CNPC conditions (Experiment 1)

def Phenomena.FillerGap.Compare.cnpc_bare_def : ProcessingModel.ProcessingProfile

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

Equations

• Phenomena.FillerGap.Compare.cnpc_bare_def = { locality := 8, boundaries := 1, referentialLoad := 2, ease := 0 }

def Phenomena.FillerGap.Compare.cnpc_which_indef : 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.FillerGap.Compare.cnpc_which_indef = { locality := 8, boundaries := 1, referentialLoad := 1, ease := 2 }

def Phenomena.FillerGap.Compare.cnpc_baseline : ProcessingModel.ProcessingProfile

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

Equations

• Phenomena.FillerGap.Compare.cnpc_baseline = { locality := 5, boundaries := 0, referentialLoad := 0, ease := 0 }

Wh-island conditions (Experiment 2)

def Phenomena.FillerGap.Compare.whIsland_bare : ProcessingModel.ProcessingProfile

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

Equations

• Phenomena.FillerGap.Compare.whIsland_bare = { locality := 7, boundaries := 1, referentialLoad := 1, ease := 0 }

def Phenomena.FillerGap.Compare.whIsland_which : ProcessingModel.ProcessingProfile

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

Equations

• Phenomena.FillerGap.Compare.whIsland_which = { locality := 7, boundaries := 1, referentialLoad := 1, ease := 2 }

inductive Phenomena.FillerGap.Compare.IslandCondition : Type

Island conditions as a sum type for typeclass instance.

• cnpcBareDef : IslandCondition
• cnpcWhichIndef : IslandCondition
• cnpcBaseline : IslandCondition
• whIslandBare : IslandCondition
• whIslandWhich : IslandCondition

instance Phenomena.FillerGap.Compare.instReprIslandCondition : Repr IslandCondition

Equations

• Phenomena.FillerGap.Compare.instReprIslandCondition = { reprPrec := Phenomena.FillerGap.Compare.instReprIslandCondition.repr }

def Phenomena.FillerGap.Compare.instReprIslandCondition.repr : IslandCondition → Nat → Std.Format

Equations

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

instance Phenomena.FillerGap.Compare.instDecidableEqIslandCondition : DecidableEq IslandCondition

Equations

• Phenomena.FillerGap.Compare.instDecidableEqIslandCondition x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.FillerGap.Compare.instBEqIslandCondition : BEq IslandCondition

Equations

• Phenomena.FillerGap.Compare.instBEqIslandCondition = { beq := Phenomena.FillerGap.Compare.instBEqIslandCondition.beq }

def Phenomena.FillerGap.Compare.instBEqIslandCondition.beq : IslandCondition → IslandCondition → Bool

Equations

• Phenomena.FillerGap.Compare.instBEqIslandCondition.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.FillerGap.Compare.instHasProcessingProfileIslandCondition : ProcessingModel.HasProcessingProfile IslandCondition

Equations

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

theorem Phenomena.FillerGap.Compare.filler_reduces_cnpc_cost : cnpc_bare_def.compare cnpc_which_indef = ProcessingModel.CompareResult.harder

Complex fillers reduce processing difficulty in CNPC. This is the filler complexity paradox: more syntactic material in the filler makes the island easier to process, contrary to any account where cost increases monotonically with phrase size.

Pareto: cnpc_which_indef is easier than cnpc_bare_def because it has lower referentialLoad (1 < 2) and higher ease (2 > 0), with locality and boundaries equal.

theorem Phenomena.FillerGap.Compare.filler_reduces_whIsland_cost : whIsland_bare.compare whIsland_which = ProcessingModel.CompareResult.harder

Complex fillers reduce processing difficulty in wh-islands.

Pareto: whIsland_which is easier than whIsland_bare because it has higher ease (2 > 0), with all other dimensions equal.

theorem Phenomena.FillerGap.Compare.bare_def_harder_than_baseline : cnpc_bare_def.compare cnpc_baseline = ProcessingModel.CompareResult.harder

Worst CNPC condition is harder than baseline.

Pareto: cnpc_bare_def is worse on locality (8 > 5), boundaries (1 > 0), and referentialLoad (2 > 0), with ease equal.

theorem Phenomena.FillerGap.Compare.bare_def_harder_than_which_indef : cnpc_bare_def.compare cnpc_which_indef = ProcessingModel.CompareResult.harder

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

Pareto: bare-def has higher referentialLoad (2 > 1) and lower ease (0 < 2), with locality and boundaries equal.

theorem Phenomena.FillerGap.Compare.which_indef_vs_baseline_incomparable : cnpc_which_indef.compare cnpc_baseline = 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 between distance costs and retrieval facilitation is genuine — Pareto honestly reports it as incomparable rather than forcing a cardinal aggregate.

structure Phenomena.FillerGap.Compare.IslandManipulation : Type

A nonstructural manipulation that changes island acceptability without altering the island configuration.

Each of the three accounts (competence, processing, discourse) makes a prediction about whether the manipulation should affect acceptability.

• description : String
• competencePredictsDifference : Bool

  Does any competence theory predict an acceptability difference?

• processingPredictsDifference : Bool

  Does the processing account predict a difference?

• discoursePredictsDifference : Bool

  Does the discourse/backgroundedness account predict a difference?

• differenceObserved : Bool

  Is a difference actually observed?

• significance : String

  Statistical significance (p-value description)

instance Phenomena.FillerGap.Compare.instReprIslandManipulation : Repr IslandManipulation

Equations

• Phenomena.FillerGap.Compare.instReprIslandManipulation = { reprPrec := Phenomena.FillerGap.Compare.instReprIslandManipulation.repr }

def Phenomena.FillerGap.Compare.instReprIslandManipulation.repr : IslandManipulation → Nat → Std.Format

Equations

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

def Phenomena.FillerGap.Compare.fillerComplexityCNPC : IslandManipulation

Filler complexity in CNPC (Experiment 1, §5). which-N vs bare wh — same island structure, different filler.

Equations

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

def Phenomena.FillerGap.Compare.fillerComplexityWhIsland : IslandManipulation

Filler complexity in wh-islands (Experiment 2, §6). which-N vs bare wh — same island structure.

Equations

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

def Phenomena.FillerGap.Compare.npTypeCNPC : IslandManipulation

NP type in CNPC (Experiment 1, §5). Definite vs indefinite island-forming NP — same CNPC configuration.

Equations

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

def Phenomena.FillerGap.Compare.fillerComplexityAdjunct : IslandManipulation

Filler complexity in adjunct islands (Experiment 3, §7). Complex vs simple temporal adjunct — same wh-island structure.

Equations

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

MoS island manipulations

def Phenomena.FillerGap.Compare.prosodicFocusMoS : IslandManipulation

Prosodic focus on embedded object in MoS islands (Experiments 1, 2a, 3b). Focus changes information structure without changing syntax or processing load.

Equations

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

def Phenomena.FillerGap.Compare.sayAdverbIsland : IslandManipulation

Say + manner adverb creates island (Experiment 3a). Adding an adverb doesn't change CP structure but adds manner weight.

Equations

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

def Phenomena.FillerGap.Compare.frequencyMoS : IslandManipulation

Verb-frame frequency in MoS islands (all experiments). Frequency is the proposed mechanism.

Equations

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

def Phenomena.FillerGap.Compare.allManipulations : List IslandManipulation

All manipulations: + @cite{lu-degen-2025}.

Equations

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

def Phenomena.FillerGap.Compare.processingCorrect (m : IslandManipulation) : Bool

Processing correctly predicts the observed difference.

Equations

• Phenomena.FillerGap.Compare.processingCorrect m = (m.differenceObserved == m.processingPredictsDifference)

def Phenomena.FillerGap.Compare.competenceCorrect (m : IslandManipulation) : Bool

Competence correctly predicts the observed (non-)difference.

Equations

• Phenomena.FillerGap.Compare.competenceCorrect m = (m.differenceObserved == m.competencePredictsDifference)

def Phenomena.FillerGap.Compare.discourseCorrect (m : IslandManipulation) : Bool

Discourse correctly predicts the observed (non-)difference.

Equations

• Phenomena.FillerGap.Compare.discourseCorrect m = (m.differenceObserved == m.discoursePredictsDifference)

def Phenomena.FillerGap.Compare.processingScore : Nat

Equations

• Phenomena.FillerGap.Compare.processingScore = (List.filter Phenomena.FillerGap.Compare.processingCorrect Phenomena.FillerGap.Compare.allManipulations).length

def Phenomena.FillerGap.Compare.competenceScore : Nat

Equations

• Phenomena.FillerGap.Compare.competenceScore = (List.filter Phenomena.FillerGap.Compare.competenceCorrect Phenomena.FillerGap.Compare.allManipulations).length

def Phenomena.FillerGap.Compare.discourseScore : Nat

Equations

• Phenomena.FillerGap.Compare.discourseScore = (List.filter Phenomena.FillerGap.Compare.discourseCorrect Phenomena.FillerGap.Compare.allManipulations).length

theorem Phenomena.FillerGap.Compare.processing_scores_4_of_7 : processingScore = 4

Processing scores 4/7: correct on all 4 H&S manipulations, but misses prosodic focus, say+adverb, and frequency (predicts effect, none found).

theorem Phenomena.FillerGap.Compare.competence_scores_1_of_7 : competenceScore = 1

Competence scores 1/7 — only the frequency null result (where it correctly predicts no effect).

theorem Phenomena.FillerGap.Compare.discourse_scores_3_of_7 : discourseScore = 3

Discourse scores 3/7: correct on prosodic focus, say+adverb, and frequency null. Misses the 4 H&S effects which are processing, not discourse.

theorem Phenomena.FillerGap.Compare.complementary_accounts : (allManipulations.all fun (m : IslandManipulation) => processingCorrect m != discourseCorrect m) = true

Processing and discourse are perfectly complementary: for every manipulation, exactly one of the two accounts is correct (XOR). This means they have full coverage (together 7/7) with zero overlap.

def Phenomena.FillerGap.Compare.islandOrderingPredictions : List (ProcessingModel.OrderingPrediction IslandCondition)

Ordering predictions that Pareto dominance can verify.

Note: which-indef CNPC vs baseline is incomparable (trade-off between distance costs and retrieval facilitation), so it is not included here. See which_indef_vs_baseline_incomparable.

Equations

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

theorem Phenomena.FillerGap.Compare.all_ordering_predictions_verified : islandOrderingPredictions.all ProcessingModel.verifyOrdering = true

All Pareto-orderable predictions verified.

theorem Phenomena.FillerGap.Compare.cnpc_is_classified_strong : constraintStrength ConstraintType.complexNP = ConstraintStrength.strong

The binary strong/weak classification (constraintStrength in Islands.Data) is challenged by H&S's data.

The CNPC is classified as "strong", yet its acceptability varies by 25 points (60 → 85) under nonstructural manipulation. If "strong" means "consistently blocks the dependency", the CNPC is not consistently strong.

Similarly, wh-islands are classified as "weak" (ameliorated with D-linking), but H&S show that the amelioration tracks processing difficulty specifically, not D-linking per se — the same effect appears with nonreferential adjuncts (Experiment 3).

theorem Phenomena.FillerGap.Compare.cnpc_acceptability_range : have worst := 60; have best := 85; best - worst ≥ 25

Yet CNPC acceptability varies by 25+ points under nonstructural manipulation — gradient, not categorical.

construction-based island analysis

@cite{deane-1991} argues that island constraints are construction-specific GAP restrictions, not universal Subjacency. This means:

• The grammar overgerates (licenses extractions freely)
• Construction-specific constraints (GAP restrictions) block some extractions
• Remaining gradient acceptability is explained by processing

This is exactly the division of labor the processing comparison reveals: grammar determines structural possibility, processing determines ease.

The F-G typology (Phenomena.FillerGap.Studies.Sag2010) classifies which constructions are islands. The processing model explains within-island gradient effects (filler complexity, NP type).

theorem Phenomena.FillerGap.Compare.sag_island_subset : Studies.Sag2010.islandConstructions.length < 5

Sag's two island constructions are a proper subset of all F-G types. The non-island types (interrogative, relative, the-clause) freely permit extraction, consistent with the processing account's prediction that apparent island effects in these are gradient, not categorical.

theorem Phenomena.FillerGap.Compare.complementary_coverage : (Studies.Sag2010.fgParams Studies.Sag2010.FGClauseType.topicalized).isIsland = true ∧ (Studies.Sag2010.fgParams Studies.Sag2010.FGClauseType.whExclamative).isIsland = true ∧ constraintStrength ConstraintType.complexNP = ConstraintStrength.strong ∧ constraintSource ConstraintType.mannerOfSpeaking = IslandSource.discourse

The constructions Sag identifies as islands (topicalization, exclamatives) are not among those tested by (CNPC, wh-islands, adjuncts). This is significant: H&S test processing-based islands, whiidentifies grammar-based islands — they explain different cases.

Together they cover both:

• Grammar-based islands: topicalization [GAP ⟨⟩], exclamatives [GAP ⟨⟩]
• Processing-based "islands": CNPC, wh-islands, adjuncts (gradient effects)

Summary: Island Effects Three-Way Comparison

Nonstructural manipulations of island acceptability

Manipulation	Competence	Processing	Discourse	Observed
Filler complexity (CNPC)	No effect	Effect ✓	No effect	p<0.0001
Filler complexity (wh-island)	No effect	Effect ✓	No effect	p=0.001
NP definiteness (CNPC)	No effect	Effect ✓	No effect	Marginal
Adjunct complexity (wh-island)	No effect	Effect ✓	No effect	p<0.01
Prosodic focus (MoS)	No effect	No effect	Effect ✓	p<0.001
Say+adverb island	No effect	No effect	Effect ✓	p<0.001
Verb-frame frequency (MoS)	No effect ✓	Effect	No effect ✓	n.s.

Score: Processing 4/7, Discourse 3/7, Competence 1/7. Together: 7/7.

Key findings

1. Filler complexity paradox (): more complex wh-phrases improve island acceptability. Predicted by processing, not by competence or discourse.

2. Prosodic amelioration: focus on embedded object ameliorates MoS islands. Predicted by discourse, not by competence or processing.

3. Say+adverb replication: adding manner adverbs to bridge verb say creates new islands. Predicted by discourse alone.

4. Perfect complementarity: processing (4/7) and discourse (3/7) cover disjoint manipulations. Together they explain all 7 observed patterns.

Theoretical upshot

Island effects arise from (at least) three distinct mechanisms:

• Grammar: categorical blocking (topicalization, exclamatives —)
• Processing: gradient difficulty from memory load (CNPC, wh-islands —)
• Discourse: information-structural backgroundedness (MoS — @cite{lu-degen-2025})

Both domains use ProcessingModel.ProcessingProfile with Pareto dominance for weight-free ordinal comparison.

Connection to

Sag's F-G typology (Phenomena.FillerGap.Studies.Sag2010) identifies grammar-based islands (topicalization, exclamatives with [GAP ⟨⟩]). covers processing-based islands (CNPC, wh-islands). @cite{lu-degen-2025} covers discourse-based islands (MoS). Together they provide a three-mechanism account.

Manner-of-Speaking Islands

@cite{lu-degen-2025} introduce a discourse-based account of island effects that complements both competence and processing accounts. MoS islands arise from information-structural backgroundedness, not syntactic configuration or processing cost. This is a third mechanism alongside grammar-based and processing-based islands.

The three sources are now tracked by constraintSource in Islands.Data:

• .syntactic → competence grammar
• .processing → performance/memory
• .discourse → information structure

Together, these three mechanisms partition the space of island phenomena:

1. Grammar-based: topicalization, exclamatives
2. Processing-based: CNPC, wh-islands () — gradient with filler complexity
3. Discourse-based: MoS complements — gradient with prosodic focus

theorem Phenomena.FillerGap.Compare.mos_distinct_from_traditional_islands : constraintSource ConstraintType.mannerOfSpeaking = IslandSource.discourse ∧ constraintSource ConstraintType.complexNP = IslandSource.syntactic ∧ constraintSource ConstraintType.embeddedQuestion = IslandSource.syntactic

MoS islands are discourse-sourced, distinct from syntactic/processing islands.