This thesis presents the Planning System DLVK, which supports the novel Planning Language K. The language allows to represent AI planning problems in a declarative way and is capable of representing incomplete knowledge as well as nondeterministic effects of actions.After explaining some basics, the syntax and semantics of this language will be formally described and some results on the computational complexity of our language will be given, proving that K is capable of expressing hard planning problems, possibly involving incomplete knowledge or uncertainty, such as secure (conformant) planning.A translation from various planning tasks specified in K to a logic programming framework will be shown subsequently. We have implemented a prototype of a planning system, DLVK, on top of the disjunctive logic programming system DLV, to show the practical use of our translation. This prototype will be presented in detail. Finally, examples and experimental results will be given, together with an outlook to further research.