Semantic difference analyses support engineers in understanding model-changes on the semantic level and thereby assist change management in Model Driven Development (MDD). A semantic differencing operator for Class Diagrams (CDs) compares two input models based on their legal instances and outputs object structures that are permitted by the first but not the second input-CD. Under the closed-world assumption only instances of explicitly-modeled elements are permitted. This closed-world approach may be less suited for semantic refinement checking in early design phases, where new elements are added to a CD in order to refine it. Instead, an open-world approach can be utilized. In this paper, we outline, evaluate and compare two approaches for extending CDDiff, an existing closed-world semantic differencing operator for CDs, to an open-world operator: The first approach reduces the open-world problem to a bounded search via Alloy. The second approach transforms the input-CDs and reduces the open-world problem to closed-world semantic differencing. It also allows for combining open- and closed-world interpretations of model-elements.