Relative Clauses in HPSG

@cite{pollard-sag-1994} @cite{ginzburg-sag-2000} @cite{sag-wasow-bender-2003}

Relative clauses are analyzed as modifiers that contain a filler-gap dependency. A relative pronoun (or complementizer "that") introduces a gapped clause; the result is a phrase with [MOD NP] that can combine with a head noun via the Head-Modifier Schema.

Derivation of "the book that John read ___"

1. "read" has COMPS ⟨NP⟩
2. Gap introduction: COMPS ⟨⟩, GAP/SLASH {NP}
3. Head-Subject with "John": S[GAP ⟨NP⟩]
4. "that" is a relativizer with [MOD NP]; it combines with the gapped clause (discharging GAP) → relative clause [MOD NP]
5. Head-Modifier: "book" + relative clause → N (modified)

Key types

• Relativizer — relative pronouns and complementizer "that"
• RelClauseDerivation — end-to-end derivation of a relative clause
• relClauseModifies — the Head-Modifier step

Connection to @cite{sag-wasow-bender-2003} Ch. 14

SWB2003 explicitly defers relative clause analysis ("beyond the scope of this text", p. 442). We follow the standard HPSG approach from @cite{pollard-sag-1994} and @cite{ginzburg-sag-2000}, using the GAP mechanism from SWB2003 Ch. 14 combined with the MOD feature.

structure HPSG.RelativeClauses.Relativizer : Type

A relativizer: either a relative pronoun (who, which) or the complementizer "that" in its relative clause use.

The relativizer has [MOD NP] — it produces a phrase that modifies a nominal.

• word : Word

  The word form

• modifiesCat : UD.UPOS

  Category of NP the relative clause modifies

def HPSG.RelativeClauses.relThat : Relativizer

Standard English relativizers.

Equations

• HPSG.RelativeClauses.relThat = { word := { form := "that", cat := UD.UPOS.SCONJ } }

def HPSG.RelativeClauses.relWho : Relativizer

Equations

• HPSG.RelativeClauses.relWho = { word := { form := "who", cat := UD.UPOS.PRON, features := { wh := true } } }

def HPSG.RelativeClauses.relWhich : Relativizer

Equations

• HPSG.RelativeClauses.relWhich = { word := { form := "which", cat := UD.UPOS.PRON, features := { wh := true } } }

def HPSG.RelativeClauses.relWhom : Relativizer

Equations

• HPSG.RelativeClauses.relWhom = { word := { form := "whom", cat := UD.UPOS.PRON, features := { wh := true } } }

structure HPSG.RelativeClauses.RelClauseDerivation : Type

A relative clause derivation: a relativizer combines with a gapped clause to produce a modifier.

This models the two-step process:

1. Inside the clause, a complement is gapped (via ARP), producing a clause with a non-empty GAP/SLASH
2. The relativizer serves as the filler, discharging the GAP
3. The result has [MOD NP, GAP ⟨⟩] — a relative clause

• rel : Relativizer

  The relativizer (who/which/that)

• gappedClause : TrackedSign

  The gapped clause (e.g., "John read ___")

• gapCompatible : self.gappedClause.slash.containsCompatible self.rel.word.cat = true ∨ self.gappedClause.slash.gaps.length > 0

  The gap in the clause must be compatible with the relativizer

def HPSG.RelativeClauses.RelClauseDerivation.result (d : RelClauseDerivation) : TrackedSign

Build the relative clause sign from a derivation.

The result is a phrase with:

• cat = VERB (it's a clause)
• mod = some NP (it modifies a noun)
• SLASH discharged (gap filled by the relativizer)

Equations

• d.result = { sign := HPSG.Sign.phrase [] { cat := UD.UPOS.VERB, mod := some d.rel.modifiesCat }, slash := d.gappedClause.slash.dischargeCompatible d.rel.word.cat }

def HPSG.RelativeClauses.RelClauseDerivation.isMod (d : RelClauseDerivation) : Bool

A relative clause has MOD set (it's a modifier).

Equations

• d.isMod = d.result.sign.synsem.mod.isSome

def HPSG.RelativeClauses.relClauseModifies (headNoun : Sign) (relClause : TrackedSign) : Option Sign

Combine a head noun with a relative clause modifier.

The relative clause's MOD value must match the head noun's category. The result is an NP with no gaps (the gap was discharged when the relative clause was formed).

Equations

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

"the book that John read ___"

Object relative clause: the gap is in object position of "read".

"the boy who saw Mary"

Subject relative clause: the gap is in subject position.

theorem HPSG.RelativeClauses.relClause_is_modifier (d : RelClauseDerivation) : d.result.sign.synsem.mod = some d.rel.modifiesCat

A relative clause derivation always produces a modifier.

theorem HPSG.RelativeClauses.headMod_succeeds_when_mod_matches (headNoun : Sign) (relClause : TrackedSign) (hMod : relClause.sign.synsem.mod = some headNoun.synsem.cat) : (relClauseModifies headNoun relClause).isSome = true

Head-Modifier succeeds when MOD matches the head's category.

theorem HPSG.RelativeClauses.headMod_fails_when_no_mod (headNoun : Sign) (relClause : TrackedSign) (hNoMod : relClause.sign.synsem.mod = none) : relClauseModifies headNoun relClause = none

Head-Modifier fails when MOD is none (non-modifier).

theorem HPSG.RelativeClauses.headMod_preserves_cat (headNoun : Sign) (relClause : TrackedSign) (result : Sign) (hSome : relClauseModifies headNoun relClause = some result) : result.synsem.cat = headNoun.synsem.cat

The Head-Modifier result preserves the head's category (HFP).