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Ambassador agents represent simulation services that are candidates to contribute to the solution of a problem. They need to know and express enough about the simulations to negotiate with other ambassador agents if the represented simulation systems can be composed to contribute to the solution. A formal approach to simulation interoperability based on set theory and date modeling theory was developed. The formal model of data in M&S capturing possible representations of real or imagined things in the world including definitions for existential and transformational dependencies is presented. Existential dependencies capture the relationships within a model while transformational dependencies capture the relationships between interactions with a model. These definitions are used to formally specify interoperation, the ability to exchange information, as a necessary condition for interoperability. The elements needed for a language needed for ambassador agents are derived using the formal approach to interoperability.