Bridge: HPSG Relative Clauses to Filler-Gap Phenomena

@cite{sag-wasow-bender-2003} @cite{pollard-sag-1994}

Connects the HPSG relative clause mechanism (MOD feature + SLASH/GAP

• Head-Modifier Schema) to empirical data in Phenomena.FillerGap.

Main results

• object_relative_licensed: object relatives derive via complement gap + relativizer + Head-Modifier
• subject_relative_licensed: subject relatives derive via subject gap + relativizer + Head-Modifier
• relClause_always_modifies: every relative clause derivation produces a modifier (has MOD set)
• modification_preserves_head_cat: Head-Modifier preserves the head noun's category

structure Phenomena.FillerGap.Studies.HPSGRelativeClauses.RelClauseConfig : Type

Configuration for a relative clause dependency.

• headCat : UD.UPOS

  Category of the head noun being modified

• gapCat : UD.UPOS

  Category of the gap inside the clause

• rel : HPSG.RelativeClauses.Relativizer

  The relativizer used

def Phenomena.FillerGap.Studies.HPSGRelativeClauses.relClauseLicensed (cfg : RelClauseConfig) : Bool

Is this relative clause configuration licensed?

A relative clause is licensed when:

1. There is a gap in the clause (modeled by gapCat)
2. The relativizer produces a modifier for the head noun's category
3. The MOD value matches the head noun

Equations

• Phenomena.FillerGap.Studies.HPSGRelativeClauses.relClauseLicensed cfg = (HPSG.categoriesMatch cfg.rel.modifiesCat cfg.headCat && cfg.gapCat != UD.UPOS.X)

def Phenomena.FillerGap.Studies.HPSGRelativeClauses.objectRelThat : RelClauseConfig

Object relative with "that": "the book that John read ___" NP head, NP gap in object position, "that" relativizer.

Equations

• Phenomena.FillerGap.Studies.HPSGRelativeClauses.objectRelThat = { headCat := UD.UPOS.NOUN, gapCat := UD.UPOS.NOUN, rel := HPSG.RelativeClauses.relThat }

def Phenomena.FillerGap.Studies.HPSGRelativeClauses.objectRelWhich : RelClauseConfig

Object relative with "which": "the book which John read ___"

Equations

• Phenomena.FillerGap.Studies.HPSGRelativeClauses.objectRelWhich = { headCat := UD.UPOS.NOUN, gapCat := UD.UPOS.NOUN, rel := HPSG.RelativeClauses.relWhich }

def Phenomena.FillerGap.Studies.HPSGRelativeClauses.subjectRelWho : RelClauseConfig

Subject relative with "who": "the boy who saw Mary" NP head, NP gap in subject position, "who" relativizer.

Equations

• Phenomena.FillerGap.Studies.HPSGRelativeClauses.subjectRelWho = { headCat := UD.UPOS.NOUN, gapCat := UD.UPOS.NOUN, rel := HPSG.RelativeClauses.relWho }

def Phenomena.FillerGap.Studies.HPSGRelativeClauses.subjectRelThat : RelClauseConfig

Subject relative with "that": "the boy that saw Mary"

Equations

• Phenomena.FillerGap.Studies.HPSGRelativeClauses.subjectRelThat = { headCat := UD.UPOS.NOUN, gapCat := UD.UPOS.NOUN, rel := HPSG.RelativeClauses.relThat }

def Phenomena.FillerGap.Studies.HPSGRelativeClauses.ppRelWho : RelClauseConfig

PP relative: "the person who(m) John talked to ___" NP head, PP gap (prep stranded), "who" relativizer.

Equations

• Phenomena.FillerGap.Studies.HPSGRelativeClauses.ppRelWho = { headCat := UD.UPOS.NOUN, gapCat := UD.UPOS.ADP, rel := HPSG.RelativeClauses.relWho }

theorem Phenomena.FillerGap.Studies.HPSGRelativeClauses.object_relative_licensed : relClauseLicensed objectRelThat = true ∧ relClauseLicensed objectRelWhich = true

Object relative clause data matches HPSG derivation.

The empirical observation (from LongDistance.relativeClauseData): "the book that John reads" ✓ is licensed by the HPSG derivation: gap(read, obj) → S[GAP ⟨NP⟩] → that + S[GAP ⟨NP⟩] → [MOD NP] → book + [MOD NP] → NP

theorem Phenomena.FillerGap.Studies.HPSGRelativeClauses.subject_relative_licensed : relClauseLicensed subjectRelWho = true ∧ relClauseLicensed subjectRelThat = true

Subject relative clause data matches HPSG derivation.

The empirical observation: "the boy that sees Mary" ✓ is licensed by the HPSG derivation: gap(see, subj) → S[GAP ⟨NP⟩] → that + S[GAP ⟨NP⟩] → [MOD NP] → boy + [MOD NP] → NP

theorem Phenomena.FillerGap.Studies.HPSGRelativeClauses.relClause_always_modifies (d : HPSG.RelativeClauses.RelClauseDerivation) : d.result.sign.synsem.mod.isSome = true

Every relative clause derivation produces a modifier (has MOD set).

theorem Phenomena.FillerGap.Studies.HPSGRelativeClauses.modification_preserves_head_cat (headNoun : HPSG.Sign) (relClause : HPSG.TrackedSign) (result : HPSG.Sign) (hMod : HPSG.RelativeClauses.relClauseModifies headNoun relClause = some result) : result.synsem.cat = headNoun.synsem.cat

The Head-Modifier Schema preserves the head noun's category.

This is the Head Feature Principle applied to Head-Modifier structures: when a relative clause modifies a noun, the result is still a noun.