Moroney (2021): definiteness and quantification in Shan

Moroney shows that Shan (Southwestern Tai) bare nouns express both unique and anaphoric definiteness, instantiating an unmarked cell that Jenks's definiteness typology had no slot for. Because Shan has no articles, no covert type-shift is blocked — ι, ι^x and ∩ are all available to bare nouns — while the optional demonstratives nâj/nân only add spatial content. The cell is derived from Shan.Determiners.inventory, the bare-noun readings as the shifts the inventory leaves unblocked that are maximal under Dayal's Meaning Preservation, her (79), and the refutation is stated against Jenks2018.attested.

Her comparison of Shan and English bare nouns (Table 2.3) finds them alike on the low-scope existential, kind and generic readings, alike in lacking a high-scope existential, and different only on the definite reading; that difference is derived here (shan_iota_english_none) rather than tabulated. On the mass/count side she adopts Deal's generalized homogeneity — a predicate is g-homogeneous when it is cumulative and, among other options, lacks minimal parts — and argues that Shan count nouns, like English furniture, are cumulative but have identifiable atomic parts (maa_cumulative_not_divisive). The demonstratives are the definite with the referent's closeness to the speaker added: nâj presupposes a unique P in the situation and refers to it if it is close (demDenotation, her (147)–(148)).

Implementation notes

Moroney leaves close.to.speaker and far.from.speaker primitive. Here a demonstrative's spatial content is the vicinity of a referent whose participants form one of its participant sets, as in Harbour's account of spatial deixis: nâj covers the sets containing the speaker and nân the others, so close.to.speaker is the vicinity of a referent including the speaker (mem_image_naj_iff) and far.from.speaker the vicinity of one excluding the speaker (mem_image_nan_iff). Where she treats far.from.speaker as the opposite of close.to.speaker, the two vicinities may overlap here, as when the addressee stands by the speaker.

References

• [Mor21]
• [Day04], [Dea17], [Har16a], [Jen18], [Sch13]

Type-shift selection

theorem Moroney2021.shan_iota_english_none : MaximalFor (Shan.Determiners.inventory.Available False) (fun (x : Genericity.CovertShift) => x ≠ Genericity.CovertShift.exists) Genericity.CovertShift.iota ∧ ∀ (τ : Genericity.CovertShift), ¬English.Determiners.inventory.Available False τ

With a non-kind predicate a Shan bare noun type-shifts by ι, the definite reading, while an English bare singular has no shift available at all, since the blocks ι and ι^x, a blocks ∃, and ∩ is undefined for a singular count noun.

theorem Moroney2021.shan_kind_ambiguity : MaximalFor (Shan.Determiners.inventory.Available True) (fun (x : Genericity.CovertShift) => x ≠ Genericity.CovertShift.exists) Genericity.CovertShift.down ∧ MaximalFor (Shan.Determiners.inventory.Available True) (fun (x : Genericity.CovertShift) => x ≠ Genericity.CovertShift.exists) Genericity.CovertShift.iota ∧ MaximalFor (Shan.Determiners.inventory.Available True) (fun (x : Genericity.CovertShift) => x ≠ Genericity.CovertShift.exists) Genericity.CovertShift.iotaAnaphoric

With a kind-compatible predicate ∩, ι and ι^x are all maximal, which is the kind and definite ambiguity of Shan bare nouns.

theorem Moroney2021.shan_thai_anaphoric_contrast : Shan.Determiners.inventory.Available False Genericity.CovertShift.iotaAnaphoric ∧ ¬Thai.Determiners.inventory.Available False Genericity.CovertShift.iotaAnaphoric

Shan blocks no ι^x, so bare nouns reach anaphoric definiteness; Thai's demonstrative marks familiarity and blocks it.

theorem Moroney2021.shan_exists_is_last_resort : Shan.Determiners.inventory.Available False Genericity.CovertShift.exists ∧ ¬MaximalFor (Shan.Determiners.inventory.Available False) (fun (x : Genericity.CovertShift) => x ≠ Genericity.CovertShift.exists) Genericity.CovertShift.exists

Under Meaning Preservation ι outranks ∃, which is available to a Shan bare noun but never selected beside ι, so Shan bare nouns default to definite or kind readings and the existential reading arises only through existential closure at vP, whence the missing high-scope existential.

The typology, derived per language

theorem Moroney2021.derive_all_languages : English.Determiners.inventory.markingStrategy = Reference.MarkingStrategy.generallyMarked ∧ German.Determiners.inventory.markingStrategy = Reference.MarkingStrategy.bipartite ∧ Thai.Determiners.inventory.markingStrategy = Reference.MarkingStrategy.markedAnaphoric ∧ Shan.Determiners.inventory.markingStrategy = Reference.MarkingStrategy.unmarked

Each language's marking strategy, computed by Determiner.Inventory.markingStrategy from its declared inventory: the four languages fill all four cells of the revised typology.

theorem Moroney2021.derive_article_types : English.Determiners.inventory.articleType = Reference.ArticleType.weakOnly ∧ German.Determiners.inventory.articleType = Reference.ArticleType.weakAndStrong ∧ Thai.Determiners.inventory.articleType = Reference.ArticleType.weakOnly ∧ Shan.Determiners.inventory.articleType = Reference.ArticleType.articleless

The [Sch13]-style article-type projection of the same inventories.

theorem Moroney2021.articleType_lossy : English.Determiners.inventory.markingStrategy ≠ Mandarin.Determiners.inventory.markingStrategy ∧ English.Determiners.inventory.articleType = Mandarin.Determiners.inventory.articleType

ArticleType is lossy where MarkingStrategy is not: English and Mandarin differ in strategy yet collapse to the same article type.

theorem Moroney2021.shan_anaphoric_without_article : ¬Shan.Determiners.inventory.Realizes Reference.Description.Kind.anaphoric ∧ Shan.Determiners.inventory.Realizes Reference.Description.Kind.demonstrative

Shan has no determiner realizing anaphoric definiteness, yet expresses it — through bare nouns (unblocked ι^x) and the optional demonstratives, which it does realize.

theorem Moroney2021.english_german_anaphoric_realized : English.Determiners.inventory.Realizes Reference.Description.Kind.anaphoric ∧ German.Determiners.inventory.Realizes Reference.Description.Kind.anaphoric

English realizes anaphoric definiteness through syncretic the and German through its dedicated strong article.

theorem Moroney2021.shan_refutes_jenks_typology : Shan.Determiners.inventory.markingStrategy ∉ Jenks2018.attested

Shan's derived strategy falls outside [Jen18]'s attested set — the fourth, unmarked cell.

Shan count nouns are cumulative but not homogeneous

def Moroney2021.LacksMinimalParts {α : Type u_1} [Preorder α] (P : α → Prop) : Prop

P lacks minimal parts, the first clause of [Dea17]'s generalized homogeneity, when every P-element has a proper P-part.

Equations

• Moroney2021.LacksMinimalParts P = ∀ (x : α), P x → ∃ y < x, P y

@[reducible, inline]

abbrev Moroney2021.isDog (x : Finset (Fin 2)) : Prop

The dog-pluralities over two dogs are the nonempty subsets.

Equations

• Moroney2021.isDog x = x.Nonempty

theorem Moroney2021.maa_cumulative_not_divisive : Mereology.CUM isDog ∧ ¬LacksMinimalParts isDog

Shan mǎa 'dog' patterns with English furniture: the sum of dogs is dogs, but the individual dogs are minimal, so the predicate is cumulative without being homogeneous.

Demonstratives add spatial content

noncomputable def Moroney2021.bareDefinite {E : Type u_1} (restrictor : E → Prop) : Option E

The bare definite description denotes the unique referent satisfying the restrictor, the uniqueness reading available to Shan bare nouns.

Equations

• Moroney2021.bareDefinite restrictor = Reference.iota restrictor

noncomputable def Moroney2021.demDenotation {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} [PartialOrder E] (c : Reference.Context W E P T) (χ : SetRel E E) (d : DemonstrativeDeterminer) (restrictor : E → Prop) : Option E

The demonstrative denotation of Moroney's (147)–(148): the unique referent satisfying the restrictor and lying in the demonstrative's deictic domain, ιx[P(x) ∧ close.to.speaker(x)] for nâj.

Equations

• Moroney2021.demDenotation c χ d restrictor = Reference.iota fun (x : E) => restrictor x ∧ x ∈ χ.image (c.participants ⁻¹' ↑d.deixis)

theorem Moroney2021.demDenotation_eq_some_of_bareDefinite {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} [PartialOrder E] (c : Reference.Context W E P T) (χ : SetRel E E) {d : DemonstrativeDeterminer} {restrictor : E → Prop} {e : E} (h : bareDefinite restrictor = some e) (hs : e ∈ χ.image (c.participants ⁻¹' ↑d.deixis)) : demDenotation c χ d restrictor = some e

The demonstrative refers to the bare definite's referent whenever that referent lies in the demonstrative's deictic domain, so nâj/nân are optional wherever the bare noun already provides the definite reading.

theorem Moroney2021.mem_image_naj_iff {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} [PartialOrder E] (c : Reference.Context W E P T) (χ : SetRel E E) {x : E} : x ∈ χ.image (c.participants ⁻¹' ↑Shan.Determiners.naj.deixis) ↔ ∃ (y : E), c.agent ≤ y ∧ (y, x) ∈ χ

nâj's close.to.speaker of (147) is the vicinity of a referent including the speaker.

theorem Moroney2021.mem_image_nan_iff {W : Type u_1} {E : Type u_2} {P : Type u_3} {T : Type u_4} [PartialOrder E] (c : Reference.Context W E P T) (χ : SetRel E E) {x : E} : x ∈ χ.image (c.participants ⁻¹' ↑Shan.Determiners.nan.deixis) ↔ ∃ (y : E), ¬c.agent ≤ y ∧ (y, x) ∈ χ

nân's far.from.speaker of (148) is the vicinity of a referent excluding the speaker.