Question Syntax: ForceP, FinP, PolP

@cite{rizzi-1997} @cite{holmberg-2016}

Syntactic projections involved in question formation.

Clause Structure for Polar Questions

@cite{rizzi-1997}'s split-CP and @cite{holmberg-2016}'s PolP analysis give the following structure for a polar question:

[ForceP Force⁰[+Q] [FinP Fin⁰[+finite] [PolP Pol⁰[uPol] [TP ...]]]]

• ForceP: Clause-typing head. Force⁰ bears [+Q] for interrogatives, [-Q] for declaratives. Corresponds to Cat.Force and FeatureVal.q.
• FinP: Finiteness head. Fin⁰ bears [±finite]. Corresponds to Cat.Fin and FeatureVal.finite.
• PolP: Polarity head. Pol⁰ bears valued [±Pol] in declaratives, unvalued [uPol] in polar questions. Corresponds to Cat.Pol and FeatureVal.pol. See Minimalism.Polarity for the Agree infrastructure.

Connection to Semantic Questions

Semantics.Questions.LeftPeriphery defines WHFeature (±WH on C) — the semantic clause-typing feature. The syntactic FeatureVal.q corresponds to the semantic WHFeature:

• FeatureVal.q true ↔ WHFeature.plusWH
• FeatureVal.q false ↔ WHFeature.minusWH

Connection to ClauseType

A clause's Core.Discourse.ClauseType (force × mood) is determined by the syntactic projections:

• Force⁰[+Q] → IllocutionaryMood.interrogative
• Force⁰[-Q] → IllocutionaryMood.declarative
• Mood is determined lower (by T/Fin morphology), not by ForceP.

inductive Minimalism.Questions.QFeature : Type

The Q-feature on Force⁰: [+Q] for interrogatives, [-Q] for declaratives.

• plusQ : QFeature
• minusQ : QFeature

instance Minimalism.Questions.instDecidableEqQFeature : DecidableEq QFeature

Equations

• Minimalism.Questions.instDecidableEqQFeature x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Minimalism.Questions.instReprQFeature : Repr QFeature

Equations

• Minimalism.Questions.instReprQFeature = { reprPrec := Minimalism.Questions.instReprQFeature.repr }

def Minimalism.Questions.instReprQFeature.repr : QFeature → ℕ → Std.Format

Equations

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def Minimalism.Questions.instBEqQFeature.beq : QFeature → QFeature → Bool

Equations

• Minimalism.Questions.instBEqQFeature.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Minimalism.Questions.instBEqQFeature : BEq QFeature

Equations

• Minimalism.Questions.instBEqQFeature = { beq := Minimalism.Questions.instBEqQFeature.beq }

def Minimalism.Questions.QFeature.toFeatureVal : QFeature → FeatureVal

Map the Q-feature to a FeatureVal for the Agree system.

Equations

• Minimalism.Questions.QFeature.plusQ.toFeatureVal = Minimalism.FeatureVal.q true
• Minimalism.Questions.QFeature.minusQ.toFeatureVal = Minimalism.FeatureVal.q false

def Minimalism.Questions.QFeature.toForce : QFeature → Core.Discourse.IllocutionaryMood

Map the Q-feature to illocutionary force.

Equations

• Minimalism.Questions.QFeature.plusQ.toForce = Core.Discourse.IllocutionaryMood.interrogative
• Minimalism.Questions.QFeature.minusQ.toForce = Core.Discourse.IllocutionaryMood.declarative

def Minimalism.Questions.polarQuestionSpine : ClauseSpine

The clause spine for a polar question: V ... T ... Pol ... Fin ... Force.

This is the full IP-to-CP spine with the projections relevant to @cite{holmberg-2016}'s analysis. The Pol head is between T and Fin.

Equations

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def Minimalism.Questions.declarativeSpine : ClauseSpine

A declarative spine has the same projections.

Equations

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

theorem Minimalism.Questions.polP_always_projected : polarQuestionSpine.projects Cat.Pol = true ∧ declarativeSpine.projects Cat.Pol = true

PolP is projected in both declaratives and polar questions.

theorem Minimalism.Questions.forceP_above_polP : fValue Cat.Force > fValue Cat.Pol

ForceP dominates PolP in the spine.

def Minimalism.Questions.clauseType (q : QFeature) (m : Core.Discourse.GramMood) : Core.Discourse.ClauseType

Derive ClauseType from the syntactic features on Force⁰ and T⁰/Fin⁰.

The Q-feature on Force determines illocutionary force; mood is determined by the morphological properties of the verb (indicative vs subjunctive), independent of Force.

Equations

• Minimalism.Questions.clauseType q m = { force := q.toForce, mood := m }

theorem Minimalism.Questions.polar_question_is_interrogative_indicative : clauseType QFeature.plusQ Core.Discourse.GramMood.indicative = Core.Discourse.ClauseType.polarQuestion

A polar question with indicative mood.

theorem Minimalism.Questions.declarative_is_decl_ind : clauseType QFeature.minusQ Core.Discourse.GramMood.indicative = Core.Discourse.ClauseType.declInd

A declarative with indicative mood.

theorem Minimalism.Questions.force_from_forceP_mood_from_fin : (clauseType QFeature.plusQ Core.Discourse.GramMood.indicative).force = Core.Discourse.IllocutionaryMood.interrogative ∧ (clauseType QFeature.plusQ Core.Discourse.GramMood.subjunctive).force = Core.Discourse.IllocutionaryMood.interrogative ∧ (clauseType QFeature.plusQ Core.Discourse.GramMood.indicative).mood = Core.Discourse.GramMood.indicative ∧ (clauseType QFeature.plusQ Core.Discourse.GramMood.subjunctive).mood = Core.Discourse.GramMood.subjunctive

Force and mood are independently set by different heads.