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The aim of the crack project is the research and the development of a knowledge representation system based on description logics. The crack language di erentiates itself from other knowledge representation systems for its high expressivity and its provably sound and complete reasoning procedures. With respect to other systems available in the research community crack is more expressive, it is expandable to new constructs, it treats the conceptual and individual levels in a homogeneous way, it is modular, it is comparably fast. However, crack algorithms do not work in polynomial space, ie in the (arguably rare in practice) worst cases they may require exponential memory. The performance of the system has been tested against several di erent classes of random knowledge bases, characterized by an order parameter generating phase transitions in the satis ability probability space.