Abstract
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.
Highlights
Numerous approaches on model inconsistency and repair operate in varying frameworks with diverse assumptions on the underlying model and consistency conditions
We develop subsequently an incremental deltabased graph repair algorithm for the scenario where a graph is subject to a sequence of updates leading to inconsistent graphs that require the computation of graph repairs after every step. We introduce to this extend an additional data structure in the form of a satisfaction tree to enable incrementality to reduce the computational cost for computing graph repairs when a graph update is provided
For the demonstration of satisfaction trees and the deltabased graph repair algorithm from the section, we extend our running example by considering the graph update u given in simplified notation in Fig. 10a that results in the graph Gu from Fig. 5c, which is inconsistent w.r.t. the graph conditions (GCs) ψ from Fig. 5a
Summary
Numerous approaches on model inconsistency and repair (see [28] for an excellent recent survey) operate in varying frameworks with diverse assumptions on the underlying model and consistency conditions. In the second scenario, which is supported by a delta-based graph repair algorithm, a graph update that changes a given graph to another possibly inconsistent graph is given. The paper is self-contained by (a) reintroducing preliminaries on typed directed graphs together with categorical notions used throughout the paper, (b) providing known results on the reasoning approach that is used for the generation of models for graph conditions in our graph repair algorithms, and (c) presenting proofs for all theorems in an appendix. We added support to generate only delta-preserving graph repairs in the delta-based case, which required substantial modifications of the underlying notions in the incremental approach. We continue with introducing satisfaction trees, which are needed for the delta-based graph repair algorithm featuring delta preservation in Sect.
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