Anaphora for Concepts, Kinds, and Parts in Dynamic Interpretation

Krifka treats the head noun of a DP as introducing a discourse referent for a concept, a property with the noun's count feature. The kind pronouns take that concept to a kind: it takes the concept of a mass noun to its kind, and they the concept of a count noun to the kind of its plural closure, so a spider is resumed by them and mold by it. Krifka takes the feature to be formal, like grammatical gender, since pollen and pollen grains can describe the same stuff and are still resumed by it and them respectively, (8) and (12) on pp. 605–606. Concept referents are presupposed by the input assignment, as the referents of names are, so they survive negation, which is a test, while an entity referent introduced under negation does not. After John doesn't own a dog, the kind pronoun them is therefore interpretable and a partitive is not.

Implementation notes

• Assignments are total functions into a heterogeneous value type with a value marking indices outside the domain; an anaphor's presupposition is a conjunct of its update, so a failed presupposition makes the update empty rather than undefined.
• Negation is the paper's VP negation, the substrate's test (neg φ); the sentential negation with its condition that the negated existential extend the input differs only in ways irrelevant to projection. The concept referent's presupposition is a hypothesis of the projection theorems; the paper derives it from the head noun's partial lexical entry.
• Which concepts sponsor kinds (dogs from the animal shelter does not) is left to the lexicon, as in the paper.
• The count feature is read off the head noun's English entry: a count noun is one a numeral counts (ClassifiedNoun.IsCount).
• Individuals form any join semilattice, as in the paper (§3); the models are Link's nonempty sets of atoms, Mereology.Individual. A kind is a function from worlds to partial individuals, and σ is ι of IsGreatest, as in (13a), so it is ∩, Kind.down. The sufficient condition for σ is stated for finite extensions (Kind.down_isSome_of_supClosed), where the paper has closure under arbitrary sums, since Link's model has no empty sum.

TODO

• cattle, police and clothes are resumed by they although no numeral counts them, so reading the feature off the counting record selects it for them. The paper does not discuss such nouns; they need the feature recorded apart from the counting record.

References

• Krifka 2026, Anaphora for Concepts, Kinds, and Parts in Dynamic Interpretation
• Chierchia 1998, Reference to Kinds across Language formalized
• Link 1983, The Logical Analysis of Plurals and Mass Terms
• Hofmann 2025, Anaphoric Accessibility with Flat Update formalized