Dependent Plurals and Three Levels of Multiplicity

Minor analyses dependent plurals in a modified Plural Compositional DRT, where a state is a set of assignments. A dref's value at an assignment can be a sum, the dref can take several values across a state, and several values across states. The singular requires atomic values that are all the same, the plural is vacuous, and a bare plural's multiplicity is Exh's negation of the singular. Numerals count atoms at every assignment. Floating all splits a sum into its atoms across the assignments of one state and floating each across singleton states, so The girls were all wearing hats holds when each girl wore one hat and the hats differ, while The girls were each wearing hats and All the girls were wearing several hats need more than one hat per girl.

Main definitions

• Minor2022.intro: dref introduction (60), the strict lift of random assignment.
• Minor2022.atomic, Minor2022.unique, Minor2022.cardinal: the conditions (75), (77) and (78), each a property of the values of a dref across the state.
• Minor2022.split, Minor2022.distW, Minor2022.distS: the split (90), and weak and strong distributivity (93) over the distributivity operator (94), Update.dist.
• Minor2022.sentence: a subject over a distributivity operator over a verb and its object.
• Minor2022.max, Minor2022.detPl, Minor2022.detSg: maximization over assignments (106) and the plural and singular quantificational determiners (108), (109).
• Minor2022.stateMax: the state-level maximization of Brasoveanu that fn. 42 contrasts with (106).

Implementation notes

• Assignments come from any register structure and values from any partial order, whose atoms are Mereology.Atom. The examples take finite sets of atoms, whose sum is union.
• Every register content is an individual, so the lexical relations (63) are Plural CDRT's atomic conditions PCDRT.atom at the identity PCDRT.ValueEmbedding.
• The event dref of event closure (72) is folded into a verb relating the values of the agent and the theme: in every derivation formalized here it is introduced together with the object.
• A model fixes the object noun and the verb. A meaning varying with the model is read as a set of model–input–output triples (acrossModels), whose strict inclusion is Generalized Strength (89), and Exh is Exhaustification.exh there.
• Exh is placed above the VP, the first site the paper considers for each sentence.
• The girls is the sum of the girls of the model, the value the maximization of fn. 45 (i) returns there. All the girls in (3) is weak distributivity over the girls, the distributivity a plural determiner places over its nuclear scope (108), without its two maximized drefs.

TODO

• The conservativity argument for the Ban on Singular Licensors ((186)–(195)) beyond its global-atomicity lemma, modified numerals (§6.3.2, §6.3.3), the other sites of Exh, the discourse rule (200), and the Schein–Kratzer sentences of Appendix 2.

References

• Minor 2022, Dependent Plurals and Three Levels of Multiplicity
• Brasoveanu 2008, Donkey pluralities: plural information states versus non-atomic individuals
• Zweig 2009, Number-neutral bare plurals and the multiplicity implicature