Dynamic Change

The central concern of dynamic change is the fact that there was an old ``process model'' F_o and now there is a new model F_n. The case wc was assumed to be consistent with F_o up to time $\hat{t}$, that is $wc, \hat{t}\;\sim\;F_o$. The issue is whether the workcase is consistent with the new model, and what should be the next activities to be executed. In other words, one would like to discover whether $wc, \hat{t}\;\sim\;F_n$, and if so, determine the set of activities psuch that $\Box F_n, wc, \hat{t}\;\rhd\;p$.

If indeed $wc, \hat{t}\;\sim\;F_o$ and $wc, \hat{t}\;\sim\;F_n$ then the workcase can be ``transfered'' to the new process. We will say that the change is safe for that workcase (at that time). If for all workcases and for all times, the change is safe, we will say that the change is everywhere safe. From the definition of logical consequence, if a change is everywhere safe then

$$F_o \rightarrow F_n$$ (22)

that is, a change is everywhere safe if the new process model is implied by the old one.

Of course it may be the case that the workcase is not consistent with the new procedures F_n. The issue is what activities should be performed in order to make the case consistent with the new procedures. One possibility is that the case is left to follow the old procedure for a while until a moment in the future in which it can be ``transfered'' to the new procedure. This can be modeled as, whether there is (will be) a time $t' > \hat{t}$ such that

$$wc, t' \;\sim\;F_n \quad \hbox{and for all~} t \leq t', \; wc,t \;\sim\; F_o$$

Another possibility is that the case may be artificially rolled back to a previous state, and allowed to continue from there on.

$$\hbox{there exists~} t' \leq \hat{t}\hbox{~and~} wc, t' \;\sim\;F_n$$

It must be noted that this operation is extra logical, we are artificially ``going back in time'' by choosing $t' < \hat{t}$, if an activity that cannot be undone (like shipping the merchandise) happened after t' that will not be taken into consideration under this scheme. In this case a better approach would be to use the scheme above: allow the case proceed in the F_o rules, possibly undoing some of those activities, until it reaches a state from which it can be transfered to F_n.

Although we could represent what was required for a case to be dynamically changed to a new procedure, in the case of an unsafe change we cannot yet determine if there are algorithms to determine when in the future (or in the past) could a case be transfered to the new procedure.