We introduce F-ALCI, a federated version of the description logic ALCI. An F-ALCI ontology, like its packagebased counterpart ALCIP, consists of multiple ALCI ontologies that can import concepts or roles defined in other modules. Unlike ALCIP, which supports only contextualized negation, F-ALCI, supports contextualization of each of the logical connectives, a feature that allows more flexible reuse of knowledge from independently developed ontologies. We provide a new semantics for F-ALCI based on image domain relations and establish the conditions that need to be imposed on domain relations to ensure properties, such as preservation of unsatisfiability and monotonicity of inference, that are desirable in distributed web applications. We also establish the decidability of F-ALCI.