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We present an approach to declaratively manage run-time errors in data-intensive applications. When large volumes of raw data meet complex third-party libraries, deterministic run-time errors become likely, and existing query processors typically stop without returning a result when a run-time error occurs. The ability to degrade gracefully in the presence of run-time errors, and partially execute jobs, is typically limited to specific operators such as bulkloading. We generalize this concept to all operators of a query processing system, introducing a novel data type "partial result with errors" and corresponding operators. We show how to extend existing error-unaware operators to support this type, and as an added benefit, eliminate side-effect based error reporting. We use declarative specifications of acceptable results to control the semantics of error-aware operators. We have incorporated our approach into a declarative query processing system, which compiles the language constructs into instrumented execution plans for clusters of machines. We experimentally validate that the instrumentation overhead is below 20% in microbenchmarks, and not detectable when running I/O-intensive workloads.