Alice and Bob want to surprise their sister Carol with a joint present
for her birthday, two weeks from now. They therefore go into a closed
room to decide on the present and to plan how they will buy it.
The plan will not work:
The following constraints must be satisfied by the solution:
- If Carol is also in the room.
- If the door is open and Carol is in the next room.
- If one of them tells Carol.
- If they do not consult together.
- If they can't agree on a present.
- If they wait until after Carol's birthday.
- It will probably not work if Carol sees that they have the present
before they give it to her.
- On the other hand, it probably will
work if Carol sees the present in the store.
- The plan will work if, instead,
- They discuss the plan during a walk outside.
- They pass a hidden written message.
- They go together to buy the present, or one of them goes singly
to buy the present.
- If Carol is not surprised, infer that she
somehow got wind of their plan.
If the plan is executed, and we know that Alice has not spent any
then infer that Bob bought the present and that Alice owes him for her
If Alice and Bob present Carol with present P on her birthday, infer
that P is the present they decided on.
Note that the problem involves a variety of domains: time, a little space and physics,
knowledge, perception, naive psychology, multi-agents.
- The events enumerated in this plan are not the only events that
transpire in the next two weeks, or even the only actions of Alice and
in the next two weeks.
Therefore, it will be considered a weakness in a theory if
it supports, either monotonically or non-monotonically, the inference
nothing else happens.
Similarly, Carol knows lots of stuff; she just doesn't know about the
present. It will be considered a weakness in a theory if it supports
inference that Carol knows nothing at all (or, more precisely, that she
knows nothing except truths that hold in all possible worlds).
Ernie Davis (
firstname.lastname@example.org), New York University,
U.S.A. (29th May 2001)