Vikner & Jensen 2002: A semantic analysis of the English genitive

[VJ02]'s uniform argument-only analysis of the English prenominal genitive: the genitive always combines with a relational noun — a non-relational head is coerced via Barker's π, the relation type supplied by the noun's qualia (availableRelations, §3.1.2). The genitive clitic itself (clitic, their (16)) embeds a narrow-scope definite: the worked examples prove iotaPresupposition and feed Possessive.Definite's existsUnique_possessee.

Qualia structure (Pustejovsky, as used by Vikner & Jensen)

structure ViknerJensen2002.NounQualia : Type

The relation-bearing lexical structure of a head noun. Telic and formal qualia license no genitive relation type and are omitted.

• isRelational : Prop

  Inherently relational (e.g. sister, teacher) — bears its own relatum.

• hasConstitutive : Prop

  Bears a constitutive quale (nose: part-of a body).

• hasAgentive : Prop

  Bears an agentive quale (poem: composed by someone).

Deriving the relation type from qualia

def ViknerJensen2002.availableRelations (q : NounQualia) : Set Possessive.PossessionRelationType

The genitive relation types a head noun licenses: inherent iff it is relational, part-whole iff it bears a constitutive quale, agentive iff it bears an agentive quale, and control unconditionally. Possessor-side selectional restrictions are left out, as in the paper's own derivations.

Equations

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

theorem ViknerJensen2002.control_always (q : NounQualia) : Possessive.PossessionRelationType.control ∈ availableRelations q

Control is available whatever the noun's qualia.

Lexical entries

def ViknerJensen2002.sister : NounQualia

sister — inherently relational.

Equations

• ViknerJensen2002.sister = { isRelational := True, hasConstitutive := False, hasAgentive := False }

def ViknerJensen2002.nose : NounQualia

nose — constitutive quale (part-of a body).

Equations

• ViknerJensen2002.nose = { isRelational := False, hasConstitutive := True, hasAgentive := False }

def ViknerJensen2002.poem : NounQualia

poem — agentive quale (composed).

Equations

• ViknerJensen2002.poem = { isRelational := False, hasConstitutive := False, hasAgentive := True }

def ViknerJensen2002.picture : NounQualia

picture — relational (picture of) and agentive (picture made by).

Equations

• ViknerJensen2002.picture = { isRelational := True, hasConstitutive := False, hasAgentive := True }

theorem ViknerJensen2002.sister_inherent : availableRelations sister = {Possessive.PossessionRelationType.inherent, Possessive.PossessionRelationType.control}

the girl's sister: inherent relation, plus the ever-present control.

theorem ViknerJensen2002.nose_partWhole : availableRelations nose = {Possessive.PossessionRelationType.partWhole, Possessive.PossessionRelationType.control}

the girl's nose: part-whole, via the constitutive quale (no inherent or agentive reading).

theorem ViknerJensen2002.poem_agentive : availableRelations poem = {Possessive.PossessionRelationType.agentive, Possessive.PossessionRelationType.control}

the girl's poem: agentive, via the agentive quale.

theorem ViknerJensen2002.picture_three_ways : availableRelations picture = {Possessive.PossessionRelationType.inherent, Possessive.PossessionRelationType.agentive, Possessive.PossessionRelationType.control}

the girl's picture is three ways ambiguous: inherent (picture of the girl), agentive (picture the girl made), and control (picture at her disposal) — but not part-whole.

The genitive clitic

def ViknerJensen2002.clitic {E : Type u_1} (Q : Quantification.Quantifier E) (R : E → E → Prop) : Quantification.Quantifier E

The genitive clitic: from the possessor quantifier and the genitive relation to the head NP's quantifier, with an implicit definite — the unique relatum — scoping under the possessor quantifier.

Equations

• ViknerJensen2002.clitic Q R P = Q fun (u : E) => ∃ (x : E), (∀ (y : E), R u y ↔ y = x) ∧ P x

The denotation: possessor + narrow-scope definite

Model over Fin 4 (girl 0, her teacher 1, her car 2, an unrelated 3), single situation. The genitive picks the unique entity standing in the resolved relation to the possessor.

def ViknerJensen2002.teacherRel : Fin 4 → Fin 4 → Unit → Prop

The (inherent) teacher relation: 0's teacher is 1.

Equations

• ViknerJensen2002.teacherRel x y x✝ = (x = 0 ∧ y = 1)

theorem ViknerJensen2002.girlsTeacher_unique (s : Unit) : ArgumentStructure.Relational.iotaPresupposition (Possessive.viaArgument 0 teacherRel) s

the girl's teacher (inherent): the relational noun's own relation applied to the possessor (viaArgument) has a unique satisfier.

def ViknerJensen2002.aGirl : Quantification.Quantifier (Fin 4)

a girl as an indefinite possessor quantifier.

Equations

• ViknerJensen2002.aGirl P = ∃ (z : Fin 4), z = 0 ∧ P z

theorem ViknerJensen2002.aGirlsTeacher (P : Fin 4 → Prop) : clitic aGirl (fun (u y : Fin 4) => teacherRel u y ()) P ↔ P 1

a girl's teacher holds of P iff some girl has a unique teacher who is P — in this model, iff P 1.

def ViknerJensen2002.theGirlsTeacher : Possessive.Definite (Fin 4) Unit

the girl's teacher as a Possessive.Definite: its unique referent is delivered by the capability API's existsUnique_possessee, no bespoke proof.

Equations

• ViknerJensen2002.theGirlsTeacher = { possessor := 0, predicate := Possessive.viaArgument 0 ViknerJensen2002.teacherRel, presupposition := ViknerJensen2002.girlsTeacher_unique }

theorem ViknerJensen2002.girlsTeacher_existsUnique (s : Unit) : ∃! y : Fin 4, HasPossesseePredicate.possesseePredicate theGirlsTeacher y s

def ViknerJensen2002.controlRel : Fin 4 → Fin 4 → Unit → Prop

The control relation: the girl 0 controls the car 2.

Equations

• ViknerJensen2002.controlRel x y x✝ = (x = 0 ∧ y = 2)

def ViknerJensen2002.carPred : Fin 4 → Unit → Prop

car as a sortal noun predicate.

Equations

• ViknerJensen2002.carPred y x✝ = (y = 2)

theorem ViknerJensen2002.girlsCar_unique (s : Unit) : ArgumentStructure.Relational.iotaPresupposition (Possessive.viaArgument 0 (ArgumentStructure.Relational.π carPred controlRel)) s

the girl's car (coerced, control): the sortal noun is π-shifted with the control relation, then combines exactly like a relational noun (viaArgument). The result again carries the definite's unique witness.