Like other components of Semantic Web-based applications, ontologies are evolving over time to reflect changes in the real world. Several of these applications require keeping a full-fledged history of ontology changes so that both ontology instance versions and their corresponding ontology schema versions are maintained. Updates to an ontology instance could be non-conservative that is leading to a new ontology instance version no longer conforming to the current ontology schema version. If, for some reasons, a non-conservative update has to be executed, in spite of its consequence, it requires the production of a new ontology schema version to which the new ontology instance version is conformant so that the new ontology version produced by the update is globally consistent. In this paper, we first propose an approach that supports ontology schema changes which are triggered by non-conservative updates to ontology instances and, thus, gives rise to an ontology schema versioning driven by instance updates. Note that in an engineering perspective, such an approach can be used as an incremental ontology construction method driven by the modification of instance data, whose exact structure may not be completely known at the initial design time. After that, we apply our proposal to the already established [Formula: see text]OWL (Temporal OWL 2) framework, which allows defining and evolving temporal OWL 2 ontologies in an environment that supports temporal versioning of both ontology instances and ontology schemas, by extending it to also support the management of non-conservative updates to ontology instance versions. Last, we show the feasibility of our approach by dealing with its implementation within a new release of the [Formula: see text] OWL-Manager tool.