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We introduce a logic-based incremental approach to graph repair, generating a sound and complete (upon termination) overview of least-changing graph repairs from which a user may select a graph repair based on non-formalized further requirements. This incremental approach features delta preservation as it allows to restrict the generation of graph repairs to delta-preserving graph repairs, which do not revert the additions and deletions of the most recent consistency-violating graph update. We specify consistency of graphs using the logic of nested graph conditions, which is equivalent to first-order logic on graphs. Technically, the incremental approach encodes if and how the graph under repair satisfies a graph condition using the novel data structure of satisfaction trees, which are adapted incrementally according to the graph updates applied. In addition to the incremental approach, we also present two state-based graph repair algorithms, which restore consistency of a graph independent of the most recent graph update and which generate additional graph repairs using a global perspective on the graph under repair. We evaluate the developed algorithms using our prototypical implementation in the tool AutoGraph and illustrate our incremental approach using a case study from the graph database domain.
Graphs play an important role in many areas of Computer Science. In particular, our work is motivated by model-driven software development and by graph databases. For this reason, it is very important to have the means to express and to reason about the properties that a given graph may satisfy. With this aim, in this paper we present a visual logic that allows us to describe graph properties, including navigational properties, i.e., properties about the paths in a graph. The logic is equipped with a deductive tableau method that we have proved to be sound and complete.