Not yet reviewed by Pith; the record is open.

In Knowledge Graphs (KGs), where the schema of the data is usually defined by particular ontologies, reasoning is a necessity to perform a range of tasks, such as retrieval of information, question answering, and the derivation of new knowledge. However, information to populate KGs is often extracted (semi-) automatically from natural language resources, or by integrating datasets that follow different semantic schemas, resulting in KG inconsistency. This, however, hinders the process of reasoning. In this survey, we focus on how to perform reasoning on inconsistent KGs, by analyzing the state of the art towards three complementary directions: a) the detection of the parts of the KG that cause the inconsistency, b) the fixing of an inconsistent KG to render it consistent, and c) the inconsistency-tolerant reasoning. We discuss existing work from a range of relevant fields focusing on how, and in which cases they are related to the above directions. We also highlight persisting challenges and future directions.