From Allen (1995)
Examples:
- A dog entered with every man
- for each man x, there is some dog y and event z, such that z involves y entering with x (i.e. the group of men is distributive; one dog/event per man)
- there is some dog x and some event y, such that for each man z, y involves x entering with z (i.e. the group of men is collective; just one dog/event)
- there is some dog x, such that for each man y, there is some event z such that z involves x entering with y (i.e. the group of men is distributive; just one dog, but one event per man)
- there is some event x, such that for each man y, there is some dog z such that x involves z entering with y (i.e. the group of men is collective; just one event, but one dog per man)
i.e. six possible scope orderings, but only four are distinct - where 'dog' and 'enter' are adjacent, there is no contrast. [Therefore, we need a representation format which allows these four fully specified structures but no others. There should also be five underspecified possibilities in the description language:
dog/man/enter
> dog/man enter
> dog man enter [3]
> [1]
> dog/enter man [2]
> man/enter dog
> [1]
> enter man dog [4]
> dog man/enter
> [3]
> [2]
> man dog/enter [1]
> enter dog/man
> [2]
> [4]
Note: this is a well-formed type hierarchy.]
- We didn't see every dog
- for all dogs x, we didn't see x
- it is not true that for all dogs x, we saw x
- Everyone thought that Fido or Fifi would win
- For all x, x thought that [Fido would win or Fifi would win]
- Everyone thought that Fido would win or everyone thought that Fifi would win
- He will feed the hungriest dog tomorrow
- Take the hungriest dog x: go to tomorrow: he will feed x then
- Go to tomorrow: take the hungriest dog x: he will feed x then
- A fat dog always loses the race
- always: there is some fat dog x such that x loses
- there is some fat dog x such that x always loses the race
Three functions of NPs:
- definite reference - the addressee should be able to identify the object/set (e.g. the, possessive determiners)
- existential quantification/indefinite reference - introduce new objects/sets into the discourse (e.g. a, some, several, many, a few, two, seven, no; test: "There are _ men who like golf")
- universal quantification - all, each, every, most
Two interpretations for NPs denoting sets:
- collective - just one event in which all members participate as a group (e.g. The men met at the corner)
- distributive - a separate event per member (e.g. each man bought a suit)
Note: a continuum of implication:
- each man bought a suit -- distributive
- every man bought a suit
- all the men bought a suit
- the men bought a suit -- strongly collective
The collectiveness/distributiveness of an NP affects how it interacts with other NPs - in "X lifted a piano", if the subject has a collective interpretation, then the object cannot take wide scope (e.g. "Together, the men lifted a piano").
-- MarkMcConville - 16 Sep 2008