As the extension of the description logic, many dynamic description logics are proposed for modeling and reasoning about Semantic Web Services. These dynamic description logics provide decidable reasoning mechanisms for the result of action execution. However, the procedure of action execution can not be described and reasoned about according to these logics. Inspired by an extended propositional dynamic logic studied by Pratt, this paper proposes two improvements to the dynamic description logic. One is that, semantics of actions in the dynamic description logic are redefined in such a way that each action is interpreted as a set of trajectories, where each trajectory is a sequence of possible worlds of the semantic model. The other is that, assertions on the procedure of action execution are introduced to the logic so that not only the result but also the procedure can be described for the execution of actions. As a result, a family of extended dynamic description logics named EDDL(X) is presented in this paper, where X represents well-studied description logics ranging from ALC (attributive language with complements) to SHOIN(D). Taking the description logic ALCQO (attributive language with complements, qualified number restrictions and nominals) as an example of the X of EDDL(X), this paper proposes a tableau decision algorithm for the logic EDDL(ALCQO) and proves that this algorithm is terminating, sound and complete. With EDDL(X), both the result and the procedure of action execution can be described and reasoned about. Therefore, compared with dynamic description logics, EDDL(X) provides further support for modeling and reasoning about semantic Web services.