We present a formal framework that can be used to specify and study a number of different semantics for rule execution in active databases. We shall consider the core of several active rule languages that are already available (e.g., Ariel, Starburst and HiPAC) but whose rule execution is specified only by informal descriptions. The framework is based on a generic active rule language and relies on a transaction rewriting technique. This technique takes a user defined transaction, which is viewed as a sequence of basic database updates forming a semantic unit, and translates it into a new transaction that explicitly includes the additional updates due to active rule triggering. We show that this framework provides a basis for the theoretical analysis and the comparison of different execution models of active rules. Moreover, it allows us to formally investigate a number of important issues related to active rule processing, such as transaction equivalence, confluence and optimization, independently of a specific rule executionmodel.