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Extension of the logic

We will define that a model m1 is a compression of a model m2after time , represented as if:

• m1|i = m2|i for .
• for all propositional symbols in , if and only if and if then
Intuitively, a model m1 is a compression of m2 after if they agree in everything up to time t, and after time all activities in m1 start before (or at the same time) as the activities in m2.

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 non-monotonic 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 Up: Figuring out what to Previous: Figuring out what to
Jacques Wainer
2000-01-06