Small Clause Predication

@cite{dendikken-1995} @cite{baker-1988}@cite{dendikken-1995}'s central thesis: all subject-predicate relationships are incarnated as small clauses [SC Subject Predicate]. The predicate head's category determines the construction type:

Pred category	Construction	Example
P	Verb-particle / dative	"lift Hsu up", "give the books to Mary"
A	Resultative	"hammer the metal flat"
V	Causative	"make the child laugh"
N	Copular / ECM	"consider John a fool"

The SC analysis unifies these constructions structurally: they share the tree shape V [SC Subj Pred] = node(leaf, node(leaf, leaf)), with differences reduced to the category of the predicate head.

Cross-linguistic extension

Bantu applicative morphemes (-il-, -el-) and Japanese causative -(s)ase are analyzed as affixal particles: grammaticalized instances of P-to-V incorporation. Low applicatives introduce the same structural configuration as particles — SC predication between a goal and a theme, mediated by a P head.

inductive Minimalism.SCPredCategory : Type

Category of the predicate head in a small clause.

@cite{dendikken-1995}: X ∈ {A, N, P, V} — the four LEXICAL categories. The SC family is parameterized by which lexical category serves as the predicate head.

• P : SCPredCategory
• A : SCPredCategory
• V : SCPredCategory
• N : SCPredCategory

instance Minimalism.instDecidableEqSCPredCategory : DecidableEq SCPredCategory

Equations

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

instance Minimalism.instBEqSCPredCategory : BEq SCPredCategory

Equations

• Minimalism.instBEqSCPredCategory = { beq := Minimalism.instBEqSCPredCategory.beq }

def Minimalism.instBEqSCPredCategory.beq : SCPredCategory → SCPredCategory → Bool

Equations

• Minimalism.instBEqSCPredCategory.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Minimalism.instReprSCPredCategory : Repr SCPredCategory

Equations

• Minimalism.instReprSCPredCategory = { reprPrec := Minimalism.instReprSCPredCategory.repr }

def Minimalism.instReprSCPredCategory.repr : SCPredCategory → ℕ → Std.Format

Equations

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

def Minimalism.SCPredCategory.toCat : SCPredCategory → Cat

Map SC predicate categories to syntactic categories.

Equations

• Minimalism.SCPredCategory.P.toCat = Minimalism.Cat.P
• Minimalism.SCPredCategory.A.toCat = Minimalism.Cat.A
• Minimalism.SCPredCategory.V.toCat = Minimalism.Cat.V
• Minimalism.SCPredCategory.N.toCat = Minimalism.Cat.N

structure Minimalism.SmallClause : Type

A small clause: subject-predicate pair where the predicate is categorially typed (@cite{dendikken-1995}:27, ex. 44).

[SC subject predicate]

The predCat field determines which member of the SC family this instance belongs to.

• subject : SyntacticObject

  The subject of predication (typically a DP)

• predicate : SyntacticObject

  The predicate head

• predCat : SCPredCategory

  Category of the predicate (determines construction type)

def Minimalism.instReprSmallClause.repr : SmallClause → ℕ → Std.Format

Equations

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

instance Minimalism.instReprSmallClause : Repr SmallClause

Equations

• Minimalism.instReprSmallClause = { reprPrec := Minimalism.instReprSmallClause.repr }

def Minimalism.SmallClause.toSO (sc : SmallClause) : SyntacticObject

Build the syntactic object for a small clause: [SC Subj Pred].

Equations

• sc.toSO = Minimalism.merge sc.subject sc.predicate

def Minimalism.SmallClause.embedUnderV (v : SyntacticObject) (sc : SmallClause) : SyntacticObject

Embed a small clause under a verb: V [SC Subj Pred].

Equations

• Minimalism.SmallClause.embedUnderV v sc = Minimalism.merge v sc.toSO

def Minimalism.SCPredCategory.constructionName : SCPredCategory → String

The construction type name for each SC predicate category.

Equations

• Minimalism.SCPredCategory.P.constructionName = "verb-particle / dative"
• Minimalism.SCPredCategory.A.constructionName = "resultative"
• Minimalism.SCPredCategory.V.constructionName = "causative"
• Minimalism.SCPredCategory.N.constructionName = "copular/ECM"

def Minimalism.ApplType.isAffixalParticle : ApplType → Bool

Whether an applicative head is analyzable as an affixal particle.

Low applicatives introduce a transfer/possession relation between goal and theme — structurally, a P head relating two DPs via SC predication. This is the same configuration as particles.

High applicatives relate the applied argument to the event, not to the theme — they are NOT affixal particles.

Equations

• Minimalism.ApplType.lowRecipient.isAffixalParticle = true
• Minimalism.ApplType.lowSource.isAffixalParticle = true
• Minimalism.ApplType.high.isAffixalParticle = false

def Minimalism.ApplType.toSCPredCategory : ApplType → Option SCPredCategory

Map low applicatives to SC predicate category P. Low Appl mediates the same structural relation as a particle: [SC Goal [XP Theme]] where the applicative head is the P.

Equations

• Minimalism.ApplType.lowRecipient.toSCPredCategory = some Minimalism.SCPredCategory.P
• Minimalism.ApplType.lowSource.toSCPredCategory = some Minimalism.SCPredCategory.P
• Minimalism.ApplType.high.toSCPredCategory = none

theorem Minimalism.low_recipient_appl_is_particle : ApplType.lowRecipient.isAffixalParticle = true

Low recipient applicatives are affixal particles.

theorem Minimalism.low_source_appl_is_particle : ApplType.lowSource.isAffixalParticle = true

Low source applicatives are affixal particles.

theorem Minimalism.high_appl_not_particle : ApplType.high.isAffixalParticle = false

High applicatives are NOT affixal particles.

theorem Minimalism.low_recipient_appl_is_P : ApplType.lowRecipient.toSCPredCategory = some SCPredCategory.P

Low recipient applicatives map to SC predicate category P.

theorem Minimalism.low_source_appl_is_P : ApplType.lowSource.toSCPredCategory = some SCPredCategory.P

Low source applicatives map to SC predicate category P.

theorem Minimalism.high_appl_no_SC : ApplType.high.toSCPredCategory = none

High applicatives have no SC predication analog.