On March 23rd, Sergey Minor defended his thesis, Dependent Plurals and the Semantics of Distributivity. Most linguists have learned about the difference between cumulative and distributive readings in examples like:
Two opponents posed twelve questions.
On the distributive reading, each of the two opponents asked twelve questions; there would have been twenty four distinct questionings involved. If a question along with its answer lasts ten minutes, then this event would take at least four hours (setting aside the possibility of simultaneous questions).
On the cumulative reading, two opponents are involved in questioning, and a total of twelve questions get asked, and the reading is compatible with different combinations of opponents posing different questions, for example they might have each posed six questions, in which case the event could have been over in two hours, or one might have posed one question and the other eleven.
Quantifiers like both and most allow the distributive reading but not the cumulative one.
Both opponents posed twelve questions.
If there were a cumulative reading, it would allow for a scenario in which twelve questions together were posed by the pair of opponents. No such reading is available.
However, quantifiers like both and most do allow what has come to be known as the dependent plural reading.
Both opponents posed questions.
For this sentence, there is a distributive reading in which the two opponents each posed questions, in the plural; hence this would take at least forty minutes. But the bare plural questions also has a dependent plural reading here. On the dependent plural reading, both opponents were involved in questioning, and multiple questions were posed, but each opponent may have only posed a single question.
Dependent plurals may also be dependent on non-quantificational referents, but not on singular (strongly distributive) quantifiers like each and every. In the following sentence, unlike the previous one, only a distributive reading is possible, and each opponent must have posed multiple questions.
Every opponent posed questions.
Minor shows in his thesis that dependent plurals are more interesting than you ever imagined, and develops an account for different ways of expressing that more than one object is present in a situation. He adopts a modified version of the framework of Plural Compositional Discourse Representation Theory, or PCDRT, adapting it with the addition of a type for events as well as operators for exhaustivity and distributivity.
I leave it as an exercise to the reader to compute the readings in the following:
Four analyses are applied to three types of determiners interactive with three types of plurals on five hundred pages.