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Imitation is a powerful mechanism whereby knowledge may be transferred between agents (both biological and artificial). Key problems on the topic of imitation have emerged in various areas close to artificial intelligence, including the cognitive and social sciences, animal behavior, robotics, human-computer interaction, embodied intelligence, software engineering, programming by example and machine learning. Artificial systems used to study imitation can both test models of imitation derived from observational or neurobiological data on imitation in animals and then apply them to different kinds of nonbiological systems ranging from robots to software agents. A crucial problem in imitation is the correspondence problem, mapping action sequences of the demonstrator and the imitator agent. This problem becomes particularly obvious when the two agents do not share the same embodiment and affordances. This paper describes a new general imitation mechanism called ALICE (action learning for imitation via correspondence between embodiments) that specifically addresses the correspondence problem. The mechanism is implemented and its efficacy illustrated on the "chessworld" testbed that was created to study imitation from an agent-based perspective, i.e., by a particular agent in a particular environment.