Partee & Borschev 2001: Some puzzles of predicate possessives

Do predicate possessives (that team is John's) refute Jensen and Vikner's uniform analysis of the genitive, on which every genitive is the argument of a relational noun, a plain noun being coerced to a relation first? A bare John's in predicate position is one of two things. Either it is an elliptical NP with an understood relational noun: that teacher is John's is John's teacher (17c), so the earlier verdict of Stockwell, Schachter and Partee that predicate possessives take only a free relation (Partee's (c) examples, repeated as (1)–(3)) is withdrawn, the oddness of that father is John's being charged to the demonstrative subject (17a). Or it is a genuine ⟨e,t⟩ predicate λx[R_POSS(John)(x)] (31), whose relation of possession or control comes from the possessive form and not from any noun; inside an NP such a possessive is an intersective modifier, the modifier genitive (6) being the noun conjoined with it (Possession.π_apply). German non-agreeing mein and Russian and Polish nominative predicate pronouns are bare predicates with the possession reading only; the agreeing and instrumental forms are elliptical NPs and admit the noun's relation as well ((28)–(30), (32)–(35)). Russian marks the split in form, postnominal genitive an argument and prenominal possessive a modifier, and on a relational noun the two constructions come apart (25).

Main statements

• elliptical_iff_bare — predicated of a P, the elliptical NP [John's P] on its possession reading and the bare predicate possessive agree: the reading the two forms share.
• ubijcaPeti_ne_petinUbijca — ubijca Peti 'murderer of Petja' (the noun's own relation applied to Petja) and Petin ubijca (the modifier over the possessor-closed noun) are distinct predicates; the latter holds exactly of a murderer Petja controls (petinUbijca_iff).

References

• [PB01]
• [JV94]
• [Par97]
• [SSP73]

Elliptical NPs and bare predicates (§2.3–2.4)

theorem ParteeBorschev2001.elliptical_iff_bare {E : Type u_1} {S : Type u_2} {P : E → S → Prop} {x : E} {s : S} (possessor : E) (R : E → E → S → Prop) (hP : P x s) : Possession.π P R possessor x s ↔ R possessor x s

Predicated of something that is a P, the elliptical NP [John's P] on its possession reading — P coerced by R, then taken as the genitive's argument — and the bare predicate possessive λx[R(John)(x)] (31) agree.

Russian genitive vs prenominal possessive (§2.2)

stul Peti and Petin stul (23)–(24) describe the same range of cases: with a plain noun the argument genitive over the coerced noun and the modifier possessive assemble the same term π stul R petja. On a relational noun they part: ubijca Peti is 'murderer of Petja', while Petin ubijca is only 'a murderer Petja has hired' (25). Model: Petja 0, the killer 1 who murdered Petja, a hireling 2 who murdered the killer and whom Petja controls.

@[reducible, inline]

abbrev ParteeBorschev2001.Ent : Type

The entities are Petja, the killer and the hireling.

Equations

• ParteeBorschev2001.Ent = Fin 3

@[reducible, inline]

abbrev ParteeBorschev2001.petja : Ent

Petja.

Equations

• ParteeBorschev2001.petja = 0

@[reducible, inline]

abbrev ParteeBorschev2001.killer : Ent

The one who murdered Petja.

Equations

• ParteeBorschev2001.killer = 1

@[reducible, inline]

abbrev ParteeBorschev2001.hireling : Ent

The murderer in Petja's employ.

Equations

• ParteeBorschev2001.hireling = 2

def ParteeBorschev2001.murderer : Ent → Ent → Unit → Prop

ubijca, where murderer v y holds iff y murdered v.

Equations

• ParteeBorschev2001.murderer v y x✝ = (v = ParteeBorschev2001.petja ∧ y = ParteeBorschev2001.killer ∨ v = ParteeBorschev2001.killer ∧ y = ParteeBorschev2001.hireling)

def ParteeBorschev2001.rPoss : Ent → Ent → Unit → Prop

R_POSS holds of Petja and the hireling, whom Petja controls.

Equations

• ParteeBorschev2001.rPoss p y x✝ = (p = ParteeBorschev2001.petja ∧ y = ParteeBorschev2001.hireling)

theorem ParteeBorschev2001.ubijcaPeti_iff (y : Ent) : murderer petja y () ↔ y = killer

ubijca Peti (25a), the relational noun applied to Petja, is the killer.

theorem ParteeBorschev2001.petinUbijca_iff (y : Ent) : Possession.π (⨆ (v : Ent), murderer v) rPoss petja y () ↔ y = hireling

Petin ubijca (25b), the modifier possessive over the noun with its possessor slot closed, is a murderer Petja controls, the hireling, never Petja's own murderer.

theorem ParteeBorschev2001.ubijcaPeti_ne_petinUbijca : murderer petja ≠ Possession.π (⨆ (v : Ent), murderer v) rPoss petja

The genitive and the prenominal possessive are distinct predicates on a relational noun.