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We will define that a model m_{1} is a compression of a model m_{2}after time ,
represented as
if:

m_{1}i = m_{2}i for
.
 for all propositional symbols in ,
if and only if
and
if
then
Intuitively, a model m_{1} is a compression of m_{2} after
if they agree in everything up to time t, and after time
all activities in m_{1} start before (or at the same time) as
the activities in m_{2}.
The relation
is reflective, transitive, and antisymmetric.
We will say that a model m' is minimal (in relation to
)
in a set M if there is no other model in M that is a
compression of m' and that is not m' itself.
Let us call X the set of all minimal models of all continuations of
the workcase, after the current time ,
that are consistent with
F. The activities that can start immediately after time ,
are
the activities
such that:

(20) 
Intuitively, the models in X are the continuations of the case after
that are consistent with F, and for which the start of all
activities is anticipated as much as possible. If an activity p is
enabled, it means it could start in the next moment, and therefore, in
minimal models they will indeed start at the next moment. The method
of defining a partial order among models and selecting only the
minimal one is the essence of the preferential nonmonotonic logics
[12].
We will denote the fact that for all
as

(21) 
that is, that given the workcase wc at time
and the
procedures and policies ,
p can start in the next moment.
Next: Modes of use of
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Jacques Wainer
20000106