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Computer software must dynamically adapt to changing conditions. In order to fully realize the benefit of dynamic adaptation, it must be performed correctly. The correctness of adaptation cannot be properly addressed without precisely specifying the requirements for adaptation. This paper introduces an approach to formally specifying adaptation requirements in temporal logic. We introduce A-LTL, an adaptation-based extension to linear temporal logic, and use this logic to specify three commonly used adaptation semantics. Neighborhood composition and sequential composition techniques are developed and applied to A-LTL to construct the specification of an adaptive system. We introduce adaptation semantics graphs to visually present the adaptation semantics. Specifications for adaptive systems can be automatically generated from adaptation semantics graphs.