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. Composition techniques are developed and applied to A-LTL to construct the specification of an adaptive program. We introduce adaptation semantics graphs to visually represent the adaptation semantics, which can also be used to automatically generate specification for adaptive programs.