Certainty Closure Reasoning About Constraint Problems with Uncertain Data

We present a generic framework to reason about constraint problems with incomplete or erroneous data. Such problems are often simplified at present to tractable deterministic models, or modified using error correction methods, with the aim of seeking a solution. However, this can lead us to solve the wrong problem because of the approximations made. Such an outcome is of little help to the user who expects the right problem to be tackled and correct information returned. The certainty closure framework aims to provide the user with reliable insight by: (1) enclosing the uncertainty using what is known for sure about the data, (2) guaranteeing the true problem is contained in the model so described, and (3) efficiently deriving the closure to an uncertain constraint problem. In this paper we define the certainty closure and show how it can be derived by transformation to an equivalent certain problem. We demonstrate the benefits of the framework on a real-world network traffic analysis problem with uncertainty.