Champollion, Lucas, Justin Bledin, and Haoze Li. 2017. Rigid and flexible quantification in plural predicate logic.
Proceedings of Semantics and Linguistic Theory (SALT) 2017.

[Full paper on lingbuzz]

Abstract:  Noun phrases with overt determiners, such as some apples¬†or a quantity of milk, differ from bare noun phrases like apples or milk in their contribution to aspectual composition. While this has been attributed to syntactic or algebraic properties of these noun phrases, such accounts have explanatory shortcomings. We suggest instead that the relevant property that distinguishes between the two classes of noun phrases derives from two modes of existential quantification, one of which holds the values of a variable fixed throughout a quantificational context while the other allows them to vary. Inspired by Dynamic Plural Logic and Dependence Logic, we propose Plural Predicate Logic as an extension of Predicate Logic to formalize this difference. We suggest that temporal for-adverbials are sensitive to aspect because of the way they manipulate quantificational contexts, and that analogous manipulations occur with spatial for-adverbials, habituals, and the quantifier all.

Keywords:  all, aspectual composition, dependence logic, dynamic plural logic, for-adverbials, plural predicate logic, quantification, quantization puzzle, team logic, telicity