Ontologies such as taxonomies, product catalogs or web directories are heavily used and hence evolve frequently to meet new requirements or to better reflect the current instance data of a domain. To effectively manage the evolution of ontologies it is essential to identify the difference (Diff) between two ontology versions. We propose a novel approach to determine an expressive and invertible diff evolution mapping between given versions of an ontology. Our approach utilizes the result of a match operation to determine an evolution mapping consisting of a set of basic change operations (insert/update/delete). To semantically enrich the evolution mapping we adopt a rule-based approach to transform the basic change operations into a smaller set of more complex change operations, such as merge, split, or changes of entire subgraphs. The proposed algorithm is customizable in different ways to meet the requirements of diverse ontologies and application scenarios. We evaluate the proposed approach by determining and analyzing evolution mappings for real-world life science ontologies and web directories.