The propositional dynamic logic PDL is one of the most successful variants of modal logic; it plays an important role in many fields of computer science and artificial intelligence. As a logical basis for the W3C-recommended Web ontology language OWL, description logic provides considerable expressive power going far beyond propositional logic as while as the reasoning is still decidable. In this paper, we bring the power and character of description logic into PDL and present a dynamic logic ALC-DL for the semantic Web. The logic ALC-DL inherits the knowledge representation ability of both the description logic ALC and the logic PDL. With an approach based on Buchi tree automaton, we prove that the satisfiability problem of ALC-DL formulas is still decidable and is EXPTIME-complete. The logic ALC-DL is suitable for modeling and reasoning about dynamic knowledge in the semantic Web environment.