Dayal (2004): Number marking and (in)definiteness in kind terms #

Dayal argues that bare nominals are kind terms or definites, never genuine indefinites, and that number morphology decides how a kind term is marked for definiteness. Revised Meaning Preservation, (39c), ranks ι with ∩ above ∃, where Chierchia ranked ∩ alone on top, so wherever ι is unblocked a bare nominal is a kind or a definite even where ∩ is undefined. ∩ is undefined for a singular count noun, whose kind term is formed by ι over the taxonomic domain instead, (77d). Section 4 places ι above ∩ on a scale of definiteness: a language's definite determiner lexicalizes ι alone or ι and ∩, and the Blocking Principle applies to its canonical meaning ι and may or may not apply to ∩.

Main definitions #

kindShift: the shift that forms the kind term of a nominal of a given number.
Lexicalization: the shifts a language's definite determiner lexicalizes and blocks.

Main results #

kind_and_definite, definite_not_indefinite: where ι is unblocked a bare nominal is a kind or a definite, even is mashiin ke TukRe 'parts of this machine', (45).
chierchia_not_definite: Chierchia's ranking pre-empts the definite readings of Hindi, Russian and Chinese bare nominals, (17) and (18).
english_chierchia_iff_dayal, exists_iff_not_down, english_bare_singular: with ι and ι^x blocked the rankings agree, ∃ applies exactly where ∩ is undefined, (43) and (44), and an English bare singular has no shift, (88a).
Lexicalization.classification: the principles admit exactly four types of language.
Lexicalization.not_englishInReverse, Lexicalization.not_germanInReverse: two impossible languages of Section 5.
rows_agree: the kind-term judgments of (6a), (14) to (16), (46), (78), (86) and (87a).

Implementation notes #

Availability is the theory layer's (Semantics/Genericity/MeaningPreservation.lean), and each ranking is written as the predicate of its upper tier, Chierchia's (· = .down) and Dayal's (· ≠ .exists). Whether ∩ is defined is a hypothesis, since it fails for plural properties anchored to particular entities, fn. 1.
The substrate's Determiner.Inventory.Blocks ignores the domain clause of the Blocking Principle, (39a): English a takes only singulars and so leaves ∃ open to a bare plural, but Blocks .exists holds of the English inventory outright. The bare-plural theorems therefore take the blocking of ∃ as a hypothesis, and the English fragment is read only for the and for the bare singular.
Which side of the cut-off each sampled language falls on is the paper's analysis (lexicalizationOf); that ι is lexicalized exactly where the fragment has a definite article is checked (iota_mem_lexicalized_iff).
A mass term is number-neutral, fn. 25, and so is a Chinese noun, which aligns with plurals, p. 413; both have the general number.

TODO #

Sections 2.2 and 2.3: number morphology and the instantiation set, (28) and (29), and the sub-group readings bare plurals have and bare singulars lack, which rule out the third impossible language of Section 5, Hindi-in-reverse.
Sections 3.2 and 3.3: the taxonomic domain, with the sub-kind hierarchy and the sum lattice of taxonomic entities kept apart, fn. 32, and the atomicity of singular kinds.
Section 4.2 on Romance plural definites in the nuclear scope, (83) to (85), and Section 4.4 on bare singulars beside definite ones in Hebrew, Hungarian and Brazilian Portuguese.

Dayal (2004): Number marking and (in)definiteness in kind terms #

Main definitions #

Main results #

Implementation notes #

TODO #

References #

Revised Meaning Preservation (Section 2.5) #

Singular kinds (Section 3.4) #

The scale of definiteness (Section 4) #

The data #