Data is underdetermined when there are variables whose values are unknown and the legal instantiations of these variables depend on given factors and the corresponding domain knowledge. The problem of instantiating the variables is a combinatorial problem. In this thesis we develop an approach to find all of the legal instantiations based on a specific knowledge formalization. We make use of a popular knowledge representation tool to make the formalization of knowledge for use cases with underdetermined data more accessible to users without programming experience. We argue that the approach is easier to use and to maintain than an alternative approach formalizing knowledge with imperative programming. We formalize a way of representing underdetermined data with an OWL ontology, and develop an algorithm to generate all of the legal instantiations based on the ontology. We also show a way of translating worlds represented in OWL to a representation of worlds in the Maude system. Furthermore, we argue for correctness of the algorithm by proving that it generates sound results and give the intuition for, and partly prove, how it generates complete results. The approach is successfully applied on parts of a use case of petroleum systems. However, the execution time of the implementation is long, and this is likely due to poor computational complexity. We discuss possible approaches to mitigate this issue.