We study the correctness of shared data structures under reads-write concurrency. A popular approach to ensuring correctness of read-only operations in the presence of concurrent update, is read-set validation, which checks that all read variables have not changed since they were first read. In practice, this approach is often too conservative, which adversely affects performance. In this paper, we introduce a new framework for reasoning about correctness of data structures under reads-write concurrency, which replaces validation of the entire read-set with more general criteria. Namely, instead of verifying that all read shared variables still hold the values read from them, we verify abstract conditions over the shared variables, which we call base conditions. We show that reading values that satisfy some base condition at every point in time implies correctness of read-only operations executing in parallel with updates. Somewhat surprisingly, the resulting correctness guarantee is not equivalent to linearizability, and is instead captured through two new conditions: validity and regularity. Roughly speaking, the former requires that a read-only operation never reaches a state unreachable in a sequential execution; the latter generalizes Lamport’s notion of regularity for arbitrary data structures, and is weaker than linearizability. We further extend our framework to capture also linearizability. We illustrate how our framework can be applied for reasoning about correctness of a variety of implementations of data structures such as linked lists.