Mereological Syntax Account of Islands

@cite{adger-2025}

@cite{adger-2025} derives island constraints from Angular Locality (AL) and Dimensionality, without stipulating phases, barriers, or subjacency. The key insight: transitivity of parthood does NOT cross dimensions. When an element's path to the target traverses both 1-part and 2-part edges, AL blocks movement.

Island derivations

• Subject islands: The subject is a 2-part of T. Elements inside the subject reach it via 1-part edges, but the subject-to-T edge is a 2-part edge — cross-dimensional. So elements inside the subject cannot be within-dimension transitive parts of any node in C's 1-part chain. But the subject DP itself can extract (it is T's direct 2-part).

• Adjunct islands: Same mechanism. The adjunct is a 2-part of v. Elements inside the adjunct traverse 1-part edges to reach the adjunct, then a 2-part edge to v — cross-dimensional.

• Definite nominal islands: When D has a filled 2-part (Det/Dem), elements inside the DP cannot subjoin to D (Dimensionality blocks it) AND cannot reach above D (the path crosses dimensions). Indefinite DPs (D with a free 2-part) are transparent.

• Successive cyclicity: Cross-clausal movement requires intermediate stops. An embedded wh must first stop at embedded C (within its EP), then reach matrix C (now in the right dimension chain).

Connection to island typology

This file cross-references the SynGraph derivations with the island constraint categories from Data.lean. The key prediction: subject, adjunct, and CNPC islands all follow from the SAME mechanism (cross- dimensional transitivity), not from separate constraints.

The core AL derivations are verified in SynGraph.lean (§ 10):

• al_blocks_superlocal: antilocality (35a)
• al_blocks_sideward: no sideward movement (35c)
• al_blocks_lowering: no lowering (35b)
• al_blocks_parallel: no parallel merge (35d)
• al_blocks_cross_dim / al_allows_within_dim: cross-dimensional transitivity restriction (35e)
• al_allows_rollup_2part / al_allows_rollup_1part: roll-up movement
• succ_cyc_blocked_cross_clause / succ_cyc_wh_reaches_C1_after_stop: successive cyclicity
• subject_island_blocks / subject_itself_can_extract: subject islands
• adjunct_island_blocks / adjunct_itself_can_extract: adjunct islands
• nominal_island_definite_blocks / nominal_island_indefinite_allows: definite nominal islands / Specificity Condition
• antilocality_sub1 / antilocality_sub12: general antilocality

theorem Phenomena.FillerGap.Islands.Studies.Adger2025.uniform_island_mechanism : (mkGraph 9 [(⟨0, ⋯⟩, ⟨1, ⋯⟩), (⟨1, ⋯⟩, ⟨2, ⋯⟩), (⟨2, ⋯⟩, ⟨3, ⋯⟩), (⟨4, ⋯⟩, ⟨5, ⋯⟩), (⟨5, ⋯⟩, ⟨6, ⋯⟩), (⟨7, ⋯⟩, ⟨8, ⋯⟩)] [(⟨1, ⋯⟩, ⟨4, ⋯⟩), (⟨5, ⋯⟩, ⟨7, ⋯⟩)]).satisfiesAL ⟨8, ⋯⟩ ⟨0, ⋯⟩ = false ∧ (mkGraph 8 [(⟨0, ⋯⟩, ⟨1, ⋯⟩), (⟨1, ⋯⟩, ⟨2, ⋯⟩), (⟨2, ⋯⟩, ⟨3, ⋯⟩), (⟨5, ⋯⟩, ⟨6, ⋯⟩), (⟨6, ⋯⟩, ⟨7, ⋯⟩)] [(⟨1, ⋯⟩, ⟨4, ⋯⟩), (⟨2, ⋯⟩, ⟨5, ⋯⟩)]).satisfiesAL ⟨7, ⋯⟩ ⟨0, ⋯⟩ = false ∧ (mkGraph 10 [(⟨0, ⋯⟩, ⟨1, ⋯⟩), (⟨1, ⋯⟩, ⟨2, ⋯⟩), (⟨2, ⋯⟩, ⟨3, ⋯⟩), (⟨5, ⋯⟩, ⟨6, ⋯⟩), (⟨6, ⋯⟩, ⟨7, ⋯⟩)] [(⟨1, ⋯⟩, ⟨4, ⋯⟩), (⟨2, ⋯⟩, ⟨5, ⋯⟩), (⟨5, ⋯⟩, ⟨8, ⋯⟩), (⟨6, ⋯⟩, ⟨9, ⋯⟩)]).satisfiesAL ⟨9, ⋯⟩ ⟨0, ⋯⟩ = false

All three strong island types (subject, adjunct, CNPC) are derived from the same mechanism: cross-dimensional transitivity failure. This contrasts with accounts that stipulate separate constraints for each island type.

We verify that AL blocks extraction from within each type using the same satisfiesAL predicate.

theorem Phenomena.FillerGap.Islands.Studies.Adger2025.adger_derives_syntactic_islands : constraintSource ConstraintType.subject = IslandSource.syntactic ∧ constraintSource ConstraintType.adjunct = IslandSource.syntactic ∧ constraintSource ConstraintType.complexNP = IslandSource.syntactic

All island types that @cite{adger-2025} derives are classified as syntactic in Data.lean's constraintSource. This is consistent: AL is a structural constraint.

theorem Phenomena.FillerGap.Islands.Studies.Adger2025.subject_island_weak : constraintStrength ConstraintType.subject = ConstraintStrength.weak

@cite{adger-2025}'s account predicts that subject islands are weak (ameliorable): the subject itself can always extract; only sub-extraction is blocked. The data classification agrees.

theorem Phenomena.FillerGap.Islands.Studies.Adger2025.adjunct_island_strong : constraintStrength ConstraintType.adjunct = ConstraintStrength.strong

Adjunct islands are strong in the data and strongly blocked by AL (the adjunct is a 2-part; cross-dimensional transitivity always fails for elements deeper than the adjunct itself).