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

Paper-anchored consumer of the relational/possessive substrate for [VJ02]. V&J give the prenominal genitive a single syntactic type (it always combines with a relational noun); a non-relational head noun is coerced to relational, with the genitive relation derived from the noun's Pustejovsky qualia rather than stipulated.

• Four lexical relation types (§3.1.2): inherent, part-whole, agentive, control. These are the project's PossessionRelationType — V&J is the source of that taxonomy (cited in Semantics/Possessive/Basic.lean), and this study is its first consumer.
• Qualia derivation (§3.2.3): the relation type follows from lexical structure — inherent from relationality, part-whole from the constitutive quale, agentive from the agentive quale; control is always available. So the three-way ambiguity of the girl's picture is derived, not listed.
• The denotation (§3.2.3, (20)–(21)): the genitive is the possessor plus a narrow-scope definite — the unique entity standing in the resolved relation to the possessor. The relation combines with the noun via Barker's π (viaArgument for a relational noun, viaModifier for a coerced sortal noun); uniqueness is iotaPresupposition, and a worked entry feeds the Possessive.Definite carrier's existsUnique_possessee.

Main statements

• control_always, picture_three_ways, nose_partWhole, … — the qualia-derivation predictions (decide-checked).
• girlsTeacher_existsUnique — V&J's inherent genitive as a carrier-API definite (unique referent via existsUnique_possessee).
• girlsCar_eq_sortal — V&J's coerced (control) genitive as viaModifier.

References

• [VJ02]: A semantic analysis of the English genitive.

Qualia structure (Pustejovsky, as used by V&J §3.2.1)

structure ViknerJensen2002.NounQualia : Type

The relation-bearing qualia V&J read off a head noun. The telic and formal qualia do not contribute a genitive relation type in V&J's four-way taxonomy, so they are omitted.

• isRelational : Bool

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

• hasConstitutive : Bool

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

• hasAgentive : Bool

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

def ViknerJensen2002.instDecidableEqNounQualia.decEq (x✝ x✝¹ : NounQualia) : Decidable (x✝ = x✝¹)

Equations

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

@[implicit_reducible]

instance ViknerJensen2002.instDecidableEqNounQualia : DecidableEq NounQualia

Equations

• ViknerJensen2002.instDecidableEqNounQualia = ViknerJensen2002.instDecidableEqNounQualia.decEq

@[implicit_reducible]

instance ViknerJensen2002.instReprNounQualia : Repr NounQualia

Equations

• ViknerJensen2002.instReprNounQualia = { reprPrec := ViknerJensen2002.instReprNounQualia.repr }

def ViknerJensen2002.instReprNounQualia.repr : NounQualia → ℕ → Std.Format

Equations

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

Deriving the relation type from qualia (V&J §3.2.3)

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

V&J's central thesis: the genitive's relation type is derived from the head noun's lexical structure, not stipulated. A noun licenses the inherent relation iff it is relational, the part-whole relation iff it bears a constitutive quale, the agentive relation iff it bears an agentive quale; the control relation is always available (the default, independent of qualia, §3.1.2). The codomain is the project's PossessionRelationType — V&J is the source of that taxonomy.

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 (V&J §3.1.2: it is always available, ownership being only one special case of control).

Lexical entries (V&J (9), §3.1.2)

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.car : NounQualia

car — agentive quale (constructed); the salient reading is control.

Equations

• ViknerJensen2002.car = { 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 (V&J §3.1.2): inherent (picture of the girl), agentive (picture the girl made), and control (picture at her disposal) — but not part-whole.

theorem ViknerJensen2002.picture_more_ambiguous_than_nose : (availableRelations picture).length = 3 ∧ (availableRelations nose).length = 2

The qualia derivation distinguishes the readings: picture is three-way ambiguous, nose only two-way.

The denotation: possessor + narrow-scope definite (V&J §3.2.3)

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 : ArgumentStructure.Relational.Pred2 (Fin 4) Unit

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, V&J (21)): the possessee predicate is the relation applied to the possessor (viaArgument), and there is a unique satisfier — V&J's narrow-scope definite, here as iotaPresupposition.

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

the girl's teacher as a Possessive.Definite carrier: its unique referent is delivered by the carrier 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 : ArgumentStructure.Relational.Pred2 (Fin 4) Unit

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

Equations

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

def ViknerJensen2002.carPred : ArgumentStructure.Relational.Pred1 (Fin 4) Unit

car as a sortal noun predicate.

Equations

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

theorem ViknerJensen2002.girlsCar_eq_sortal (y : Fin 4) : Possessive.viaModifier 0 carPred controlRel y () ↔ y = 2

the girl's car (coerced, control): the sortal noun is shifted to a relation via Barker's π (viaModifier), and the result selects the controlled car. This is V&J's coercion of a non-relational head noun.