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Current aspect specification methods do not provide enough support for explicitly specifying aspects and their weaving logic, nor do they provide effective and suitable mechanisms for aspect analysis and evaluation. A formal approach for specifying architecture aspects and their weaving logic is presented. In this approach, architecture aspects and their weaving logic are specified in independent abstract mechanisms. More importantly, Petri Nets are used as the common foundations for describing their behaviors. Owing to the powerful specification capability of these mechanisms, the main advantages of this approach lie in that it can not only specify complex aspect architecture structures and behaviors and their complex weaving logic, but also make it possible for reasoning about and evaluating the weaving results. A simple example is given to illustrate the approach and its advantages.