Bare NPs: Kind-Referring, Indefinites, Both, or Neither?

Krifka treats bare noun phrases as properties that type shifts, applied locally, turn into indefinites or kinds: in the terms of the title, they are neither, but can become both. A count noun relates numbers to individuals, so a singular count noun cannot be an argument, and the semantic plural fills the number argument without requiring more than one, since Yes, one answers Do you have dogs?. The existential shift applies where a predicate meets a verbal predicate, so a bare plural takes narrow scope under negation even when moved over it, while a determiner phrase scopes wide. Kind reference is Chierchia's down operator, which Krifka does not confine to cumulative properties.

Implementation notes

• Composition is stated on extensions at a world. The composition rule (51) is Den.app: functional application whichever way is well formed, and otherwise the existential shift of a predicate meeting a verbal predicate. Movement over negation binds a type-neutral variable, which substitutes the moved denotation at its trace, or an entity variable, which abstracts over the trace; a property has no rule for meeting the abstract, which is the paper's requirement that the trace of a bare noun phrase be untyped.
• Individuals are finite sets of atoms, and a count noun holds of nonempty ones only: the non-overlap of (53b), ¬∃z[z ≤ x ∧ z ≤ y], presupposes a domain without a null individual, so no individual consists of zero dogs and without dogs the semantic plural holds of nothing. Counting atoms is the extensive measure Finset.card of Mereology.IsExtensiveMeasure, so the count of an individual is unique and adds over non-overlapping individuals, (53), numeral phrases are quantized, and the semantic plural is cumulative. Link's nonempty sets of atoms (Mereology.Individual) would also exclude the null individual, but their cardinality, Set.ncard, is no extensive measure, being 0 on infinite sets.
• The down operator is Kind.down, the largest member of the extension at each world, which Krifka defines wherever there is one, as for one dog in a world with one dog (down_withNumber_one).
• The topic condition on kind reference, the choice-function reading of some, and the singular definite generics of the paper's last section are not formalized.

References

• Krifka 2003, Bare NPs: Kind-Referring, Indefinites, Both, or Neither?
• Chierchia 1998, Reference to Kinds across Language formalized
• Partee 1987, Noun Phrase Interpretation and Type-shifting Principles formalized
• Krifka 1989, Nominal Reference, Temporal Constitution and Quantification in Event Semantics formalized