8 Concluding Remarks

concern the introduction of disjunctions or even general formulas for the add and delete sets, and the integration of evaluable function symbols in order to cope with arithmetics, for instance. References [1] M. Decker. Entwurf und Implementierung eines Planers basierend auf einem Konsi-stenzerhaltungsmechanismus einer deduktiven Datenbank. Diplomarbeit, 1991. 15 loc-constr-1: 8x; y; z : on(x,y) ^ on(x,z)) y = z loc-constr-2: 8x; y; z : on(x,y) ^ on(z,y)) x = z loc-constr-3: 8x 9y : is(x,block)) on(x,y) ^ is(y,location) connected-rule-1: 8x; y : is(connected,x,y) ^ on(x,loc1)) on(y,loc2) connected-rule-2: 8x; y : is(connected,x,y) ^ on(x,loc2)) on(y,loc3) Figure 8: Constraints and rules for the Dumbbell Problem Assume we want to have a at loc2, thus on(a; loc2) is the goal to achieve. If this is added to the initial world, the following repair is generated to make the resulting world consistent again: This computation proceeds in principle as follows. If we assert on(a; loc2), but also have on(a; loc1), constraint 1 is violated. The only choice to repair it is deleting on(a; loc1), expressed by the literal :on(a; loc1). Now, on(b; loc2) violates two constraints: constraint 1, because b is both at loc2 and loc3, and constraint 2, because both b and c are at the same place 6. This is resolved by removing on(b; loc2) and on(c; loc3). Finally, both b and c cause problems with constraint 3, because it requires a location for each existing block. The only choice to repair this is obvious. Note that a goal world will be complete, if it satises the repair set. Last not least, some remarks to nding a plan for this problem. First, an appropriate 'move' operator must not have the precondition that the target location is empty, because we want to handle qualications implicitly. When looking for a plan, we have to nd a sequence of 'move's that 'perform' the repair; [move(a; loc1; loc2), move(c; loc3; loc1)] would do the job. However, this does not mean that the goal world is actually achievable: the intermediate world is inconsistent, because c blocks loc3. This plan could only be carried out if we had two actors that can 'move' in parallel. The current implementation of our planner does not handle parallel actions, but future research will investigate this. We have described a novel approach to planning based on deduction. The deductive system consists of a deductive database enhanced by a procedure for maintaining …