In this paper, we consider the setting of graph-structured data that evolves as a result of operations carried out by users or applications. We study different reasoning problems, which range from ensuring the satisfaction of a given set of integrity constraints after a given sequence of updates, to deciding the (non-)existence of a sequence of actions that would take the data to an (un)desirable state, starting either from a specific data instance or from an incomplete description of it. We consider an action language in which actions are finite sequences of conditional insertions and deletions of nodes and labels, and use Description Logics for describing integrity constraints and (partial) states of the data. We then formalize the above data management problems as a static verification problem and several planning problems. We provide algorithms and tight complexity bounds for the formalized problems, both for an expressive DL and for a variant of DL-Lite.
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