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The imperfect nature of context in Ambient Intelligence environments and the special characteristics of the entities that possess and share the available context information render contextual reasoning a very challenging task. The accomplishment of this task requires formal models that handle the involved entities as autonomous logic-based agents and provide methods for handling the imperfect and distributed nature of context. This paper proposes a solution based on the Multi-Context Systems paradigm in which local context knowledge of ambient agents is encoded in rule theories (contexts), and information flow between agents is achieved through mapping rules that associate concepts used by different contexts. To handle imperfect context, we extend Multi-Context Systems with nonmonotonic features: local defeasible theories, defeasible mapping rules, and a preference ordering on the system contexts. On top of this model, we have developed an argumentation framework that exploits context and preference information to resolve potential conflicts caused by the interaction of ambient agents through the mappings, and a distributed algorithm for query evaluation.