Purpose: The rise of intraoperative information threatens to outpace our abilities to process it. Context-aware systems, filtering information to automatically adapt to the current needs of the surgeon, are necessary to fully profit from computerized surgery. To attain context awareness, representation of medical knowledge is crucial. However, most existing systems do not represent knowledge in a reusable way, hindering also reuse of data. Our purpose is therefore to make our computational models of medical knowledge sharable, extensible and interoperational with established knowledge representations in the form of the LapOntoSPM ontology. To show its usefulness, we apply it to situation interpretation, i.e., the recognition of surgical phases based on surgical activities. Methods: Considering best practices in ontology engineering and building on our ontology for laparoscopy, we formalized the workflow of laparoscopic adrenalectomies, cholecystectomies and pancreatic resections in the framework of OntoSPM, a new standard for surgical process models. Furthermore, we provide a rule-based situation interpretation algorithm based on SQWRL to recognize surgical phases using the ontology. Results: The system was evaluated on ground-truth data from 19 manually annotated surgeries. The aim was to show that the phase recognition capabilities are equal to a specialized solution. The recognition rates of the new system were equal to the specialized one. However, the time needed to interpret a situation rose from 0.5 to 1.8 s on average which is still viable for practical application. Conclusion: We successfully integrated medical knowledge for laparoscopic surgeries into OntoSPM, facilitating knowledge and data sharing. This is especially important for reproducibility of results and unbiased comparison of recognition algorithms. The associated recognition algorithm was adapted to the new representation without any loss of classification power. The work is an important step to standardized knowledge and data representation in the field on context awareness and thus toward unified benchmark data sets.