Discovering semantic relations between heterogeneous ontologies is one of the key research topics in the Semantic Web. As the matching strategies adopted are largely heuristic, wrong mappings often exist in alignments generated by ontology matching systems. The mainstream methods for mapping revision deal with logical inconsistencies, so erroneous mappings not causing an inconsistency may be left out. Therefore, manual validations from domain experts are required. In this paper, we propose a graph-based method for interactive mapping revision with the purpose of reducing manual efforts as much as possible. Source ontologies are encoded into an integrated graph, where its mapping arcs are obtained by transforming mappings and will be evaluated by the expert. We specify the decision space for mapping revision and the corresponding operations that can be applied in the graph. After a human decision is made in each interaction, the mappings entailed by the manually confirmed ones are automatically approved. Conversely, those that would entail the rejected mappings or make the graph incoherent are declined. The whole update process modeled in the decision space can be done in polynomial time. Moreover, we define an impact function based on the integrated graph to identify the most influential mappings that will be displayed to the expert. In this way, the efforts of manual evaluation could be reduced further. The experiment on real-world ontology alignments shows that our method can save more decisions made by the expert than other revisions in most cases.
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