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##

Actions by Persons and Joint Actions of Groups

When there is more than one actor acting, we can consider three levels
of complexity. The simplest level is when the actors act jointly to
achive the goal. The second level is when one actor (or more than
one) does something to motivate the others, e.g. one person pays
another to do something. This generalizes to a hierarchy of
influence. The hard level is when the actors have competing
motivations and must negotiate or fight. This is the subject of game
theory, and we won't pursue it in this article.

As MCP was originally formulated, the missionaries and cannibals are
moved like pieces on a chessboard. Let's consider elaborations in
which the actions of individual missionaries and cannibals are
considered. One eventual goal might be to allow a formalization in
which a cannibal has to be persuaded to row another cannibal across
the river and bring the boat back. However, our discussion starts
with simpler phenomena.

We now consider an action by a person as a particular kind of event.
What we have written we now write
. If there is only one person, nothing is
gained by the expansion.

Consider a proposition
, meaning
that the person can achieve the goal starting from the
situation . For the time being we shall not say what goals are,
because our present considerations are independent of that decision.
The simplest case is that there is a sequence of actions
such that

satisfies .
Now let's consider achievement by a group. We will say
provided there is a sequence of
events
,
where each is in , and the s are not assumed
to be distinct, and such that

satisfies .
We can now introduce a simple notion of a person leading a group,
written
or more generally
. We want the axioms

Thus a leader of a group can achieve whatever the group can achieve.
Note that need not be a member of for this definition
to work.

We could give the same definition for
, but
maybe it would be better to make a definition that requires that
maintain his leadership of in the succeeding
situations.

is too strong a statement in general, because
the members of a group only accept leadership in some activities.

** Next:** Formalizing some elaborations
** Up:** Situation Calculus Representations
** Previous:** Not so simple situation
*John McCarthy *

2003-09-29