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This article applies the theory of argumentation to ontology engineering. Recent research in ontology engineering has highlighted the importance of controlled discussions for creating commonly agreed-on and widely accepted ontologies. The article analyzes how agreement is reached in the context of ontology development using rhetorical structure theory and identifies the most frequently used argument types. Case study-based investigations have shown that restricting the set of arguments participants use to express their positions can significantly facilitate reaching an agreement. The DILIGENT argumentation framework, consisting of a process, a formal model and a support tool, was built on the basis of these empirical findings. The formal model complies to the IBIS methodology, which was adapted to the ontology-specific requirements. It helps capture and record the design deliberations in ontology-engineering discussions, makes consensus building tasks more efficient, and provides detailed guidance for nonexperts. The authors successfully evaluated the framework in several case studies. This article is part of a special issue on argumentation technology.