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We introduce the concept of a security language, used to express security statements in a distributed system. Most existing security languages encode security statements as schematized data structures, such as ACLs and X.509 certificates. In contrast, Binder is an open logic-based security language that encodes security statements as components of communicating distributed logic programs. Binder programs can be more expressive than statements in standard security languages, and the meanings of standard security constructs and operations such as certificates and delegation are simplified and clarified by their formulation in Binder. Translation into Binder has been used to explore the design of other new and existing security languages.