From Allen (1995)

Examples:

• A dog entered with every man
  1. 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)
  2. 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 X 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]

-- MarkMcConville - 16 Sep 2008