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Abstract. The traditional notion of instantiation in Object-Oriented Modeling (OOM) requires objects to be complete, i.e., be fully certain about their existence and attributes. This paper explores the notion of partial instantiation of class diagrams, which allows the modeler to omit some details of objects depending on modeler's intention. Partial instantiation allows modelers to express optional existence of some objects and slots (links) as well as uncertainty of values in some slots. We show that partial instantiation is useful and natural in domain modeling and requirements engineering. It is equally useful in architecture modeling with uncertainty (for design exploration) and with variability (for modeling software product lines). Partial object diagrams can be (partially) completed by resolving (some of) optional objects and replacing (some of) unknown values with actual ones. Under the Closed World Assumption (CWA), completion reduces uncertainty of already existing objects, or deletes them if their existence is optional. Under the Open World Assumption (OWA), completion may additionally introduce new elements, perhaps uncertain. The paper presents a simple theory of partial instantiation and completion under the CWA. It shows that partial object diagrams can be modeled by subclassing and multiplicity constraints. As a result, class diagrams can implement partial instances with the well-known notions of subtyping and inheritance.