Ahn and Zhu (2025): A Bridge to Definiteness: Identifying Unique and Relational Definites through Bridging

Mandarin marks definiteness with bare nouns and with na-CL-N demonstrative descriptions. Ahn and Zhu probe which mechanism each form carries through bridging, a definite whose referent was never mentioned: part-whole bridging is resolvable by situational uniqueness, relational bridging needs an anaphoric relatum. Four studies find that both forms bridge both ways, with a preference for bare nouns in part-whole bridging; that English that is degraded where na is not; and, decisively, that a bare noun bridges relationally only when the noun is lexically relational (zuozhe 'author' but not xiaoshuo-jia 'novelist'), while na bridges with either. Neither an anti-uniqueness presupposition on na nor an Index! principle forcing the indexed form whenever an antecedent is available survives the data.

The analysis keeps the uniqueness ι for the bare noun and re-analyses na as a relationalizing definite whose restrictor is the π-shifted noun, ιx[P(x)(sᵣ) ∧ R(z,x)(sᵣ)] for a contextual relation R and an index z. That restrictor is Possession.π P R z (na); a relational noun applied to the index is Rel z; felicity is ∃! uniqueness. na_of_two_satisfiers shows the relation restoring uniqueness where the bare ι fails, na_identity_iff recovers the strong article as the identity-relation case, and na_iff_bare_of_related isolates the situations where R is redundant and the two forms compete on economy, which covers part-whole bridging (na_seat_redundant) and the moon. The Study 4 item runs through both routes: the bare non-relational noun fails (bare_novelist_fails) while na_novelist, bare_author and na_ex_author each pick the author. index_contradicted_by_bare_relational states the comparison drawn with Index!, and the closing theorems check the rows: na bridges everywhere (na_bridges), English that is out in the paper's own bridging example (that_degraded), and the of and de diagnostics classify the nouns (of_iff_relational, de_of_relational).

TODO

The Studies' stimuli are printed unmarked, with mean ratings. The rating contrasts, that the bare noun bridges relationally better with relational author than with sortal novelist (Study 4) and that English that is degraded in bridging (Study 2), are results for Data/Experiments; the claims over them are not yet stated.

References

• [AZ25c]
• [Bar11]
• [Jen18]
• [Sch09b]
• [DJ23]
• [BLvdKLB22]
• [VJ02]

Bare nouns and na

@[reducible, inline]

abbrev AhnZhu2025.na {E : Type u_1} {S : Type u_2} (P : E → S → Prop) (R : E → E → S → Prop) (z : E) : E → S → Prop

The na restrictor na P R z x s ↔ P x s ∧ R z x s is the noun relationalized by π with the index z in the relatum slot, and the definite ιx[P(x)(sᵣ) ∧ R(z,x)(sᵣ)] is its ∃! witness.

Equations

• AhnZhu2025.na P R z = Possession.π P R z

theorem AhnZhu2025.na_of_two_satisfiers {E : Type u_1} {S : Type u_2} (P : E → S → Prop) (R : E → E → S → Prop) (z : E) (s : S) (h : ∃ (a : E) (b : E), a ≠ b ∧ P a s ∧ P b s) (hR : ∃! x : E, P x s ∧ R z x s) : (¬∃! x : E, P x s) ∧ ∃! x : E, na P R z x s

Two satisfiers of the noun defeat the bare noun's uniqueness presupposition; the relation to the index can restore it.

theorem AhnZhu2025.na_identity_iff {E : Type u_1} {S : Type u_2} (P : E → S → Prop) (z : E) (s : S) : (∃! x : E, na P (fun (a b : E) (x : S) => a = b) z x s) ↔ P z s

With the identity relation na is the strong article, felicitous iff the indexed entity is P.

theorem AhnZhu2025.na_iff_bare_of_related {E : Type u_1} {S : Type u_2} (P : E → S → Prop) (R : E → E → S → Prop) (z : E) (s : S) (h : ∀ (x : E), P x s → R z x s) (x : E) : na P R z x s ↔ P x s

When every P in s bears R to the index, the relation is redundant, and na and the bare noun have the same extension.

theorem AhnZhu2025.existsUnique_na_iff {E : Type u_1} {S : Type u_2} (P : E → S → Prop) (R : E → E → S → Prop) (z : E) (s : S) (h : ∀ (x : E), P x s → R z x s) : (∃! x : E, na P R z x s) ↔ ∃! x : E, P x s

Part-whole bridging: bike and seat

inductive AhnZhu2025.Thing : Type

The bike and its seat.

• bike : Thing
• seat : Thing

@[instance_reducible]

instance AhnZhu2025.instDecidableEqThing : DecidableEq Thing

Equations

• AhnZhu2025.instDecidableEqThing x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def AhnZhu2025.seat : Thing → Unit → Prop

chezuo 'seat'.

Equations

• AhnZhu2025.seat x x✝ = (x = AhnZhu2025.Thing.seat)

def AhnZhu2025.partOf : Thing → Thing → Unit → Prop

partOf z x holds when x is a part of z.

Equations

• AhnZhu2025.partOf z x x✝ = (z = AhnZhu2025.Thing.bike ∧ x = AhnZhu2025.Thing.seat)

theorem AhnZhu2025.bare_seat : ∃! x : Thing, seat x ()

The bare chezuo picks the unique seat of the situation.

theorem AhnZhu2025.na_seat_redundant (x : Thing) : na seat partOf Thing.bike x () ↔ seat x ()

na ge chezuo with R resolved to part-of has the same extension as the bare noun, so the demonstrative's restriction is redundant and economy prefers the bare noun.

Relational bridging: the novel, its author, and another novelist

inductive AhnZhu2025.Ind : Type

The novel found, its author, and another novelist.

• theNovel : Ind
• itsAuthor : Ind
• anotherNovelist : Ind

@[instance_reducible]

instance AhnZhu2025.instDecidableEqInd : DecidableEq Ind

Equations

• AhnZhu2025.instDecidableEqInd x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def AhnZhu2025.novelist : Ind → Unit → Prop

xiaoshuo-jia 'novelist', a sortal noun true of both novelists.

Equations

• AhnZhu2025.novelist x x✝ = (x = AhnZhu2025.Ind.itsAuthor ∨ x = AhnZhu2025.Ind.anotherNovelist)

def AhnZhu2025.author : Ind → Ind → Unit → Prop

zuozhe 'author', where author z x holds when x is an author of z.

Equations

• AhnZhu2025.author z x x✝ = (z = AhnZhu2025.Ind.theNovel ∧ x = AhnZhu2025.Ind.itsAuthor)

theorem AhnZhu2025.bare_novelist_fails : ¬∃! x : Ind, novelist x ()

The bare non-relational noun has no relatum slot, and situational uniqueness fails with two novelists.

theorem AhnZhu2025.na_novelist : ∃! x : Ind, na novelist author Ind.theNovel x ()

na wei xiaoshuo-jia: the demonstrative supplies the relatum, and R resolved to authorship picks the author.

theorem AhnZhu2025.bare_author : ∃! x : Ind, author Ind.theNovel x ()

The bare zuozhe with its relatum argument covertly filled by the novel.

theorem AhnZhu2025.na_ex_author : ∃! x : Ind, na (⨆ (z : Ind), author z) author Ind.theNovel x ()

na wei zuozhe (53) is na over the relational noun with its relatum slot closed, and with R resolved to the noun's own relation it is the bare relational reading.

The Studies' rows

theorem AhnZhu2025.na_bridges (row : Datum) : row ∈ Examples.all → row.feature? "definite_form" = some "naCL" → row.feature? "bridging_type" ≠ some "none" → row.judgment = Judgment.acceptable

na is acceptable in every bridging row, part-whole and relational, with sortal and relational nouns alike.

theorem AhnZhu2025.bare_partWhole (row : Datum) : row ∈ Examples.all → row.feature? "definite_form" = some "bare" → row.feature? "bridging_type" = some "partWhole" → row.judgment = Judgment.acceptable

theorem AhnZhu2025.index_contradicted_by_bare_relational : ¬Jenks2018.BareLicit Mandarin.Determiners.inventory Jenks2018.Environment.producerBridging Jenks2018.Topic.none ∧ ∀ row ∈ Examples.all, row.feature? "definite_form" = some "bare" → row.feature? "bridging_type" = some "relational" → row.feature? "noun_arity" = some "relational" → row.judgment = Judgment.acceptable

Index! excludes the bare noun from relational bridging, predicting complementary distribution; the bare noun is nonetheless acceptable with every relational noun in the relational-bridging rows.

theorem AhnZhu2025.that_degraded (row : Datum) : row ∈ Examples.all → row.feature? "study" = some "none" → row.feature? "definite_form" = some "that" → row.feature? "bridging_type" ≠ some "none" → row.judgment ≠ Judgment.acceptable

English that is out in the paper's own bridging example.

theorem AhnZhu2025.the_acceptable (row : Datum) : row ∈ Examples.all → row.feature? "definite_form" = some "the" → row.judgment = Judgment.acceptable

theorem AhnZhu2025.of_iff_relational (row : Datum) : row ∈ Examples.all → row.feature? "diagnostic" = some "of" → (row.judgment = Judgment.acceptable ↔ row.feature? "noun_arity" = some "relational")

The English of-possessive classifies the nouns: it is grammatical exactly with a relational noun.

theorem AhnZhu2025.de_of_relational (row : Datum) : row ∈ Examples.all → row.feature? "diagnostic" = some "de" → row.feature? "noun_arity" = some "relational" → row.judgment = Judgment.acceptable

Mandarin de admits every relational noun; the converse fails, since the sortal hua 'flower' passes too.