First, we observe that temporally annotated conditions and effects can be accumulated, because the temporal annotation distributes through logical conjunction. Therefore, we can convert conditional effects so that their conditions are simple conjunctions of at most one at start condition, at most one at end condition and at most one over all condition. It should be noted that we do not allow logical connectives other than conjunction in combining temporally annotated propositions. Allowing other connectives would create significant further complexity in the semantics and create potentially paradoxical opportunities for communication from future states to earlier states. Similarly to conditions, durative action effects can be reduced to a conjunction of at most one at start effect and at most one at end effect. Treatment of conditional effects then divides into three cases. The first case is very straightforward: any effect in a durative action of the form (when (at t p) (at t q)), where the condition and the effect bear the same single temporal annotation, can be transformed into a simple conditional effect of the form (when p q) attached to the start or end simple action according to whether is start or end. Since this case is straightforward we will not explicitly extend the previous definitions to cope with it. The second case is one in which the condition of a condition effect has at start conditions and the effect has at end effects.
Note that we consider conditional effects in which the effects occur at the start, but with conditions dependent on the state at the end or over the duration of the action, to be meaningless. This is because they reverse the expected behaviour of causality, where cause precedes effect. In any attempt to validate a plan by constructing a trace such reversed causality would be a huge problem, since we could not determine the initial effects of applying a durative action until we had seen what conditions held over the subsequent interval and conclusion of its activity, but, equally, we could not see what the effects of activity during the interval would be without seeing the initial effects of applying the durative action. This paradox is created by the opportunity for an action to change the past.
To handle this second case we need to modify the state after the start of the durative action to ``remember'' whether the start conditions were satisfied and communicate this to the end of the durative action where it can then be simply looked up in the (then) current state to determine whether the conditional effect should be applied. We apply a transformation to conditional effects of the form (when (and (at start ps) (at end pe)) (at end q)) into a conditional effect added to the start simple action, (when ps (M)), and a conditional effect added to the end simple action, (when (and pe (M)) q), where M is a special new proposition, unique to the particular conditional effect of the particular application of the durative action being transformed. By ensuring that this proposition is unique in this way, there is no possibility of any other action in the plan interfering with it, so it represents an isolated memory of the fact that ps held in the state at which the durative action was started. If a conditional effect does not have at end conditions, the same transformation can be applied, simply ignoring pe in the previous discussion. Figure 15 depicts the transformation of a single durative action, , with a conditional effect, into a collection of level 2 actions, complete with the appropriate ``memory'' proposition (in this case called ).
The importance of the memory introduced in this transformation is explained in Figures 16 and 17. Figure 16 shows the ambiguity that results from not remembering how a state, on the trajectory of a plan, was reached. The figure illustrates that if one is in a state at the point when durative action (as described in Figure 15) ends, it is impossible to determine from the state alone whether should be added or not. This is because it is possible to have reached the state by at least two different paths, with at least one path having seen started in a state in which held and at least one path having seen started in a state in which did not hold (using an action, achieve, with as its only effect). The state does not contain any information to disambiguate which path was used to reach it, and hence cannot determine the correct value of after ends.
The third, and final, case is where the durative action has conditional effects of the form:


The addition of these new memorychecking actions means that it is no longer true to claim that the added actions cannot change the state. However, memory propositions are unique to the task of communication for a single action instance, so the effects that memorychecking actions might have on these have no implications for other invariants.