Certainty Closure On Tackling Constraint Problems with Uncertain Data

We present a generic framework to model and solve real-world constraint problems with incomplete or inconsistent data. Such problems are often simplified at present to tractable deterministic models, in order to find a solution; so doing, however, can lead us to solve the wrong problem or to introduce unsatisfiability because of the approximations made. The certainty closure framework addresses the data uncertainty by specifying what can be said with certainty, given what is known about the data. The aim is to provide a formal framework that considers all three aspects: (1) the modelling of uncertain data, (2) the definition of a closure to an uncertain constraint problem, (3) the guarantee that the closure derived is correct, i.e. holds under every satisfiable realisation of the data. We address these points by defining the certainty closure and outlining how it can be derived by transformation to an equivalent certain problem. We show the use of the framework in an uncertain network optimisation problem.