  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.
