We propose a history-based approximation of the Possible Worlds Semantics (PWS) for reasoning about knowledge and action. A respective planning system is implemented by a transformation of the problem domain to an Answer-Set Program. The novelty of our approach is elaboration tolerant support for postdiction under the condition that the plan existence problem is still solvable in NP, as compared to ΣP2 for non-approximated PWS of Son and Baral [20]. We demonstrate our planner with standard problems and present its integration in a cognitive robotics framework for high-level control in a smart home.