IslandNPType

Equations

• Phenomena.Islands.Studies.HofmeisterSag2010.instDecidableEqIslandNPType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

structure Phenomena.Islands.Studies.HofmeisterSag2010.IslandCondition : Type

An experimental condition from @cite{hofmeister-sag-2010}. Acceptability stored as Nat (judgment ratio x 100, so 78 means 0.78).

• island : ConstraintType
• filler : FillerType
• npType : Option IslandNPType
• acceptability : ℕ

  Mean judgment ratio x 100

• citation : String

def Phenomena.Islands.Studies.HofmeisterSag2010.instReprIslandCondition.repr : IslandCondition → ℕ → Std.Format

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@[implicit_reducible]

instance Phenomena.Islands.Studies.HofmeisterSag2010.instReprIslandCondition : Repr IslandCondition

Equations

• Phenomena.Islands.Studies.HofmeisterSag2010.instReprIslandCondition = { reprPrec := Phenomena.Islands.Studies.HofmeisterSag2010.instReprIslandCondition.repr }

def Phenomena.Islands.Studies.HofmeisterSag2010.cnpcAcceptability : List IslandCondition

Experiment 1: CNPC violations (section 5). 36 items, (2 x 3) + 1 design. Acceptability ratings on 1-8 scale, normalized as ratio of subject mean. Data from Figure 3 (p. 393).

Equations

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

def Phenomena.Islands.Studies.HofmeisterSag2010.whIslandAcceptability : List IslandCondition

Experiment 2: Wh-island violations (section 6). 24 items, 2 + 1 design. Acceptability on 1-7 scale, normalized. Data from Figure 5 (p. 397). Key finding: F1(1,15)=15.964, p=0.001; F2(1,19)=14.428, p=0.001.

Equations

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

def Phenomena.Islands.Studies.HofmeisterSag2010.cnpcBaseline : ℕ

Non-island baseline acceptability (CNPC experiment, Figure 3).

Equations

• Phenomena.Islands.Studies.HofmeisterSag2010.cnpcBaseline = 108

def Phenomena.Islands.Studies.HofmeisterSag2010.avgAcceptability (conditions : List IslandCondition) (f : FillerType) : ℕ

Average acceptability for a filler type across a set of conditions.

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theorem Phenomena.Islands.Studies.HofmeisterSag2010.cnpc_whichN_gt_bare : avgAcceptability cnpcAcceptability FillerType.whichN > avgAcceptability cnpcAcceptability FillerType.bare

Filler complexity effect in CNPC: which-N > bare wh (section 5.2). F1(1,20)=48.741, p<0.0001; F2(1,35)=39.494, p<0.0001. The structure is identical -- only the filler changes.

theorem Phenomena.Islands.Studies.HofmeisterSag2010.whIsland_whichN_gt_bare : avgAcceptability whIslandAcceptability FillerType.whichN > avgAcceptability whIslandAcceptability FillerType.bare

Filler complexity effect in wh-islands: which-N > bare wh (section 6.2). F1(1,15)=15.964, p=0.001.

theorem Phenomena.Islands.Studies.HofmeisterSag2010.cnpc_indefinite_gt_definite : have indef := List.filter (fun (x : IslandCondition) => x.npType == some IslandNPType.indefinite) cnpcAcceptability; have def_ := List.filter (fun (x : IslandCondition) => x.npType == some IslandNPType.definite) cnpcAcceptability; List.foldl (fun (x1 : ℕ) (x2 : IslandCondition) => x1 + x2.acceptability) 0 indef > List.foldl (fun (x1 : ℕ) (x2 : IslandCondition) => x1 + x2.acceptability) 0 def_

NP type effect: indefinite > definite across both filler types (section 5.2). Consistent with lower referential processing cost for indefinites.

theorem Phenomena.Islands.Studies.HofmeisterSag2010.best_island_lt_baseline : 85 < cnpcBaseline

Even the best island condition (which-PL, 85) remains below the non-island baseline (108). Islands are ameliorated, not eliminated.

Pareto profiles re-encode H&S's key conditions in the format used by Theories.Processing.Cost.Profile, supporting weight-free ordinal comparison via Pareto dominance.

def Phenomena.Islands.Studies.HofmeisterSag2010.cnpcBareDefProfile : ProcessingModel.ProcessingProfile

Bare wh + definite island-forming NP: worst CNPC condition. "I saw who Emma doubted the report that we had captured ___"

Equations

• Phenomena.Islands.Studies.HofmeisterSag2010.cnpcBareDefProfile = { locality := 8, boundaries := 1, referentialLoad := 2, ease := 0 }

def Phenomena.Islands.Studies.HofmeisterSag2010.cnpcWhichIndefProfile : ProcessingModel.ProcessingProfile

Which-N + indefinite island-forming NP: best CNPC condition. "I saw which convict Emma doubted a report that we had captured ___"

Equations

• Phenomena.Islands.Studies.HofmeisterSag2010.cnpcWhichIndefProfile = { locality := 8, boundaries := 1, referentialLoad := 1, ease := 2 }

def Phenomena.Islands.Studies.HofmeisterSag2010.cnpcBaselineProfile : ProcessingModel.ProcessingProfile

Non-island baseline (no extraction): "I saw who Emma doubted that ___"

Equations

• Phenomena.Islands.Studies.HofmeisterSag2010.cnpcBaselineProfile = { locality := 5, boundaries := 0, referentialLoad := 0, ease := 0 }

def Phenomena.Islands.Studies.HofmeisterSag2010.whIslandBareProfile : ProcessingModel.ProcessingProfile

Bare wh into wh-island: "Who did Albert learn whether they dismissed ___"

Equations

• Phenomena.Islands.Studies.HofmeisterSag2010.whIslandBareProfile = { locality := 7, boundaries := 1, referentialLoad := 1, ease := 0 }

def Phenomena.Islands.Studies.HofmeisterSag2010.whIslandWhichProfile : ProcessingModel.ProcessingProfile

Which-N into wh-island: "Which employee did Albert learn whether they dismissed ___"

Equations

• Phenomena.Islands.Studies.HofmeisterSag2010.whIslandWhichProfile = { locality := 7, boundaries := 1, referentialLoad := 1, ease := 2 }

inductive Phenomena.Islands.Studies.HofmeisterSag2010.ProcessingCondition : Type

Conditions tagged for use with OrderingPrediction.

• cnpcBareDef : ProcessingCondition
• cnpcWhichIndef : ProcessingCondition
• cnpcBaseline : ProcessingCondition
• whIslandBare : ProcessingCondition
• whIslandWhich : ProcessingCondition

@[implicit_reducible]

instance Phenomena.Islands.Studies.HofmeisterSag2010.instReprProcessingCondition : Repr ProcessingCondition

Equations

• Phenomena.Islands.Studies.HofmeisterSag2010.instReprProcessingCondition = { reprPrec := Phenomena.Islands.Studies.HofmeisterSag2010.instReprProcessingCondition.repr }

def Phenomena.Islands.Studies.HofmeisterSag2010.instReprProcessingCondition.repr : ProcessingCondition → ℕ → Std.Format

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@[implicit_reducible]

instance Phenomena.Islands.Studies.HofmeisterSag2010.instDecidableEqProcessingCondition : DecidableEq ProcessingCondition

Equations

• Phenomena.Islands.Studies.HofmeisterSag2010.instDecidableEqProcessingCondition x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Phenomena.Islands.Studies.HofmeisterSag2010.instHasProcessingProfileProcessingCondition : ProcessingModel.HasProcessingProfile ProcessingCondition

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theorem Phenomena.Islands.Studies.HofmeisterSag2010.filler_reduces_cnpc_cost : cnpcBareDefProfile.compare cnpcWhichIndefProfile = ProcessingModel.CompareResult.harder

Complex fillers reduce processing difficulty in CNPC. Pareto: cnpcWhichIndefProfile is easier than cnpcBareDefProfile because referentialLoad is lower (1 < 2) and ease is higher (2 > 0); locality and boundaries are equal.

theorem Phenomena.Islands.Studies.HofmeisterSag2010.filler_reduces_whIsland_cost : whIslandBareProfile.compare whIslandWhichProfile = ProcessingModel.CompareResult.harder

Complex fillers reduce processing difficulty in wh-islands. Pareto: whIslandWhichProfile is easier than whIslandBareProfile because ease is higher (2 > 0) with all other dimensions equal.

theorem Phenomena.Islands.Studies.HofmeisterSag2010.bare_def_harder_than_baseline : cnpcBareDefProfile.compare cnpcBaselineProfile = ProcessingModel.CompareResult.harder

Worst CNPC condition is harder than baseline. Pareto: cnpcBareDefProfile dominates on locality (8 > 5), boundaries (1 > 0), and referentialLoad (2 > 0); ease is equal.

theorem Phenomena.Islands.Studies.HofmeisterSag2010.bare_def_harder_than_which_indef : cnpcBareDefProfile.compare cnpcWhichIndefProfile = ProcessingModel.CompareResult.harder

Worst CNPC condition (bare-def) is strictly harder than best (which-indef).

theorem Phenomena.Islands.Studies.HofmeisterSag2010.which_indef_vs_baseline_incomparable : cnpcWhichIndefProfile.compare cnpcBaselineProfile = ProcessingModel.CompareResult.incomparable

Which-indef CNPC vs baseline is incomparable under Pareto: which-indef is worse on locality (8 > 5), boundaries (1 > 0), and referentialLoad (1 > 0) but better on ease (2 > 0). The trade-off is genuine — Pareto reports it as incomparable rather than forcing a cardinal aggregate.

def Phenomena.Islands.Studies.HofmeisterSag2010.islandOrderingPredictions : List (ProcessingModel.OrderingPrediction ProcessingCondition)

Pareto-orderable predictions over the H&S conditions. Which-indef CNPC vs baseline is omitted because it is incomparable under Pareto (see which_indef_vs_baseline_incomparable).

Equations

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

theorem Phenomena.Islands.Studies.HofmeisterSag2010.all_ordering_predictions_verified : islandOrderingPredictions.all ProcessingModel.verifyOrdering = true

Every Pareto-orderable prediction is verified by the data.