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What is Branching time semantics and why to use it?

The concept of branching time in the semantics of concurrent systems is well known and well understood. Still a formal deenition of what it means for a model or equivalence to respect branching time has never explicitly be given. This note proposes such a deenition. Additionally the opportunity is taken to voice an old but poorly understood argument for using branching time semantics instead of models or equivalences that are fully abstract with respect to some notion of observability.