If an agent executes an action, this will not only change the world physically, but also the agent's knowledge about the world. Therefore the occurrence of an action can be modeled as an epistemic state transition which maps the knowledge state of an agent to a successor knowledge state. For example, consider that an agent in a state s_0 executes an action a. This causes a transition to a state s_1. Subsequently, the agent executes a sensing action a_s, which produces knowledge and causes a transition to a state s_2. With the information which is gained by the sensation, the agent can not only extend its knowledge about s_2, but also infer additional knowledge about the initial state s_0. That is, the agent uses knowledge about the present to retrospectively acquire additional information about the past. We refer to this temporal form of epistemic inference as postdiction. Existing action theories are not capable of efficiently performing postdictive reasoning because they require an exponential number of state variables to represent an agent's knowledge state. The contribution of this thesis is an approximate epistemic action theory which is capable of postdictive reasoning while it requires only a linear number of state variables to represent an agent's knowledge state. In addition, the theory is able to perform a more general temporal form of postdiction, which most existing approaches do not support. We call the theory the h-approximation (HPX) because it explicitly represents historical knowledge about past world states. In addition to the operational semantics of HPX, we present its formalization in terms of Answer Set Programming (ASP) and provide respective soundness results. The ASP implementation allows us to apply HPX in real robotic applications by using off-the-shelf ASP solvers. Specifically, we integrate of HPX in an online planning framework for Cognitive Robotics where planning, plan execution and abductive explanation tasks are interleaved. As a proof-of-concept, we provide a case-study which demonstrates the application of HPX for high-level robot control in a Smart Home. The case-study emphasizes the usefulness of postdiction for abnormality detection in robotics: actions which are performed by robots are often not successful due to unforeseen practical problems. A solution is to verify action success by observing the effects of the action. If the desired effects do not hold after action execution, then one can postdict the existence of an abnormality
