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Many transaction processing applications execute at isolation levels lower than SERIALIZABLE in order to increase throughput and reduce response time. The problem is that non-serializable schedules are not guaranteed to be correct for all applications. The semantics of a particular application determines whether that application will run correctly at a lower isolation level, and in practice it appears that many applications do. Unfortunately, we know of no analysis technique that has been developed to test an application for its correctness at a particular level. Apparently decisions of this nature are made on an informal basis. In this paper we describe such a technique in a formal way.We use a new definition of correctness, semantic correctness, which is weaker than serializability, to investigate the correctness of such executions. For each isolation level, we prove a condition under which transactions that execute at that level will be semantically correct. In addition to the ANSI/ISO isolation levels of READ UNCOMMITTED, READ COMMITTED, and REPEATABLE READ, we also prove a condition for correct execution at the READ COMMITTED with first-committer-wins (a variation of READ COMMITTED) and at the SNAPSHOT isolation level. We assume that different transactions can be executing at different isolation levels, but that each transaction is executing at least at the READ UNCOMMITTED level.