OWL is a powerful language to formalize terminologies in an ontology. Its main
strength lies in its foundation on description logics, allowing systems to automatically deduce implicit information through logical reasoning. However, since ontologies are often complex, understanding the outcome of the reasoning process is not always straightforward. Unlike already existing tools for exploring ontologies, our visualization tool Evonne is tailored towards explaining logical consequences. In addition, it supports the debugging of unwanted consequences and allows for an interactive comparison of the impact of removing statements from the ontology. Our visual approach combines (1) specialized views for the explanation of logical consequences and the structure of the ontology, (2) employing multiple layout modes for iteratively exploring explanations, (3) detailed explanations of specific reasoning steps, (4) cross-view highlighting and color coding of the visualization components, (5) features for dealing with visual complexity and (6) comparison and exploration of possible fixes to the ontology. We evaluated Evonne in a qualitative study with 16 experts in logics, and their positive feedback confirms the value of our concepts for explaining reasoning and debugging ontologies.