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UML Class Diagrams (UCDs) are the best known class-based formalism for conceptual modeling. They are used by software engineers to model the intensional structure of a system in terms of classes, attributes and operations, and to express constraints that must hold for every instance of the system. Reasoning over UCDs is of paramount importance in design, validation, maintenance and system analysis; however, for medium and large software projects, reasoning over UCDs may be impractical. Query answering, in particular, can be used to verify whether a (possibly incomplete) instance of the system modeled by the UCD, i.e., a snapshot, enjoys a certain property. In this work, we study the problem of querying UCD instances, and we relate it to query answering under guarded Datalog +/-, that is, a powerful Datalog-based language for ontological modeling. We present an expressive and meaningful class of UCDs, named UCDLog, under which conjunctive query answering is tractable in the size of the instances.